The EMBRS Scope and Sequence

Explore our K-12 Curriculum, lesson by lesson.

Featuring:

120 lessons per grade

Slide Decks for Every Lesson

Printable Worksheets for Every Lesson

Small Group Instruction for Every Lesson

Acceleration Activities for Every Lesson

Misconception Alerts

Concrete-Representational-Abstract Lesson Flow

EMBRS Math Curriculum Accordion

EMBRS Math Scope and Sequence

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Kindergarten ▼

Unit 1: Numbers 0-5 – Counting, Cardinality, “One More,” Writing ▼

1.Count to 5 by ones (Rote Counting).
2.Pair objects with number names when counting up to 5 objects (One-to-One Correspondence).
3.Understand that the last number name said tells the number of objects counted (Cardinality for up to 5 objects).
4.Understand that the number of objects is the same regardless of their arrangement or the order counted (Conservation for up to 5 objects).
5.Understand that each successive number name refers to a quantity that is one larger (for numbers 1-5).
6.Count forward beginning from a given number within the known sequence (1-5, instead of starting at 1).
7.Write numbers from 0 to 3.
8.Write numbers from 0 to 5.
9.Represent a number of objects (0-5) with a written numeral and count to answer “how many?”.
10.Unit 1 Review: Numbers 0-5 – Counting, Cardinality, “One More,” Writing.

Unit 2: Comparing Numbers 0-5; Introduction to 2D Shapes & Positional Language ▼

11.Identify whether the number of objects in one group is greater than the number in another group (up to 5 objects, using matching or counting).
12.Identify whether the number of objects in one group is less than the number in another group (up to 5 objects, using matching or counting).
13.Identify whether the number of objects in two groups is equal (up to 5 objects, using matching or counting).
14.Compare two numbers between 1 and 5 presented as written numerals.
15.Describe objects in the environment using names of 2D shapes (Circle, Square, Triangle, Rectangle).
16.Correctly name 2D shapes (Circle, Square, Triangle, Rectangle) regardless of their orientations or overall size.
17.Describe the relative positions of objects using terms such as above, below, beside, in front of, behind, and next to.
18.Practice using positional language in various contexts (following directions, describing scenes).
19.Identify shapes as two-dimensional (“flat”) versus three-dimensional (“solid”) – Introduction.
20.Unit 2 Review: Comparing Numbers 0-5; Introduction to 2D Shapes & Positional Language.

Unit 3: Numbers 6-10 – Counting, Cardinality, “One More,” Writing, Scattered Configuration ▼

21.Count to 10 by ones (Rote Counting – Review and Fluency).
22.Pair objects with number names when counting 6-10 objects (One-to-One Correspondence).
23.Understand that the last number name said tells the number of objects counted (Cardinality for 6-10 objects).
24.Understand that the number of objects is the same regardless of arrangement or order counted (Conservation for 6-10 objects).
25.Understand “one larger” for numbers 1-10.
26.Count forward beginning from a given number within 1-10.
27.Write numbers from 0 to 10.
28.Represent a number of objects (0-10) with a written numeral.
29.Count to answer “how many?”
30.Unit 3 Review: Numbers 6-10 – Counting, Cardinality, “One More,” Writing, Scattered Configuration.

Unit 4: Comparing Numbers 0-10; Exploring Patterns; 2D Shapes (Rectangle, Hexagon, Attributes, Modeling, Composing) ▼

31.Identify whether the number of objects in one group is greater than/less than in another group (up to 10 objects).
32.Identify whether the number of objects in two groups is equal (up to 10 objects).
33.Compare two numbers between 1 and 10 presented as written numerals.
34.Exploring Simple Repeating Patterns (AB).
35.Exploring Simple Repeating Patterns (ABC, AAB, ABB).
36.Correctly name 2D shapes (Rectangle, Hexagon) regardless of their orientations or overall size (Review Circle, Square, Triangle).
37.Analyze and compare two-dimensional shapes by their attributes (number of sides and vertices/”corners”, and side lengths – informal).
38.Model shapes in the world by drawing 2D shapes (circles, squares, triangles, rectangles, hexagons).
39.Compose simple 2D shapes to form larger or different shapes.
40.Unit 4 Review: Comparing Numbers 0-10; Exploring Patterns; 2D Shapes (Rectangle, Hexagon, Attributes, Modeling, Composing).

Unit 5: Addition Concepts and Word Problems within 10 ▼

41.Represent addition as “putting together” distinct groups with objects or fingers (sums up to 5, then extend to 10).
42.Represent addition as “adding to” an existing group with drawings (sums up to 5, then extend to 10).
43.Represent addition situations with simple expressions or equations (spoken or written) for sums up to 10.
44.Solve addition word problems (add to/put together, result unknown) within 10, using objects or drawings.
45.Practice solving various “add to” word problems within 10 using preferred strategies (objects, fingers, drawings).
46.Practice solving various “put together” word problems within 10 using preferred strategies.
47.Solve “how many in all” addition problems by counting all (within 10).
48.Solve “how many in all” addition problems by counting on (within 10, from larger number).
49.Introduction to commutative property of addition (order doesn’t change sum) using objects within 10.
50.Unit 5 Review: Addition Concepts and Word Problems within 10.

Unit 6: Subtraction Concepts and Word Problems within 10 ▼

51.Represent subtraction as “taking away” with objects or fingers (minuends up to 10).
52.Represent subtraction as “taking apart” or “separating” with drawings (minuends up to 10).
53.Represent subtraction situations with simple expressions or equations (spoken or written) for minuends up to 10.
54.Solve subtraction word problems (take from/take apart, result unknown) within 10, using objects or drawings.
55.Practice solving various “take from” word problems within 10 using preferred strategies (objects, fingers, drawings).
56.Practice solving various “take apart” word problems within 10 using preferred strategies.
57.Solve “how many are left” subtraction problems by counting the remaining (within 10).
58.Solve “how many are left” subtraction problems by counting back (within 10).
59.Introduction to subtraction as finding the missing addend (within 10).
60.Unit 6 Review: Subtraction Concepts and Word Problems within 10.

Unit 7: Numbers 11-20 – Teen Numbers as “10 and some ones”; Counting & Writing to 20 ▼

61.Count to 20 by ones (Review and Fluency).
62.Write numbers from 0 to 20.
63.Represent 11-20 objects with numerals and count to answer “how many?”
64.Compose numbers from 11 to 19 into ten ones and some further ones using objects or drawings.
65.Decompose numbers from 11 to 19 into ten ones and some further ones using objects or drawings.
66.Record composition/decomposition for numbers 11-19 by a drawing or equation (e.
67.Understand teen numbers as “10 and some ones” – Reinforce meaning.
68.Count to answer “how many?”
69.Practice with numbers 0-20: Counting, representing, and understanding “ten and some ones.
70.Unit 7 Review: Numbers 11-20 – Teen Numbers as “10 and some ones”; Counting & Writing to 20.

Unit 8: Counting to 100; 3D Shapes & Comparing 2D/3D ▼

71.Count to 50 by ones (Practice and Hundred Chart Introduction).
72.Count to 100 by ones (using Hundred Chart for support).
73.Count to 100 by tens (using Hundred Chart and bundles of tens).
74.Patterns on the Hundred Chart (Numbers in rows and columns).
75.Count forward beginning from a given number (other than 1, within 1-100).
76.Correctly name 3D shapes (Cube, Cone, Cylinder, Sphere) regardless of orientation/size (Review).
77.Identify shapes as two-dimensional (“flat”) versus three-dimensional (“solid”) – Review and Sort.
78.Analyze and compare two-dimensional and three-dimensional shapes by their attributes (informal: sides, corners, faces, rolling/stacking).
79.Model shapes in the world by drawing 2D shapes and building 3D shapes from components.
80.Unit 8 Review: Counting to 100; 3D Shapes & Comparing 2D/3D.

Unit 9: Decomposing Numbers to 10; Making 10; Fluency +/- within 5 ▼

81.Decompose numbers less than or equal to 10 into pairs in more than one way using objects or drawings (Focus 7, 8, 9 – Review).
82.Record decompositions of numbers up to 10 with drawings or equations (Review).
83.For any number from 1 to 9, find the number that makes 10 when added to the given number, using objects or drawings (Focus on speed and visual memory with ten-frames).
84.Record “make 10” pairs with drawings or equations (Focus on all pairs).
85.Fluently add within 5 (Games and Timed Practice).
86.Fluently subtract within 5 (Games and Timed Practice).
87.Practice “Make 10” strategy for sums slightly above 10 (e.
88.Solve addition and subtraction word problems within 10 (Mixed types, focus on representation with equations).
89.Problem Solving: Using decomposing, making 10, and fluency in contextual tasks.
90.Unit 9 Review: Decomposing Numbers to 10; Making 10; Fluency +/- within 5.

Unit 10: Measurement – Describing and Directly Comparing Measurable Attributes (Length, Weight) ▼

91.Describe measurable attributes of objects (Length – long, short, tall, etc.).
92.Describe measurable attributes of objects (Weight – heavy, light).
93.Directly compare two objects with respect to length/height, and describe which has “more of”/”less of” the attribute.
94.Directly compare two objects with respect to weight, and describe which has “more of”/”less of” the attribute.
95.Ordering three objects by length or height.
96.Practice directly comparing objects by various measurable attributes (length, height, weight, capacity – full/empty).
97.Introduce non-standard units for measuring length (e.
98.Practice measuring length with simple non-standard units.
99.Describing objects using a combination of attributes (e.
100.Unit 10 Review: Measurement – Describing and Directly Comparing Measurable Attributes (Length, Weight).

Unit 11: Data – Classifying Objects, Counting, and Sorting Categories; Counting to 100 ▼

101.Classify objects into given categories based on a single attribute (e.
102.Count the number of objects in each category after classifying (up to 10 per category).
103.Sort the categories by count (identify category with most, least, or equal – up to 3 categories).
104.Practice classifying, counting, and sorting by count with various object sets and attributes.
105.Represent classified data with simple concrete graphs or drawings.
106.Count to 100 by ones (Fluency practice and identifying missing numbers on hundred chart sections).
107.Count to 100 by tens (Fluency practice and relating to groups of ten).
108.Count forward from any given number up to 100 (not just 1).
109.Solving simple put-together or take-apart problems based on classified and counted data (linking K.
110.Unit 11 Review: Data – Classifying Objects, Counting, and Sorting Categories; Counting to 100.

Unit 12: Geometry (Identifying, Analyzing, Comparing, Modeling & Composing 2D & 3D Shapes); Overall Kindergarten Math Application ▼

111.Correctly name 2D shapes (Circle, Square, Triangle, Rectangle, Hexagon) and 3D shapes (Cube, Cone, Cylinder, Sphere) – Review.
112.Identify shapes as two-dimensional (“flat”) or three-dimensional (“solid”) – Review and Application.
113.Analyze and compare two-dimensional shapes by various attributes (sides, vertices, side lengths – equal/unequal, curved/straight).
114.Analyze and compare three-dimensional shapes by various attributes (faces – number and shape, vertices, edges, ability to roll/stack/slide).
115.Model shapes in the world by drawing 2D shapes (more complex scenes).
116.Model shapes in the world by building 3D shapes from components (blocks, clay, straws and connectors).
117.Compose simple 2D shapes to form larger or different shapes (using pattern blocks, tangrams, or cutouts).
118.Practice composing various 2D shapes to form specified larger shapes.
119.Kindergarten Year-End Review of Core Counting, Cardinality, Operations, and NBT Skills.
120.Unit 12 Review: Geometry (Identifying, Analyzing, Comparing, Modeling & Composing 2D & 3D Shapes); Overall Kindergarten Math Application.

Grade 1 (Ontario) ▼

Unit 1: Building Number Sense to 20 – Counting, Comparing, and Zero ▼

1.Rote Count to 20 (and beyond).
2.Object Counting to 20 (One-to-One Correspondence & Cardinality).
3.Understanding the Concept of Zero.
4.Read and Represent Numbers 0-10.
5.Read and Represent Numbers 11-20.
6.Compose and Decompose Numbers up to 10.
7.Compose and Decompose Numbers 11-20 (Ten and Some Ones).
8.Compare and Order Numbers up to 20.
9.Everyday Uses of Numbers up to 20.
10.Unit 1 Review: Building Number Sense to 20.

Unit 2: Numbers to 50 – Place Value, Estimation, and Skip Counting ▼

11.Estimate Collections up to 20 and Verify.
12.Read and Represent Numbers 21-50 (Tens and Ones).
13.Compose and Decompose Numbers 21-50 (Tens and Ones).
14.Compare and Order Numbers up to 50.
15.Estimate Collections up to 50 and Verify.
16.Count to 50 by 1s and 10s (Forward and Backward).
17.Count to 50 by 5s.
18.Count to 50 by 2s.
19.Everyday Uses of Numbers up to 50.
20.Unit 2 Review: Numbers to 50.

Unit 3: Mastering Addition and Subtraction Facts to 10 ▼

21.Addition Facts to 10: Counting On & Number Lines.
22.Addition Facts to 10: Doubles & Near Doubles.
23.Addition Facts to 10: Making Ten Strategy.
24.Subtraction Facts from 10: Counting Back & Number Lines.
25.Subtraction Facts from 10: Relating to Addition (Think Addition/Fact Families).
26.Properties of Addition: Commutative Property (Order Doesn’t Matter).
27.Relationship Between Addition and Subtraction (Fact Families).
28.Demonstrating Fluency with Addition Facts to 10.
29.Demonstrating Fluency with Subtraction Facts from 10.
30.Unit 3 Review: Mastering Addition and Subtraction Facts to 10.

Unit 4: Mental Math Strategies for Sums and Differences to 20 ▼

31.Mental Math: Making Ten to Add (Sums to 20).
32.Mental Math: Using Doubles and Near Doubles to Add (Sums to 20).
33.Mental Math: Adding in Parts (Splitting a Number, Sums to 20).
34.Mental Math: Subtracting by Making Ten (Differences from up to 20).
35.Mental Math: Relating Subtraction to Addition (Thinking Missing Addend, up to 20).
36.Mental Math: Subtracting in Parts (Differences from up to 20).
37.Estimation in Addition and Subtraction (Sums/Differences to 20).
38.Explaining Chosen Mental Math Strategies.
39.Problem Solving using Mental Math Strategies for +/- to 20.
40.Unit 4 Review: Mental Math Strategies for Sums and Differences to 20.

Unit 5: Adding and Subtracting Two-Digit Numbers (to 50) ▼

41.Adding 2-Digit Numbers (No Regrouping) using Base-Ten Blocks & Drawings.
42.Adding 2-Digit Numbers (With Regrouping) using Base-Ten Blocks.
43.Adding 2-Digit Numbers (With Regrouping) using Drawings & Expanded Form.
44.Subtracting 2-Digit Numbers (No Regrouping) using Base-Ten Blocks & Drawings.
45.Subtracting 2-Digit Numbers (With Regrouping) using Base-Ten Blocks.
46.Subtracting 2-Digit Numbers (With Regrouping) using Drawings & Expanded Form.
47.Representing Word Problems with Equations (+/- to 50).
48.Solving Word Problems (+/- to 50) using Chosen Strategies.
49.Checking Calculations (+/- to 50) using Inverse Operations.
50.Unit 5 Review: Adding and Subtracting Two-Digit Numbers (to 50).

Unit 6: Patterns All Around Us – Identifying, Creating, and Extending ▼

51.Identifying Regularities in Patterns (Real-Life Contexts).
52.Creating Repeating Patterns (Movements, Sounds, Objects).
53.Creating Repeating Patterns (Shapes, Letters, Numbers).
54.Translating Patterns (e.g., Sound to Shape).
55.Determining Pattern Rules and Extending Repeating Patterns.
56.Making and Justifying Predictions in Repeating Patterns.
57.Identifying Missing Elements in Repeating Patterns.
58.Creating and Describing Growing Patterns with Numbers up to 50 (e.g., +2, +5).
59.Exploring Number Patterns on a Hundred Chart (Numbers up to 50).
60.Unit 6 Review: Patterns All Around Us.

Unit 7: Exploring Shapes and Spaces – Geometry and Spatial Sense ▼

61.Sorting 3D Objects by One Attribute and Identifying the Rule.
62.Sorting 2D Shapes by One Attribute and Identifying the Rule.
63.Constructing 3D Objects.
64.Identifying 2D Shapes within 3D Structures and Objects.
65.Constructing and Describing 2D Shapes with Matching Halves (Symmetry).
66.Exploring Symmetrical Properties in 3D Objects.
67.Describing Relative Locations of Objects using Positional Language.
68.Giving Directions for Movement (e.g., to a classmate).
69.Following Directions for Movement.
70.Unit 7 Review: Exploring Shapes and Spaces.

Unit 8: Measuring Our World – Non-Standard Units and Time ▼

71.Identifying Measurable Attributes: Length & Area.
72.Identifying Measurable Attributes: Mass & Capacity.
73.Measuring Length with Non-Standard Units.
74.Comparing and Ordering Lengths using Non-Standard Units.
75.Measuring Area with Non-Standard Units.
76.Comparing and Ordering Areas using Non-Standard Units.
77.Measuring Mass with Non-Standard Units & Comparing/Ordering.
78.Measuring Capacity with Non-Standard Units & Comparing/Ordering.
79.Reading Dates & Using a Calendar (Days, Weeks, Months, Holidays, Seasons).
80.Unit 8 Review: Measuring Our World.

Unit 9: Data Explorers – Sorting, Collecting, and Displaying Information ▼

81.Sorting Sets of Data by One Attribute and Describing Rules.
82.Collecting Data through Observations and Interviews.
83.Recording and Organizing Data in Tally Tables.
84.Displaying Data in Concrete Graphs.
85.Displaying Data in Pictographs.
86.Ordering Categories of Data from Greatest to Least Frequency.
87.Analyzing Data: Asking and Answering Questions.
88.Analyzing Data: Drawing Conclusions.
89.Analyzing Data: Making Convincing Arguments & Informed Decisions.
90.Unit 9 Review: Data Explorers.

Unit 10: Fair Shares & Equal Groups – Fraction and Multiplication Foundations ▼

91.Fair-Share Problems: 2 Sharers (Halves) with Remainders.
92.Fair-Share Problems: 4 Sharers (Fourths) with Remainders.
93.Equivalence: One Half and Two Fourths.
94.Introduction to Unit Fractions (1/2, 1/3, 1/4 from a Whole).
95.Comparing Unit Fractions (Individual Portions from up to 10 Sharers).
96.Ordering Unit Fractions (e.g., 1/2, 1/3, 1/4).
97.Representing and Solving Equal-Group Problems (Total up to 10).
98.Solving Equal-Group Problems Involving Halves (Total up to 10).
99.Problem Solving with Fair Shares and Equal Groups.
100.Unit 10 Review: Fair Shares & Equal Groups.

Unit 11: Money, Equality, and Early Algebra ▼

101.Identifying Canadian Coins up to 50¢ and their Values.
102.Identifying Canadian Coins and Bills up to $50.
103.Comparing Values of Canadian Coins and Bills.
104.Identifying Quantities that Change vs. Remain the Same.
105.Determining if Addition/Subtraction Expressions are Equivalent (up to 20).
106.Understanding the Equals Sign as “the same as” (Balance).
107.Identifying Equivalent Relationships for Whole Numbers up to 50 (e.g., different ways to make a number).
108.Using Equivalent Relationships to Solve Problems.
109.Finding Missing Numbers in Equations (Addition/Subtraction to 20).
110.Unit 11 Review: Money, Equality, and Early Algebra.

Unit 12: Applying Skills – Likelihood, Logic, and Problem Integration ▼

111.Describing Likelihood of Events (Impossible, Possible, Certain) – Deeper Dive.
112.Making Predictions and Informed Decisions based on Simple Chance.
113.Testing Predictions about Data Frequencies (Comparing Two Small Groups).
114.Unplugged Coding: Understanding Sequential Instructions (Following a Recipe/Path).
115.Unplugged Coding: Giving Sequential Instructions (Creating a Path for a “Robot”).
116.Unplugged Coding: Identifying Errors in Sequential Instructions (Debugging a Path).
117.Unplugged Coding: Modifying Sequential Instructions to Change an Outcome.
118.Integrated Problem Solving: Numbers and Operations with Data.
119.Integrated Problem Solving: Geometry and Positional Language in Logical Tasks.
120.Unit 12 Review: Likelihood, Unplugged Coding Logic, and Integrated Problems.

