## Grade 7 Math

## CONTENTS

## Number theory

Prime or composite

Prime factorization

Multiplicative inverses

Divisibility rules

Greatest common factor

Least common multiple

GCF and LCM: word problems

Scientific notation

Compare numbers written in scientific notation

Classify numbers

## Integers

Understanding integers

Integers on number lines

Graph integers on horizontal and vertical number lines

Absolute value and opposite integers

Compare and order integers

Integer inequalities with absolute values

## Operations with integers

Integer addition and subtraction rules

Add and subtract integers using counters

Add and subtract integers

Complete addition and subtraction sentences with integers

Add and subtract integers: word problems

Integer multiplication and division rules

Multiply and divide integers

Complete multiplication and division sentences with integers

Evaluate numerical expressions involving integers

## Decimals

Decimal numbers review

Compare and order decimals

Decimal number lines

Round decimals

II

## Operations with decimals

Add and subtract decimals

Add and subtract decimals: word problems

Multiply decimals

Multiply decimals and whole numbers: word problems

Divide decimals

Divide decimals by whole numbers: word problems

Estimate sums, differences and products of decimals

Add, subtract, multiply and divide decimals: word problems

Multi-step inequalities with decimals

Maps with decimal distances

Evaluate numerical expressions involving decimals

## Fractions and mixed numbers

Understanding fractions: word problems

Equivalent fractions

Write fractions in lowest terms

Fractions: word problems with graphs and tables

Least common denominator

Compare and order fractions

Compare fractions using benchmarks

Compare fractions: word problems

Convert between mixed numbers and improper fractions

Compare mixed numbers and improper fractions

Round mixed numbers

Put a mix of decimals, fractions and mixed numbers in order

## Add and subtract fractions

Add and subtract fractions with like denominators

Add and subtract fractions with like denominators: word problems

Add fractions with unlike denominators using models

Subtract fractions with unlike denominators using models

Add fractions with unlike denominators

Subtract fractions with unlike denominators

Add and subtract fractions with unlike denominators: word problems

Add and subtract mixed numbers

Add and subtract mixed numbers: word problems

Inequalities with addition and subtraction of fractions and mixed numbers

Estimate sums and differences of mixed numbers

## Multiply fractions

Multiply unit fractions by whole numbers using number lines

Multiply unit fractions by whole numbers using models

Multiply fractions by whole numbers using number lines

Multiply fractions by whole numbers using models

Multiply fractions and whole numbers

Multiply fractions and whole numbers: word problems

Multiply two fractions using models

Multiply fractions

Multiply fractions: word problems

Multiply three or more fractions and whole numbers

## Divide fractions

Divide whole numbers by unit fractions using models

Reciprocals

Divide whole numbers and unit fractions

Divide whole numbers by fractions

Divide fractions

Divide fractions: word problems

## Rational numbers

Identify rational numbers

Convert between decimals and fractions or mixed numbers

Absolute value of rational numbers

Compare rational numbers

Put rational numbers in order

Add and subtract rational numbers

Apply addition and subtraction rules

Multiply and divide rational numbers

Apply multiplication and division rules

Estimate products and quotients of rational numbers

Add, subtract, multiply and divide rational numbers: word problems

Evaluate numerical expressions involving fractions

## Exponents and square roots

Understanding exponents

Evaluate exponents

Solve equations with variable exponents

Exponents with negative bases

Exponents with decimal and fractional bases

Evaluate numerical expressions involving exponents

Square roots of perfect squares

Estimate square roots

## Ratios, rates and proportions

Understanding ratios

Identify equivalent ratios

Write an equivalent ratio

Equivalent ratios: word problems

Unit rates

Compare ratios: word problems

Scale drawings: word problems

Do the ratios form a proportion?

Do the ratios form a proportion: word problems

Solve proportions

Solve proportions: word problems

Estimate population size using proportions

Rate of change

Constant rate of change

## Proportional relationships

Find the constant of proportionality from a table

Write equations for proportional relationships from tables

Identify proportional relationships by graphing

Find the constant of proportionality from a graph

Write equations for proportional relationships from graphs

Identify proportional relationships

Interpret graphs of proportional relationships

Write and solve equations for proportional relationships

## Percents

What percentage is illustrated?

