A: Social-Emotional Learning (SEL) Skills in Mathematics and the Mathematical Processes

A1: Throughout this grade, in order to promote a positive identity as a math learner, to foster well-being and the ability to learn, build resilience, and thrive, students will: apply, to the best of their ability, a variety of social-emotional learning skills to support their use of the mathematical processes and their learning in connection with the expectations in the other five strands of the mathematics curriculum

1.1.2: … as they apply the mathematical processes:

A1.MP.2: reasoning and proving: develop and apply reasoning skills (e.g., classification, recognition of relationships, use of counter-examples) to justify thinking, make and investigate conjectures, and construct and defend arguments

Biconditional Statements
Conditional Statements

B: Number

B1: By the end of each grade, students will: demonstrate an understanding of numbers and make connections to the way numbers are used in everyday life

2.1.1: Rational Numbers

B1.1: By the end of each grade, students will: read and represent whole numbers up to and including one million, using appropriate tools and strategies, and describe various ways they are used in everyday life

Modeling Whole Numbers and Decimals (Base-10 Blocks)
Whole Numbers with Base-10 Blocks

B1.2: By the end of each grade, students will: read and represent integers, using a variety of tools and strategies, including horizontal and vertical number lines

Integers, Opposites, and Absolute Values

B1.3: By the end of each grade, students will: compare and order integers, decimal numbers, and fractions, separately and in combination, in various contexts

Comparing and Ordering Decimals
Equivalent Fractions (Fraction Tiles)
Fraction Garden (Comparing Fractions)
Fraction, Decimal, Percent (Area and Grid Models)
Integers, Opposites, and Absolute Values
Modeling Decimals (Area and Grid Models)
Modeling Fractions (Area Models)
Ordering Percents, Fractions, and Decimals Greater Than 1
Treasure Hunter (Decimals on the Number Line)

2.1.2: Fractions, Decimals, and Percents

B1.4: By the end of each grade, students will: read, represent, compare, and order decimal numbers up to thousandths, in various contexts

Comparing and Ordering Decimals
Fraction, Decimal, Percent (Area and Grid Models)
Modeling Decimals (Area and Grid Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Ordering Percents, Fractions, and Decimals Greater Than 1
Treasure Hunter (Decimals on the Number Line)

B1.6: By the end of each grade, students will: describe relationships and show equivalences among fractions and decimal numbers up to thousandths, using appropriate tools and drawings, in various contexts

Fraction, Decimal, Percent (Area and Grid Models)
Ordering Percents, Fractions, and Decimals Greater Than 1
Percents, Fractions, and Decimals

B2: By the end of each grade, students will: use knowledge of numbers and operations to solve mathematical problems encountered in everyday life

2.2.1: Properties and Relationships

B2.1: By the end of each grade, students will: use the properties of operations, and the relationships between operations, to solve problems involving whole numbers, decimal numbers, fractions, ratios, rates, and whole number percents, including those requiring multiple steps or multiple operations

Part-to-part and Part-to-whole Ratios
Percent of Change
Percents and Proportions
Proportions and Common Multipliers

2.2.2: Math Facts

B2.2: By the end of each grade, students will: understand the divisibility rules and use them to determine whether numbers are divisible by 2, 3, 4, 5, 6, 8, 9, and 10

Factor Trees (Factoring Numbers)

2.2.4: Addition and Subtraction

B2.4: By the end of each grade, students will: represent and solve problems involving the addition and subtraction of whole numbers and decimal numbers, using estimation and algorithms

Adding Whole Numbers and Decimals (Base-10 Blocks)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Sums and Differences with Decimals

B2.5: By the end of each grade, students will: add and subtract fractions with like and unlike denominators, using appropriate tools, in various contexts

Adding Fractions (Fraction Tiles)
Fractions Greater than One (Fraction Tiles)
Fractions with Unlike Denominators
Improper Fractions and Mixed Numbers

2.2.5: Multiplication and Division

B2.6: By the end of each grade, students will: represent composite numbers as a product of their prime factors, including through the use of factor trees

Factor Trees (Factoring Numbers)
Finding Factors with Area Models

B2.9: By the end of each grade, students will: multiply whole numbers by proper fractions, using appropriate tools and strategies

Multiplying Fractions

B2.10: By the end of each grade, students will: divide whole numbers by proper fractions, using appropriate tools and strategies

Dividing Fractions

B2.12: By the end of each grade, students will: solve problems involving ratios, including percents and rates, using appropriate tools and strategies

Part-to-part and Part-to-whole Ratios
Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Proportions and Common Multipliers

C: Algebra

C1: By the end of each grade, students will: identify, describe, extend, create, and make predictions about a variety of patterns, including those found in real-life contexts

3.1.1: Patterns

C1.1: By the end of each grade, students will: identify and describe repeating, growing, and shrinking patterns, including patterns found in real-life contexts, and specify which growing patterns are linear

Finding Patterns
Pattern Flip (Patterns)

C1.2: By the end of each grade, students will: create and translate repeating, growing, and shrinking patterns using various representations, including tables of values, graphs, and, for linear growing patterns, algebraic expressions and equations

Finding Patterns
Function Machines 2 (Functions, Tables, and Graphs)
Pattern Flip (Patterns)

C1.3: By the end of each grade, students will: determine pattern rules and use them to extend patterns, make and justify predictions, and identify missing elements in repeating, growing, and shrinking patterns, and use algebraic representations of the pattern rules to solve for unknown values in linear growing patterns

