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Solving Linear Equations by Graphing: Time-Distance Relationships

Demonstrate understanding of powers with integral bases and whole number exponents

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Using exponents to describe numbers

Expanded powers

Exponent rules

Single Power Expressions

Dividing powers

Multiplying powers

Order of operations with exponents

Using exponents to solve problems

Demonstrate understanding of operations on powers with integral bases and whole number exponents

Scientific notation

Demonstrate understanding of 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 order of operations including exponents with and without technology

Order of operations (PEMDAS)

Identify the Order of Operations

Order of Operations — Word Problem

Demonstrate understanding of perfect square and square root concretely pictorially and symbolically

Squares and square roots

Square Root of a Perfect Square

Estimating square roots

Determine square root of positive rational numbers that are perfect squares

Determine square roots of rational numbers

Square roots of rational numbers

Generalize pattern arising from problem-solving context using linear equations and verify by substitution

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

Influencing factors in data collection

Data collection

Probability

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 with rational coefficients

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 understanding of polynomials limited to degree less than or equal to 2

Characteristics of polynomials

What are polynomials

Equivalent expressions of polynomials

Adding and subtracting polynomials

Model record and explain operations of multiplication and division of polynomial expressions by monomials

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

Develop and apply Pythagorean theorem to solve problems

Angles in a circle

Chord properties

Tangent properties

Pythagorean theorem

Pythagorean Theorem

Using the pythagorean relationship

Applications of pythagorean theorem

Determine surface area of composite 3D objects to solve problems

Line symmetry

Rotational symmetry and transformations

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 understanding of similarity of triangles

Similar triangles

Similar polygons

Draw and interpret scale diagrams of 2D shapes

Enlargements and reductions with scale factors

Scale diagrams

Grade 9

Number

Patterns and Relations

Shape and Space

math

Intro

Ex. 1:

Ex. 2:

Ex. 3:

Ex. 4:

- Hi, welcome to this question right here. So we&apos;ve got a graph here set up for us already, trying to show us the relationship between the temperature in degree Celsius versus the time underneath right here which is in minute, okay? It looks like a very straight single straight lines. So guess what, if you see a straight line it means you're looking at a y equals mx plus b graph, okay? 
Now remember, the y is your y-axis. So in this case I'm going to put down the degree Celsius right here in the position of the y. The m, if you don't remember what m is, it's the slope of the graph, okay? So we're going to figure out the slope later. The x, so we draw a box with a slope and the x is the x axis. So it's in the time and we just use the variable t, but just remember as in terms of a minute for this question. Now the b is known as the y-intercept on the graph. The y-intercept is where the graph would touch the y-axis. If I just kind of look at the graph right here. If it is just going straight down like this, it will probably enter the zero go across the zero. So in this question here, you don't have a b for your equation, okay? Just leave it out, but the problem is how do you figure out the slope? Well remember, you might want to learn it right now, the slope is equal to the rise over run, okay? It's basically how the graphs behaves, going up first and turn left or right. Now, this is how we do it. You can pick two points. Let's say I pick these two points right here. Now just ask yourself, 
"How can I go from here to here?" Well, if I'm just using the rise over run which is the slope, which is the m over here, okay? 
All we had to do is just think about that in order for me to go from here to here, I need to go up 20 units first, okay? So this is 20, this is 40, so the difference is that I need to go up 20. So the rise in this case will be 20 and it's positive. Why, because you're going up. If you're going down, it'll be negative. Okay? Then in order for me to go from this point to here, I need to travel from two minutes to four minutes. That's a difference of two minutes. So that means I need to go to my right side two minutes. So it's positive because you're going toward the right. If you're going towards the left, it's negative. Okay? So 20 over two, what do you get? You don't need a calculator for that, at least for me I don't need one. Ten, okay so the 10 is actually your slope which is represented by the m in the equation. So guess what, it goes in here, 10t okay? 
So the relationship between the degree Celsius right here versus the time is just that the degree, the temperature is equal to 10 times the t, that's it. So the equation here, the equation for that relationship is right over here. You can either use this one right here or feel free to go y equals to 10 times the x. You can also use this equation, okay? Oh, where did it go? 
Y equals to 10 times the x, okay? So that way, it's easier. All right, but if you want to use the variables from the question, then it will be the degree Celsius equals the 10 times the t. All right? Let's check on the next--

We will learn how to plot linear equations, and then use the graphs as an aid to answer questions about the linear relations. Alternatively, we can find out the linear equations from their graphs. In addition, we will learn how to plot graphs and determine their equations when we are given the table of values of linear relations. We will also explore the concepts of interpolating and extrapolating data from graphs of linear equations.  