Grade 1 ▼

Unit 1: Counting and Representation (up to 50) ▼

1.Counting Forward to 20
2.Counting Forward to 50
3.Reading and Writing Numerals to 20
4.Representing Numbers with Objects & Relating Counts to Numerals (up to 20)
5.Reading and Writing Numerals to 50
6.Representing Numbers with Objects & Relating Counts to Numerals (up to 50, using grouping)
7.Comparing Quantities and Numerals (up to 50)
8.Ordering Numerals to 50
9.One More, One Less (within 50)
10.Unit 1 Review: Counting and Representation Practice (up to 50)

Unit 2: Counting to 120 and Place Value Introduction ▼

11.Counting Forward from 50 to 100
12.Counting Forward from 100 to 120
13.Reading and Writing Numerals up to 100
14.Reading and Writing Numerals from 100 to 120
15.Understanding a “Ten”
16.Representing Multiples of 10 (e.g., 70 is 7 tens) up to 100
17.Exploring the 120 Chart: Structure and Patterns
18.Using the 120 Chart for Counting On and Counting Back
19.Representing numbers to 120 with tens and ones
20.Unit 2 Review: Counting to 120 and Place Value Introduction Practice

Unit 3: Place Value (Tens and Ones) and Comparing Two-Digit Numbers ▼

21.Understanding Numbers 11-19 as Ten and Ones
22.Representing Two-Digit Numbers with Tens and Ones (Models & Drawings)
23.Decomposing Two-Digit Numbers into Tens and Ones
24.Identifying the Value of Digits in Two-Digit Numbers
25.Comparing Two-Digit Numbers using Models and Symbols (>, <, =)
26.Comparing Two-Digit Numbers Strategy: Based on the Tens Digit
27.Comparing Two-Digit Numbers Strategy: Based on the Ones Digit (when tens are equal)
28.Ordering Sets of Two-Digit Numbers
29.Mentally Finding 10 More than a Given Two-Digit Number
30.Unit 3 Review: Place Value (Tens and Ones) and Comparing Two-Digit Numbers Practice

Unit 4: Equality and Basic Equations (within 10) ▼

31.Mentally Finding 10 Less than a Given Two-Digit Number
32.Understanding the Meaning of the Equal Sign
33.Understanding Balanced Equations (Introduction)
34.Determining if Addition/Subtraction Equations are True or False (within 10)
35.Solving for Result Unknowns in Addition/Subtraction Equations (within 10)
36.Introduction to Change Unknowns in Addition Equations (within 10)
37.Introduction to Change Unknowns in Subtraction Equations (within 10)
38.Relating Counting to Addition & Subtraction for Basic Equations
39.Fluency Practice: Mixed Addition and Subtraction within 10 with Unknowns (Result/Change)
40.Unit 4 Review: Equality and Basic Equations (Result/Change Unknowns within 10)

Unit 5: Properties of Operations and Solving for Unknowns (within 20) ▼

41.Commutative Property of Addition
42.Applying the Commutative Property to Simplify and Solve Problems
43.Associative Property of Addition (for adding three numbers) (Addition Only)
44.Applying the Associative Property to Make Ten when Adding Three Numbers
45.Understanding Subtraction as an Unknown-Addend Problem
46.Solving Subtraction Problems by Finding the Unknown Addend
47.Solving for Start Unknowns in Addition Equations (within 20)
48.Solving for Start Unknowns in Subtraction Equations (within 20)
49.Mixed Practice: Solving for Unknowns in All Positions (within 20)
50.Unit 5 Review: Properties and Solving for All Unknown Types Practice

Unit 6: Addition Strategies and Fluency (within 20) ▼

51.Addition Strategy: Making Ten
52.Practice and Application of Making Ten Strategy
53.Addition Strategy: Using Doubles
54.Addition Strategy: Using Doubles Plus/Minus One
55.Practice with Doubles and Near Doubles Strategies
56.Adding Three Whole Numbers (Sum $\le 20$) by Making Ten or Using Known Facts
57.Choosing Efficient Strategies for Addition within 20
58.Fluency Development Drills: Addition within 20
59.Cumulative Addition Practice within 20
60.Unit 6 Review: Mastering Addition Strategies and Fluency within 20

Unit 7: Subtraction Strategies and Fluency (within 20) ▼

61.Subtraction Strategy: Decomposing to Make Ten
62.Practice and Application of Decomposing to Make Ten Strategy
63.Understanding the Relationship Between Addition and Subtraction (Introducing Fact Families)
64.Using Fact Families and Thinking of Addition to Solve Subtraction Problems
65.Practice with Fact Families and Relating Addition to Subtraction
66.Choosing Efficient Strategies for Subtraction within 20
67.Fluency Development Drills: Subtraction within 20
68.Cumulative Subtraction Practice within 20
69.Mixed Fluency Practice: Addition AND Subtraction within 20
70.Unit 7 Review: Mastering Subtraction Strategies and Fluency within 20

Unit 8: Word Problem Solving (within 20) ▼

71.Solving Add To Word Problems (Result, Change, and Start Unknown)
72.Solving Take From Word Problems (Result, Change, and Start Unknown)
73.Solving Put Together/Take Apart Word Problems (Total Unknown and Addend Unknown)
74.Introduction to Compare Word Problems (Difference Unknown)
75.Solving Compare Word Problems (Bigger Unknown)
76.Solving Compare Word Problems (Smaller Unknown)
77.Solving Word Problems with Three Addends
78.Representing Word Problems with Equations and a Symbol for the Unknown
79.Solving a Mix of Word Problem Types (Students identify type and strategy)
80.Unit 8 Review: Comprehensive Word Problem Solving within 20

Unit 9: Addition within 100 (Two-Digit + One-Digit) ▼

81.Adding a Two-Digit Number and a One-Digit Number (No Regrouping, Concrete/Drawings)
82.Adding a Two-Digit Number and a One-Digit Number (No Regrouping, Strategy/Written, Place Value)
83.Understanding Composing a Ten when Adding Ones
84.Adding a Two-Digit Number and a One-Digit Number (With Regrouping, Concrete/Drawings)
85.Adding a Two-Digit Number and a One-Digit Number (With Regrouping, Strategy/Written, Place Value)
86.Practice: Adding Two-Digit and One-Digit Numbers (With and Without Regrouping)
87.Explaining Addition Strategies for 2-digit + 1-digit (No Regrouping and Regrouping)
88.Word Problems: Adding Two-Digit and One-Digit Numbers (within 100)
89.Cumulative Practice: Addition within 20 and 2-digit + 1-digit within 100
90.Unit 9 Review: Addition within 100 (Two-Digit + One-Digit)

Unit 10: Place Value Operations with Tens (within 100) ▼

91.Adding a Two-Digit Number and a Multiple of 10 (Concrete/Drawings & Strategy)
92.Practice: Adding a Two-Digit Number and a Multiple of 10
93.Subtracting Multiples of 10 from Multiples of 10 (Concrete/Drawings & Strategy)
94.Practice: Subtracting Multiples of 10
95.Adding Two Two-Digit Numbers (No Regrouping, Tens with Tens, Ones with Ones)
96.Practice: Adding Two Two-Digit Numbers (No Regrouping)
97.Explaining Place Value Strategies for Adding/Subtracting Tens & Adding 2-Digit Numbers (No Regrouping)
98.Word Problems Involving Adding/Subtracting with Multiples of 10
99.Mixed Practice: Addition and Subtraction with Tens (within 100)
100.Unit 10 Review: Place Value Operations with Tens Practice

Unit 11: Measurement (Length and Time) ▼

101.Comparing Lengths: Direct Comparison of Two Objects
102.Ordering Three Objects by Length
103.Comparing Lengths Indirectly using a Third Object
104.Understanding Length Units: Iteration of Same-Size Units with No Gaps or Overlaps
105.Measuring the Length of Objects using Non-Standard Units
106.Practice: Measuring and Comparing Lengths with Non-Standard Units
107.Telling and Writing Time to the Hour (Analog and Digital Clocks)
108.Telling and Writing Time to the Half-Hour (Analog and Digital Clocks)
109.Relating Analog Clock Features (Hour and Minute Hands) to Telling Time
110.Unit 11 Review: Measurement Application (Length and Time Problems)

Unit 12: Data Analysis and Geometry ▼

111.Organizing Data with up to Three Categories (Tally Charts, Lists)
112.Representing Data with up to Three Categories (Simple Bar Graphs)
113.Interpreting Data: Total Number of Data Points and How Many in Each Category
114.Interpreting Data: Comparing Categories
115.Distinguishing Between Defining Attributes and Non-Defining Attributes of Shapes
116.Building and Drawing Shapes to Possess Defining Attributes
117.Composing Two-Dimensional Shapes (Rectangles, Squares, Trapezoids, Triangles, Half-circles, Quarter-circles)
118.Composing Three-Dimensional Shapes (Cubes, Right Rectangular Prisms, Cones, Cylinders)
119.Partitioning Circles and Rectangles into Two and Four Equal Shares (Halves, Fourths, Quarters)
120.Unit 12 Review: Data Analysis and Geometry Application

Grade 2 ▼

Unit 1: Fluency with Addition & Subtraction within 20 ▼

1.Fluently add within 20 using mental strategies (Adding 0, 1, 2).
2.Fluently add within 20 using mental strategies (Doubles).
3.Fluently add within 20 using mental strategies (Doubles Plus/Minus 1).
4.Fluently add within 20 using mental strategies (Making 10).
5.Fluently add within 20 using mental strategies (Commutative Property).
6.Fluently subtract within 20 using mental strategies (Think Addition).
7.Fluently subtract within 20 using mental strategies (Make 10).
8.Fluently subtract within 20 using mental strategies (Relating to Doubles).
9.Know from memory sums of two one-digit numbers and related subtraction facts (Practice).
10.Unit 1 Review: Fluency with Addition & Subtraction within 20.

Unit 2: Place Value – Understanding Hundreds, Tens, and Ones ▼

11.Understand Place Value (Tens and Ones Review).
12.Understand that 100 can be thought of as a bundle of ten tens — called a “hundred.”
13.Understand that the numbers 100, 200, , 900 refer to one, two, , nine hundreds.
14.Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones (Identifying Place & Value).
15.Represent three-digit numbers using base-ten blocks or drawings (connecting to place value).
16.Read and write numbers to 1000 using base-ten numerals and number names (Part 1 – standard forms).
17.Read and write numbers to 1000 using expanded form (connecting to place value).
18.Mentally add 10 or 100 to a given three-digit number (100-900).
19.Mentally subtract 10 or 100 from a given three-digit number (100-900).
20.Unit 2 Review: Place Value – Understanding Hundreds, Tens, and Ones.

Unit 3: Counting, Comparing, and Ordering Numbers to 1000 ▼

21.Count within 1000 by ones, forwards and backwards, across hundreds.
22.Skip-count by 10s within 1000, from any number.
23.Skip-count by 100s within 1000, from any number.
24.Skip-count by 5s within 1000.
25.Identify and describe number patterns in counting and skip-counting sequences.
26.Compare two three-digit numbers using place value (Hundreds, then Tens, then Ones).
27.Use >, =, and < symbols to accurately record the results of comparisons of two three-digit numbers.
28.Order a set of three or more three-digit numbers from least to greatest.
29.Order a set of three or more three-digit numbers from greatest to least.
30.Unit 3 Review: Counting, Comparing, and Ordering Numbers to 1000.

Unit 4: Addition within 100 ▼

31.Add two-digit numbers without regrouping (Place Value Strategy: Tens + Tens, Ones + Ones; Open Number Line).
32.Add two-digit numbers with regrouping ones to make a new ten (Using Models and Partial Sums).
33.Add two-digit numbers with regrouping ones (Standard Algorithm).
34.Practice adding two-digit numbers with and without regrouping ones.
35.Add a two-digit number and a multiple of 10 within 100.
36.Add a column of three two-digit numbers, regrouping ones if necessary.
37.Add a column of four two-digit numbers, regrouping ones if necessary.
38.Choose efficient strategies for adding two-digit numbers.
39.Explain why addition strategies work for 2-digit numbers (Place Value & Properties).
40.Unit 4 Review: Addition within 100.

Unit 5: Subtraction within 100 ▼

41.Subtract two-digit numbers from multiples of 10 (e.g., $90-47$).
42.Subtract two-digit numbers without regrouping (Place Value Strategy; Open Number Line).
43.Subtract two-digit numbers with regrouping a ten into 10 ones (Using Models).
44.Subtract two-digit numbers with regrouping a ten into 10 ones (Standard Algorithm).
45.Practice subtracting two-digit numbers with and without regrouping.
46.Subtract multiples of 10 from two-digit numbers (e.g., $84-30$).
47.Choose efficient strategies for subtracting two-digit numbers.
48.Use addition to check subtraction within 100.
49.Explain why subtraction strategies work for 2-digit numbers (Place Value & Relationship to Addition).
50.Unit 5 Review: Subtraction within 100.

Unit 6: One-Step Word Problems (within 100) ▼

51.Solve one-step Add To/Take From word problems (Result Unknown & Change Unknown) within 100.
52.Solve one-step Add To/Take From word problems (Start Unknown) within 100.
53.Solve one-step Put Together/Take Apart word problems (Total Unknown & Addend Unknown) within 100.
54.Solve one-step Compare word problems (Difference Unknown: “How many more/fewer?”) within 100.
55.Solve one-step Compare word problems (Bigger Unknown or Smaller Unknown) within 100.
56.Represent one-step word problems (all types) using drawings (bar models/tape diagrams).
57.Represent one-step word problems (all types) using equations with a symbol for the unknown number.
58.Mixed practice: Solving various one-step word problems within 100.
59.Review: Identifying & Representing Different One-Step Word Problem Types (within 100).
60.Unit 6 Review: One-Step Word Problems (within 100); Add up to Four 2-Digit Numbers.

Unit 7: Measurement – Length ▼

61.Estimate lengths using units of inches and feet (Introduce before measuring).
62.Estimate lengths using units of centimeters and meters (Introduce before measuring).
63.Select and use appropriate tools for measuring length (rulers, yardsticks, meter sticks, measuring tapes).
64.Measure the length of an object using inches and feet accurately (aligning at zero, nearest whole unit).
65.Measure the length of an object using centimeters and meters accurately (aligning at zero, nearest whole unit).
66.Measure the length of an object twice using different standard length units (e.g., inches and feet; inches and cm).
67.Describe how two measurements of the same object (using different units) relate to the size of the unit chosen.
68.Measure to determine how much longer one object is than another (expressing difference in same standard units).
69.Solve one-step word problems involving lengths given in the same units (using addition/subtraction within 100).
70.Unit 7 Review: Measurement – Length.

Unit 8: Addition within 1000 ▼

71.Mentally add 10 or 100 to a given three-digit number (100-900).
72.Add three-digit numbers (no regrouping) using place value strategies and models/written methods.
73.Add three-digit numbers with regrouping ones (e.g., $348+125$) using place value strategies and models/written methods.
74.Add three-digit numbers with regrouping tens (e.g., $472+153$) using place value strategies and models/written methods.
75.Add three-digit numbers with regrouping in both ones and tens places (e.g., $378+245$) using place value strategies and models/written methods.
76.Develop fluency adding three-digit numbers using the standard algorithm (or other efficient written method).
77.Add up to three or four two-digit numbers (Review and conceptual link to three-digit addition).
78.Explain why addition strategies for three-digit numbers work (Place Value, Properties).
79.Mixed addition practice within 1000 (including word problem context).
80.Unit 8 Review: Addition within 1000.

Unit 9: Subtraction within 1000 ▼

81.Mentally subtract 10 or 100 from a given three-digit number (100-900).
82.Subtract three-digit numbers (no regrouping) using place value strategies and models/written methods.
83.Subtract three-digit numbers with regrouping tens to ones (e.g., $673-248$) using strategies and models/written methods.
84.Subtract three-digit numbers with regrouping hundreds to tens (e.g., $825-371$) using strategies and models/written methods.
85.Subtract three-digit numbers with regrouping in multiple places (e.g., $735-278$, no zeros first) using strategies and models/written methods.
86.Subtract three-digit numbers with regrouping across zeros (e.g., $804-327$) using place value strategies and models/written methods.
87.Develop fluency subtracting three-digit numbers using the standard algorithm (or other efficient written method).
88.Use addition to check subtraction within 1000.
89.Explain why subtraction strategies for three-digit numbers work (Place Value & Relationship to Addition).
90.Unit 9 Review: Subtraction within 1000.

Unit 10: Word Problems (One- and Two-Step, Add/Sub within 1000) ▼

91.Solve one-step addition and subtraction word problems within 1000 (All types).
92.Represent one-step word problems (within 1000) using drawings (bar models/tape diagrams).
93.Represent one-step word problems (within 1000) using equations with a symbol for the unknown number.
94.Introduction to two-step word problems involving addition and subtraction (Numbers within 100 first for structure).
95.Solve two-step word problems involving addition and subtraction (Numbers within 100).
96.Solve two-step word problems involving addition and subtraction (Numbers up to 1000).
97.Represent two-step word problems (up to 1000) using drawings (bar models/tape diagrams).
98.Represent two-step word problems (up to 1000) using equations with symbols for unknowns for each step.
99.Determine reasonableness of answers in one- and two-step word problems using estimation or mental math.
100.Unit 10 Review: Word Problems (One- and Two-Step, Add/Sub within 1000, Representing).

Unit 11: Money and Time ▼

101.Identify coins (penny, nickel, dime, quarter) and $1, $5, $10 bills, and state their values in cents and dollars.
102.Count collections of mixed coins (pennies, nickels, dimes, quarters) to find total value, expressing in cents or dollars/cents.
103.Solve one-step word problems involving coin collections (total value, comparing values, simple transactions).
104.Solve one-step word problems involving dollar bills and coins (making change from $1, $5, or $10, or simple purchases).
105.Show equivalent amounts of money using different combinations of coins and bills.
106.Tell and write time from analog and digital clocks to the nearest five minutes.
107.Associate a.m. and p.m. with daily events and correctly write time using a.m./p.m.
108.Calculate simple elapsed time (durations in hours or half-hours, or minutes within the hour, focusing on start/end on 5-min marks).
109.Solve simple word problems involving time (finding end times given start and duration, or finding duration).
110.Unit 11 Review: Money and Time.

Unit 12: Data, Geometry, & Foundations ▼

111.Determine whether a number (up to 20) is odd or even (by pairing or counting by 2s); Write an equation for an even number (sum of two equal addends).
112.Use addition to find the total number of objects arranged in rectangular arrays (up to 5 rows and 5 columns); write a repeated addition equation.
113.Identify 2D shapes (triangles, quadrilaterals, pentagons, hexagons) by their defining attributes (number of sides and angles).
114.Identify cubes and their defining attributes (6 square faces, all equal; 8 vertices, 12 edges).
115.Partition a rectangle into rows and columns of same-size squares and count to find the total number of squares.
116.Partition circles and rectangles into two, three, or four equal shares; describe shares using vocabulary (halves, thirds, fourths/quarters) and the whole.
117.Generate measurement data (lengths to nearest whole unit) and create a line plot to display the data.
118.Draw picture graphs and bar graphs (single-unit scale) to represent a data set with up to four categories.
119.Solve simple put-together, take-apart, and compare problems using information from picture graphs and bar graphs.
120.Unit 12 Review: Data, Geometry, & Foundations of Multiplication/Fractions.

Grade 2 (Ontario) ▼

Unit 1: Building Number Sense to 200 – Place Value and Flexibility ▼

1.Reading and Representing Numbers to 100 (Review: Tens and Ones using Base-Ten Blocks).
2.Flexible Decomposition of Numbers to 100 (e.g., 52 as 5T 2O or 4T 12O).
3.Practice: Flexible Decomposition to 100 using Drawings & Recording.
4.Reading and Representing Numbers 101-200 (Hundreds, Tens, Ones).
5.Composing and Decomposing Numbers 101-200 (Standard & Expanded Form).
6.Comparing and Ordering Numbers up to 200.
7.Estimating Quantities up to 200 and Verifying by Counting.
8.Identifying Even and Odd Numbers by Pairing.
9.Unit 1 Review and Application: Number Sense to 200.

Unit 2: Developing Fact Fluency & Mental Math Power ▼

10.Addition Facts to 20: Strategies for Efficient Recall.
11.Subtraction Facts from 20: Strategies (Think Addition) for Efficient Recall.
12.Mental Math: Adding 2-Digit + 1-Digit/2-Digit (No Regrouping, Sums to 50) – Concrete/Pictorial Bridge & Explanation.
13.Mental Math: Subtracting 2-Digit – 1-Digit/2-Digit (No Regrouping, within 50) – Concrete/Pictorial Bridge & Explanation.
14.Mental Math Strategies: Making Friendly Numbers (Compensating +/- to 50) & Explanation.
15.Mental Math: Estimation for Addition and Subtraction (Sums to 50).
16.Counting to 200 by 1s, 10s, and 100s (Forwards and Backwards).
17.Counting to 200 by 20s, 25s, and 50s (Forwards and Backwards).
18.Unit 2 Review: Fact Fluency & Mental Math.

Unit 3: Mastering 2-Digit Addition & Subtraction (to 100) ▼

19.Adding 2-Digit Numbers (No Regrouping) with Base-Ten Blocks & Place Value Charts.
20.Adding 2-Digit Numbers (Regrouping Ones to Tens) with Base-Ten Blocks.
21.Transition: Adding with Regrouping from Blocks to Place Value Drawings.
22.Adding with Regrouping using Drawings & Expanded Form.
23.Adding with Regrouping using the Standard Algorithm.
24.Subtracting 2-Digit Numbers (No Regrouping) with Base-Ten Blocks & Place Value Charts.
25.Subtracting 2-Digit Numbers (Regrouping Tens to Ones) with Base-Ten Blocks.
26.Transition: Subtracting with Regrouping from Blocks to Place Value Drawings.
27.Subtracting with Regrouping using Drawings & Expanded Form.
28.Subtracting with Regrouping using the Standard Algorithm.
29.Properties of Addition (Commutative, Associative) & Checking Calculations (+/-).
30.Unit 3 Review: 2-Digit Addition & Subtraction (to 100).

Unit 4: Foundations of Multiplication and Division ▼

31.Multiplication as Repeated Equal Groups and Arrays (Totals to 30).
32.Division as Equal Sharing (Up to 25 items, 2-5 sharers, Whole Number Answers).
33.Division as Equal Grouping (How many groups?, Up to 25 items).
34.Relationship between Addition and Multiplication.
35.Relationship between Subtraction and Division (Equal Grouping).
36.Simple Multiplicative Rate Problems (Whole Numbers – Concrete/Pictorial).
37.Solving Word Problems (Equal Groups/Sharing – Whole Numbers) using Models.
38.Fair Share Problems Resulting in Whole or Mixed Numbers (Concrete/Pictorial).
39.Unit 4 Review: Multiplication and Division Foundations.

Unit 5: Deepening Understanding of Fractions ▼

40.Fair Share Problems Resulting in Fractional Amounts (halves, thirds, fourths, sixths).
41.Comparing Unit Fractions from Fair Share Problems.
42.Introduction to Unit Fractions (halves, thirds, fourths, sixths) as Parts of a Whole (Area Models).
43.Representing Non-Unit Fractions (e.g., 2/3, 3/4) as Multiple Parts of a Whole (Area Models).
44.Recognizing Equivalence: One Half and Two Fourths, One Third and Two Sixths.
45.Finding Unit Fractions of a Set (halves, thirds, fourths, sixths).
46.Finding Non-Unit Fractions of a Set (e.g., 2/3 of 9).
47.Repeated Addition of a Unit Fraction (Concrete/Pictorial) and Recording Totals.
48.Connecting Repeated Addition of Unit Fractions to Numerator and Denominator.
49.Multiplication as Groups of Unit Fractions (1/2, 1/4) related to Repeated Addition.
50.Unit 5 Review: Fractions.

Unit 6: Geometry: Analyzing 2D Shapes ▼

51.Sorting 2D Shapes by Number of Sides and Side Lengths (Equal/Unequal).
52.Sorting 2D Shapes by Angles (Informal: “Corners,” Identifying Right Angles).
53.Identifying Lines of Symmetry in 2D Shapes.
54.Composing 2D Shapes from Simpler Shapes.
55.Decomposing 2D Shapes into Simpler Shapes.
56.Investigating Area Constancy through Rearranging Parts.
57.Determining Congruence of 2D Shapes (Direct Matching of Sides/Angles, Slides, Flips, Turns).
58.Creating Geometric Designs and Exploring Tessellations (Informal).
59.Unit 6 Review: 2D Shapes.

Unit 7: Measurement: Length and Time ▼

60.Choosing Appropriate Non-Standard Units for Measuring Length.
61.Inverse Relationship: Size of Unit and Number of Units (Length).
62.Relationship Between Centimetres and Metres (100cm = 1m).
63.Establishing Benchmarks for Centimetres and Metres.
64.Estimating Lengths in Centimetres and Metres using Benchmarks.
65.Measuring and Drawing Lengths in Centimetres (Starting at Zero Mark).
66.Measuring Lengths in Metres.
67.Units of Time: Relative Duration of Seconds, Minutes, Hours.
68.Describing Duration of Events using Standard and Non-Standard Time Units.
69.Unit 7 Review: Length and Time.

