# Welcome to Coach Cowland's 8th Grade Math Resource

**Do you know how scientists do calculations with very big and/or very small numbers (without making mistakes)?**

**Did you know that square roots and exponents are connected?**

**Do you know how to calculate the volume of the Earth?**

**Do you know how to look for relationships between a dependent and independent variable?**

**Do you know how equations are used in every day circumstances (often without people even thinking that they are doing math)?**

These are all parts of seventh grade math. If you need help with your seventh grade math, check out some of the videos below to help you with your homework.

# Contents

CLICK ON ANY OF THE LINKS BELOW TO HELP YOU WITH YOUR MATH HOMEWORK.

Topic 1. Number definitions

Topic 2. Integer Operations

Topic 3. Order of Operations/a>

Topic 4. Exponents

Topic 5. Scientific Notation

Topic 6. Radicals

Topic 7. Equations

Topic 7a. Equation Word Problems

Topic 8. Contradictions and Identities

Topic 9. Angle Geometry

Topic 10. Plane Geometry and Circles

Topic 11. Shape Translation, Rotation, Reflection and Dilation

Topic 12. Pythagorean Theorem

Topic 13. Graphing Straight Lines

Topic 14. Slope, Functions and Equations of a straight line

Topic 15. Parallel and Perpendicular Lines

Topic 16. Identifying Linear Equations and Word Problems

Topic 17. 3 Dimensional Geometry (Volume)

Topic 18. Properties of Bivariate Data

Topic 18a. Interpreting Bivariate Scatter Plots

# Topic 1. Number definitions

**Do you know what is meant by a whole number?** **What about an integer? **

**Why two different definitions?** **Are they always the same? **

# Topic 2. Integer Operations

**What happens when you add two negative numbers together? **

**What about when you subtract a negative from a positive? Does it get bigger or smaller? **

**How do you know if adding a positive to a negative will give you a positive or a negative?**

**What about when you multiply or divide positives with negatives? **

# Topic 3. Order of Operations

**What is all this PEMDAS business and what do I do if I dont have an Aunt Sally?**

**What if I have to multiply more than once?**

**Does a subtract always come before an addition?**

# Topic 4. Exponents

**What are those pesky little numbers that hover in mid air?**

**What is the difference between them and the bigger numbers next to them?**

**What do they mean. What happens if you multiply them together or divide? **

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# Topic 5. Scientific Notation

**What is scientific notation?**

** How do scientists express very big and very small numbers? **

**How do you add, subtract, multiply and divide scientific notation?**

practice multiplying and dividing scientific notation

**Scientific Notation Activity**

Students research interesting numerical facts and share the answers in both scientific and standard notation. Students then calculate speed, time and distance using scientific notation.

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# Topic 6. Radicals

**What is a square root? ****What is a cubed root? **

**What is the cube root of a negative number?**

**How do you find the square or cube root of a number? **

# Topic 7. Equations

**EQUATION GOLDEN RULE: ****Whatever you do to one side of the equation, you have to do to the other side of the equation.**

**Whatever you do to one side of the equation, you have to do to the other side of the equation.**

**What is an equation?**

**How do you solve a one or two step equation?**

**What is the distributive property?**

**How do you distribute an equation?**

# Equation Word Problems

**Have you ever wondered when you are going to use equations? So have I.**

It might not be obvious that equations are used in many different parts of life - that don't obviously include math, but they are. From working out mileage and gas for a road trip to calculating the how much of something there is after a sequence of events (adding a few, losing half etc).

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# Topic 8. Contradictions and Identities

**What kind of equations are contradictions? **

**What kind of equations are identities? **

**How are these different to equations with solutions?**

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# Topic 9. Angle Geometry

**What is a supplementary pair?**

**What is a complementary pair? **

**What are vertical angles?**

**Did you know that when you have a transversal line crossing parallel lines, that you only need one angle to be able to calculate all the others?**

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# Plane Geometry and Circles

Students review 7th grade plane geometry finding area and perimeter of parallelograms, trapezoids and triangles as well as finding the area and circumference of circles. Beyond this, students find the area and perimeter of complex shapes (combinations of two or more shapes together).*****

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# Topic 11. Shape Translation, Rotation, Reflection and Dilation

**What does a shape look like when it is translated, rotated, reflected or dilated?**

**What happens to the co-ordinates of a shape that has been transformed like this?**

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# Topic 12. Pythagorean Theorem

**What is the pythagorean theorem? **

**Which sides of a right triangle are the legs and which is the hypotenuse? **

**How can you tell which side is the hypotenuse of a right triangle?**

** If you know the lengths of the sides of a triangle, is there a way to determine (without measuring) if it is a right triangle?**

**Pythagorean Theorem Activity**

Pythagoras' Theorem is really useful. Don't believe me? Have you ever wondered how long a diagonal short cut around a rectangle will be compared to the distance around the out side? You need Pythagoras for that.

Have you ever wondered how high the top of a ladder will reach when leaning against a wall? You need Pythagoras for that.

In class we use Pythagoras Theorem to do some measurements around the school.

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# Topic 13. Graphing Straight Lines

Equations of straight lines are used anywhere that there is a constant ratio of two variables. For example if you are traveling the same distance in the same time (or going the same speed), you can use an equation of a straight line to calculate either the time or the distance that traveling takes.

**In Case you forgot how to plot a graph:**

# Topic 14. Slope, Functions and Equations of a Straight Line

**How do you calculate the slope of a line? ****What does 'b' in the equation of a straight line mean? **

**What is the definition of a function? ****How do you make an equation of a line with a couple of co-ordinates? **

**What does it mean if the slope of a line is negative? ****Is it possible to have horizontal or vertical lines? **

**How can you tell if two equations make lines that are parallel (or perpendicular) to each other?**

We answer all these questions in the next few sections.

slope from 2 co-ordinates interactive practice

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# Topic 15. Parallel and Perpendicular Lines

Students continue with theme of equations of lines by learning to identify lines that are are parallel or perpendicular based on the equation of the line given. Equivalent equations. Students examine equations of lines to identify the point where one line meets the other line. Students use their skills in algebra to find the solution.

# Topic 16. Identifying Linear Equations and Word Problems

This topic requires students to examine equations to determine which are linear (form a straight line graph) and which are not. Students also look at scatter plots and determine if there is a linear relationship. Once a linear relationship has been determined, students then go about calculating the equation of the line in *y=mx+b* format. Finally, students must identify the equation of a line in *y=mx+b* format given a word problem and then plot the line.

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# Topic 17. 3 Dimensional Geometry (Volume)

Students examine cylinders, spheres, cones and hemispheres and calculate the volume of the shapes. In addition, we shall be examining prisms, cuboids and pyramids.*****

*3 Dimensional Geometry Project*

Students will design a house made of the geometric shapes above. Each room/section of the house will be one of the shapes. Students will calculate the cubic volume of their living residence. The design can be an actual model, Minecraft model, 3D Cad design or simple drawing on paper. All models will require (for grade) the calculations and the measurements of the house.

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# Topic 18. Properties of Bivariate Data

Students examine bivariate (One variable on the x axis and one on the y axis) graphs and tables of data. Students then have the opportunity to examine the data for patterns, linear or non linear relationships, outliers and clusters.

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# Topic 18a. Interpreting Bivariate Scatter Plots

Students should be able to interpret the data in bivariate plots, not only to find the equation of a line (should one exist) but also to infer qualitatively the relationship that the data suggests. The data analysis is probably the most challenging aspect of topic 18.

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***Students are required to memorize these equations before the EOG as the test does not include any equation sheet.**