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Learn to represent patterns in linear relations

Demonstrate understanding of powers with integral bases and whole number exponents

Using exponents to describe numbers

Expanded powers

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Exponent rules

Single Power Expressions

Dividing powers

Multiplying powers

Order of operations with exponents

Using exponents to solve problems

Demonstrate understanding of rational numbers by comparing and ordering rational numbers

Comparing and ordering rational numbers

Comparing decimal numbers

Comparing fractions

Solving problems with rational numbers in decimal form

Mixed Operations with Decimals

Mixed Operations

Mixed Operations with Decimals Bracket

Mixed Operations with Bracket Square

Solving problems with rational numbers in fraction form

Operations with fractions

Explain and apply the order of operations including exponents with and without technology

Order of operations (PEMDAS)

Identify the Order of Operations

Order of Operations — Word Problem

Determine the square root of positive rational numbers that are perfect squares

Determine square roots of rational numbers

Square roots of rational numbers

Squares and square roots

Square Root of a Perfect Square

Determine the approximate square root of positive rational numbers that are non-perfect squares

Estimating square roots

Generalize a pattern arising from a problem-solving context using linear equations

Representing patterns in linear relations

Represent Patterns in Linear Relations Equation Decimal

Represent Patterns in Linear Relations Equation Integer Start From 0

Represent Patterns in Linear Relations Equation Integer Start From 1

Represent Patterns in Linear Relations Equation Negative Decimal

Identify the Linear Equation

Reading linear relation graphs

Solving linear equations by graphing

Graph linear relations analyze the graph and interpolate or extrapolate to solve problems

Understanding graphs of linear relationships

Linear relations

Understanding tables of values of linear relationships

Linear relation

Applications of linear relationships

Model and solve problems using linear equations of various forms

Solving linear equations using multiplication and division

Two-step Linear Equations LHS

Two-step Linear Equations RHS

Solving two-step linear equations: ax + b = c, x/a + b = c

Solving linear equations using distributive property: a(x + b) = c

Solving linear equations with variables on both sides

Solving literal equations

Explain and illustrate strategies to solve single variable linear inequalities

Compound inequalities

Analyze the Alternate Form of Compound Inequalities: AND

Compound linear inequalities

Evaluate Compound Inequalities: And

Express linear inequalities graphically and algebraically

Graph the Inequality

Linear Inequalities – Word Problem 

Linear inequalities

Solving one-step linear inequalities

One-step Linear Inequalities

One-step linear inequalities

One-step Linear Inequalities Decimal

One-step Linear Inequalities Decimal with Fraction

One-step Linear Inequalities Fraction

Solve One Step Linear Inequalities Find Solution– Word Problem

One-step Linear Inequalities — Word Problem

Solving multi-step linear inequalities

Multi-step Linear Inequalities

Two-step Linear Inequalities

Multi-step linear inequalities

Two-step linear inequalities

Solve Multi-step Linear Inequalities – Word Problem 

Solve Multi Step Linear Inequalities Solve Equation – Word Problem

Solve Multi Step Linear Inequalities Equation – Word Problem

Demonstrate an understanding of polynomials

Characteristics of polynomials

What are polynomials

Equivalent expressions of polynomials

Adding and subtracting polynomials

Model record and explain the operations of multiplication and division of polynomial expressions

Multiplying and dividing monomials

Divide a monomial by a monomial

Multiply a monomial by a monomial

Multiplying polynomials by monomials

Multiply a polynomial by a monomial

Dividing polynomials by monomials

Model and solve problems using linear equations

Model and solve one-step linear equations: ax = b, x/a = b

One-step Linear Equations

One Step Linear Equations — Word Problem

One-step equations

One-step Equations LHS

One-step Equations RHS

Model And Solve One Step Linear Equations Divide – Word Problem

Model And Solve One Step Linear Equations Multiply – Word Problem

Solving two-step linear equations using addition and subtraction: ax + b = c

Two-step Linear Equations

Solve Linear Equations Using Addition and Subtraction – Word Problem

Two-step Linear Equations — Word Problem

Solving two-step linear equations using multiplication and division: x/a + b = c

Solving two-step linear equations using distributive property: a(x + b) = c

Solve Linear Equations Using Distributive Property – Word Problem

Describe the effect of various factors on the collection of data

Influencing factors in data collection

Data collection

Select and defend the choice of using either a population or a sample of a population