Unit 8: Pattern Detectives: Geometry, Numbers, and Hundred Charts ▼

70.Identifying, Describing, and Creating Geometric Patterns with Multiple Attributes (including Real-Life Contexts).
71.Translating Patterns Between Different Representations (Shape, Number, Sound, Action).
72.Determining Pattern Rules for Shape and Number Patterns (Repeating, Growing/Shrinking).
73.Extending Patterns and Identifying Missing Elements based on Rules.
74.Making and Justifying Predictions in Various Patterns.
75.Creating and Describing Patterns on a Hundred Chart (to 100).
76.Exploring Number Patterns in Input/Output Tables (Simple Addition/Subtraction Rules).
77.Unit 8 Review: Patterns.

Unit 9: Advanced Data Analysis: Two Attributes and New Graphs ▼

78.Sorting Data by Two Attributes using Two-Way Tables.
79.Sorting Data by Two Attributes using Venn Diagrams.
80.Sorting Data by Two Attributes using Carroll Diagrams.
81.Collecting Data for Two Attributes & Organizing in Two-Way Tally Tables.
82.Creating Line Plots from Numerical Data.
83.Interpreting Line Plots to Analyze Data.
84.Creating Bar Graphs from Categorical Data.
85.Interpreting Bar Graphs and Identifying the Mode(s).
86.Analyzing and Comparing Data from Various Displays (Tables, Logic Diagrams, Graphs).
87.Unit 9 Review: Advanced Data Analysis.

Unit 10: Money, Maps, and Early Algebraic Ideas ▼

88.Representing Money Amounts up to 200¢ ($2.00) using Coins.
89.Representing Money Amounts up to $10.00 using Coins & Bills (to $10).
90.Adding and Subtracting Money Amounts (Cents, and Dollars/Cents without regrouping over $1).
91.Making Change from Amounts up to $1.00 (Counting Up).
92.Identifying Symbols as Variables in Equations.
93.Describing How Symbols are Used as Variables to Make Equations True.
94.Equivalent Expressions: Finding What to Add/Subtract to Make Them Equal (Balancing).
95.Identifying and Using Equivalent Numerical Expressions for Numbers up to 100.
96.Creating and Interpreting Simple Maps of Familiar Places (Classroom, Schoolyard).
97.Using Maps: Describing Relative Positions and Simple Routes.
98.Problem Solving with Money (to $10), Variables, and Equivalence.
99.Unit 10 Review: Money, Maps, Algebra.

Unit 11: Exploring Chance and Probability ▼

100.Likelihood Language (Impossible, Unlikely, Equally Likely, Likely, Certain) for Events.
101.Describing the Likelihood of Complementary Events.
102.Making Predictions Based on Likelihood in Simple Chance Experiments.
103.Conducting Simple Chance Experiments and Recording Outcomes (Tally Tables).
104.Comparing Experimental Results to Initial Predictions.
105.Making and Testing Predictions about Mode(s) in Data from Different Populations.
106.Discussing Fairness in Simple Games of Chance.
107.Relating Likelihood to Simple Fractions (Informal Introduction).
108.Unit 11 Review: Chance and Probability.

Unit 12: Integrating Concepts – Probability, Code Logic, Applications ▼

109.Describing Likelihood of Events and Their Complements on a Probability Scale.
110.Making and Testing Predictions about the Mode of Data Sets by Comparing Two Populations.
111.Problem Solving by Interpreting Data with Likelihood Language.
112.Coding Logic: Understanding Sequential and Concurrent Events through Flowcharts/Diagrams.
113.Coding Logic: Designing Unplugged Algorithms with Sequential and Concurrent Steps.
114.Coding Logic: Analyzing Provided Code Snippets (Block-Based, Sequential & Concurrent).
115.Coding Logic: Describing Effects of Changes in Provided Code Snippets.
116.Integrated Problem Solving: Measurement (Length, Time, Money) and Operations.
117.Integrated Problem Solving: Patterns, Geometry, and Data.
118.Year-End Review of Key Fluencies: Addition/Subtraction Facts & 2-Digit Calculations.
119.Year-End Review of Key Concepts: Place Value, Fractions, Multiplication/Division Foundations.
120.Unit 12 Review & Course Culmination: Probability, Code Logic, and Integrated Applications.

Grade 3 (Ontario) ▼

Unit 1: Place Value Power to 1000 – Building and Understanding ▼

1.Read and Represent Numbers up to 1000 using Base-Ten Blocks.
2.Compose and Decompose Whole Numbers up to 1000 (Standard and Expanded Form).
3.Flexible Decomposition of 3-Digit Numbers using Base-Ten Blocks.
4.Using Place Value to Describe the Value of Digits in Multi-Digit Numbers.
5.Comparing and Ordering Whole Numbers up to 1000.
6.Rounding Whole Numbers to the Nearest Ten.
7.Rounding Whole Numbers to the Nearest Hundred.
8.Counting to 1000 by 1s, 10s, 100s (Forwards and Backwards).
9.Counting to 1000 by 25s, 50s, and 200s (Forwards and Backwards).
10.Unit 1 Review: Place Value to 1000.

Unit 2: Mastering Addition and Subtraction Algorithms to 1000 ▼

11.Mental Math Strategies for Addition to 1000 (Break Apart, Compensation).
12.Mental Math Strategies for Subtraction to 1000 (Counting Up, Constant Difference).
13.Estimating Sums and Differences to 1000.
14.Adding 3-Digit Numbers (No Regrouping & Regrouping Ones) – Concrete to Algorithm.
15.Adding 3-Digit Numbers (Regrouping Tens & Regrouping Ones/Tens) – Concrete to Algorithm & Practice.
16.Subtracting 3-Digit Numbers (No Regrouping & Regrouping Tens to Ones) – Concrete to Algorithm.
17.Subtracting 3-Digit Numbers (Regrouping Hundreds to Tens & Multiple Regroupings) – Concrete to Algorithm.
18.Subtracting 3-Digit Numbers (Regrouping Across Zeros) – Concrete to Algorithm & Practice.
19.Checking Calculations (+/-) and Solving 1-Step Word Problems (+/- to 1000 using SBI).
20.Unit 2 Review: Addition and Subtraction to 1000.

Unit 3: Multiplication & Division Foundations – Facts and Relationships ▼

21.Multiplication Facts of 2, 5, and 10 (Represent and Recall).
22.Related Division Facts for 2, 5, and 10 (Think Multiplication).
23.Representing Multiplication up to 10×10 using Arrays.
24.Representing Multiplication up to 10×10 using Equal Groups and Number Lines.
25.Representing Division up to 100÷10 as Equal Sharing.
26.Representing Division up to 100÷10 as Equal Grouping.
27.Relationship between Multiplication and Division (Fact Families).
28.Solving Multiplication Word Problems (up to 10×10 using SBI – Equal Groups Schema).
29.Solving Division Word Problems (up to 100÷10 using SBI – Sharing/Grouping Schemas).
30.Unit 3 Review: Multiplication & Division.

Unit 4: Fractions – Fair Shares and Equivalence ▼

31.Fair Share Problems Resulting in Whole or Mixed Numbers (halves, fourths, eighths).
32.Fair Share Problems Resulting in Proper Fractions (thirds, sixths, fifths, tenths).
33.Comparing Unit Fractions using Models and Reasoning from Fair Shares.
34.Equivalent Fractions: Halves, Fourths, Eighths using Area Models.
35.Equivalent Fractions: Thirds and Sixths using Area Models.
36.Equivalent Fractions: Fifths and Tenths using Area Models.
37.Placing Unit and Common Non-Unit Fractions on a Number Line (0 to 1).
38.Comparing Fractions with Like Denominators or Like Numerators.
39.Multiplication as Repeated Addition of Unit Fractions.
40.Unit 4 Review: Fractions.

Unit 5: Geometry – Exploring 3D Objects and 2D Shapes ▼

41.Sort, Construct, and Identify Cubes and Prisms by Attributes.
42.Sort, Construct, and Identify Pyramids by Attributes.
43.Sort, Construct, and Identify Cylinders and Cones by Attributes.
44.Composing and Decomposing 3D Structures.
45.Identifying 2D Shapes as Faces of 3D Objects and within Structures.
46.Identifying Congruent Lengths (Edges) of 3D Objects.
47.Identifying Congruent Faces of 3D Objects.
48.Determining if Two 3D Objects are Congruent.
49.Giving and Following Multistep Instructions for Movement (Location, Distance, Turns on a Grid).
50.Unit 5 Review: Geometry.

Unit 6: Measurement – Perimeter and Area Explorations ▼

51.Estimating and Measuring Perimeter of Polygons using Non-Standard Units.
52.Estimating and Measuring Perimeter of Polygons using Standard Units (cm, m).
53.Constructing Different Polygons with a Given Perimeter.
54.Estimating and Comparing Perimeter of Curved Shapes using Flexible Units.
55.Comparing Areas by Direct Matching, Covering, or Decomposing/Recomposing Shapes.
56.Demonstrating that Different Shapes Can Have the Same Area.
57.Measuring Area with Appropriate Non-Standard Units (Tessellating Units).
58.Explaining the Effect of Gaps and Overlaps on Area Measurement Accuracy.
59.Estimating, Measuring, and Comparing Areas using cm² (Grids) and m² (Cutouts); Connecting Area of Rectangles to Multiplication.
60.Unit 6 Review: Perimeter and Area.

Unit 7: Expanding Measurement Skills – Length, Mass, Capacity, Time ▼

61.Relationships, Benchmarks, and Estimation for Metric Length (mm, cm, m, km).
62.Measuring Mass: Non-Standard Units & Pan Balance; Introduction to Grams (g) and Kilograms (kg).
63.Measuring Capacity: Non-Standard Units; Introduction to Millilitres (mL) and Litres (L).
64.Conservation of Measurement (Different-Sized Units for the Same Attribute).
65.Telling Time to the Nearest Minute (Analog and Digital Clocks, AM/PM).
66.Elapsed Time in Minutes (within the hour).
67.Elapsed Time in Hours and Minutes (across the hour, simple cases).
68.Solving Problems Involving Time (Duration, Start/End Times).
69.Problem Solving with Length, Mass, Capacity (Choosing Units, Simple Conversions, Comparing).
70.Unit 7 Review: Length, Mass, Capacity, Time.

Unit 8: Patterns in Operations and Numbers to 1000 ▼

71.Identifying Repeating Elements and Operations in Patterns (Real-Life and Mathematical).
72.Creating Patterns with Repeating Elements, Movements, or Operations (Shapes, Numbers).
73.Translating Patterns Between Representations (Shapes, Numbers, Tables of Values, Descriptions).
74.Determining Pattern Rules for Repeating, Growing, and Shrinking Patterns.
75.Extending Patterns, Making Justified Predictions, and Identifying Missing Elements.
76.Creating and Describing Patterns Illustrating Number Relationships on Hundred Charts (to 1000).
77.Exploring Growing Patterns Involving Multiplication (e.g., Doubling, Tripling).
78.Input/Output Tables with Addition, Subtraction, and Simple Multiplication/Division Rules.
79.Using Patterns to Solve Contextual Problems.
80.Unit 8 Review: Patterns.

Unit 9: Data Management – Sorting, Graphing, and Interpreting ▼

81.Sorting Data by Two and Three Attributes using Tables.
82.Sorting Data by Two or Three Attributes using Venn Diagrams (Intersecting Circles).
83.Sorting Data by Two Attributes using Carroll Diagrams and Simple Tree Diagrams.
84.Collecting Qualitative Data (Categorical) and Quantitative Data (Numerical).
85.Organizing Collected Data using Frequency Tables (with Tally Marks and Frequencies).
86.Displaying Data: Creating Pictographs with Many-to-One Correspondence.
87.Displaying Data: Creating Bar Graphs with Many-to-One Correspondence and Appropriate Scales.
88.Determining the Mean for Simple Data Sets (Conceptual: Fair Share/Levelling Out).
89.Identifying the Mode(s) in Data Sets and Explaining its Meaning.
90.Analyzing Data from Various Displays (Frequency Tables, Graphs with Different Scales), Drawing Conclusions, and Making Arguments.

Unit 10: Algebraic Thinking and Financial Literacy ▼

91.Describing How Variables are Used as Placeholders for Unknowns and in Generalizations.
92.Using Variables in Various Contexts (Simple Formulas, Equations).
93.Determining if Sets of Addition, Subtraction, Multiplication, and Division Expressions are Equivalent.
94.Identifying and Using Equivalent Numerical Relationships for Numbers up to 1000.
95.Estimating and Calculating Change for Whole Dollar Transactions up to $100.
96.Estimating and Calculating Change for Transactions involving Dollars and Cents up to $10.
97.Understanding Concepts of Spending, Saving, Earning, Investing, and Donating.
98.Relationship between Spending and Saving & Recognizing Differing Financial Behaviors.
99.Determining if Something is Reasonably Priced (Making a Good Purchase).
100.Unit 10 Review: Algebra and Financial Literacy.

Unit 11: Probability and Making Predictions ▼

101.Likelihood Language (Impossible to Certain) & Representing on a Probability Line.
102.Using Likelihood to Make Predictions and Informed Decisions in Simple Chance Situations.
103.Conducting Simple Chance Experiments and Comparing Experimental Results to Predictions.
104.Introduction to Theoretical Probability for Simple Events with Equally Likely Outcomes.
105.Making Predictions about Mean and Mode in Different but Related Populations.
106.Testing Predictions about Mean and Mode by Comparing Data from Two Groups.
107.Designing Fair and Unfair Games of Chance and Explaining Fairness.
108.Discussing How Probability Influences Real-Life Decisions and Events.
109.Exploring Independent Events (Conceptual Understanding).
110.Unit 11 Review: Probability.

Unit 12: Advanced Coding Logic and Integrated Mathematical Applications ▼

111.Coding Logic: Understanding Sequential, Concurrent, and Repeating Events in Provided Code.
112.Coding Logic: Designing Unplugged Algorithms with Repeating Events (Loops).
113.Coding Logic: Analyzing and Predicting Effects of Altering Provided Code Snippets with Loops.
114.Coding Logic: Debugging Simple Unplugged Algorithms or Provided Code Snippets with Loops.
115.Describing How Changes to Parameters of Repeating Events (Loops) in Code Affect Outcomes.
116.Problem Solving: Multiplication/Division with Unit Fractions.
117.Problem Solving: Area and Perimeter of Simple Composite Shapes (Rectangles).
118.Problem Solving: Financial Literacy – Multi-Step Transactions.
119.Problem Solving: Using Data Analysis (Mode, Frequency) to Make Simple Probability Statements.
120.Unit 12 Review: Coding Logic (Loops) and Integrated Mathematical Problem Solving.

Grade 3 ▼

Unit 1: Understanding Multiplication Concepts ▼

1.Interpret products of whole numbers (Equal Groups)
2.Represent multiplication situations using drawings and equations (Equal Groups)
3.Interpret products of whole numbers (Arrays)
4.Represent multiplication situations using drawings and equations (Arrays)
5.Solve one-step multiplication word problems (Equal Groups)
6.Solve one-step multiplication word problems (Arrays)
7.Solve one-step multiplication word problems (Measurement Quantities – equal groups)
8.Differentiating between additive and multiplicative situations in word problems
9.Writing and solving multiplication stories involving equal groups and arrays
10.Unit 1 Review: Understanding Multiplication Concepts

Unit 2: Properties of Multiplication ▼

11.Apply the Commutative Property of Multiplication (Order Property)
12.Apply the Associative Property of Multiplication (Grouping Property – Introduction)
13.Using the Associative Property to make multiplying three factors easier
14.Apply the Distributive Property of Multiplication (Breaking apart a factor using addition – Introduction with Area Models)
15.Using the Distributive Property to solve multiplication problems (Focus on known facts)
16.Apply the Distributive Property when a factor is decomposed using subtraction (e.g., x9 as x10-x1)
17.Practice applying properties of multiplication (Commutative, Associative, Distributive) to solve problems
18.Using properties as strategies for mental math in multiplication
19.Solving multi-step problems that involve applying properties of multiplication
20.Unit 2 Review: Properties of Multiplication

Unit 3: Understanding Division, Its Relationship to Multiplication, & Finding Unknowns ▼

21.Interpret whole-number quotients (Equal Sharing – finding number in each group)
22.Interpret whole-number quotients (Equal Grouping – finding number of groups)
23.Understand division as an unknown-factor problem
24.Using multiplication and division fact families to solve problems
25.Determine the unknown whole number in a multiplication equation
26.Determine the unknown whole number in a division equation
27.Solve one-step division word problems (Equal Sharing or Equal Grouping)
28.Represent division word problems using drawings and equations with a symbol/letter for the unknown
29.Differentiating and solving one-step multiplication and division word problems
30.Unit 3 Review: Understanding Division, Its Relationship to Multiplication, & Finding Unknowns

Unit 4: Multiplication & Division Fluency (Part 1: Facts of 0,1,2,5,10 & patterns) ▼

31.Multiplication Fact Strategies & Fluency (Factor 0 – Zero Property; Factor 1 – Identity Property)
32.Multiplication Fact Strategies & Fluency (Factor 2 – Doubles; Factor 10 – Place Value Pattern)
33.Multiplication Fact Strategies & Fluency (Factor 5 – Skip Counting, Half of x10)
34.Division Fact Strategies & Fluency (Relating to x0,x1,x2,x5,x10 multiplication facts)
35.Identifying Arithmetic Patterns in Multiplication (Focus on 0,1,2,5,10 facts)
36.Solving one-step word problems with multiplication/division facts (0,1,2,5,10)
37.Mixed Practice & Games for Fluency (Facts of 0,1,2,5,10 – Multiplication and Division)
38.Applying strategies to derive unknown facts from known “easy” facts
39.Cumulative Practice: Multiplication & Division with factors 0,1,2,5,10 and simple word problems
40.Unit 4 Review: Multiplication & Division Fluency (Part 1: Facts of 0,1,2,5,10 & patterns)

Unit 5: Multiplication & Division Fact Strategies & Fluency (Part 2: Facts of 3,4,6,7,8,9 & patterns) ▼

41.Multiplication Fact Strategies & Fluency (Factor 3 – Skip Counting, Doubling +1 group; Factor 4 – Double Double)
42.Multiplication Fact Strategies & Fluency (Factor 6 – Using x5 +1 group or x3 doubled; Factor 8 – Using x4 doubled)
43.Multiplication Fact Strategies & Fluency (Factor 9 – Using x10 minus 1 group, patterns; Factor 7 – Using known facts and distributive property)
44.Multiplication Fluency: Square Numbers (e.g., 3×3, …, 9×9)
45.Division Fact Strategies & Fluency (Relating to multiplication facts of 3,4,6,7,8,9)
46.Identifying Arithmetic Patterns in Multiplication (Focus on all factors, general properties)
47.Solving one-step word problems with multiplication/division facts (all factors 0-10)
48.Know from memory all products of two one-digit numbers (Consolidated Practice & Assessment Goal)
49.Cumulative Fluency Practice: Multiplication and Division (All Facts within 100)
50.Unit 5 Review: Multiplication & Division Fact Strategies & Fluency (Part 2: Facts of 3,4,6,7,8,9 & patterns)

Unit 6: Place Value; Rounding; Estimating; Adding & Subtracting Fluently within 1000 ▼

51.Rounding to the Nearest 10 (Review and Application)
52.Rounding to the Nearest 100 (Review and Application)
53.Estimating Sums by Rounding addends to the nearest 10 or 100
54.Estimating Differences by Rounding to the nearest 10 or 100
55.Adding within 1000 using strategies based on place value (e.g., partial sums, open number line)
56.Adding within 1000 using the standard algorithm with regrouping
57.Subtracting within 1000 using strategies based on place value (e.g., open number line – counting up or back, partial differences)
58.Subtracting within 1000 using the standard algorithm with regrouping (including across zeros)
59.Solving one- and two-step word problems involving addition/subtraction within 1000 using estimation and precise calculation
60.Unit 6 Review: Place Value; Rounding; Estimating; Adding & Subtracting Fluently within 1000

Unit 7: Multiplying by Multiples of 10; Solving Two-Step Word Problems (All Operations) ▼

61.Multiplying one-digit whole numbers by multiples of 10 (in the range 10-90) using place value understanding
62.Multiplying one-digit whole numbers by multiples of 10 using properties of operations
63.Practice multiplying one-digit numbers by multiples of 10 (10-90)
64.Solving one-step word problems involving multiplying by multiples of 10
65.Solving two-step word problems involving addition and subtraction (Review and Extension to 1000)
66.Solving two-step word problems involving multiplication and division (Products/dividends within 100)
67.Solving two-step word problems using a mix of any two operations (numbers appropriate for G3 fluency)
68.Representing two-step word problems using equations with a letter for the unknown quantity
69.Assessing the reasonableness of answers in two-step word problems using estimation (rounding or mental math)
70.Unit 7 Review: Multiplying by Multiples of 10; Solving Two-Step Word Problems (All Operations)

Unit 8: Understanding Fractions & Representing (Unit Fractions, a/b, Partitioning Shapes, Number Line) ▼

71.Understand a fraction 1/b as one part when a whole is partitioned into ‘b’ equal parts (Emphasize Equal Parts)
72.Represent unit fractions (1/b where b=2,3,4,6,8) using area models (circles, rectangles, squares) and linear models (fraction strips)
73.Understand a fraction a/b as the quantity formed by ‘a’ parts of size 1/b (Composing non-unit fractions from unit fractions)
74.Represent fractions a/b (where b=2,3,4,6,8) using various area models and linear models
75.Partition shapes (rectangles, circles) into parts with equal areas and express the area of each part as a unit fraction of the whole
76.Introduction to fractions on a number line: Defining the interval from 0 to 1 as the whole and partitioning it into ‘b’ equal parts
77.Represent unit fractions (1/b) on a number line, recognizing that each part has size 1/b and its endpoint locates the number 1/b
78.Represent fractions (a/b) on a number line by marking off ‘a’ lengths of 1/b from 0
79.Placing fractions greater than 1 (improper fractions like 5/4 or 7/3) on the number line by extending partitioning beyond 1
80.Unit 8 Review: Understanding Fractions & Representing (Unit Fractions, a/b, Partitioning Shapes, Number Line)

Unit 9: Fractions on the Number Line & Equivalent Fractions; Whole Numbers as Fractions ▼

81.Understand two fractions as equivalent (equal) if they are the same size, using visual fraction models (area models, fraction strips)
82.Understand two fractions as equivalent (equal) if they are at the same point on a number line
83.Recognize simple equivalent fractions (e.g., 1/2 = 2/4, 4/6 = 2/3) using visual reasoning and models
84.Generate simple equivalent fractions (e.g., for 1/2, 1/3, 1/4, 2/3, 3/4) using visual fraction models
85.Explain why fractions are equivalent using visual fraction models (focus on size and number of parts)
86.Express whole numbers (1, 2, 3) as fractions (e.g., 3 = 3/1)
87.Recognize fractions that are equivalent to whole numbers (e.g., 6/1 = 6; 3/3 = 1; 8/2 = 4)
88.Practice with equivalent fractions and whole numbers as fractions
89.Introduce comparing fractions with unlike denominators by finding common numerators or common denominators (visual, simple cases)
90.Unit 9 Review: Fractions on the Number Line & Equivalent Fractions; Whole Numbers as Fractions

