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Understanding surface area of 3D shapes

EQAO Grade 9 Math: Master Core Concepts & Skills

Ratios, Rates, and Proportions

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Ratios

Ratios - Find The Missing Value LHS

Ratios - Find The Missing Value RHS

Equivalent Ratios

Rates

Find the Biggest Rate 

Find the Unit Price 

Unit Rate Fill in Box

Find the Quickest Rate 

Unit Rate

Proportions

Proportions — Missing Denominator

Proportions — Missing Numerator

Proportions - Find the Missing Denominator LHS

Proportions - Find the Missing Denominator RHS

Proportions - Find the Missing Numerator LHS

Proportions - Find the Missing Numerator RHS

Square Roots

Squares and square roots

Square Root of a Perfect Square

Estimating square roots

Pythagorean Theorem

Introduction to pythagorean theorem

Using the pythagorean relationship

Applications of pythagorean theorem

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

Determine square roots of rational numbers

Square roots of rational numbers

Powers and Exponents

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

Proportional Relationships

Understanding graphs of proportional relationships

Linear relations

Using tables of values to graph proportional relationships

Linear relation

Applications of proportional relationships

Identifying proportional relationships

Linear Ralations

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

Solving Linear Equations

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

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

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

Solving linear equations with variables on both sides

Introduction to Relations and Functions

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Function notation

Linear Functions

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Distance formula: <katex>d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}</katex>

Distance formula

Midpoint formula: \(M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)\)

Midpoint formula

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

Slope equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Slope equation: <katex>m = \frac{y_2-y_1}{x_2- x_1}</katex>

Slope intercept form: y = mx + b

General form: Ax + By + C = 0

Point-slope form: \(y - y_1 = m (x - x_1)\)

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Word problems of graphing linear functions

Rate of change

Parallel and perpendicular lines in linear functions

Applications of linear relations

Introduction to Polynomials

Characteristics of polynomials

What are polynomials

Equivalent expressions of polynomials

Adding and subtracting polynomials

Multiplication and Division of Polynomials

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

Introduction to 3-Dimensional Objects

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

Surface Area and Volume

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

Circle Geometry

Angles in a circle

Chord properties 

Tangent properties

Data Management

Influencing factors in data collection

Classification of data

Characteristics of Quantitative Data

Classify the Level of Measurement

Identify the Level of Measurement

Sampling methods

Sampling Methods

Scatter plots and correlation

Census and bias

Census and Bias

Classifying Bias

Linear Programming

What is linear programming?

Finding Optimal Values Given Constraints In Slope-Intercept Form

Finding Optimal Values Given Constraints In Standard Form

Linear programming word problems

EQAO Grade 9 Principles of Math

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Identifying top, front, and side views of a 3D object

Drawing new views of a cereal box rotated 90 degrees

- Hi, welcome to this question right here. So this kind of a fun problem, cause right now, you're gonna outline the front, the top, and the left view of this diagram right here. Okay? So, let's do the front first. Okay? Since that was the first one. So, if you look at the front, basically, what we have is, you're looking from this direction. Okay? So, I'm doing the blue ones. So, I got 1, 2, 3, 4, 5, 6. Okay? I got six blocks. If I'm looking from this direction, I have only seen the six blocks. So basically, I got a bottom three. Basically, 1, 2, and 3, it's all there. And I got a top two right here. Okay. So, there's another two and following there is one more on the top. So, that's basically the graph for the front part. Okay? It's good that you havea different color pen, and then you're just gonna dot them and then just visualize and draw just a two-dimensional of the front. Then let's go to the top. Let's change the color of the pen right here. Let's go to the top. Okay? So, doing it from the top, that means you're looking it from the top-down. So, there is your 1, 2, 3, 4, and 5. Okay. So, let's put the dots on that. They're clear but as you can see, there's only two rows if you're looking from the top. And clearly you got the back row all completed. So, I can see it from the back that there is three pieces and then there's two more in the front on the further left right here. So basically, this is what you have from the top view. Okay? Now, let's do it from the side view here. Let's grab the last color right here, which is the red. The side view, pretend that you're looking from this way. Okay? So, there is your 1, 2, and the 3 and there is a 4 on the top. Okay? So, here is my side view right here, let's go to the bottom right there. Here is my side view. I got the first three on the left all completed. Okay? Draw a big one right here and cut it into three equal parts. And then I have one more at the bottom and that's it. Okay? So, that is my side view right here. Again, grab a color pen, pen or pencil, blue pen, black pen, dot them and then you will be able to draw them really easily. Okay? Have fun with them. Thanks for watching.

Drawing the front, top, and side views of a 3D block structure

Drawing front, top, and side views of a 3D block structure

Drawing front, top, and side views of an irregular 3D shape

Imagine you are looking at a 3-dimensional shape, for example, a cereal box. It looks like large rectangle from the front. From the side, it may look like a much thinner rectangle. However, you are sure that it is the same cereal box. It is because 3-dimensional shapes have many surfaces, and they do not necessarily look the same from different angles.

Surface area of three-dimensional (3D) objects

Surface area of 3-dimensional shapes