Sampling methods

Sampling Methods

Census and bias

Census and Bias

Classifying Bias

Develop and implement a project plan for the collection display and analysis of data

Classification of data

Characteristics of Quantitative Data

Classify the Level of Measurement

Identify the Level of Measurement

Bivariate, scatter plots and correlation

Demonstrate an understanding of the role of probability in society

Probability

Solve problems and justify the solution strategy using circle properties

Angles in a circle

Chord properties

Tangent properties

Determine the surface area of composite 3-D objects to solve problems

Surface area of 3-dimensional shapes

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

Surface area of prisms

Surface Area of Prisms Rectangle

Calculate the Surface Area

Surface area of cylinders

Demonstrate an understanding of similarity of polygons

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Demonstrate an understanding of line and rotation symmetry

Line symmetry

Rotational symmetry and transformations

Grade 9

Develop number sense

Use patterns to describe the world and solve problems

Represent algebraic expressions in multiple ways

Collect display and analyze data to solve problems

Use direct or indirect measurement to solve problems

math

Ex. 1:

Ex. 2:

Ex. 3:

Building a table from square tile figures

Using slope formula to find the linear equation from a table

Finding the figure number that gives 84 squares

Finding the number of squares in figure 14 using the linear equation

Verifying the equation y = 4x + 1 against each figure

Building a table for connected octagons and their side counts

<p>- Let's take a look. We're going to come up with an equation to represent the relationship between the number of sides we have, sorry the number of octagons that we have versus the number of sides that we have right here. This is the input and this is the output. The purpose of this chapter here is to figure out the relationship between the two variables and the relationship is always called the linear. They are all linear functions in this chapter. It's a good thing. Why?<br />
Because if you're doing linear functions, guess what? You have one equation. It's y equals to mx plus a b. That's the equation you are trying to get. This is the output, which is the y. This is the x, which is the input. Basically, one times something and add another thing should give you that eight over here. It should work for all the points here. Are we going to take a guess or are we going to calculate? Personal suggestion, we should calculate. Because guessing might take forever. What we're going to do is this. It's very simple. We're going to calculate the m and we're calculate the b. To calculate m right now, we're just going to give you an equation. It's very straightforward. It's y2 minus y1 divided by x2 minus the x1. What are the twos? What are the ones? It's just representing the second point versus the first point. And they don't have to be the second versus the first. They can be any two points from your data sets right here. So for example, I can pick the third one versus the second one. But try to pick the later one subtracting the preceding ones. Let's say I pick this set here and let's pick another set right here. What happened here we're just following the equation. It's says y two, so let's say this is my y two, which is right here, the 20 because this is the y and that's the x. This is the second point and this is the first point that we're going to pick. 20 minus 14. Be careful you're subtracting the two y's together. Then x two minus the x one. We've got three minus one. We've got a six over here on the top and a two down here. We've got ourselves a three for our m. You see right here, we've got m right here now which is three. What about b? For b, it's a little bit easier. What happened is, if you write down that equation one more time and this time you can pick any points that you wish. Just pick one. Let's say you pick this one right here. Let's say you like the five better. You put 32 into your y position. The m that you just calculated is a three. The x with the 32, make sure it is coming from the same pair. You're going to put the five right there and there's your b that's missing. Let's do a little bit of math right here for you. We've got 32 equals to 15 plus the b. If you subtract the 15 over to the other side, your b turns out to be 17. That's your b right there. Once you have your b, and once you have your m, guess what happens? Your final answer for this question here is actually just going to be-- therefore, three triangles we're going to go y equals the m, 3x plus the 17 and this is your final answer for this question. Without any guessing, the process may seem a little messy but you just have to remember apply this m calculation right here. Then solve for b by writing down the equation one more time but plug in the m you just calculated which is a three and you can pick any points you like. Just plug it in and you will find the b. Rewrite them one more time, leave out the y, leave out the x. Why is that? Because we're going to put different numbers for x in here to calculate the y for future questions. That's it for this part. Let's take a look at what's happening for the next part.</p>


Deriving the linear equation from the octagon pattern table

Finding the number of sides for 15 octagons using the equation

Finding the number of octagons given 84 sides

Writing a linear equation from a table of values