Unit 10: Comparing Fractions; Measurement: Time (to minute, intervals), Liquid Volume & Mass ▼

91.Compare two fractions with the same numerator by reasoning about their size (using models, number lines, and symbols >,=,<)
92.Compare two fractions with the same denominator by reasoning about their size (using models, number lines, and symbols >,=,<)
93.Comparing fractions to benchmarks like 1/2 or 1 whole
94.Understanding that fraction comparisons are valid only when the two fractions refer to the same size whole
95.Mixed practice comparing fractions (same numerator, same denominator, or to benchmarks)
96.Tell and write time to the nearest minute using analog and digital clocks
97.Measure time intervals in minutes (elapsed time) using number lines or clock faces (counting on/back within 1-2 hours)
98.Solve one-step word problems involving addition and subtraction of time intervals in minutes
99.Measure and estimate liquid volumes (Liters/milliliters conceptually) and masses (grams/kilograms)
100.Unit 10 Review: Comparing Fractions; Measurement: Time (to minute, intervals), Liquid Volume & Mass

Unit 11: Measurement Word Problems (Volume/Mass); Data Analysis (Scaled Graphs, Line Plots)

101.Solve one-step word problems involving multiplication and division of liquid volumes (liters) or masses (grams/kilograms)
102.Draw a scaled picture graph (choosing an appropriate scale where each symbol represents 2, 5, or 10 units)
103.Draw a scaled bar graph (choosing an appropriate scale where intervals are 2, 5, 10, or other suitable number)
104.Solve one- and two-step “how many more” and “how many less” problems using information from scaled picture graphs and bar graphs
105.Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
106.Show measurement data (lengths to whole, half, or quarter inch) by making a line plot with an appropriate fractional horizontal scale
107.Interpret data from line plots with fractional scales
108.Mixed practice with data representation and interpretation
109.Review all types of word problems using the four operations
110.Unit 11 Review: Measurement Word Problems (Volume/Mass); Data Analysis (Scaled Graphs, Line Plots)

Unit 12: Geometry (Lines, Angles, 2D Figures, Symmetry); Angle Measurement; Data (Line Plots with Fractions)

111.Understand area as an attribute of plane figures and measure area by counting unit squares (sq cm, sq m, sq in, sq ft)
112.Relate area to multiplication: Find the area of a rectangle with whole-number side lengths by tiling it and showing it is the same as multiplying side lengths
113.Solve real-world and mathematical problems involving area of rectangles by multiplying side lengths
114.Use area models to represent the distributive property in multiplication
115.Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding their areas
116.Understand and find the perimeter of polygons by adding side lengths
117.Solve problems involving perimeter, including finding an unknown side length given the perimeter and other side lengths
118.Distinguish between area and perimeter; Explore rectangles with the same perimeter and different areas, or same area and different perimeters
119.Understand attributes of shapes; Categorize shapes (e.g., quadrilaterals) based on shared attributes
120.Unit 12 Review: Geometry (Lines, Angles, 2D Figures, Symmetry); Angle Measurement; Data (Line Plots with Fractions)

Grade 4 (Ontario) ▼

Unit 1: Mastering Place Value to 10 000 and Fractions Foundations ▼

1.Read and Represent Whole Numbers up to 10 000 using Base-Ten Blocks & Place Value Charts.
2.Compose and Decompose Whole Numbers up to 10 000 (Standard & Expanded Form).
3.Flexible Decomposition of 4-Digit Numbers.
4.Practice Flexible Decomposition and its Applications (Total Units).
5.Comparing and Ordering Whole Numbers up to 10 000.
6.Rounding Whole Numbers to the Nearest Ten, Hundred, and Thousand using Number Lines.
7.Rounding Whole Numbers to the Nearest Ten, Hundred, and Thousand using Place Value Rules.
8.Representing Fractions (Halves to Tenths) and Understanding Denominator/Numerator.
9.Identifying Everyday Uses of Numbers to 10 000 and Fractions.
10.Unit 1 Review: Place Value to 10 000 & Fraction Foundations.

Unit 2: Building Multiplication and Division Fluency ▼

11.Multiplication Facts of 0s, 1s, 2s, 5s, 10s (Strategies and Recall).
12.Related Division Facts for 0s, 1s, 2s, 5s, 10s (Fact Families).
13.Multiplication Facts of 3s, 4s, 6s (Strategies: Doubles, Arrays, Known Facts).
14.Related Division Facts for 3s, 4s, 6s (Fact Families).
15.Multiplication Facts of 7s, 8s, 9s (Strategies: Distributive Property, Patterns).
16.Related Division Facts for 7s, 8s, 9s (Fact Families).
17.Properties of Operations (Commutative and Associative for Multiplication).
18.Relationships Between All Four Operations.
19.Solving Multi-Step Word Problems Involving All Four Operations.
20.Unit 2 Review: Multiplication and Division Fluency & Relationships.

Unit 3: Operations with Larger Numbers and Decimals ▼

21.Adding Whole Numbers up to 10 000 using the Standard Algorithm.
22.Subtracting Whole Numbers up to 10 000 using the Standard Algorithm (Including Zeros).
23.Multiplication: 2-Digit by 1-Digit using Area Models and Partial Products.
24.Multiplication: 3-Digit by 1-Digit using Area Models and Standard Algorithm.
25.Multiplication: 2-Digit by 2-Digit using Area Models (Conceptual).
26.Mental Math: Multiplying Whole Numbers by 10, 100, 1000.
27.Reading and Representing Decimal Tenths and Hundredths using Models and Fraction Equivalents.
28.Comparing, Ordering, and Rounding Decimal Tenths and Hundredths.
29.Adding and Subtracting Decimal Tenths and Hundredths using Models and Standard Algorithm.
30.Unit 3 Review: Larger Number Operations & Decimal Foundations.

Unit 4: Mastering Division and Decimal Operations ▼

31.Division: 2-Digit by 1-Digit using Base-Ten Blocks (Equal Sharing & Grouping).
32.Division: 2-Digit by 1-Digit using the Partial Quotients Strategy.
33.Division: 3-Digit by 1-Digit using the Partial Quotients Strategy.
34.Division: Interpreting Remainders and Expressing Remainders as Fractions.
35.Mental Math: Dividing Whole Numbers by 10, 100, 1000.
36.Multiplying Decimals (Tenths/Hundredths) by Whole Numbers.
37.Mental Math Strategies for Adding and Subtracting Decimal Tenths and Hundredths.
38.Solving Word Problems (All 4 Ops with Whole Numbers; Add/Sub/Multiply Decimals by Whole Numbers).
39.Solving Division Problems (2/3-Digit by 1-Digit) in Context, Interpreting Remainders.
40.Unit 4 Review: Division & Decimal Operations.

Unit 5: Expanding Fraction and Decimal Understanding ▼

41.Counting Forwards and Backwards by Halves, Thirds, Fourths, Fifths (Including Mixed Numbers).
42.Counting Forwards and Backwards by Sixths, Eighths, Tenths (Including Mixed Numbers).
43.Fair-Share Scenarios: Comparing Portions when Wholes and Sharers Differ.
44.Ordering Fractions (Like/Unlike Denominators) using Benchmarks (0, 1/2, 1) and Common Denominators.
45.Relationships and Equivalences: Fractions (Tenths/Hundredths) and Decimal Tenths/Hundredths.
46.Generating Equivalent Fractions using Multiplication and Division.
47.Adding and Subtracting Fractions with Like Denominators (Halves to Tenths).
48.Multiplying Whole Numbers by Unit Fractions (Interpreting as “Fraction of a Set”).
49.Multiplying Whole Numbers by Non-Unit Proper Fractions (e.g., 2/3 of 18).
50.Unit 5 Review: Fractions & Decimals.

Unit 6: Geometry – 2D/3D Shapes, Transformations, and Spatial Views ▼

51.Geometric Properties of Rectangles, Squares, Parallelograms, Rhombuses, Trapezoids.
52.Identifying and Constructing Congruent 2D Shapes (Triangles, Quadrilaterals).
53.Plotting and Reading Coordinates in the First Quadrant of the Cartesian Plane.
54.Describing Translations from One Coordinate to Another on a Grid.
55.Performing Translations of 2D Shapes on a Grid.
56.Performing Reflections of 2D Shapes on a Grid (across horizontal/vertical lines of reflection).
57.Performing Rotations of 2D Shapes on a Grid (90° CW/CCW about a vertex or origin).
58.Drawing Top, Front, and Side Views of Simple 3D Objects.
59.Matching 2D Orthographic Views (Top, Front, Side) with their Corresponding 3D Objects.
60.Unit 6 Review: 2D Geometry, Transformations & Spatial Views.

Unit 7: Measurement All Around – Metric System, Angles, and Area ▼

61.Relationships Between Metric Units of Mass (g/kg) & Capacity (mL/L); Simple Conversions.
62.Estimating Mass (g/kg) & Capacity (mL/L) using Benchmarks and Choosing Appropriate Units.
63.Understanding Metric Prefixes (kilo, centi, milli) and Relative Size across Length, Mass, Capacity.
64.Selecting Appropriate Metric Units and Tools for Measurement (Length, Mass, Capacity, Temperature).
65.Identifying and Classifying Angles (Right, Straight, Acute, Obtuse) and Relating to Degrees (90°, 180°).
66.Estimating, Measuring, and Drawing Angles using a Protractor (to nearest degree).
67.Area of Rectangles: Using the Formula A=lxw.
68.Applying Area Formula for Rectangles to Find an Unknown Side Length.
69.Solving Problems involving Area of Rectangles and Simple Composite Shapes (made of rectangles).
70.Unit 7 Review: Metric Measurement, Angles, Area.

Unit 8: Time, Patterns, and Algebraic Relationships ▼

71.Solving Problems Involving Elapsed Time (Hours, Minutes, Seconds, including 24-hour clock).
72.Identifying and Describing Repeating and Growing/Shrinking Patterns (Numerical, Geometric, Real-Life).
73.Creating and Representing Repeating and Growing Patterns using Tables of Values, Graphs, and Simple Algebraic Expressions.
74.Determining Pattern Rules (Repeating & Growing/Shrinking) and Extending Patterns.
75.Making Justified Predictions and Identifying Missing Elements in Various Patterns.
76.Creating Patterns to Illustrate Relationships Among Whole Numbers & Decimal Tenths/Hundredths.
77.Identifying and Using Symbols (Letters) as Variables in Expressions and Simple Equations.
78.Solving One-Step Equations Involving Whole Numbers (All Operations, up to 100) using Inverse Operations and Substitution.
79.Solving Simple One-Step Inequalities (Addition/Subtraction of Whole Numbers up to 20) and Graphing Solutions on a Number Line.
80.Unit 8 Review: Time, Patterns, Algebra.

Unit 9: Data Management – Sorting, Graphing, and Interpreting ▼

81.Differentiating Between Qualitative and Quantitative Data.
82.Collecting Data from Primary Sources (Surveys, Experiments) & Secondary Sources (Websites, Books) to Compare Two or More Sets.
83.Organizing Comparative Data in Frequency Tables and Stem-and-Leaf Plots.
84.Selecting and Justifying Appropriate Graph Types for Displaying Data (Including Multiple-Bar Graphs and Line Graphs).
85.Constructing Multiple-Bar Graphs and Simple Line Graphs from Data Sets.
86.Analyzing Data in Stem-and-Leaf Plots, Multiple-Bar Graphs, and Line Graphs.
87.Determining Mean, Median, and Mode(s) for Whole Number Data Sets.
88.Explaining What Mean, Median, and Mode Indicate About a Data Set.
89.Planning and Creating a Simple Infographic to Tell a Story with Data.
90.Unit 9 Review: Data Handling.

Unit 10: Financial Literacy – Payments, Transactions, and Decisions ▼

91.Identifying and Describing Various Methods of Payment (Cash, Debit Card, Credit Card, E-transfer).
92.Estimating the Total Cost of Multiple Items (Whole Dollars and Simple Cents, No Tax).
93.Calculating the Exact Cost of Multiple Items and Change Needed (Cash Payments, including Dollars and Cents).
94.Understanding Concepts of Spending, Saving, Earning, Investing, and Donating (Key Factors and Goals).
95.Analyzing the Relationship Between Spending and Saving and Recognizing Differing Financial Behaviors.
96.Determining if Something is Reasonably Priced (Making a Good Purchase Decision).
97.Identifying Types of Taxes in Canada (e.g., Sales Tax like GST/HST/PST, Income Tax basics, Property Tax) and How Tax Revenue is Used by Governments.
98.Designing Sample Basic Budgets for Specific Goals (Earning/Spending/Saving Scenarios).
99.Understanding Basic Concepts of Credit and Debt and their Impact on Financial Decisions.
100.Unit 10 Review: Financial Literacy.

Unit 11: Probability and Predictions ▼

101.Describing Likelihood of Single Events using Words (Impossible to Certain) & Representing on a Probability Line.
102.Using Likelihood to Make Predictions and Informed Decisions in Chance Situations with Unequal Likelihoods.
103.Conducting Multi-Trial Chance Experiments and Systematically Recording Data.
104.Comparing Experimental Probability (Relative Frequency) to Theoretical Probability (for simple events).
105.Making Justified Predictions about Mean, Median, and Mode for Different but Related Populations.
106.Testing Predictions about Mean, Median, and Mode by Analyzing Provided Data Sets from Two Populations.
107.Designing and Analyzing Fair and Unfair Spinner Games, Explaining Fairness Based on Outcomes.
108.Identifying and Discussing Probability in Real-World Contexts (e.g., Weather Forecasts, Games of Chance, Surveys, Basic Insurance Ideas).
109.Determining Sample Space for Simple Combined Events using Lists and Tree Diagrams.
110.Unit 11 Review: Probability & Predictions.

Unit 12: Applying Unit Rates, Advanced Coding Logic, and Mathematical Reasoning ▼

111.Calculating and Applying Unit Rates in Varied Contexts.
112.Identifying Which Purchase Offers the Best Value by Comparing Unit Rates.
113.Solving Problems Involving Unit Rates and Proportional Reasoning (Informal).
114.Coding Logic: Understanding Sequential, Concurrent, Repeating, and Nested Events from Visual Code.
115.Coding Logic: Designing Unplugged Algorithms with Sequential, Repeating, and Nested Events.
116.Coding Logic: Analyzing and Predicting the Effect of Altering Visual Code with Loops and Nested Structures.
117.Coding Logic: Describing How Changes to Parameters in Nested Code Structures Affect Outcomes.
118.Solving Multi-Step Financial Problems with Decimals and Fractions.
119.Analyzing Data and Rates to Make Probabilistic Judgments.
120.Unit 12 Review: Applying Unit Rates, Coding Logic, and Mathematical Concepts.

Grade 4 ▼

Unit 1: Place Value of Multi-Digit Whole Numbers

1.Recognize Place Value Relationships: Ten Times the Value
2.Read and Write Multi-Digit Whole Numbers (up to 1,000,000) using Standard Form and Number Names
3.Write Multi-Digit Whole Numbers using Expanded Form
4.Practice Reading and Writing Multi-Digit Numbers in All Forms
5.Compare Two Multi-Digit Numbers using Place Value
6.Record Comparisons of Multi-Digit Numbers using >, =, and < Symbols
7.Order a Set of Multi-Digit Numbers from Least to Greatest
8.Order a Set of Multi-Digit Numbers from Greatest to Least
9.Problem Solving with Place Value (Reading, Writing, Comparing Numbers)
10.Unit 1 Review: Place Value of Multi-Digit Whole Numbers

Unit 2: Rounding; Fluently Adding & Subtracting Multi-Digit Numbers

11.Rounding Multi-Digit Numbers to the Nearest Ten or Hundred (Using Number Lines and Place Value)
12.Rounding Multi-Digit Numbers to Any Place (Thousands, Ten Thousands, etc., Using Place Value Rule)
13.Practice Rounding Multi-Digit Numbers to Various Places
14.Fluently Add Multi-Digit Whole Numbers using the Standard Algorithm (Conceptual Anchoring with Base-Ten Blocks/Drawings)
15.Practice Fluently Adding Multi-Digit Whole Numbers (up to 1,000,000)
16.Fluently Subtract Multi-Digit Whole Numbers using the Standard Algorithm (Conceptual Anchoring with Base-Ten Blocks/Drawings, including regrouping)
17.Practice Fluently Subtracting Multi-Digit Whole Numbers (up to 1,000,000, including across zeros)
18.Mixed Addition and Subtraction Fluency Practice with Multi-Digit Numbers (Standard Algorithm)
19.Solving One- and Two-Step Word Problems Involving Addition/Subtraction of Multi-Digit Numbers and Rounding/Estimation
20.Unit 2 Review: Rounding; Fluently Adding & Subtracting Multi-Digit Numbers

Unit 3: Multiplication as Comparison; Factors, Multiples, Prime & Composite; Number Patterns

21.Interpret a Multiplication Equation as a Comparison
22.Represent Verbal Statements of Multiplicative Comparisons as Multiplication Equations
23.Solve Multiplicative Comparison Word Problems (Result Unknown or Product Unknown)
24.Solve Multiplicative Comparison Word Problems (Group Size Unknown or Number of Groups/Multiplier Unknown)
25.Distinguish Multiplicative Comparison from Additive Comparison in Word Problems
26.Find all Factor Pairs for a Whole Number in the range 1-100
27.Recognize that a Whole Number is a Multiple of Each of its Factors; Determine if a number is a multiple of a given 1-digit number
28.Determine whether a given Whole Number (1-100) is Prime or Composite (Using Factor Pairs)
29.Generate and Analyze Number Patterns based on a given rule (linking to factors/multiples)
30.Unit 3 Review: Multiplication as Comparison; Factors, Multiples, Prime & Composite; Number Patterns

Unit 4: Multi-Digit Multiplication

31.Multiply a Whole Number of up to Four Digits by a One-Digit Whole Number (Place Value Strategies & Partial Products, Conceptual Anchoring with Models)
32.Multiply a Whole Number of up to Four Digits by a One-Digit Whole Number (Standard Algorithm, with connection to models)
33.Practice: Multiply up to 4-digit by 1-digit numbers using the standard algorithm and other strategies
34.Multiply Two Two-Digit Numbers (Place Value Strategies & Partial Products, Conceptual Anchoring with Area Models)
35.Multiply Two Two-Digit Numbers (Standard Algorithm – or efficient method based on partial products, with connection to models)
36.Practice: Multiply 2-digit by 2-digit numbers using the standard algorithm and other strategies
37.Solving Word Problems Involving Multi-Digit Multiplication (up to 4-digit x 1-digit, and 2-digit x 2-digit)
38.Choosing between Multiplication and Addition in Word Problems
39.Estimating Products and Assessing Reasonableness of Answers in Multiplication
40.Unit 4 Review: Multi-Digit Multiplication

Unit 5: Multi-Digit Division

41.Divide up to Four-Digit Dividends by One-Digit Divisors (Place Value Strategies – Partial Quotients, Conceptual Anchoring with Models)
42.Divide up to Four-Digit Dividends by One-Digit Divisors (Relationship to Multiplication – Estimating Quotients with known facts)
43.Divide up to Four-Digit Dividends by One-Digit Divisors (Arrays/Area Models – relating to partial quotients)
44.Divide up to Four-Digit Dividends by One-Digit Divisors (Standard Algorithm – Introduction, with connection to models/strategies)
45.Interpreting Remainders in Division Word Problems
46.Practice: Divide up to 4-digit by 1-digit numbers, finding quotients and remainders using various strategies
47.Solving One-Step Word Problems Involving Multi-Digit Division (with and without remainders)
48.Checking Division Calculations using Multiplication and the Remainder
49.Choosing between Multiplication and Division in Word Problems
50.Unit 5 Review: Multi-Digit Division

Unit 6: Solving One-Step & Two-Step Word Problems (All Four Operations)

51.Solve One-Step Word Problems Using All Four Operations (Review and Mixed Practice)
52.Introduction to Two-Step Word Problems: Identifying the Steps and Operations
53.Solve Two-Step Word Problems involving Addition and Subtraction of Whole Numbers
54.Solve Two-Step Word Problems involving Multiplication and Addition/Subtraction
55.Solve Two-Step Word Problems involving Division and Addition/Subtraction (including interpreting remainders)
56.Represent Multi-Step Word Problems using Equations with a Letter for the Unknown Quantity
57.Assess the Reasonableness of Answers to Multi-Step Word Problems using Estimation Strategies (Rounding, Compatible Numbers)
58.Practice: Solving a Variety of One- and Two-Step Word Problems (All Four Operations)
59.Writing Own One- and Two-Step Word Problems
60.Unit 6 Review: Solving One-Step & Introduction to Two-Step Word Problems (All Four Operations)

Unit 7: Fraction Equivalence and Ordering

61.Explain Fraction Equivalence using Visual Fraction Models (a/b = (n×a)/(n×b))
62.Recognize and Generate Equivalent Fractions using Visual Models (Consolidated)
63.Generate Equivalent Fractions using Multiplication or Division (Symbolic)
64.Practice: Recognizing and Generating Various Equivalent Fractions
65.Compare Two Fractions with Different Numerators and Different Denominators by Creating Common Denominators
66.Compare Two Fractions with Different Numerators and Different Denominators by Creating Common Numerators
67.Compare Two Fractions with Different Numerators and Different Denominators by Comparing to Benchmark Fractions (0, 1/2, 1)
68.Record Comparisons of Fractions with Symbols >, =, or <, and Justify Conclusions using Visual Models or Reasoning
69.Ordering a Set of Fractions with Unlike Denominators
70.Unit 7 Review: Fraction Equivalence and Ordering

Unit 8: Building Fractions – Adding & Subtracting Fractions and Mixed Numbers with Like Denominators

71.Understand Addition/Subtraction of Fractions as Joining/Separating Parts of the Same Whole (Like Denominators)
72.Add and Subtract Fractions with Like Denominators using Visual Models and Equations
73.Decompose a Fraction into a Sum of Fractions with the Same Denominator in More Than One Way (Visual Models & Equations)
74.Understand Mixed Numbers as a Sum of a Whole Number and a Fraction
75.Convert Mixed Numbers to Improper Fractions
76.Convert Improper Fractions to Mixed Numbers
77.Add Mixed Numbers with Like Denominators (Adding whole parts and fractional parts, regrouping fractions if sum ≥ 1)
78.Subtract Mixed Numbers with Like Denominators (Subtracting whole/fractional parts, regrouping a whole into a fraction if needed)
79.Solve Word Problems Involving Addition and Subtraction of Fractions and Mixed Numbers (Like Denominators)
80.Unit 8 Review: Building Fractions – Adding & Subtracting Fractions and Mixed Numbers with Like Denominators