Finding Patterns
Pattern Flip (Patterns)

C1.4: By the end of each grade, students will: create and describe patterns to illustrate relationships among whole numbers and decimal numbers

Finding Patterns
Function Machines 2 (Functions, Tables, and Graphs)
Pattern Flip (Patterns)

C2: By the end of each grade, students will: demonstrate an understanding of variables, expressions, equalities, and inequalities, and apply this understanding in various contexts

3.2.1: Variables and Expressions

C2.1: By the end of each grade, students will: add monomials with a degree of 1 that involve whole numbers, using tools

Simplifying Algebraic Expressions II

C2.2: By the end of each grade, students will: evaluate algebraic expressions that involve whole numbers and decimal tenths

Equivalent Algebraic Expressions I

3.2.2: Equalities and Inequalities

C2.3: By the end of each grade, students will: solve equations that involve multiple terms and whole numbers in various contexts, and verify solutions

Modeling and Solving Two-Step Equations
Solving Algebraic Equations I
Solving Algebraic Equations II
Solving Two-Step Equations

C2.4: By the end of each grade, students will: solve inequalities that involve two operations and whole numbers up to 100, and verify and graph the solutions

Exploring Linear Inequalities in One Variable

D: Data

D1: By the end of each grade, students will: manage, analyse, and use data to make convincing arguments and informed decisions, in various contexts drawn from real life

4.1.1: Data Collection and Organization

D1.2: By the end of each grade, students will: collect qualitative data and discrete and continuous quantitative data to answer questions of interest about a population, and organize the sets of data as appropriate, including using intervals

Estimating Population Size
Polling: Neighborhood
Stem-and-Leaf Plots

4.1.2: Data Visualization

D1.3: By the end of each grade, students will: select from among a variety of graphs, including histograms and broken-line graphs, the type of graph best suited to represent various sets of data; display the data in the graphs with proper sources, titles, and labels, and appropriate scales; and justify their choice of graphs

Graphing Skills
Histograms

D1.4: By the end of each grade, students will: create an infographic about a data set, representing the data in appropriate ways, including in tables, histograms, and broken-line graphs, and incorporating any other relevant information that helps to tell a story about the data

Graphing Skills
Histograms
Mascot Election (Pictographs and Bar Graphs)
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram
Stem-and-Leaf Plots

4.1.3: Data Analysis

D1.5: By the end of each grade, students will: determine the range as a measure of spread and the measures of central tendency for various data sets, and use this information to compare two or more data sets

Describing Data Using Statistics
Mean, Median, and Mode
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots

D1.6: By the end of each grade, students will: analyse different sets of data presented in various ways, including in histograms and broken-line graphs and in misleading graphs, by asking and answering questions about the data, challenging preconceived notions, and drawing conclusions, then make convincing arguments and informed decisions

Elevator Operator (Line Graphs)
Graphing Skills
Histograms
Stem-and-Leaf Plots

D2: By the end of each grade, students will: describe the likelihood that events will happen, and use that information to make predictions

4.2.1: Probability

D2.1: By the end of each grade, students will: use fractions, decimals, and percents to express the probability of events happening, represent this probability on a probability line, and use it to make predictions and informed decisions

Spin the Big Wheel! (Probability)

D2.2: By the end of each grade, students will: determine and compare the theoretical and experimental probabilities of two independent events happening

Independent and Dependent Events

E: Spatial Sense

E1: By the end of each grade, students will: describe and represent shape, location, and movement by applying geometric properties and spatial relationships in order to navigate the world around them

5.1.1: Geometric Reasoning

E1.1: By the end of each grade, students will: create lists of geometric properties of various types of quadrilaterals, including the properties of the diagonals, rotational symmetry, and line symmetry

Classifying Quadrilaterals

E1.2: By the end of each grade, students will: construct three-dimensional objects when given their top, front, and side views

3D and Orthographic Views

5.1.2: Location and Movement

E1.3: By the end of each grade, students will: plot and read coordinates in all four quadrants of a Cartesian plane, and describe the translations that move a point from one coordinate to another

Points in the Coordinate Plane
Rotations, Reflections, and Translations

E1.4: By the end of each grade, students will: describe and perform combinations of translations, reflections, and rotations up to 360° on a grid, and predict the results of these transformations

Rock Art (Transformations)
Rotations, Reflections, and Translations

E2: By the end of each grade, students will: compare, estimate, and determine measurements in various contexts

5.2.1: The Metric System

E2.1: By the end of each grade, students will: measure length, area, mass, and capacity using the appropriate metric units, and solve problems that require converting smaller units to larger ones and vice versa

Cannonball Clowns (Number Line Estimation)
Unit Conversions

5.2.2: Angles

E2.3: By the end of each grade, students will: use the properties of supplementary angles, complementary angles, opposite angles, and interior and exterior angles to solve for unknown angle measures

Investigating Angle Theorems

5.2.3: Area and Surface Area

E2.4: By the end of each grade, students will: determine the areas of trapezoids, rhombuses, kites, and composite polygons by decomposing them into shapes with known areas

Area of Triangles

E2.5: By the end of each grade, students will: create and use nets to demonstrate the relationship between the faces of prisms and pyramids and their surface areas

Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

E2.6: By the end of each grade, students will: determine the surface areas of prisms and pyramids by calculating the areas of their two-dimensional faces and adding them together

Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones