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 and Irrational Numbers

B1.1: By the end of each grade, students will: represent and compare very large and very small numbers, including through the use of scientific notation, and describe various ways they are used in everyday life

Number Systems

B1.2: By the end of each grade, students will: describe, compare, and order numbers in the real number system (rational and irrational numbers), separately and in combination, in various contexts

Comparing and Ordering Decimals
Modeling Decimals (Area and Grid Models)
Ordering Percents, Fractions, and Decimals Greater Than 1
Rational Numbers, Opposites, and Absolute Values

B1.3: By the end of each grade, students will: estimate and calculate square roots, in various contexts

Ordering and Approximating Square Roots
Square Roots

2.1.2: Fractions, Decimals, and Percents

B1.4: By the end of each grade, students will: use fractions, decimal numbers, and percents, including percents of more than 100% or less than 1%, interchangeably and flexibly to solve a variety of problems

Fraction, Decimal, Percent (Area and Grid Models)
Part-to-part and Part-to-whole Ratios
Percent of Change
Percents and Proportions
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 and order of operations, and the relationships between operations, to solve problems involving rational numbers, ratios, rates, and percents, including those requiring multiple steps or multiple operations

Adding and Subtracting Integers
Adding on the Number Line
Order of 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 and recall commonly used square numbers and their square roots

Ordering and Approximating Square Roots
Square Roots

2.2.4: Addition and Subtraction

B2.4: By the end of each grade, students will: add and subtract integers, using appropriate strategies, in various contexts

Adding and Subtracting Integers
Adding and Subtracting Integers with Chips
Adding on the Number Line

B2.5: By the end of each grade, students will: add and subtract fractions, using appropriate strategies, 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: multiply and divide fractions by fractions, as well as by whole numbers and mixed numbers, in various contexts

Dividing Fractions
Dividing Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers

B2.8: By the end of each grade, students will: compare proportional situations and determine unknown values in proportional situations, and apply proportional reasoning to solve problems in various contexts

Percent of Change
Percents and Proportions

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 compare a variety of repeating, growing, and shrinking patterns, including patterns found in real-life contexts, and compare linear growing and shrinking patterns on the basis of their constant rates and initial values

Finding Patterns
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 and subtract monomials with a degree of 1, and add binomials with a degree of 1 that involve integers, using tools

Simplifying Algebraic Expressions II

3.2.2: Equalities and Inequalities

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

Modeling and Solving Two-Step Equations
Solving Algebraic Equations I
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Two-Step Equations

C2.4: By the end of each grade, students will: solve inequalities that involve integers, and verify and graph the solutions

Exploring Linear Inequalities in One Variable
Solving 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 continuous data to answer questions of interest involving two variables, and organize the data sets as appropriate in a table of values

Solving Using Trend Lines

4.1.2: Data Visualization

D1.3: By the end of each grade, students will: select from among a variety of graphs, including scatter plots, 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

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 and scatter plots, and incorporating any other relevant information that helps to tell a story about the data

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

4.1.3: Data Analysis

D1.5: By the end of each grade, students will: use mathematical language, including the terms “strong”, “weak”, “none”, “positive”, and “negative”, to describe the relationship between two variables for various data sets with and without outliers

Trends in Scatter Plots

D1.6: By the end of each grade, students will: analyse different sets of data presented in various ways, including in scatter plots 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

Graphing Skills
Solving Using Trend Lines
Stem-and-Leaf Plots
Trends in Scatter 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: solve various problems that involve probability, using appropriate tools and strategies, including Venn and tree diagrams

Geometric Probability
Lucky Duck (Expected Value)
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

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

E1.2: By the end of each grade, students will: make objects and models using appropriate scales, given their top, front, and side views or their perspective views

3D and Orthographic Views

E1.3: By the end of each grade, students will: use scale drawings to calculate actual lengths and areas, and reproduce scale drawings at different ratios

Perimeters and Areas of Similar Figures

5.1.2: Location and Movement

E1.4: By the end of each grade, students will: describe and perform translations, reflections, rotations, and dilations on a Cartesian plane, and predict the results of these transformations

Dilations
Reflections
Rotations, Reflections, and Translations
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: represent very large (mega, giga, tera) and very small (micro, nano, pico) metric units using models, base ten relationships, and exponential notation

Unit Conversions 2 - Scientific Notation and Significant Digits

5.2.2: Lines and Angles

E2.2: By the end of each grade, students will: solve problems involving angle properties, including the properties of intersecting and parallel lines and of polygons

Classifying Quadrilaterals
Investigating Angle Theorems
Parallelogram Conditions
Special Parallelograms
Triangle Angle Sum

5.2.3: Length, Area, and Volume

E2.3: By the end of each grade, students will: solve problems involving the perimeter, circumference, area, volume, and surface area of composite two-dimensional shapes and three-dimensional objects, using appropriate formulas

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

E2.4: By the end of each grade, students will: describe the Pythagorean relationship using various geometric models, and apply the theorem to solve problems involving an unknown side length for a given right triangle

Pythagorean Theorem
Pythagorean Theorem with a Geoboard