Unit 9: Multiplying Fractions by Whole Numbers

81.Understand a Fraction a/b as a Multiple of 1/b (e.g., 3/4 = 3 × (1/4))
82.Understand a Multiple of a/b as a Multiple of 1/b (e.g., 3 × (2/5) as 6 × (1/5), which is 6/5)
83.Multiply a Fraction by a Whole Number using the understanding n × (a/b) = (n × a)/b
84.Practice Multiplying a Fraction by a Whole Number (using models to verify and the formula)
85.Convert Products of Whole Numbers and Fractions to Mixed Numbers
86.Solve Word Problems Involving Multiplication of a Fraction by a Whole Number (Result as a fraction or mixed number)
87.Solve Word Problems Involving Multiplication of a Fraction by a Whole Number (Interpreting the product in context and units)
88.Finding a Fractional Part of a Whole Number (e.g., 1/4 of 12)
89.Practice solving a variety of word problems involving multiplication of fractions by whole numbers
90.Unit 9 Review: Multiplying Fractions by Whole Numbers

Unit 10: Decimal Fractions (Tenths & Hundredths); Comparing Decimals

91.Express a Fraction with Denominator 10 as an Equivalent Fraction with Denominator 100
92.Add Two Fractions with Respective Denominators 10 and 100
93.Use Decimal Notation for Fractions with Denominator 10 (Tenths)
94.Use Decimal Notation for Fractions with Denominator 100 (Hundredths)
95.Relate decimal notation for tenths and hundredths (e.g., 0.3 = 0.30)
96.Compare Two Decimals to Hundredths by Reasoning About Their Size (Using Visual Models – Grids or Number Lines)
97.Compare Two Decimals to Hundredths by Reasoning About Their Size (Place Value)
98.Record Comparisons of Decimals with Symbols >, =, or <, and Justify Conclusions
99.Solving word problems involving comparison of decimals to hundredths (e.g., money, measurements)
100.Unit 10 Review: Decimal Fractions (Tenths & Hundredths); Comparing Decimals

Unit 11: Measurement Conversions; Area and Perimeter

101.Know Relative Sizes of Measurement Units (Length: km, m, cm; Mass: kg, g; Volume: l, ml; Time: hr, min, sec)
102.Express Measurements in a Larger Unit in Terms of a Smaller Unit (Length, Mass, Volume Conversions)
103.Express Measurements in a Larger Unit in Terms of a Smaller Unit (Time Conversions)
104.Record Measurement Equivalents in a Two-Column Table (All unit types)
105.Solve One-Step Word Problems Involving Measurement Conversions (Distances, Liquid Volumes, Masses of Objects, Time)
106.Apply the Area Formula for Rectangles in Real-World and Mathematical Problems
107.Apply the Perimeter Formula for Rectangles in Real-World and Mathematical Problems
108.Solve Real-World Problems Involving Both Area and Perimeter of Rectangles, distinguishing between them
109.Practice: Solving Mixed Measurement Conversion and Area/Perimeter Word Problems in realistic scenarios
110.Unit 11 Review: Measurement Conversions; Area and Perimeter

Unit 12: Geometry (Lines, Angles, 2D Figures, Symmetry); Angle Measurement; Data (Line Plots with Fractions)

111.Draw and Identify Points, Lines, Line Segments, Rays, and Angles (Right, Acute, Obtuse)
112.Draw and Identify Perpendicular and Parallel Lines in Two-Dimensional Figures
113.Classify Two-Dimensional Figures Based on the Presence or Absence of Parallel or Perpendicular Lines
114.Classify Two-Dimensional Figures Based on the Presence or Absence of Angles of a Specified Size (Right, Acute, Obtuse)
115.Understand Angle Measurement: Degrees and relationship to a circle (1 degree = 1/360 of a circle)
116.Measure Angles in Whole-Number Degrees using a Protractor and Sketch Angles of Specified Measure
117.Recognize and Identify Lines of Symmetry in Two-Dimensional Figures
118.Draw Lines of Symmetry for Symmetric Figures
119.Make a Line Plot to Display a Data Set of Measurements in Fractions of a Unit (1/2, 1/4, 1/8)
120.Unit 12 Review: Geometry (Lines, Angles, 2D Figures, Symmetry); Angle Measurement; Data (Line Plots with Fractions)

Grade 5 ▼

Unit 1: Place Value System & Powers of Ten

1.Recognize Place Value: A Digit Represents 10 Times the Value to its Right
2.Recognize Place Value: A Digit Represents 1/10 the Value to its Left
3.Powers of 10: Understanding Exponents
4.Use Whole-Number Exponents to Denote Powers of 10
5.Explain Patterns in Zeros when Multiplying a Whole Number by Powers of 10
6.Explain Patterns in Decimal Point Placement when Multiplying a Decimal by Powers of 10
7.Explain Patterns in Decimal Point Placement when Dividing a Decimal by Powers of 10
8.Practice: Multiplying and Dividing Whole Numbers and Decimals by Powers of 10
9.Solving Word Problems Involving Powers of 10
10.Unit 1 Review: Place Value System & Powers of Ten

Unit 2: Multi-Digit Whole Number Multiplication

11.Multiply Multi-Digit Whole Numbers (e.g., 2-digit by 2-digit) using Place Value Strategies (Partial Products)
12.Multiply Multi-Digit Whole Numbers (e.g., 2-digit by 2-digit) using Area Models
13.Multiply Multi-Digit Whole Numbers (e.g., 2-digit by 2-digit) using the Standard Algorithm
14.Multiply Multi-Digit Whole Numbers (e.g., 3-digit by 2-digit) using Place Value Strategies and Area Models
15.Multiply Multi-Digit Whole Numbers (e.g., 3-digit by 2-digit) using the Standard Algorithm
16.Multiply Multi-Digit Whole Numbers (e.g., 3-digit by 3-digit, 4-digit by 2-digit) using the Standard Algorithm
17.Develop Fluency with the Standard Algorithm for Multi-Digit Multiplication
18.Estimate Products of Multi-Digit Numbers to Assess Reasonableness
19.Solve Word Problems Involving Multiplication of Multi-Digit Whole Numbers
20.Unit 2 Review: Multi-Digit Whole Number Multiplication

Unit 3: Multi-Digit Whole Number Division (2-Digit Divisors)

21.Divide Multi-Digit Dividends by Two-Digit Divisors using Place Value Strategies (e.g., Partial Quotients – Conceptual Introduction)
22.Divide Multi-Digit Dividends by Two-Digit Divisors using the Relationship between Multiplication and Division (Estimating Quotients)
23.Illustrate and Explain Division Calculations using Equations and Rectangular Arrays/Area Models
24.Divide Multi-Digit Dividends by Two-Digit Divisors using the Standard Algorithm (Introduction and connection to strategies)
25.Practice: Finding Whole-Number Quotients with Up to Four-Digit Dividends and Two-Digit Divisors using the Standard Algorithm
26.Interpreting Remainders in Division Problems (Contextual)
27.Solve Word Problems Involving Division of Whole Numbers (Quotients and Remainders)
28.Checking Division with Multiplication and Remainders
29.Develop Fluency with the Standard Algorithm for Multi-Digit Division
30.Unit 3 Review: Multi-Digit Whole Number Division (2-Digit Divisors)

Unit 4: Numerical Expressions (Order of Operations, Writing & Interpreting); Patterns

31.Use Parentheses, Brackets, or Braces in Numerical Expressions (Introduction to Order of Operations)
32.Evaluate Numerical Expressions with Parentheses
33.Evaluate Numerical Expressions with Brackets and Braces in addition to Parentheses
34.Order of Operations (PEMDAS/BEDMAS without exponents explicitly yet, focus on grouping and M/D before A/S)
35.Write Simple Expressions that Record Calculations with Numbers (Using Parentheses for Order)
36.Interpret Numerical Expressions Without Evaluating Them (Focus on Structure)
37.Practice Writing and Interpreting Numerical Expressions in Various Contexts
38.Solving problems involving order of operations with all four operations
39.Generate Two Numerical Patterns Using Two Given Rules and Identify Relationships
40.Unit 4 Review: Numerical Expressions (Order of Operations, Writing & Interpreting); Patterns

Unit 5: Decimals – Place Value, Reading, Writing, Comparing, & Rounding

41.Read and Write Decimals to Thousandths using Base-Ten Numerals
42.Read and Write Decimals to Thousandths using Number Names
43.Read and Write Decimals to Thousandths using Expanded Form (Fractional and Decimal Forms)
44.Practice Reading and Writing Decimals in All Forms (Standard, Word, Expanded)
45.Compare Two Decimals to Thousandths based on Meanings of the Digits in Each Place
46.Record Comparisons of Decimals to Thousandths using >, =, and < Symbols
47.Order a Set of Decimals to Thousandths
48.Use Place Value Understanding to Round Decimals to Any Place (Whole Number, Tenth, Hundredth, Thousandth)
49.Practice Rounding Decimals to Various Places
50.Unit 5 Review: Decimals – Place Value, Reading, Writing, Comparing, & Rounding

Unit 6: Adding and Subtracting Decimals to Hundredths

51.Add Decimals to Hundredths using Concrete Models or Drawings and Place Value Strategies
52.Add Decimals to Hundredths using the Standard Algorithm (Relating to strategy)
53.Practice Adding Decimals to Hundredths
54.Subtract Decimals to Hundredths using Concrete Models or Drawings and Place Value Strategies
55.Subtract Decimals to Hundredths using the Standard Algorithm (Relating to strategy)
56.Practice Subtracting Decimals to Hundredths
57.Estimating Sums and Differences of Decimals to Assess Reasonableness
58.Solve Word Problems Involving Addition and Subtraction of Decimals to Hundredths (Money context)
59.Solve Word Problems Involving Addition and Subtraction of Decimals to Hundredths (Measurement context)
60.Unit 6 Review: Adding and Subtracting Decimals to Hundredths

Unit 7: Multiplying Decimals to Hundredths

61.Multiply Decimals to Hundredths using Concrete Models or Drawings (Area Models) and Place Value Strategies
62.Multiply Decimals to Hundredths by Whole Numbers (Relating to Repeated Addition and Place Value)
63.Multiply Decimals to Hundredths by Decimals (Relating to Fraction Multiplication and Area Models)
64.Practice Multiplying Decimals to Hundredths (Whole x Decimal, Decimal x Decimal)
65.Estimating Products of Decimals to Assess Reasonableness
66.Multiply Decimals by Powers of 10 (Revisiting with Fluency)
67.Solve Word Problems Involving Multiplication of Decimals to Hundredths (Money context)
68.Solve Word Problems Involving Multiplication of Decimals to Hundredths (Measurement context)
69.Practice Solving Word Problems Involving Decimal Multiplication
70.Unit 7 Review: Multiplying Decimals to Hundredths

Unit 8: Dividing Decimals to Hundredths

71.Divide Decimals to Hundredths by Whole Numbers using Concrete Models or Drawings and Place Value Strategies
72.Divide Decimals to Hundredths by Whole Numbers using the Standard Algorithm (Relating to strategy)
73.Practice Dividing Decimals by Whole Numbers
74.Divide Decimals to Hundredths by Decimals (Using Models/Strategies like Relationship to Multiplication or Equivalent Problems)
75.Divide Decimals to Hundredths by Decimals (Written Method – Making Divisor a Whole Number)
76.Practice Dividing Decimals by Decimals
77.Estimating Quotients of Decimals to Assess Reasonableness
78.Divide Decimals by Powers of 10 (Revisiting with Fluency)
79.Solve Word Problems Involving Division of Decimals to Hundredths (Money, Measurement contexts)
80.Unit 8 Review: Dividing Decimals to Hundredths

Unit 9: Adding and Subtracting Fractions (Unlike Denominators, including Mixed Numbers)

81.Add Fractions with Unlike Denominators using Equivalent Fractions (Visual Models)
82.Add Fractions with Unlike Denominators by Finding Common Denominators (Symbolic)
83.Subtract Fractions with Unlike Denominators using Equivalent Fractions (Visual Models)
84.Subtract Fractions with Unlike Denominators by Finding Common Denominators (Symbolic)
85.Add Mixed Numbers with Unlike Denominators (Convert to Improper or Add Parts)
86.Subtract Mixed Numbers with Unlike Denominators (Convert to Improper or Subtract Parts with Regrouping)
87.Estimate Sums and Differences of Fractions and Mixed Numbers using Benchmark Fractions and Number Sense
88.Solve Word Problems Involving Addition and Subtraction of Fractions (Unlike Denominators, Same Whole)
89.Practice Adding and Subtracting Fractions & Mixed Numbers with Unlike Denominators
90.Unit 9 Review: Adding and Subtracting Fractions (Unlike Denominators, including Mixed Numbers)

Unit 10: Multiplying Fractions & Mixed Numbers; Fraction as Division; Scaling

91.Interpret a Fraction as Division of the Numerator by the Denominator (a/b = a ÷ b)
92.Solve Word Problems Involving Division of Whole Numbers Leading to Answers in the Form of Fractions or Mixed Numbers
93.Interpret Multiplication of a Fraction by a Whole Number (a/b × q) as finding a part of a quantity
94.Multiply a Fraction or Whole Number by a Fraction (Visual Models and a/b × c/d = ac/bd)
95.Find the Area of a Rectangle with Fractional Side Lengths by Tiling and by Multiplying Side Lengths
96.Interpret Multiplication as Scaling (Resizing) – Comparing Product to Factors
97.Interpret Multiplication as Scaling (Resizing) – Explaining Why
98.Solve Real-World Problems Involving Multiplication of Fractions and Mixed Numbers
99.Practice Solving Real-World Problems with Fraction Multiplication
100.Unit 10 Review: Multiplying Fractions & Mixed Numbers; Fraction as Division; Scaling

Unit 11: Dividing Fractions; Measurement Conversions & Line Plots

101.Interpret Division of a Unit Fraction by a Non-Zero Whole Number, and Compute Such Quotients (Visual Models & Equations)
102.Interpret Division of a Whole Number by a Unit Fraction, and Compute Such Quotients (Visual Models & Equations)
103.Compute Quotients of Unit Fractions by Whole Numbers and Whole Numbers by Unit Fractions (Using Relationship to Multiplication)
104.Solve Real-World Problems Involving Division of Unit Fractions by Whole Numbers
105.Solve Real-World Problems Involving Division of Whole Numbers by Unit Fractions
106.Convert among Different-Sized Standard Measurement Units within a Given System (Length, Weight, Capacity – Customary & Metric)
107.Use Measurement Conversions in Solving Multi-Step, Real-World Problems
108.Make a Line Plot to Display a Data Set of Measurements in Fractions of a Unit (1/2, 1/4, 1/8)
109.Solve Problems Involving Information Presented in Line Plots (Using Operations on Fractions)
110.Unit 11 Review: Dividing Fractions; Measurement Conversions & Line Plots

Unit 12: Geometric Measurement (Volume); Coordinate Plane & Classifying 2D Figures

111.Recognize Volume as an Attribute of Solid Figures and Understand Concepts of Volume Measurement (Unit Cube, Packing)
112.Measure Volumes by Counting Unit Cubes (Using Standard and Improvised Units)
113.Relate Volume to Multiplication: Find the Volume of a Right Rectangular Prism by Packing and Showing it equals Multiplying Edge Lengths (V = l × w × h)
114.Relate Volume to Multiplication: Find the Volume of a Right Rectangular Prism by Multiplying the Height by the Area of the Base (V = B × h)
115.Apply Volume Formulas (V = l × w × h and V = B × h) to Find Volumes of Right Rectangular Prisms with Whole-Number Edge Lengths in Real-World Problems
116.Find Volumes of Solid Figures Composed of Two Non-Overlapping Right Rectangular Prisms (Additive Volume)
117.Define a Coordinate System (Axes, Origin, Coordinates) and Graph Points in the First Quadrant
118.Interpret Coordinate Values of Points in the Context of a Real-World or Mathematical Problem
119.Classify Two-Dimensional Figures in a Hierarchy Based on Properties
120.Unit 12 Review: Geometric Measurement (Volume); Coordinate Plane & Classifying 2D Figures

Grade 5 (Ontario) ▼

Unit 1: Place Value to 100 000, Rounding, and Decimal Foundations ▼

1.Read and Represent Whole Numbers up to 100 000 using Base-Ten Blocks & Place Value Charts.
2.Compose and Decompose Whole Numbers up to 100 000 (Standard & Expanded Form).
3.Flexible Decomposition of 5-Digit Numbers.
4.Practice Flexible Decomposition and its Applications (Total Units).
5.Comparing and Ordering Whole Numbers up to 100 000.
6.Rounding Whole Numbers to the Nearest Ten, Hundred, or Thousand.
7.Introduction to Decimal Hundredths: Reading and Representing with Grids.
8.Representing Decimal Hundredths with Base-Ten Blocks (Redefining the Whole).
9.Comparing, Ordering, and Rounding Decimal Numbers (Hundredths) to the Nearest Tenth.
10.Unit 1 Review: Whole Numbers to 100 000 & Decimal Hundredths.

Unit 2: Multiplication and Division – Fluency and Early Algorithms ▼

11.Multiplication Facts 0x0 to 12×12: Strategies for Fluency.
12.Related Division Facts for 0x0 to 12×12: Using Fact Families.
13.Properties of Operations (Commutative, Associative, Distributive for Multiplication).
14.Mental Math: Multiplying Whole Numbers by 0.1 (as ÷10) and 0.01 (as ÷100).
15.Multiplication: 2-Digit by 2-Digit using the Area Model (Partial Products).
16.Connecting the Area Model to the Standard Algorithm for 2-Digit x 2-Digit Multiplication.
17.Practicing 2-Digit by 2-Digit Multiplication with the Standard Algorithm.
18.Division: 3-Digit by 2-Digit using Estimation and Partial Quotients (Flexible Method).
19.Connecting Partial Quotients to the Standard Long Division Algorithm (3-Digit by 2-Digit).
20.Unit 2 Review: Multiplication and Division Algorithms.

Unit 3: Mastering Operations with Whole and Decimal Numbers ▼

21.Adding & Subtracting Whole Numbers to 100 000 (Algorithm Fluency).
22.Adding Decimal Numbers up to Hundredths (Models & Algorithm).
23.Subtracting Decimal Numbers up to Hundredths (Models & Algorithm).
24.Estimating Sums and Differences of Decimal Numbers.
25.Solving Multi-Step Word Problems (Whole Numbers & Decimals, All Operations).
26.Checking Calculations Involving Whole & Decimal Numbers.
27.Multiplying Decimals by Whole Numbers (Conceptual Understanding).
28.Dividing Decimals by Whole Numbers (Conceptual: Equal Sharing Model).
29.Practice: Multiplying and Dividing Decimals by Whole Numbers (Conceptual Focus).
30.Unit 3 Review: Whole/Decimal Operations.

Unit 4: Advanced Fractions: Equivalence, Comparison, and Operations ▼

31.Representing Equivalent Fractions (Halves to Twelfths) using Various Tools.
32.Representing Improper Fractions and Mixed Numbers (Halves to Twelfths) – Conversion.
33.Comparing and Ordering Fractions (Like/Unlike Denominators, Improper/Mixed) using Benchmarks and Conceptual Common Denominators.
34.Relationships Among Fractions, Decimal Hundredths, and Whole Number Percents.
35.Converting Common Fractions to Decimals and Percents.
36.Converting Decimals (to hundredths) and Percents to Fractions.
37.Adding Fractions with Like Denominators (Including Improper/Mixed Numbers).
38.Subtracting Fractions with Like Denominators (Including Improper/Mixed Numbers).
39.Solving Word Problems: Adding/Subtracting Fractions with Like Denominators.
40.Unit 4 Review: Fractions Deep Dive.

Unit 5: Geometric Explorations – Triangles, 3D Objects, and Coordinate Plane ▼

41.Identifying Geometric Properties of Triangles (Scalene, Isosceles, Equilateral; Acute, Obtuse, Right) and Classifying.
42.Constructing Different Types of Triangles Given Side/Angle Measurements (Exploring Triangle Inequality).
43.Identifying and Constructing Congruent Triangles, Rectangles, Parallelograms (Focus on Properties).
44.Drawing Top, Front, and Side Views of More Complex 3D Objects (Multiple Components).
45.Matching Multiple 2D Views with their Corresponding 3D Objects.
46.Plotting and Reading Coordinates in the First Quadrant (Using Various Scales, Including Fractional/Decimal).
47.Describing Translations That Move a Point from One Coordinate to Another (Scaled Grids).
48.Performing Translations and Reflections on a Coordinate Grid (Complex Shapes, Predicting Outcomes).
49.Performing Rotations up to 180° on a Coordinate Grid (Around a Vertex, Origin, or Other Point).
50.Unit 5 Review: Geometry & Transformations.

Unit 6: Mastering Measurement – Metric System, Angles, Area Formulas ▼

51.Estimating and Measuring Length, Area, Mass, Capacity using Appropriate Metric Units in Problem Solving Contexts.
52.Solving Problems Involving Converting Larger Metric Units to Smaller Ones and Vice-Versa (Length, Mass, Capacity).
53.Describing Base-Ten Relationships Among Metric Units using Place Value Charts and Exponents (Powers of 10).
54.Comparing Angles and Determining Relative Size by Matching and Using Non-Standard Units (Focusing on Precision).
55.Explaining How Protractors Work (Semi-circular Scale, Degrees) & Using Benchmark Angles to Estimate Accurately.
56.Measuring and Constructing Angles up to 180° with Precision using a Protractor.
57.Developing and Applying the Formula for the Area of a Parallelogram (A=base x height).
58.Developing and Applying the Formula for the Area of a Triangle (A = 1/2 x base x height or A = (bxh)/2).
59.Solving Complex Problems involving Area of Parallelograms and Triangles (e.g., finding a missing dimension given the area).
60.Unit 6 Review: Metric Measurement, Angles, Area Formulas.

Unit 7: Exploring Area, Perimeter, and Advanced Operations ▼

61.Investigating the Relationship: Same Area, Different Perimeters (Rectangles and Other Polygons).
62.Investigating the Relationship: Same Perimeter, Different Areas (Rectangles and Other Polygons).
63.Solving Optimization Problems involving Area and Perimeter in Context.
64.Multiplying One-Digit Whole Numbers by Unit Fractions (Conceptual Understanding & Problem Solving).
65.Dividing One-Digit Whole Numbers by Unit Fractions (Conceptual Understanding & Problem Solving).
66.Practicing Multiplication and Division of Whole Numbers by Unit Fractions (Using Tools and Drawings).
67.Solving Multi-Step Word Problems with Whole Numbers, Decimals, and Simple Fractions (All Operations).
68.Checking Calculations in Complex Multi-Step Problems (Estimation, Inverse Operations, Reasonableness).
69.Real-World Design Challenges Integrating Area, Perimeter, and Cost.
70.Unit 7 Review: Area/Perimeter Optimization & Advanced Operations.

