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Catching up with learning how to code? It's never too late...
Learn how to code with your child this winter holiday. It's a fun way to switch from playing video games to writing them.

# Grade 8 Math, Alberta Curriculum

## Shortcuts

Give it a try with easy to follow Scratch 3.0 Workbooks that walk you through all major programming concepts like: loops, variables, screen coordinates and much more.    ## Math in Person...

Books

Volumes

(Back to Shortcuts...) ## Do you memorize or calculate the volume?

The volume of any right, uniform shape is easy to calculate, so it does not need to be memorized.

The 3D shape has a base. Imagine you cut out identical paper copies of the base. Then stack them one on top of the other until the full 3D shape is formed. The volume is then akin to the area of one sheet times the number of sheets stacked, which is just another way of saying the height. Such constructs would be similar to the shown below, but using identical slices rather than changing ones.

Verify this in the volumes of the following right, uniform, not tilted prisms and cylinders.
These simpler volumes equal the base area times the height. But this is only the case for regular shapes. The base area repeats along the entire height, as is, everywhere.
That is not the case with the pyramid, and the cone, which has stacked triangles and circles, but with the raising height the shapes are getting smaller, so they are not identical. The formula for these volumes are harder to remember.

Tricks to remember

The volume of the pyramid is one third of the volume of the circumscribing rectangular prism. Thus, if the base of the pyramid is rectangular then its volume is (L*W*h)/3.
The volume of the cone is one third of the volume of the circumscribing cylinder. Thus, since the base of the cone is circular then its volume is ( π*r2*h)/3.

All you have to memorize is the ratio: one third, the rest you can calculate from the predictable volume of the rectangular prism and cone.  ## Divisibility Rules

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Quick ways to determine divisibility:

A number is divisible by 2 if it terminates with 2, 4, 6, 8, or 0.
A number is divisible by 3 if the sum of its digits is divisible by 3.
A number is divisible by 4 if the last two digits are divisible by 4.
A number is divisible by 5 if it terminates with 5 or 0.
A number is divisible by 6 if it is divisible by both 2 and 3.
A number is divisible by 8 if the last three digits are divisible by 8.
A number is divisible by 9 if the sum of digits is divisible by 9.
A number is divisible by 10 if it terminates with 0.

## Equations, Linear

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Lectures,
• Equations with variables on both sides
• Equations with parentheses
• Number of solutions to equations
• Equations word problems
• Equations & geometry
• Graphing proportional relationships
• Solutions to linear equations
• Intercepts
• Slope
• Intro to slope-intercept form
• Graphing slope-intercept form
• Writing slope-intercept equations
• Functions and function notation
• Linear models
• Comparing linear functions
• Constructing linear models for real-world relationships
• Recognizing functions
• Linear and nonlinear functions
Learn how to code with the latest
Scratch 3.0 from MIT:
.    Practice: Make sure you know how to work with negative numbers   http://highered.mheducation.com/sites/0070917612/student_view0/chapter11/study_quiz.html

Worksheet   McGraw-Hill Global Education:

## Probability

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Probability Lesson:

http://highered.mheducation.com/sites/0070973350/student_view0/chapter5/study_quiz.html

Probability Lecture
(see examples)
http://www.mathsisfun.com/data/probability.html
Probability Lesson & Practice   https://njctl.org/courses/math/geometry/probability/attachments/probability-3/
Practice   Probability Quiz on Mathopolis

Experiment with Digital Spinner
(Hands on...)
Classroom Activity   https://illuminations.nctm.org/Lesson.aspx?id=2895
Graphing Probability activity: https://illuminations.nctm.org/Lesson.aspx?id=2898

Class Activity: Large Areas of the Spinner, less likely or more likely?   https://teacher.desmos.com/activitybuilder/custom/59233c9aefd17610dbbd684e    Activities   You can buy large batches of dice at various stores and run dice rolling experiments. Use worksheets to record the outcome.  Play Skunk - A Probability Game
A Student’s Guide to Probability and Statistics   The following page provides numerous links about Probability.

## Ratios, Rates, Proportions & Percents

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Finding percents

Converting decimals to percents

Converting percents to decimals

Converting percents and fractions

Percent word problems

Decimals and Percents Worksheets on Wired Math

Ratios Quiz   https://www.mathopolis.com/questions/q.php?id=5040

Quizzes, Videos, Games on Ratios   http://www.mrfischer.ca/rates-ratios-and-percents/

## Squares & Exponents

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What is an Exponent n?    The exponent n means some number a to the power of n: an  = a*a*... *a, multiplied n times.
What is a Square?   A square is the specific exponent 2. It means some number a, to the power of 2: a2  = a*a
Practice See Page 15.