Convert between percents, fractions and decimals

Compare percents to fractions and decimals

Estimate percents of numbers

Percents of numbers and money amounts

Percents of numbers: word problems

Solve percent equations

Solve percent equations: word problems

## Consumer math

Add, subtract, multiply and divide money amounts: word problems

Price lists

Unit prices

Unit prices: find the total price

Percent of a number: tax, discount and more

Find the percent: tax, discount and more

Sale prices: find the original price

Multi-step problems with percents

Estimate tips

Simple interest

Compound interest

## Problem solving and estimation

Estimate to solve word problems

Multi-step word problems

Guess-and-check word problems

Use Venn diagrams to solve problems

Find the number of each type of coin

Elapsed time word problems

## Units of measurement

Estimate metric measurements

Compare and convert metric units

Metric mixed units

Convert square and cubic units of length

Convert between cubic metres and litres

Precision

## Coordinate plane

Coordinate plane review

Quadrants and axes

Follow directions on a coordinate plane

Distance between two points

## Number sequences

Identify arithmetic and geometric sequences

Arithmetic sequences

Geometric sequences

Number sequences: mixed review

Number sequences: word problems

Evaluate variable expressions for number sequences

Write variable expressions for arithmetic sequences

## Expressions and properties

Write variable expressions

Write variable expressions: word problems

Evaluate linear expressions

Evaluate multi-variable expressions

Evaluate absolute value expressions

Evaluate nonlinear expressions

Identify terms and coefficients

Sort factors of expressions

Properties of addition and multiplication

Multiply using the distributive property

Solve equations using properties

Write equivalent expressions using properties

Add and subtract like terms

Add, subtract and multiply linear expressions

Factors of linear expressions

Identify equivalent linear expressions

## One-variable equations

Which x satisfies an equation?

Write an equation from words

Model and solve equations using algebra tiles

Write and solve equations that represent diagrams

Solve one-step equations

Solve two-step equations

Solve equations: word problems

Solve equations involving like terms

Solve equations: complete the solution

## Two-variable equations

Does (x, y) satisfy the equation?

Identify independent and dependent variables

Solve word problems involving two-variable equations

Complete a table for a two-variable relationship

Write a two-variable equation

Identify the graph of an equation

Graph a two-variable equation

Interpret a graph: word problems

Write an equation from a graph using a table

## Two-dimensional figures

Identify and classify polygons

Name, measure and classify angles

Classify triangles

Identify trapezoids

Classify quadrilaterals

Graph triangles and quadrilaterals

Find missing angles in triangles and quadrilaterals

Interior angles of polygons

Lines, line segments and rays

Parallel, perpendicular and intersecting lines

Identify complementary, supplementary, vertical, adjacent and congruent angles

Find measures of complementary, supplementary, vertical and adjacent angles

Transversal of parallel lines

Find lengths and measures of bisected line segments and angles

Parts of a circle

## Transformations and congruence

Symmetry

Identify reflections, rotations and translations

Translations: graph the image

Translations: find the coordinates

Reflections: graph the image

Reflections: find the coordinates

Rotations: graph the image

Rotations: find the coordinates

Similar and congruent figures

Side lengths and angle measures of congruent figures

Congruence statements and corresponding parts

Side lengths and angle measures of similar figures

Similar figures and indirect measurement

## Constructions

Construct the midpoint or perpendicular bisector of a segment

Construct an angle bisector

Construct a congruent angle

Construct a perpendicular line

Construct parallel lines

Construct an equilateral triangle or regular hexagon

## Three-dimensional figures

Bases of three-dimensional figures

Nets of three-dimensional figures

Front, side and top view

## Geometric measurement

Perimeter

Area of rectangles and parallelograms

Area of triangles

Area of trapezoids

Area with mixed numbers

Area and perimeter: word problems

Circles: calculate area, circumference, radius and diameter

Circles: word problems

Semicircles: calculate area, perimeter, radius and diameter

Quarter circles: calculate area, perimeter and radius

Area of compound figures with triangles, semicircles and quarter circles

Area between two shapes

Surface area

Perimeter, area and volume: changes in scale

## Data and graphs

Construct the midpoint or perpendicular bisector of a segment

Construct an angle bisector

Construct a congruent angle

Construct a perpendicular line

Construct parallel lines

Construct an equilateral triangle or regular hexagon

## Statistics

Calculate mean, median, mode and range

Interpret charts to find mean, median, mode and range

Mean, median, mode and range: find the missing number

Changes in mean, median, mode and range

Identify representative, random and biased samples

## Probability

Probability of simple events

Probability of simple events – word problems

Probability of opposite, mutually exclusive and overlapping events

Experimental probability

Make predictions

Compound events: find the number of outcomes

Counting principle