Unit 8: Patterns, Algebra, and Functions on the Coordinate Plane ▼

71.Identifying and Describing Repeating, Growing, and Shrinking Patterns (Increasing Complexity).
72.Creating Growing/Shrinking Patterns using Tables of Values (Linear, Introduction to Quadratic and Exponential).
73.Graphing Growing/Shrinking Patterns (Linear, Visual Recognition of Quadratic and Exponential Curves).
74.Translating Patterns Between Representations: Words, Algebraic Expressions (with two variables or two steps), Tables, and Graphs.
75.Determining Pattern Rules for Complex Patterns (including multi-step linear and simple non-linear) and Extending them.
76.Making Justified Predictions and Identifying Missing Elements in Complex Patterns.
77.Creating Patterns to Illustrate Relationships (Involving Whole Numbers, Decimals to Hundredths, and Fractions).
78.Plotting and Reading Coordinates in the First Quadrant (Application to Geometric Patterns & Simple Functions).
79.Describing and Performing Combined Transformations (e.g., a Rotation then a Reflection) on the Coordinate Plane.
80.Unit 8 Review: Advanced Patterns, Algebra, and the Cartesian Plane.

Unit 9: Mastering Algebraic Expressions, Equations, and Inequalities ▼

81.Translating Complex Word Problems into Algebraic Expressions and Equations.
82.Evaluating Algebraic Expressions with Multiple Variables and Order of Operations (BEDMAS/PEDMAS).
83.Solving Two-Step Equations Involving Whole Numbers up to 100 (All Operations) and Verifying Solutions.
84.Solving Equations with Variables on Both Sides (Simple Cases, Whole Numbers up to 100).
85.Solving Inequalities Involving One Operation (Whole Numbers up to 50) – Verifying and Representing Solutions.
86.Solving Two-Step Inequalities (Whole Numbers up to 50) and Graphing Solutions.
87.Using Variables to Model and Solve Real-World Problems (Involving Equations & Inequalities).
88.Exploring Equivalent Algebraic Expressions through Simplification (Introduction to Combining Like Terms).
89.Creating Word Problems from Given Equations or Inequalities.
90.Unit 9 Review: Algebraic Mastery.

Unit 10: Comprehensive Data Analysis and Representation ▼

91.Importance and Application of Various Sampling Techniques (Introduction to Stratified and Systematic Sampling).
92.Collecting Data (Qualitative & Quantitative) using Appropriate Sampling Methods (Comparing Two or More Sets).
93.Organizing Data in Relative-Frequency Tables (for Comparing Proportions in Different Data Sets).
94.Selecting and Justifying Appropriate Graph Types (Including Stacked-Bar Graphs and Multiple-Line Graphs for trends).
95.Displaying Data in Stacked-Bar Graphs and Interpreting Part-to-Whole Relationships.
96.Determining Mean, Median, and Mode for Whole Number and Decimal Number Data Sets (More Complex Sets).
97.Explaining What Mean, Median, and Mode Indicate About Data, Considering Skewness and Outliers.
98.Analyzing Data in Stacked-Bar Graphs and Critiquing Potentially Misleading Graphs.
99.Creating a Comprehensive Infographic (Including Multiple Data Representations, Analysis, and a Clear Narrative).
100.Unit 10 Review: Comprehensive Data Analysis.

Unit 11: Probability, Financial Planning, and Unit Rates ▼

101.Using Fractions to Express Theoretical Probability (for Single and Simple Combined Independent Events) & Representing on a Probability Line.
102.Making Predictions and Informed Decisions using Fractional Probability (More Complex Scenarios).
103.Determining and Comparing Theoretical and Experimental Probabilities (Analyzing Discrepancies).
104.Describing Ways Money Can Be Transferred (Including Electronic Funds Transfer – EFT, Online Payment Platforms).
105.Estimating and Calculating the Cost of Transactions (Involving Multiple Items and Sales Tax – common rates like 5%, 10%, 13%).
106.Calculating Complex Unit Rates and Identifying Best Value (e.g., multi-packs, items with different units of measure).
107.Designing Detailed Budgets to Manage Personal or Household Finances (Considering Long-Term Goals and Unexpected Expenses).
108.Understanding Concepts of Credit (Interest Rates, Credit Scores – basic introduction) and Debt (Distinguishing “Good” vs. “Bad” Debt).
109.Analyzing the Impact of Financial Decisions on Credit and Debt.
110.Unit 11 Review: Advanced Probability & Financial Planning.

Unit 12: Advanced Coding Logic and Mathematical Concepts and Synthesis ▼

111.Coding Logic: Designing Unplugged Algorithms with Sequential, Concurrent, and Repeating Events for Mathematical Tasks.
112.Coding Logic: Understanding and Implementing Conditional Statements (If-Then-Else) in Mathematical Contexts by Analyzing Code Snippets.
113.Coding Application: Using Loops and Conditionals to Generate Number Patterns (Guided Creation of Code Snippets).
114.Coding Logic: Understanding Nested Control Structures (Loops within Loops, Conditionals within Loops) in Provided Mathematical Code Examples.
115.Coding Application: Altering Provided Visual Code Snippets to Solve Variations of Mathematical Problems.
116.Coding Logic: Describing How Changes to Variables, Operators, and Control Structures in Mathematical Code Affect Outcomes.
117.Synthesizing Mathematical Concepts: Multi-Step Financial Scenarios.
118.Synthesizing Mathematical Concepts: Area, Perimeter, and Volume of Rectangular Prisms.
119.Synthesizing Mathematical Concepts: Data Analysis (Mean, Median, Mode) and Probability.
120.Unit 12 Culminating Review: Applying Coding Logic and Synthesizing Mathematical Concepts.

Grade 6 ▼

Unit 1: Understanding Ratios and Unit Rates

1.Understand the Concept of a Ratio
2.Use Ratio Language to Describe Relationships (Part-to-Part and Part-to-Whole)
3.Represent Ratios using Visual Models (Tape Diagrams, Double Number Lines)
4.Make Tables of Equivalent Ratios
5.Find Missing Values in Tables of Equivalent Ratios
6.Plot Pairs of Values from Ratio Tables on the Coordinate Plane
7.Understand the Concept of a Unit Rate a/b Associated with a Ratio a:b
8.Use Rate Language and Solve Unit Rate Problems (Unit Pricing, Constant Speed)
9.Solve Multi-Step Ratio and Rate Problems using Various Strategies
10.Unit 1 Review: Understanding Ratios and Unit Rates

Unit 2: Applying Ratios – Percent & Measurement Conversions

11.Understand Percent as a Rate per 100
12.Find a Percent of a Quantity (Using Fractions or Decimals)
13.Practice Finding a Percent of a Quantity (Mental Math and Calculation)
14.Solve Problems Involving Finding the Whole, Given a Part and the Percent (Introduction using Models)
15.Solve Problems Involving Finding the Whole, Given a Part and the Percent (Using Equations)
16.Solve Real-World Problems Involving Percents (Discounts, Sales Tax)
17.Solve Real-World Problems Involving Percents (Tips, Simple Interest – Conceptual)
18.Use Ratio Reasoning to Convert Measurement Units (Length, Weight, Capacity – Customary & Metric)
19.Use Ratio Reasoning to Convert Measurement Units in Multi-Step, Real-World Problems
20.Unit 2 Review: Applying Ratios – Percent & Measurement Conversions

Unit 3: Operations with Multi-Digit Decimals

21.Add Multi-Digit Decimals using the Standard Algorithm
22.Subtract Multi-Digit Decimals using the Standard Algorithm
23.Practice Adding and Subtracting Multi-Digit Decimals (Fluency and Word Problems)
24.Multiply Multi-Digit Decimals using the Standard Algorithm
25.Practice Multiplying Multi-Digit Decimals (Fluency and Estimating Products)
26.Solve Word Problems Involving Multiplication of Multi-Digit Decimals
27.Multiply Decimals by Powers of 10
28.Divide Decimals by Powers of 10
29.Solve Word Problems Involving All Four Operations with Decimals (Multi-Step Focus)
30.Unit 3 Review: Operations with Multi-Digit Decimals (Adding, Subtracting, Multiplying)

Unit 4: Dividing Multi-Digit Decimals; GCF & LCM

31.Divide Multi-Digit Decimals by Whole Numbers using the Standard Algorithm
32.Divide Multi-Digit Decimals by Decimals (Making the Divisor a Whole Number)
33.Practice Dividing Multi-Digit Decimals (by Whole Numbers and Decimals)
34.Solve Word Problems Involving Division of Multi-Digit Decimals
35.Find the Greatest Common Factor (GCF) of Two Whole Numbers (≤ 100) by Listing Factors
36.Find the Greatest Common Factor (GCF) using Prime Factorization (Conceptual Introduction)
37.Find the Least Common Multiple (LCM) of Two Whole Numbers (≤ 12) by Listing Multiples
38.Use the Distributive Property to Express a Sum of Two Whole Numbers with a Common Factor
39.Solve Real-World Problems involving GCF and LCM
40.Unit 4 Review: Dividing Multi-Digit Decimals; GCF & LCM

Unit 5: Fluency with Multi-Digit Division and Applications

41.Fluently Divide Multi-Digit Numbers using the Standard Algorithm (Review and Practice)
42.Choosing Operations in Multi-Step Word Problems involving Whole Numbers and Decimals
43.Solving Multi-Step Word Problems Involving Whole Number Division and Other Operations
44.Solving Multi-Step Word Problems Involving Decimal Operations (All Four)
45.Practice: Solving Complex Multi-Step Real-World Problems
46.Interpreting Quotients of Fractions using Visual Models
47.Compute Quotients of Fractions using the Standard Algorithm (Invert and Multiply)
48.Solve Word Problems Involving Division of Fractions by Fractions
49.Mixed Practice: All Operations with Whole Numbers, Decimals, and Fractions in Context
50.Unit 5 Review: Fluency with Multi-Digit Division and Applications

Unit 6: Rational Numbers – Integers, Opposites, Absolute Value

51.Understand Positive and Negative Numbers to Describe Quantities with Opposite Directions/Values
52.Explain the Meaning of 0 in Contexts with Positive and Negative Numbers
53.Understand a Rational Number as a Point on the Number Line
54.Recognize Opposite Signs of Numbers as Locations on Opposite Sides of 0
55.Understand Ordering of Rational Numbers: Interpret Inequality Statements
56.Write, Interpret, and Explain Statements of Order for Rational Numbers in Real-World Contexts
57.Understand the Absolute Value of a Rational Number as its Distance from 0 on the Number Line
58.Interpret Absolute Value as Magnitude in Real-World Situations
59.Distinguish Comparisons of Absolute Value from Statements about Order
60.Unit 6 Review: Rational Numbers – Integers, Opposites, Absolute Value, Number Line Ordering

Unit 7: The Coordinate Plane

61.Understand Signs of Numbers in Ordered Pairs as Indicating Locations in Quadrants
62.Find and Position Pairs of Integers and Other Rational Numbers on a Coordinate Plane
63.Recognize Reflections Across Axes and Origin: When Two Ordered Pairs Differ Only by Signs
64.Find Distances Between Points with the Same First Coordinate or Same Second Coordinate
66.Solve Real-World Problems by Graphing Points in All Four Quadrants
67.Draw Polygons in the Coordinate Plane Given Coordinates for the Vertices
68.Use Coordinates to Find the Length of a Side of a Polygon
69.Solve Real-World Problems Involving Polygons in the Coordinate Plane
70.Unit 7 Review: The Coordinate Plane (All Quadrants, Reflections, Distances)

Unit 8: Expressions – Numerical & Algebraic

71.Write and Evaluate Numerical Expressions Involving Whole-Number Exponents
72.Order of Operations including Exponents, Parentheses, Brackets, and Braces
73.Write Algebraic Expressions from Verbal Phrases (Using Letters for Numbers)
74.Identify Parts of an Algebraic Expression using Mathematical Terms
75.View One or More Parts of an Expression as a Single Entity
76.Evaluate Algebraic Expressions at Specific Values of Their Variables
77.Apply Properties of Operations to Generate Equivalent Expressions (Commutative and Associative)
78.Apply the Distributive Property to Generate Equivalent Expressions
79.Apply the Distributive Property to Generate Equivalent Expressions (Factoring)
80.Unit 8 Review: Expressions – Numerical & Algebraic

Unit 9: Equivalent Expressions & Solving One-Step Equations

81.Identify when Two Algebraic Expressions are Equivalent
82.Understand Solving an Equation as Finding Values that Make it True
83.Use Variables to Represent Numbers and Write One-Step Equations (x+p=q)
84.Solve One-Step Equations of the form x+p=q
85.Use Variables to Represent Numbers and Write One-Step Equations (px=q)
86.Solve One-Step Equations of the form px=q
87.Practice Solving One-Step Equations with Non-Negative Rational Numbers
88.Write an Inequality to Represent a Constraint or Condition
89.Represent Solutions of Inequalities on Number Line Diagrams
90.Unit 9 Review: Equivalent Expressions & Solving One-Step Equations and Inequalities

Unit 10: Relationships Between Variables; Geometry: Area

91.Use Variables to Represent Two Quantities in a Real-World Problem
92.Write an Equation to Express One Quantity in Terms of the Other Quantity
93.Analyze the Relationship Between Variables using Tables from an Equation
94.Analyze the Relationship Between Variables using Graphs from an Equation/Table
95.Relate Tables, Graphs, and Equations Representing the Same Quantitative Relationship
96.Solve Real-World Problems Involving Area of Right Triangles
97.Solve Real-World Problems Involving Area of Other Triangles
98.Solve Real-World Problems Involving Area of Special Quadrilaterals
99.Solve Real-World Problems Involving Area of Polygons by Composition or Decomposition
100.Unit 10 Review: Relationships Between Variables; Geometry: Area

Unit 11: Geometry: Volume, Nets & Surface Area

101.Draw Polygons in the Coordinate Plane Given Coordinates for the Vertices
102.Use Coordinates to Find the Length of Horizontal and Vertical Sides of Polygons
103.Solve Real-World Problems by Finding Perimeters and Areas of Polygons in the Coordinate Plane
104.Find the Volume of a Right Rectangular Prism with Fractional Edge Lengths
105.Apply the Formulas V = lwh and V = Bh to Find Volumes of Right Rectangular Prisms
106.Solve Real-World Problems Involving Volume of Right Rectangular Prisms
107.Represent Three-Dimensional Figures using Nets Made Up of Rectangles and Triangles
108.Use Nets to Find the Surface Area of Three-Dimensional Figures (Prisms)
109.Use Nets to Find the Surface Area of Three-Dimensional Figures (Pyramids)
110.Unit 11 Review: Geometry: Area & Coordinate Geometry Applications; Volume; Nets & Surface Area

Unit 12: Statistics & Probability

111.Recognize a Statistical Question as One that Anticipates Variability in Data
112.Understand Data Distributions: Center, Spread, and Overall Shape
113.Reporting Number of Observations; Describing Attribute, Measurement Method, and Units
114.Display Numerical Data in Plots on a Number Line: Dot Plots
115.Display Numerical Data in Plots on a Number Line: Histograms
116.Calculate Measures of Center: Mean
117.Calculate Measures of Center: Median
118.Calculate Measures of Variation: Range and Interquartile Range (IQR)
119.Display Numerical Data in Plots on a Number Line: Box Plots
120.Unit 12 Review: Geometry (Volume with Fractional Edges, Nets & Surface Area); Statistics & Probability

Grade 6 (Ontario) ▼

Unit 1: Understanding Whole Numbers to 1 000 000 and Decimal Foundations ▼

1.Read and Represent Whole Numbers to 1 000 000.
2.Compose and Decompose Whole Numbers to 1 000 000 (Standard, Expanded Form & Powers of Ten).
3.Using Place Value to Describe and Represent Multi-Digit Numbers (up to 1 000 000).
4.Comparing and Ordering Whole Numbers up to 1 000 000.
5.Rounding Whole Numbers to the Nearest Ten, Hundred, Thousand, Ten Thousand, or Hundred Thousand.
6.Reading and Representing Decimal Numbers up to Thousandths.
7.Comparing and Ordering Decimal Numbers up to Thousandths.
8.Rounding Terminating Decimal Numbers to the Nearest Whole Number, Tenth, or Hundredth.
9.Rounding Repeating Decimal Numbers (e.g., 0.666…) to the Nearest Tenth, Hundredth, or Whole Number.
10.Unit 1 Review: Place Value (Whole Numbers to 1 Million & Decimals to Thousandths), Rounding.

Unit 2: Number Theory and Operations – Building Blocks ▼

11.Introduction to Integers: Reading, Representing, Comparing, and Ordering.
12.Addition and Subtraction of Integers using Number Lines and Models.
13.Divisibility Rules for 2, 5, and 10.
14.Divisibility Rules for 3, 9, 4, 8, and 6.
15.Identifying and Representing Perfect Squares and Their Square Roots (up to 144).
16.Prime Factorization of Composite Numbers (Using Factor Trees).
17.Determining the Greatest Common Factor (GCF) for Two or Three Whole Numbers.
18.Determining the Lowest Common Multiple (LCM) for Two and Three Whole Numbers.
19.Using GCF and LCM to Solve Contextual Problems.
20.Unit 2 Review: Integers, Divisibility, Perfect Squares & Roots, Prime Factorization, GCF/LCM.

Unit 3: Mastering Operations with Whole Numbers and Decimals ▼

21.Properties and Order of Operations (BEDMAS/PEDMAS) with Whole Numbers and Decimals.
22.Adding and Subtracting Whole Numbers up to 1 000 000 (Algorithm Fluency).
23.Adding and Subtracting Decimal Numbers up to Thousandths (Algorithm Fluency).
24.Multiplication of Two-Digit Whole Numbers by Two-Digit Whole Numbers (Connecting Area Model & Standard Algorithm).
25.Division of Three-Digit Whole Numbers by Two-Digit Whole Numbers (Connecting Partial Quotients/Area Model & Standard Algorithm, Remainders as Fractions).
26.Multiplying Three-Digit Whole Numbers by Decimal Tenths using Algorithms.
27.Dividing Three-Digit Whole Numbers by Decimal Tenths (Using Equivalent Divisions).
28.Dividing Decimal Numbers up to Thousandths by Whole Numbers up to 10 (Using Algorithms).
29.Solving Multi-Step Word Problems Involving Whole Numbers and Decimals (All Operations).
30.Unit 3 Review: Operations with Whole Numbers and Decimals.

Unit 4: Fractions – Deep Dive into Equivalence, Comparison, & Operations ▼

31.Representing Equivalent Fractions (Halves to Twelfths), Improper Fractions, and Mixed Numbers (Using Tools, Contexts, and Simplification with GCF).
32.Comparing and Ordering Fractions (Halves to Twelfths, All Forms, Including Integers).
33.Relationships & Equivalences: Fractions, Decimals (to Thousandths), and Percents.
34.Commonly Used Percents, Fractions, and Decimal Equivalents (Recall & Application).
35.Adding Fractions with Like and Unlike Denominators (Including Mixed Numbers).
36.Subtracting Fractions with Like and Unlike Denominators (Including Mixed Numbers, with Regrouping).
37.Multiplying Fractions by Fractions (Using Area Models and the Standard Algorithm).
38.Dividing Fractions by Fractions (Using Common Denominators or “Invert and Multiply” Algorithm).
39.Solving Multi-Step Word Problems with Fractions (Involving All Four Operations).
40.Unit 4 Review: Advanced Fractions, Decimals, and Percents.

Unit 5: Proportional Reasoning, Rates, and Percent Applications ▼

41.Mental Math Strategies to Increase or Decrease a Whole Number by 1%, 5%, 10%, 25%, 50%, 100%.
42.Identifying Proportional and Non-Proportional Situations from Tables, Graphs, and Descriptions.
43.Solving Problems using Proportional Reasoning (Setting up and Solving Equivalent Ratios/Proportions).
44.Solving Problems Involving Ratios (Part-to-Part and Part-to-Whole Relationships).
45.Solving Problems Involving Percents (Finding Percent of a Number, Finding What Percent One Number is of Another, Finding the Whole Given a Part and Percent).
46.Solving Problems Involving Rates (e.g., Speed, Density, Price per Unit).
47.Identifying and Comparing Exchange Rates Between Currencies.
48.Converting Foreign Currencies to Canadian Dollars and Vice Versa using Given Exchange Rates.
49.Solving Multi-Step Problems Involving Ratios, Rates, Percents, and Proportions.
50.Unit 5 Review: Proportional Reasoning, Ratios, Rates, Percents, and Currency Exchange.

Unit 6: Geometry – Properties, Views, and Transformations ▼

51.Classifying Cylinders, Pyramids, and Prisms by their Geometric Properties (Number/Shape of Faces, Edges, Vertices, Plane and Rotational Symmetry).
52.Drawing Top, Front, and Side Views of Complex 3D Objects and Physical Spaces.
53.Drawing Perspective Views of Simple Objects (Introduction to One-Point Perspective).
54.Performing Dilations on a Coordinate Grid (From the Origin, Using Whole Number Scale Factors).
55.Describing Similarity Between an Original Shape and its Image After Dilation.
56.Performing Combinations of Translations, Reflections, and Rotations on a Cartesian Plane (All Four Quadrants).
57.Predicting Results of Combined Transformations (More Complex Sequences and Predicting Final Orientation/Location).
58.Identifying Congruent Triangles, Rectangles, and Parallelograms by their Properties (Using SSS, SAS, ASA congruence conditions for triangles informally, and side/angle properties for quadrilaterals).
59.Using a Protractor to Measure and Construct Angles up to 360° (Review and Application).
60.Unit 6 Review: 3D Properties, 2D/3D Views, All Transformations (including Dilations and Combined).

Unit 7: Measurement – Circles, Area, Surface Area, and Volume ▼

61.Relationship Between Radius, Diameter, and Circumference of a Circle (Investigating and Discovering Pi).
62.Explaining and Using the Formulas for the Circumference of a Circle (C=πd or C=2πr).
63.Constructing Circles Given Radius, Diameter, or Circumference.
64.Relationships Between Radius, Diameter, and Area of a Circle (Developing the Formula A=πr²).
65.Using the Formula for the Area of a Circle (A=πr²).
66.Distinguishing Between Volume and Capacity and their Units.
67.Understanding the Relationship Between Millilitres (mL) and Cubic Centimetres (cm³).
68.Determining the Volume of Prisms by Multiplying the Area of the Base by the Height (V=Bh).
69.Determining the Volume of Cylinders by Multiplying the Area of the Circular Base by the Height (V=πr²h).
70.Unit 7 Review: Circles (Circumference, Area) and Volume (Prisms, Cylinders).

Unit 8: Surface Area of 3D Objects and Metric Conversions ▼

71.Representing Cylinders and Prisms as Nets.
72.Determining the Surface Area of Cylinders by Adding the Areas of their Parts (Two Circles + Rectangle from Net).
73.Determining the Surface Area of Prisms (Rectangular, Triangular) by Summing the Areas of their Faces.
74.Solving Problems Involving Perimeter, Area, Volume, and Surface Area that Require Converting Metric Units.
75.Finding Unknown Dimensions (e.g., Base Area, Height, Radius) of Prisms or Cylinders Given the Volume and One Other Measurement.
76.Comparing Volumes of Different Shaped Prisms or Cylinders that may have the Same Base Area or Same Height.
77.Solving Real-World Applications of Surface Area and Volume (e.g., Packaging Design, Construction Materials, Capacity of Containers).
78.Solving Capacity vs. Volume Word Problems (Requiring Conversions like cm³ to mL or L).
79.Introduction to Optimization Problems (e.g., Minimizing Surface Area for a Given Volume of a Rectangular Prism).
80.Unit 8 Review: Surface Area, Volume, and Metric Conversions.

