## Grade 9 Math

## CONTENTS

## Numbers

Classify numbers

Compare rational numbers

Put rational numbers in order

Number lines

Convert between decimals and fractions

Square roots of perfect squares

Square roots of fractions and decimals

Estimate square roots

## Operations

Add, subtract, multiply and divide integers

Evaluate numerical expressions involving integers

Evaluate variable expressions involving integers

Add and subtract rational numbers

Add and subtract rational numbers: word problems

Multiply and divide rational numbers

Multiply and divide rational numbers: word problems

Evaluate numerical expressions involving rational numbers

Evaluate variable expressions involving rational numbers

## Ratios, rates and proportions

Identify equivalent ratios

Write an equivalent ratio

Unit rates

Unit prices

Solve proportions

Solve proportions: word problems

Scale drawings: word problems

## Percents

Convert between percents, fractions and decimals

Solve percent equations

Percent word problems

Percent of change

Percent of change: word problems

## Geometry

Perimeter

Area

Area of compound figures

Area between two shapes

Symmetry

Count lines of symmetry

Draw lines of symmetry

Interior angles of polygons

Transversal of parallel lines

Volume of prisms and pyramids

Volume of cones and cylinders

Volume of spheres

Nets of three-dimensional figures

Surface area of prisms and pyramids

Surface area of cones and cylinders

Surface area of spheres

Similar figures: side lengths and angle measures

Similar triangles and indirect measurement

Area and perimeter of similar figures

Similar solids

Volume and surface area of similar solids

Perimeter, area and volume: changes in scale

Identify reflections, rotations and translations

Reflections, rotations and translations: find the coordinates

Reflections, rotations and translations: graph the image

Dilations and scale factors

Pythagorean theorem

Pythagorean theorem: word problems

Converse of the Pythagorean theorem: is it a right triangle?

## Circles

Parts of a circle

Circles: calculate area, circumference, radius and diameter

Circles: word problems

Central angles

Arc measure and arc length

Area of sectors

Circle measurements: mixed review

Arcs and chords

Tangent lines

Perimeter of polygons with an inscribed circle

Inscribed angles

Angles in inscribed right triangles

Angles in inscribed quadrilaterals I

Angles in inscribed quadrilaterals II

## Coordinate plane

Coordinate plane review

Quadrants and axes

Distance between two points

## Properties

Properties of addition and multiplication

Distributive property

Simplify variable expressions using properties

Properties of equality

## Exponents

Understanding exponents

Exponents with integer bases

Exponents with decimal and fractional bases

Negative exponents

Multiplication with exponents – integral bases

Division with exponents – integral bases

Multiplication and division with exponents – integral bases

Power rule – integral bases

Multiplication with exponents – variable bases

Division with exponents – variable bases

Multiplication and division with exponents – variable bases

Power rule – variable bases

Evaluate expressions using properties of exponents

Identify equivalent expressions involving exponents

## Scientific notation

Convert between standard and scientific notation

Compare numbers written in scientific notation

Multiply numbers written in scientific notation

Divide numbers written in scientific notation

## Problem solving

Word problems: mixed review

Word problems with money

Consecutive integer problems

Rate of travel: word problems

Weighted averages: word problems

## Number sequences

Identify arithmetic and geometric sequences

Arithmetic sequences

Geometric sequences

Evaluate variable expressions for number sequences

Write variable expressions for arithmetic sequences

Write variable expressions for geometric sequences

Number sequences: mixed review

## Variable expressions and equations

Write variable expressions

Simplify variable expressions involving like terms and the distributive property

Identify equivalent linear expressions

Write variable equations

Does x satisfy the equation?

Solve equations using order of operations

Rearrange multi-variable equations

## Solve equations

Model and solve equations using algebra tiles

Write and solve equations that represent diagrams

Solve one-step linear equations

Solve two-step linear equations

Solve advanced linear equations

Solve equations with variables on both sides

Solve equations: complete the solution

Find the number of solutions

Create equations with no solutions or infinitely many solutions

Solve linear equations: word problems

Solve linear equations: mixed review

## Single-variable inequalities

Graph inequalities

Write inequalities from graphs

Identify solutions to inequalities

Solve one-step linear inequalities: addition and subtraction

Solve one-step linear inequalities: multiplication and division

Solve one-step linear inequalities

Graph solutions to one-step linear inequalities

Solve two-step linear inequalities

Graph solutions to two-step linear inequalities

Solve advanced linear inequalities

Graph solutions to advanced linear inequalities

## Data and graphs

Interpret bar graphs, line graphs and histograms

Create bar graphs, line graphs and histograms

Interpret circle graphs

Interpret stem-and-leaf plots

Interpret box-and-whisker plots

Interpret a scatter plot

Scatter plots: line of best fit

## Relations and functions

Relations: convert between tables, graphs, mappings and lists of points

Identify independent and dependent variables

Identify functions

Identify functions: vertical line test

Find values using function graphs

Evaluate a function

Evaluate a function: plug in an expression

Complete a function table from a graph

Complete a function table from an equation

Interpret the graph of a function: word problems

## Direct variation

Identify proportional relationships

Find the constant of variation

Graph a proportional relationship

Write direct variation equations

Write and solve direct variation equations

## Linear functions

Identify linear functions

Find the slope of a graph

Find the slope from two points

Find a missing coordinate using slope

Slope-intercept form: find the slope and y-intercept

Slope-intercept form: graph an equation

Slope-intercept form: write an equation from a graph

Slope-intercept form: write an equation

Slope-intercept form: write an equation from a table

Slope-intercept form: write an equation from a word problem

Linear equations: solve for y

Write linear functions to solve word problems

Complete a table and graph a linear function

Compare linear functions: graphs, tables and equations

Write equations in standard form

Standard form: find x- and y-intercepts

Standard form: graph an equation

Equations of horizontal and vertical lines

Graph a horizontal or vertical line

Point-slope form: graph an equation

Point-slope form: write an equation

Point-slope form: write an equation from a graph

Slopes of parallel and perpendicular lines

Write an equation for a parallel or perpendicular line

Transformations of linear functions

## Systems of linear equations

Is (x, y) a solution to the system of equations?

Solve a system of equations by graphing

Solve a system of equations by graphing: word problems

Find the number of solutions to a system of equations by graphing

## Monomials

Identify monomials

Multiply monomials

Multiply monomials to find area

Divide monomials

Multiply and divide monomials

Powers of monomials

## Polynomials

Polynomial vocabulary

Model polynomials with algebra tiles

Add and subtract polynomials using algebra tiles

Add and subtract polynomials

Add polynomials to find perimeter

Multiply a polynomial by a monomial

Multiply polynomials to find area

Divide a polynomial by a monomial

## Logic

Identify hypotheses and conclusions

Counterexamples

## Probability

Theoretical probability

Experimental probability

Compound events: find the number of outcomes

Identify independent and dependent events

Probability of independent and dependent events

## 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

Quartiles

Identify biased samples