Lesson and Practice   https://courseware.cemc.uwaterloo.ca/27/71/assignments/543/0
Order of Operations with Exponents   https://courseware.cemc.uwaterloo.ca/27/72/assignments/552

## Square Roots

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Perfect Squares   To do well on most square root tasks you should memorize most of the ones listed below. See more squares...

What is a square root?   The square root of a number is easy to spot when the number is formatted as a square.
For example, when formatting 9 as a square: 9 = 32, it is easy to see the "root" of the square is 3.
The identified root of such a square is called a "square root" or "radical".

The method to find the square root of a is as follows:
Step 1: Step 2: format a as a square, ask yourself, what number squared will give you a: a = b2
Step 3: replace a in the original expression Step 4: Conclude that: Thus the problem of square-rooting becomes a much simpler problem of formatting a number as a square. If in doubt, check the table of perfect squares above.

CAVEAT: If a number cannot be formatted as a perfect square, we typically use a calculator, as the algorithm to extract a decimal square root is more complicated.    Sorting Square Roots How do we know this is true for sure?
Check out the Radical function below (in this case a radical of order II = square root)
and notice the function is continuously rising. As long as a is "earlier" than b on the horizontal number line, the result of the square root is also "earlier" on the vertical number line. Drag a and b tto experiment on the demonstration below. (Click on the image to experiment with this graph).

Since any number can be fitted between two perfect squares, you can easily estimate roughly, approximations of the square root of all such numbers.
Here is an example: All the numbers n between 64 and 81 are larger than 64 and smaller than 81: Thus the square root of any number between 64 and 81 must be between 8 and 9. You can use this technique to place the approximate roots of any radicals (square roots) between two consecutive known perfect squares.

Practice Square Roots on Khan Academy
Square roots

Roots of decimals & fractions

Approximating square roots

Decomposing into primes will be useful when solving the next exercise.
Example: (Note sure how this example works? then watch this video)

Simplify square roots (Remove all perfect squares from inside the square root)

Square Roots, Lesson and Practice   https://courseware.cemc.uwaterloo.ca/27/72/assignments/551/0

(may require registration, it's free).

## Symmetry

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Visualize Symmetry and
Rotational Symmetry
(animation)
http://www.learnalberta.ca/content/memg/Division03/Symmetric/index.html

## Fractions

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Circle Model and Fraction Names: http://www.aaamath.com/fra.htm

Quizlet Flash Cards on Fractions and other topics

Fractions and Rationals Worksheet on "Wired Math"  (answers here).

Advanced: University of Waterloo, Math Circles on Continued Fractions:
https://cemc.math.uwaterloo.ca/events/mathcircles/2016-17/Fall/Junior78_Oct11.pdf

Fractions Formula Sheet     Simplifying Fractions

SBA Math - Grade 8: Introduction to Fractions Chapter Exam  Scroll down to "Unit 3: Operations with Fractions"
https://www.rsf.gsacrd.ab.ca/eteachers/1064/math-8

http://www.cbv.ns.ca/morrison/modules/mastop_publish/files/files_4b0bdce7da311.pdf

https://www.onlinemathlearning.com/grade8-math-worksheets.html, Scroll down to "Fraction Worksheets"

Printable Worksheets:
http://www.math-aids.com/Fractions/

Comparing Fractions and Decimals: http://www.bbc.co.uk/skillswise/worksheet/ma18comp-l1-w-compare-decimals-and-percentages

## Geometry

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McGraw-Hill Global Education:

http://highered.mheducation.com/sites/0070917612/student_view0/chapter13/study_quiz.html

Geometry on Mathopolis
(scroll down to the Geometry section)  ## Answers to Waterloo Math Circle Presentations

Winter 2010 3D Geometry I

Question 12

A fly lands on the outside of a cylindrical drinking glass 6 cm from the top. Diametrically opposite the fly and 7 cm from the bottom, but on the inside of the glass, there is a drop of honey. The glass has circumference 24 cm, height 10 cm. Find the shortest path, in cm, that the fly must walk on the surface of the glass to reach the honey.

 McGraw-Hill Global Education Download worksheets as PDF: http://highered.mheducation.com/sites/007092242x/student_view0/get_ready_for_grade_9.html ## Competitions

Gauss Mathematics Contests, for Grades 7-8

AMC 8 for middle school students

Math Games

## Exams

New York State Grade 8 Exams (each book has scoring keys).

 PDF, Mathematics Test     