Unit 9: Advanced Patterns, Algebra, and Equations ▼

81.Identifying and Comparing Repeating, Growing, and Shrinking Patterns (Distinguishing Linear vs. Non-Linear Growth).
82.Creating and Translating Patterns (Focus on Linear Growing Patterns) using Tables, Graphs, Algebraic Expressions (y=mx+b form), and Equations.
83.Determining Pattern Rules and Using Algebraic Representations to Solve for Unknown Values in Linear Growing Patterns (e.g., find the term number given a specific value, or find the value of a specific term number).
84.Making Justified Predictions and Identifying Missing Elements in More Complex Repeating, Growing, or Shrinking Patterns (Non-Linear).
85.Creating and Describing Patterns to Illustrate Relationships Among Integers (e.g., patterns involving addition or subtraction of positive and negative numbers on a number line).
86.Adding Monomials with a Degree of 1 (Like Terms) Involving Whole Number Coefficients, Using Tools like Algebra Tiles.
87.Subtracting Monomials with a Degree of 1 (Like Terms) Involving Whole Number Coefficients, Using Tools like Algebra Tiles.
88.Evaluating Algebraic Expressions (with Whole Numbers, Decimals, and Simple Fractions as coefficients or values) using Order of Operations (BEDMAS/PEDMAS).
89.Solving Equations Involving Multiple Terms, Whole Numbers, and Decimals (One-Variable, Multi-Step Linear Equations) and Verifying Solutions.
90.Unit 9 Review: Advanced Patterns & Algebra.

Unit 10: Data Analysis – Populations, Samples, and Representations ▼

91.Explaining the Importance of Various Sampling Techniques for Ensuring a Sample is Representative of the Population (Random, Stratified, Systematic, Convenience Sampling; Introduction to Bias).
92.Collecting Both Qualitative & Quantitative Data using Appropriate Sampling Methods (Comparing Two or More Sets).
93.Organizing Data in Relative-Frequency Tables (Using Fractions, Decimals, or Percents to Compare Proportions).
94.Selecting and Justifying Appropriate Types of Graphs for Displaying Data (Including Circle Graphs for Part-to-Whole Comparisons, and Stacked-Bar Graphs for Comparing Proportions within Different Categories).
95.Displaying Data in Circle Graphs (Calculating Sector Angles from Frequencies or Using Percentages with Technology).
96.Determining Mean, Median, and Mode(s) for Various Data Sets (Including Whole Numbers and Decimal Numbers) and Explaining Their Meaning as Measures of Central Tendency.
97.Analyzing the Impact of Adding or Removing Data Points (Especially Outliers) on Measures of Central Tendency (Mean, Median, Mode) and the Shape of the Data Distribution.
98.Analyzing Data Presented in Various Graphs (Stacked-Bar Graphs, Circle Graphs, Line Graphs) and Critiquing Potentially Misleading Graphical Representations.
99.Creating a Comprehensive Infographic Incorporating Multiple Data Representations (e.g., Relative-Frequency Tables, Stacked-Bar Graphs, Circle Graphs) and Analytical Text.
100.Unit 10 Review: Comprehensive Data Analysis.

Unit 11: Probability and Financial Management ▼

101.Describing the Difference Between Independent and Dependent Events, with Clear Examples.
102.Determining the Theoretical Probability of Two Independent Events Happening (Using Multiplication Rule or Tree Diagrams/Area Models).
103.Determining the Experimental Probability of Two Independent Events Happening (Conducting Trials and Calculating Relative Frequency).
104.Determining the Theoretical Probability of Two Dependent Events Happening (Simple Cases, e.g., Drawing without Replacement).
105.Determining the Experimental Probability of Two Dependent Events Happening (Conducting Trials for Dependent Events).
106.Comparing Theoretical and Experimental Probabilities for Both Independent and Dependent Events, Analyzing Discrepancies.
107.Identifying and Describing Reliable Sources of Information for Financial Planning (e.g., Government Websites, Reputable Non-Profit Financial Education Organizations, Licensed Financial Advisors).
108.Creating, Tracking, and Adjusting Sample Budgets for Achieving Longer-Term Financial Goals.
109.Identifying and Analyzing Societal and Personal Factors that Influence Financial Decision Making (e.g., Advertising, Peer Pressure, Economic Trends, Personal Values, Cultural Background).
110.Unit 11 Review: Probability (Independent/Dependent Events) & Financial Management (Information Sources, Budgeting, Influencing Factors).

Unit 12: Computational Thinking and Efficient Coding Structures ▼

111.Analyzing Efficiency in Sequential Algorithms.
112.Understanding Concurrent Events in Code through Analysis of Visual Snippets.
113.Designing Unplugged Algorithms Incorporating Concurrent Events.
114.Understanding Repeating Events (Loops: Count-Controlled and Condition-Controlled) in Provided Code.
115.Designing Unplugged Algorithms with Various Types of Repeating Events (Loops).
116.Understanding Conditional Statements (If-Then-Else and simple nested Ifs) in Provided Code.
117.Designing Unplugged Algorithms with Conditional Statements (Including Simple Nested Conditions).
118.Understanding Nested Control Structures in Provided Code (e.g., a loop within a loop, a conditional within a loop, or a loop within a conditional).
119.Reading, Altering, and Describing the Effects of Changes in Visual Code with Multiple Control Structures (Focus on Logic and Efficiency).
120.Unit 12 Review: Coding Logic, Structures, and Efficiency.

Grade 7 (Ontario) ▼

Unit 1: Understanding Whole Numbers to 1 000 000 000 and Decimal Foundations ▼

1.Reading & Writing Whole Numbers to One Billion (Standard Form & Words).
2.Identifying Place Value in Whole Numbers to One Billion.
3.Expanded Form of Whole Numbers (Standard Method).
4.Introduction to Powers of Ten.
5.Expanded Form of Whole Numbers Using Powers of Ten.
6.Comparing Whole Numbers to One Billion.
7.Ordering Sets of Whole Numbers to One Billion.
8.Problem Solving with Large Whole Numbers in Context.
9.Real-World Uses of Numbers to One Billion (Contextual Exploration).
10.Unit 1 Review: Whole Numbers to One Billion.

Unit 2: Exponents, Squares & Roots ▼

11.Understanding Exponential Notation (Whole Number Bases & Exponents).
12.Evaluating Expressions with Exponents (Whole Numbers).
13.Identifying Perfect Squares (Up to 144) Using Models & Exponents.
14.Determining Square Roots of Perfect Squares (Up to 144).
15.Exploring Patterns in Powers and Special Cases (Powers of 0 and 1).
16.Relating Squares and Square Roots to Area Problems.
17.Order of Operations with Exponents (Whole Numbers).
18.Problem Solving Involving Exponents and Square Roots.
19.Estimating Square Roots of Non-Perfect Squares.
20.Unit 2 Review: Exponents, Perfect Squares, and Square Roots.

Unit 3: Rational Numbers (Fractions & Decimals) ▼

21.Representing Positive Fractions (Proper, Improper, Mixed) Using Models.
22.Representing Positive Decimals to Thousandths Using Models & Place Value.
23.Introducing Negative Integers on the Number Line (Contextual).
24.Representing Negative Fractions on the Number Line.
25.Representing Negative Decimals to Thousandths on the Number Line.
26.Comparing and Ordering Positive Fractions and Decimals.
27.Comparing and Ordering Integers and Negative Rational Numbers.
28.Comparing and Ordering Sets of All Rational Numbers.
29.Rounding Decimals to Nearest Whole, Tenth, and Hundredth.
30.Unit 3 Review: Representing, Comparing & Ordering Rational Numbers; Rounding.

Unit 4: Fraction Equivalence ▼

31.Understanding and Finding Equivalent Fractions (Models & Multiplication/Division).
32.Factors, Prime/Composite Numbers.
33.Determining the Greatest Common Factor (GCF).
34.Simplifying Fractions to Lowest Terms (Using GCF).
35.Converting Fractions to Decimals (Terminating & Repeating).
36.Converting Terminating Decimals to Fractions.
37.Understanding Percent and Converting Decimals & Fractions to Percents.
38.Converting Percents to Decimals and Fractions.
39.Recalling and Applying Common FDP Equivalents.
40.Unit 4 Review: Equivalent Fractions, GCF, FDP Conversions.

Unit 5: Integer Operations & BEDMAS ▼

41.Adding Integers Using Models (Counters & Number Lines).
42.Developing and Applying Rules for Adding Integers.
43.Subtracting Integers Using Models (Take-Away & Difference).
44.Connecting Subtraction of Integers to Adding the Opposite (Models & Rule).
45.Problem Solving with Integer Addition and Subtraction in Context.
46.Order of Operations with Whole Numbers and Decimals (No Exponents, Brackets emphasis).
47.Order of Operations with Fractions (No Exponents, Brackets emphasis).
48.Order of Operations Involving Integers (No Exponents).
49.Full Order of Operations (BEDMAS) with All Rational Numbers and Exponents.
50.Unit 5 Review: Integer Operations and Full Order of Operations.

Unit 6: Fraction Operations ▼

51.Adding & Subtracting Fractions with Like Denominators (Models & Algorithm).
52.Finding the Lowest Common Multiple (LCM) for Common Denominators.
53.Adding Fractions with Unlike Denominators (Conceptual Understanding & LCM).
54.Subtracting Fractions with Unlike Denominators (Conceptual Understanding & LCM).
55.Adding Mixed Numbers (Like & Unlike Denominators, Regrouping).
56.Subtracting Mixed Numbers (Like & Unlike Denominators, with Regrouping).
57.Multiplying Fractions by Whole Numbers & Fractions (Models First).
58.Developing and Applying the Algorithm for Multiplying Fractions.
59.Dividing Fractions (Conceptual Understanding Leading to “Invert & Multiply” Algorithm).
60.Unit 6 Review: All Operations with Fractions.

Unit 7: Decimal Operations & Percent ▼

61.Adding and Subtracting Decimals (Estimation, Algorithm Fluency).
62.Multiplying Decimals (Estimation, Algorithm Fluency).
63.Dividing Decimals by Whole Numbers (Algorithm Fluency).
64.Dividing Decimals by Decimals (Understanding Equivalence & Algorithm Fluency).
65.Problem Solving with All Decimal Operations (Multi-Step).
66.Mental Math: Increasing/Decreasing by Key Percentages (1%, 5%, 10%, 25%, 50%, 100%).
67.Finding a Percent of a Number (Tax, Tip, Discount).
68.Finding What Percent One Number is of Another.
69.Solving Percent Problems (Finding the Whole given a Part and Percent).
70.Unit 7 Review: Decimal Operations and Percent Applications.

Unit 8: Ratios, Rates & Proportionality ▼

71.Introduction to Ratios: Writing and Interpreting (Part-to-Part, Part-to-Whole).
72.Equivalent Ratios & Simplest Form.
73.Introduction to Rates and Unit Rates.
74.Identifying Proportional Relationships from Tables (Constant Ratio/Unit Rate).
75.Identifying Proportional Relationships from Graphs (Line Through Origin).
76.Identifying Non-Proportional Situations (Contexts, Tables, Graphs).
77.Solving Problems using Proportions (Equivalent Ratios, Unit Rate, Cross-Multiplication).
78.Exchange Rates and Currency Conversions using Proportional Reasoning.
79.Problem Solving with Ratios, Rates, and Proportions (Multi-Step Contexts).
80.Unit 8 Review: Ratios, Rates, Proportional Relationships, and Currency.

Unit 9: Patterns & Algebra Intro ▼

81.Identifying and Describing Repeating, Growing, Shrinking Patterns (Numerical & Geometric).
82.Extending Patterns, Predicting Terms, Finding Missing Elements (Systematic Approach).
83.Comparing Linear Growing Patterns (Constant Rate/Difference, Initial Value from Tables/Sequences).
84.Creating Patterns (Whole/Decimal Numbers, Integers) from Given Rules or Starting Points.
85.Representing Linear Patterns with Variables and Informal Language (Input/Output).
86.Translating Linear Growing Patterns into Algebraic Expressions (an+b or similar).
87.Introduction to Monomials (Degree 1, Coefficient, Variable from Pattern Expressions).
88.Adding and Subtracting Monomials (Degree 1, Whole Number Coefficients, Using Algebra Tiles).
89.Evaluating Algebraic Expressions (Whole/Decimal Values from Patterns or Given).
90.Unit 9 Review: Patterns, Algebraic Expressions, Monomials.

Unit 10: Equations & Inequalities ▼

91.Understanding Equations (Balance Concept) & Verifying Solutions.
92.Solving One-Step Equations (Addition/Subtraction with Inverse Operations & Balance).
93.Solving One-Step Equations (Multiplication/Division with Inverse Operations & Balance).
94.Solving Two-Step Equations (ax+b=c, Whole/Decimal Numbers).
95.Solving Equations with Multiple Terms (e.g., ax + bx = c, ax + b = cx + d – simple cases).
96.Translating Word Problems into One- and Two-Step Equations.
97.Solving Word Problems using Equations.
98.Introduction to Inequalities (<, >, ≤, ≥) & Verifying Solutions (Whole Numbers).
99.Solving One-Step & Multi-Term Inequalities (Whole Numbers, Graphing Solutions).
100.Unit 10 Review: Solving Equations and Inequalities.

Unit 11: Geometry & Measurement ▼

101.Classifying Prisms, Pyramids, Cylinders by Geometric Properties.
102.Drawing Top, Front, Side Views & Perspective Views of Objects.
103.Radius, Diameter, Circumference of Circles (Discovering Pi, Formulas).
104.Constructing Circles & Area of a Circle (Developing Formula, Calculations).
105.Volume vs. Capacity (mL/cm³) & Metric Unit Conversions (Length, Area, Volume).
106.Nets of Cylinders & Prisms; Surface Area by Adding Parts.
107.Volume of Prisms and Cylinders (Area of Base x Height).
108.Finding Missing Dimensions of Prisms & Cylinders (Given Volume).
109.Geometric Transformations on Cartesian Plane (Translations, Reflections, Rotations, Dilations & Similarity).
110.Unit 11 Review: 2D/3D Geometry, Measurement (Circles, Volume, SA), Conversions, Transformations.

Unit 12: Advanced Coding Logic and Mathematical Concepts and Synthesis ▼

111.Data: Collecting, Organizing (Frequency Tables with Percentages), Graph Selection.
112.Data: Creating Circle Graphs (Sector Angles) & Analyzing Data including Misleading Graphs.
113.Data: Impact of Adding/Removing Data on Mean, Median, Mode.
114.Probability: Independent vs. Dependent Events (Definitions & Identification).
115.Probability of Two Independent Events (Tree Diagrams, Multiplication Rule).
116.Probability of Two Dependent Events (Simple Cases using Tree Diagrams).
117.Coding: Writing Code (Events, Count-Controlled Loops, Sub-programs).
118.Coding: Reading, Altering Existing Code & Describing Effects.
119.Financial Literacy: Budgets, Interest Rates, Societal/Personal Factors.
120.Unit 12 Review: Data Analysis, Probability, Coding & Financial Literacy.

Grade 7 ▼

Unit 1: Rational Number Operations – Addition & Subtraction

1.Understand Addition of Rational Numbers on a Number Line
2.Understand Additive Inverses and Situations where Opposite Quantities Combine to Make 0
3.Understand Subtraction of Rational Numbers as Adding the Additive Inverse
4.Show that the Distance Between Two Rational Numbers on the Number Line is the Absolute Value of their Difference
5.Add Rational Numbers with the Same Sign (Integers, Fractions, Decimals)
6.Add Rational Numbers with Different Signs (Integers, Fractions, Decimals)
7.Subtract Rational Numbers by Adding the Additive Inverse (Fluency Practice)
8.Interpret Sums and Differences of Rational Numbers in Real-World Contexts
9.Mixed Practice Adding and Subtracting Rational Numbers Fluently (Integers, Decimals, Fractions)
10.Unit 1 Review: Rational Number Operations – Addition & Subtraction

Unit 2: Rational Number Operations – Multiplication & Division

11.Understand Multiplication of Integers (Rules and Properties, including (-1)(-1)=1)
12.Multiply Integers Fluently (Positive and Negative)
13.Multiply Rational Numbers (Fractions and Decimals, Positive and Negative)
14.Understand Division of Integers (Rules and Relationship to Multiplication)
15.Understand and Write Equivalent Forms of Negative Quotients
16.Divide Rational Numbers (Fractions and Decimals, Positive and Negative)
17.Convert Rational Numbers (Fractions) to Decimals using Long Division
18.Solve Real-World Problems Involving All Four Operations with Rational Numbers
19.Practice: All Four Operations with Rational Numbers
20.Unit 2 Review: Rational Number Operations – Multiplication & Division

Unit 3: Expressions – Generating Equivalent Linear Expressions

21.Write Algebraic Expressions from Verbal Phrases Involving Rational Numbers
22.Identify Parts of an Algebraic Expression with Rational Coefficients
23.Add and Subtract Linear Expressions with Rational Coefficients
24.Expand Linear Expressions using the Distributive Property
25.Factor Linear Expressions (GCF with Rational Coefficients)
26.Practice Generating Various Equivalent Linear Expressions
27.Understand How Rewriting an Expression Clarifies Problem Context (Percents)
28.Understand How Rewriting an Expression Clarifies Problem Context (Other Scenarios)
29.Use Variables to Represent Quantities in Real-World Problems
30.Unit 3 Review: Expressions – Generating Equivalent Linear Expressions

Unit 4: Equations & Inequalities – Solving Multi-step Problems

31.Solve Multi-step Real-Life Problems with Positive and Negative Rational Numbers
32.Solve Multi-step Real-Life Problems (Conversions Between Forms of Rational Numbers)
33.Assess the Reasonableness of Answers using Mental Computation and Estimation
34.Construct Simple Equations of the form px+q=r from Word Problems
35.Solve Equations of the form px+q=r Fluently (Rational Numbers)
36.Construct Simple Equations of the form p(x+q)=r from Word Problems
37.Solve Equations of the form p(x+q)=r Fluently (Rational Numbers)
38.Compare an Algebraic Solution to an Arithmetic Solution for Multi-Step Word Problems
39.Construct and Solve Simple Inequalities from Word Problems
40.Unit 4 Review: Equations & Inequalities – Solving Multi-step Problems

Unit 5: Ratios & Proportional Relationships – Unit Rates & Proportionality

41.Compute Unit Rates Associated with Ratios of Fractions (Lengths, Areas)
42.Compute Unit Rates with Fractions in Other Quantities
43.Decide Whether Two Quantities are in a Proportional Relationship
44.Identify the Constant of Proportionality (Unit Rate) in Tables
45.Identify the Constant of Proportionality (Unit Rate) in Graphs
46.Identify the Constant of Proportionality (Unit Rate) in Equations
47.Identify the Constant of Proportionality in Diagrams and Verbal Descriptions
48.Represent Proportional Relationships by Writing Equations (y = kx)
49.Explain What a Point (x, y) on the Graph of a Proportional Relationship Means
50.Unit 5 Review: Ratios & Proportional Relationships

Unit 6: Proportional Relationships – Applications & Percent Problems

51.Use Proportional Relationships to Solve Multistep Ratio Problems
52.Use Proportional Relationships to Solve Multistep Percent Problems (Finding a Percent of a Quantity)
53.Use Proportional Relationships to Solve Multistep Percent Problems (Simple Interest)
54.Use Proportional Relationships to Solve Multistep Percent Problems (Tax and Gratuities)
55.Use Proportional Relationships to Solve Multistep Percent Problems (Markups and Markdowns)
56.Use Proportional Relationships to Solve Multistep Percent Problems (Commissions and Fees)
57.Use Proportional Relationships to Solve Multistep Percent Problems (Percent Increase and Decrease)
58.Use Proportional Relationships to Solve Multistep Percent Problems (Percent Error)
59.Mixed Multistep Ratio and Percent Problem Solving
60.Unit 6 Review: Proportional Relationships – Applications & Percent Problems

Unit 7: Geometry – Scale Drawings & Constructing Triangles

61.Solve Problems Involving Scale Drawings (Computing Actual Lengths)
62.Solve Problems Involving Scale Drawings (Computing Actual Areas)
63.Reproducing a Scale Drawing at a Different Scale
64.Draw Geometric Shapes with Given Conditions
65.Conditions for Unique Triangles (Given 3 Side Lengths – SSS)
66.Conditions for Unique Triangles (Given SAS or ASA)
67.Conditions for Unique Triangles (Given 3 Angle Measures – AAA)
68.Conditions for Unique Triangles (Exploring Ambiguous Cases)
69.Practice Constructing and Analyzing Triangles with Various Given Conditions
70.Unit 7 Review: Geometry – Scale Drawings & Constructing Triangles

Unit 8: Geometry – Circles & Angle Relationships

71.Know the Formulas for Area and Circumference of a Circle
72.Use Formulas to Solve Problems Involving Circumference of a Circle
73.Use Formulas to Solve Problems Involving Area of a Circle
74.Give an Informal Derivation of the Relationship Between Circumference and Area
75.Use Facts About Supplementary and Complementary Angles to Solve Problems
76.Use Facts About Vertical and Adjacent Angles to Solve Problems
77.Use Angle Relationships to Write and Solve Simple Equations
78.Solving for Unknown Angles in More Complex Figures
79.Practice: Solving Mixed Problems with Circles and Angle Relationships
80.Unit 8 Review: Geometry – Circles & Angle Relationships

Unit 9: Geometry – Area, Volume & Surface Area

81.Solve Real-World Problems Involving Area of Triangles and Quadrilaterals
82.Solve Real-World Problems Involving Area of Other Polygons
83.Describe the Two-Dimensional Figures that Result from Slicing Three-Dimensional Figures
84.Solve Real-World Problems Involving Volume of Cubes and Right Rectangular Prisms
85.Solve Real-World Problems Involving Volume of Right Triangular Prisms
86.Solve Real-World Problems Involving Surface Area of Cubes and Right Rectangular Prisms
87.Solve Real-World Problems Involving Surface Area of Right Triangular Prisms
88.Solve Real-World Problems Involving Volume and Surface Area of Composite 3D Figures
89.Practice: Solving Mixed Real-World Problems Involving Area, Volume, and Surface Area
90.Unit 9 Review: Geometry – Area, Volume & Surface Area

Unit 10: Statistics – Sampling & Comparing Populations

91.Understand that Statistics Can Be Used to Gain Information About a Population
92.Understand that Random Sampling Tends to Produce Representative Samples
93.Use Data from a Random Sample to Draw Inferences About a Population (Proportions)
94.Use Data from a Random Sample to Draw Inferences About a Population (Means)
95.Generate Multiple Samples to Gauge Variation in Estimates or Predictions
96.Informally Assess the Degree of Visual Overlap of Two Numerical Data Distributions
97.Measure the Difference Between Centers of Two Data Distributions
98.Use Measures of Center from Random Samples to Draw Comparative Inferences
99.Use Measures of Variability from Random Samples to Draw Comparative Inferences
100.Unit 10 Review: Statistics – Sampling & Comparing Populations

Unit 11: Probability – Likelihood & Compound Events

101.Understand Probability Scale (0 to 1) and Likelihood of Events
102.Approximate Probability of a Chance Event by Collecting Data (Experimental Probability)
103.Predict Approximate Relative Frequency Given Theoretical Probability
104.Develop a Uniform Probability Model and Use it to Find Probabilities
105.Develop a Non-Uniform Probability Model by Observing Frequencies
106.Compare Probabilities from a Model to Observed Frequencies
107.Understand that the Probability of a Compound Event is a Fraction of Outcomes
108.Represent Sample Spaces for Compound Events using Organized Lists and Tables
109.Represent Sample Spaces for Compound Events using Tree Diagrams
110.Unit 11 Review: Probability – Likelihood & Compound Events

Unit 12: Probability – Compound Events & Simulations

111.Find Probabilities of Compound Events using Organized Lists, Tables, or Tree Diagrams
112.Identify Outcomes in the Sample Space which Compose an Event
113.Introduction to Simulations: Understanding Purpose for Compound Events
114.Designing Simple Simulations to Generate Frequencies for Compound Events
115.Designing Simulations to Generate Frequencies for Compound Events (Using Random Digits)
116.Using a Designed Simulation to Generate Frequencies for Compound Events
117.Using Frequencies from a Simulation to Estimate the Probability of a Compound Event
118.Practice Designing and Using Simulations for Various Compound Events
119.Comparing Experimental Probability to Theoretical Probability
120.Unit 12 Review: Probability – Compound Events & Simulations

Grade 8 (Ontario) ▼

Unit 1: The Real Number System, Integers, and Square Roots ▼

1.Understanding Rational Numbers: Definition, Representation, and Examples.
2.Understanding Irrational Numbers: Definition and Examples.
3.Comparing and Ordering Real Numbers (Rational and Irrational).
4.Adding Integers using Rules and Strategies.
5.Subtracting Integers using Rules and Strategies (Relating to Adding the Opposite).
6.Multiplying Integers: Understanding Rules for Signs.
7.Dividing Integers: Understanding Rules for Signs.
8.Understanding and Recalling Commonly Used Perfect Squares and Their Principal Square Roots.
9.Estimating and Calculating Square Roots of Non-Perfect Squares.
10.Unit 1 Review: Real Numbers, Integer Operations, Square Roots.

Unit 2: Powers, Scientific Notation, and Large/Small Scale ▼

11.Representing Very Large Numbers (Standard Form and Place Value up to Trillions).
12.Introduction to Scientific Notation for Large Numbers.
13.Representing Very Small Numbers (Standard Form and Place Value to Millionths/Billionths).
14.Scientific Notation for Small Numbers.
15.Comparing Numbers in Scientific Notation and Identifying Everyday Uses.
16.Representing Very Large Metric Units (Mega-, Giga-, Tera-) using Powers of Ten.
17.Representing Very Small Metric Units (Micro-, Nano-, Pico-) using Powers of Ten.
18.Mental Math: Multiplying Whole Numbers and Decimals by Powers of Ten (Positive and Negative Exponents).
19.Mental Math: Dividing Whole Numbers and Decimals by Powers of Ten (Positive Exponents).
20.Unit 2 Review: Powers, Scientific Notation, Large/Small Scale Applications.

Unit 3: Fraction Operations and Problem Solving ▼

21.Adding Fractions with Like and Unlike Denominators (Including Positive and Negative Fractions and Mixed Numbers).
22.Subtracting Fractions with Like and Unlike Denominators (Including Positive and Negative Fractions and Mixed Numbers).
23.Problem Solving with Addition and Subtraction of Fractions.
24.Multiplying Fractions by Fractions (Positive and Negative).
25.Multiplying Fractions by Whole Numbers and Mixed Numbers (Positive and Negative).
26.Dividing Fractions by Fractions (Positive and Negative, Using Reciprocals).
27.Dividing Fractions by Whole Numbers and Mixed Numbers (Positive and Negative, Using Reciprocals).
28.Problem Solving with Multiplication and Division of Fractions.
29.Order of Operations with Fractions (Positive and Negative).
30.Unit 3 Review: Fraction Operations.

Unit 4: Rational Numbers: Decimals, Percents, Ratios, Rates, and Order of Operations ▼

31.Converting Fractions to Decimals (Terminating and Repeating) and Percents.
32.Converting Decimals (Terminating and Repeating) to Fractions (Simplest Form) and Percents.
33.Converting Percents (Including >100% and <1%) to Fractions (Simplest Form) and Decimals.
34.Solving Problems Using Fractions, Decimals, and Percents Flexibly and Strategically.
35.Order of Operations with Rational Numbers (Fractions, Decimals, Integers, including Exponents).
36.Problem Solving with Order of Operations Involving Rational Numbers in Context.
37.Ratios and Rates involving Rational Numbers (Fractions and Decimals).
38.Solving All Types of Percent Problems (Finding Part, Whole, Percent) Involving Rational Numbers.
39.Multi-Step Problems Involving Ratios, Rates, and Percents with Rational Numbers (Complex Contexts).
40.Unit 4 Review: Rational Numbers (FDP Conversions, Operations, Order of Ops, Ratios/Rates/Percents).

Unit 5: Proportional Reasoning and Applications ▼

41.Identifying Proportional Situations from Tables, Graphs, and Equations.
42.Comparing Proportional Situations using Unit Rates, Ratios, or Graphs.
43.Determining Unknown Values in Proportional Situations using Unit Rates.
44.Determining Unknown Values in Proportional Situations using Scale Factors (Multiplicative Relationships).
45.Determining Unknown Values in Proportional Situations using Cross-Multiplication (Setting up and Solving Proportions).
46.Applying Proportional Reasoning to Solve Problems in Various Contexts (e.g., mixtures, similar figures, conversions involving rates).
47.Scale Drawings: Calculating Actual Lengths and Perimeters from Scaled Representations.
48.Scale Drawings: Calculating Actual Areas from Scaled Representations (Understanding Area Scale Factor).
49.Reproducing Scale Drawings at Different Ratios (Enlarging or Reducing Existing Scaled Drawings).
50.Unit 5 Review: Proportional Reasoning and Scale Drawings.

Unit 6: Financial Literacy: Planning, Spending, and Interest ▼

51.Analyzing Advantages and Disadvantages of Various Payment Methods When Dealing with Multiple Currencies (Cash, Credit Cards, Debit Cards, Online Payment Services, considering exchange rates and fees).
52.Optimizing Value for Money: Analyzing Sales, Discounts, and Promotions.
53.Evaluating Customer Loyalty and Incentive Programs for Actual Value.
54.Comparing Credit Card Offers: Analyzing Interest Rates (APR), Annual Fees, Grace Periods, and Penalties.
55.Comparing Credit Card Offers: Evaluating Rewards Programs and Incentives.
56.Comparing Consumer Contracts for Services (e.g., Cell Phone Plans, Streaming Services, Gym Memberships).
57.Creating a Comprehensive Financial Plan for a Significant Long-Term Goal (Considering Income, All Expense Categories, Savings Targets, Timelines).
58.Financial Planning: Accounting for Tax Implications (Sales Tax, Basic Income Tax Deductions) on Income and Expenses.
59.Maintaining a Balanced Budget, Tracking Actual Income and Spending, and Making Necessary Adjustments.
60.Unit 6 Review: Financial Literacy (Payment Methods, Value, Credit/Contracts, Planning, Budgeting, Taxes, Interest).

Unit 7: Patterns and Introduction to Algebra ▼

61.Identifying and Comparing Repeating, Growing, and Shrinking Patterns (Linear and Introduction to Non-Linear).
62.Creating and Describing Patterns to Illustrate Relationships Among Rational Numbers (Growing Patterns with Fractions or Decimals).
63.Creating and Describing Patterns to Illustrate Relationships Among Rational Numbers (Shrinking Patterns with Fractions or Decimals).
64.Creating Repeating, Growing, and Shrinking Patterns with Rational Numbers and Representing them using Tables of Values.
65.Translating Linear Growing/Shrinking Patterns (with Rational Numbers) into Algebraic Expressions (nth term).
66.Translating Linear Growing/Shrinking Patterns (with Rational Numbers) into Equations.
67.Determining Pattern Rules (for patterns with rational numbers) and Using Them to Extend Patterns and Make Predictions.
68.Using Algebraic Representations of Linear Pattern Rules (Equations) to Solve for Unknown Values.
69.Adding and Subtracting Monomials with a Degree of 1 (Involving Integer Coefficients).
70.Unit 7 Review: Patterns with Rational Numbers and Introduction to Monomials.

Unit 8: Algebraic Expressions, Equations, and Inequalities ▼

71.Adding Binomials with a Degree of 1 (Involving Integer Coefficients) using Tools and Symbolically.
72.Evaluating Algebraic Expressions Involving Rational Numbers (Fractions as Coefficients or Values).
73.Evaluating Algebraic Expressions Involving Rational Numbers (Decimals as Coefficients or Values).
74.Solving Multi-Term Equations with Integer Coefficients and Constants (Variables on One Side, Including Distributive Property).
75.Solving Multi-Term Equations with Decimal Number Coefficients and Constants (Variables on One Side).
76.Solving Equations with Variables on Both Sides of the Equation (Integer and Decimal Coefficients).
77.Solving Inequalities Involving Integers (One-Step and Two-Step Linear Inequalities).
78.Solving Multi-Term Inequalities Involving Integers (Requiring Distributive Property or Combining Like Terms).
79.Verifying Solutions to Inequalities and Graphing Solution Sets on a Number Line.
80.Unit 8 Review: Algebraic Operations (Adding Binomials, Evaluating Expressions with Rationals), Solving Equations (Multi-Step, Variables on Both Sides) and Inequalities (Integers).

Unit 9: Geometric Properties, Transformations, and Spatial Reasoning ▼

81.Describing and Classifying Prisms According to their Geometric Properties (Number/Shape of Faces, Edges, Vertices, Type of Base, Parallelism of Faces).
82.Describing and Classifying Pyramids and Cylinders According to their Geometric Properties (Number/Shape of Faces, Edges, Vertices, Apex, Circular Bases, Curved Surface).
83.Identifying Planes of Symmetry in 3D Shapes (Prisms and Pyramids) and Axes of Rotational Symmetry in Prisms and Cylinders.
84.Drawing Top, Front, and Side Views (Orthographic Projections) of 3D Objects Composed of Simple Geometric Solids.
85.Drawing Basic Perspective Views of Objects and Simple Physical Spaces (One-Point and Introduction to Two-Point Perspective).
86.Understanding and Using Appropriate Scales in Geometric Drawings and Models.
87.Performing Dilations (Enlargements and Reductions) of 2D Shapes on a Cartesian Plane and Describing Similarity.
88.Describing and Performing Sequences of Translations and Reflections on the Cartesian Plane.
89.Describing and Performing Rotations on the Cartesian Plane (90°, 180°, 270° about the origin) and Predicting Results of Combined Transformations.
90.Unit 9 Review: Geometric Properties, 2D/3D Views, Scale, and All Four Transformations.

Unit 10: Measurement – 2D Shapes, Pythagorean Theorem, and 3D Solids ▼

91.Calculating Perimeter and Circumference of Composite 2D Shapes (Made from Rectangles, Triangles, Circles/Semicircles).
92.Calculating Area of Composite 2D Shapes (Adding/Subtracting Areas of Simpler Shapes).
93.Describing the Pythagorean Relationship (a² + b² = c²) Using Geometric Models (Squares on Sides of a Right Triangle).
94.Applying the Pythagorean Theorem to Find the Length of the Hypotenuse in a Right-Angled Triangle.
95.Applying the Pythagorean Theorem to Find the Length of a Leg in a Right-Angled Triangle.
96.Calculating Surface Area of Right Prisms (Rectangular, Triangular) and Cylinders (Review and Composite Parts).
97.Calculating Surface Area of Composite 3D Objects (Made from Prisms and Cylinders).
98.Calculating Volume of Right Prisms (Rectangular, Triangular) and Cylinders (Review and Composite Parts).
99.Calculating Volume of Composite 3D Objects (Made from Prisms and Cylinders).
100.Unit 10 Review: Perimeter/Area of Composite 2D Shapes, Pythagorean Theorem, Surface Area/Volume of Composite 3D Solids.

Unit 11: Data Analysis and Probability ▼

101.Identifying Situations Involving One-Variable Data (Descriptive Statistics) and Two-Variable Data (Exploring Relationships).
102.Collecting Continuous Data for Two Variables from Various Sources (Primary and Secondary) and Organizing it in a Table of Values.
103.Selecting Appropriate Types of Graphs, Including Scatter Plots, to Represent Different Types of Data and Relationships, and Justifying the Choice.
104.Displaying Data in Scatter Plots with Proper Formatting (Titles, Labeled Axes with Units, Appropriate Scales, Source Citation).
105.Describing Relationships (Correlations) Between Two Variables as Displayed in Scatter Plots (Using terms like Strong, Weak, None, Positive, Negative, Linear, Non-linear).
106.Identifying Outliers in Scatter Plots and Discussing Their Potential Impact on the Perceived Relationship and Line of Best Fit (Informal).
107.Analyzing Data Presented in Scatter Plots and Potentially Misleading Graphs; Drawing Conclusions and Making Inferences.
108.Solving Probability Problems Involving Two or More Events Using Venn Diagrams.
109.Solving Probability Problems Using Tree Diagrams for Multiple Independent or Dependent Events.
110.Unit 11 Review: One- and Two-Variable Data Analysis (Scatter Plots, Correlations, Outliers, Misleading Graphs) and Probability (Venn Diagrams, Tree Diagrams for Multiple Events).

Unit 12: Coding for Data Analysis and Decision Making ▼

111.Introduction to Coding for Data Analysis: Setting up Variables and Basic Input/Output Operations.
112.Using Lists or Arrays to Store and Access Sets of Numerical Data in Code.
113.Implementing Control Structures: Using Loops (e.g., For Loops) for Iterating Through Data Sets to Perform Calculations (e.g., Sum, Average, Counting).
114.Implementing Control Structures: Using Conditional Statements (If/Else If/Else) for Data Analysis and Categorization.
115.Creating Sub-programs (Functions or Procedures) for Reusable Data Analysis Tasks (e.g., finding min/max, calculating range).
116.Reading Data into Programs from Simple Sources (e.g., Predefined Lists within Code, User Input for Multiple Items to form a list).
117.Altering Existing Code: Modifying Logic for Different Data Analysis Tasks.
118.Altering Existing Code: Describing How Changes to Code (Variables, Operators, Control Structures) Affect Outcomes and Efficiency.
119.Developing Computational Representations of Mathematical Situations: Using Code to Communicate Decisions Based on Processed Data.
120.Unit 12 Review: Coding Concepts for Data Analysis and Decision Making.

Grade 8 ▼

Unit 1: The Number System (Rational & Irrational Numbers)

1.Define Rational and Irrational Numbers
2.Decimal Expansions of Rational Numbers: Terminating or Repeating
3.Converting Repeating Decimals to Fractions
4.Exploring Irrational Numbers: Non-Repeating, Non-Terminating Decimals
5.Approximate Irrational Numbers on a Number Line using Rational Approximations
6.Compare the Size of Irrational Numbers using Rational Approximations
7.Estimate the Value of Expressions Involving Irrational Numbers
8.Ordering Sets of Real Numbers (Rational and Irrational)
9.Problem Solving with Rational and Irrational Numbers
10.Unit 1 Review: The Number System (Rational & Irrational Numbers, Approximations)

Unit 2: Integer Exponents and Scientific Notation

11.Integer Exponents – Product Rule
12.Integer Exponents – Quotient Rule
13.Integer Exponents – Zero Exponent
14.Integer Exponents – Negative Exponents
15.Integer Exponents – Power of a Power
16.Integer Exponents – Power of a Product and Power of a Quotient
17.Applying Multiple Exponent Properties to Simplify Expressions
18.Introduction to Scientific Notation: Expressing Very Large Numbers
19.Introduction to Scientific Notation: Expressing Very Small Numbers
20.Unit 2 Review: Integer Exponents and Scientific Notation

Unit 3: Square Roots, Cube Roots & The Pythagorean Theorem

21.Square Roots: Understanding and Evaluating Square Roots of Perfect Squares
22.Cube Roots: Understanding and Evaluating Cube Roots of Perfect Cubes
23.Estimating Square Roots of Non-Perfect Squares
24.The Pythagorean Theorem: Understanding a² + b² = c²
25.Explain a Proof of the Pythagorean Theorem
26.Apply the Pythagorean Theorem to Find the Hypotenuse
27.Apply the Pythagorean Theorem to Find a Leg
28.Apply the Converse of the Pythagorean Theorem
29.Apply the Pythagorean Theorem to Find Distance Between Points
30.Unit 3 Review: Square Roots, Cube Roots & The Pythagorean Theorem

Unit 4: Proportional Relationships, Lines, and Linear Equations

31.Graph Proportional Relationships, Interpreting Unit Rate as Slope
32.Compare Different Proportional Relationships Represented in Different Ways
33.Use Similar Triangles to Explain Why Slope is Constant
34.Derive the Equation y = mx for a Line Through the Origin
35.Derive the Equation y = mx + b for a Line with y-intercept b
36.Identify Slope and y-intercept from an Equation
37.Graph a Linear Equation in the form y = mx + b
38.Write the Equation of a Line Given its Graph
39.Practice with Slope and Linear Equations
40.Unit 4 Review: Proportional Relationships, Lines, and Linear Equations

Unit 5: Solving Linear Equations in One Variable

41.Solve Linear Equations with Integer Coefficients (Variables on One Side)
42.Solve Linear Equations with Integer Coefficients (Variables on Both Sides)
43.Solve Linear Equations with Rational Coefficients (Fractions)
44.Solve Linear Equations with Rational Coefficients (Decimals)
45.Give Examples of Linear Equations with One Solution
46.Give Examples of Linear Equations with Infinitely Many Solutions
47.Give Examples of Linear Equations with No Solutions
48.Practice Solving Linear Equations (All Types of Solutions)
49.Solve Real-World Problems Leading to Linear Equations
50.Unit 5 Review: Solving Linear Equations in One Variable

Unit 6: Systems of Linear Equations

51.Understand Solutions to a System of Two Linear Equations
52.Solve Systems of Two Linear Equations by Graphing
53.Practice Solving Systems by Graphing (Including Special Cases)
54.Solve Systems Using Substitution (Simple Cases)
55.Solve Systems Using Substitution (More Complex Cases)
56.Solve Systems Using Elimination (Adding or Subtracting Equations)
57.Solve Systems Using Elimination (Multiplying Equations First)
58.Choose the Best Method for Solving a System
59.Solve Real-World Problems Using Systems of Equations
60.Unit 6 Review: Systems of Linear Equations

Unit 7: Introduction to Functions

61.Understand that a Function Assigns Each Input Exactly One Output
62.Understand the Graph of a Function as Ordered Pairs
63.Use Function Notation to Evaluate Functions
64.Compare Properties of Two Functions Represented in Different Ways
65.Compare Properties of Two Functions (Rates of Change / Slopes)
66.Interpret the Equation y = mx + b as Defining a Linear Function
67.Give Examples of Functions that are Not Linear
68.Practice Identifying Linear and Non-Linear Functions
69.Determine Rate of Change and Initial Value from a Description
70.Unit 7 Review: Introduction to Functions

Unit 8: Using Functions to Model Relationships

71.Determine Rate of Change and Initial Value from Two Points
72.Determine Rate of Change and Initial Value from a Graph
73.Construct a Function to Model a Linear Relationship
74.Interpret Rate of Change and Initial Value in Context
75.Practice Modeling Linear Relationships
76.Describe Qualitative Features of Functions from Graphs
77.Sketch Graphs from Verbal Descriptions of Functions
78.Analyzing and Sketching Qualitative Graphs for Real-World Scenarios
79.Comparing Qualitative Features of Different Functional Relationships
80.Unit 8 Review: Using Functions to Model Relationships

Unit 9: Transformations & Congruence

81.Verify Properties of Rotations
82.Verify Properties of Reflections
83.Verify Properties of Translations
84.Understand Congruence in Terms of Rigid Motions
85.Describe Sequences of Transformations Between Congruent Figures
86.Describe the Effect of Translations Using Coordinates
87.Describe the Effect of Reflections Using Coordinates
88.Describe the Effect of Rotations Using Coordinates
89.Practice Describing Sequences of Transformations Using Coordinates
90.Unit 9 Review: Transformations & Congruence

Unit 10: Transformations & Similarity

91.Verify Properties of Dilations
92.Understand Similarity in Terms of Transformations
93.Describe Sequences of Transformations Between Similar Figures
94.Describe the Effect of Dilations Using Coordinates
95.Use Informal Arguments to Establish Angle Sum in Triangles
96.Use Informal Arguments to Establish Exterior Angle Theorem
97.Use Informal Arguments to Establish Angles from Parallel Lines
98.Use Informal Arguments to Establish the AA Criterion for Similarity
99.Apply AA Similarity to Determine if Triangles are Similar
100.Unit 10 Review: Transformations & Similarity

Unit 11: Volume of Cylinders, Cones, and Spheres

101.Know and Understand the Formula for Volume of a Cylinder
102.Use the Formula to Solve Problems Involving Volume of Cylinders
103.Know and Understand the Formula for Volume of a Cone
104.Use the Formula to Solve Problems Involving Volume of Cones
105.Know and Understand the Formula for Volume of a Sphere
106.Use the Formula to Solve Problems Involving Volume of Spheres
107.Comparing Volumes of Cylinders, Cones, and Spheres
108.Solve Real-World Problems Involving Volumes of 3D Shapes
109.Practice: Mixed Problems with Volume of 3D Shapes
110.Unit 11 Review: Volume of Cylinders, Cones, and Spheres

Unit 12: Bivariate Data (Scatter Plots, Linear Models, Two-Way Tables)

111.Construct and Interpret Scatter Plots
112.Describe Patterns in Scatter Plots: Clustering, Outliers, Association
113.Describe Patterns in Scatter Plots: Linear and Nonlinear Association
114.Informally Fit a Straight Line to Scatter Plots
115.Informally Assess the Model Fit
116.Find an Approximate Equation for a Fitted Line
117.Use a Linear Model to Solve Problems
118.Interpret Slope and Intercept of a Linear Model in Context
119.Understand Patterns of Association in Bivariate Categorical Data
120.Unit 12 Review: Bivariate Data Analysis