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Math, Alberta Curriculum

(Free Resources)

Alberta Program Overview

Specific Units

Shortcuts

Divisibility, Quick Rules

Equations, Linear

Fractions

Geometry

Probability

Ratios, Rates & Proportions

Squares & Exponents

Square Roots

 

Symmetry

Volumes

 

Jump to:

Competitions

Exams

Answers to Waterloo Math Circle Presentations

 
           
 

Books:

 

Math Makes Sense 8


Additional Resources

 

Self Guiding Lessons
for Grade 8 Math

https://www.khanacademy.org/math/cc-eighth-grade-math
Various Lessons https://im.openupresources.org/8/students/index.html 

Math Challenge

Mr. Jones' Classroom

Worksheets and Automated Quizzes

Grade 8 Worksheets (+answers and automated tests)

Fun Math on MAA

https://www.maa.org/programs/students/fun-math
Find a reason why an element does not belong http://wodb.ca/
Self Grading Chapter Based Quizes Mathematics 8 Making Connections (McGraw - Hill Ryerson)
Online Course, numerous practice sheets Grade 8 Math Course Outline
Nelson's Math Focus 8, online practice http://www.nelson.com/mathfocus/grade8/student/tryout.html
Grade 8 Math: Newfoundland and Labrador School District Ms. Fewer's resources, click on Grade 8
Grade 8 resource compilation http://www.mrfischer.ca/grade-8-math/
SPJH Math Department - Resource Compilation (English and French) https://sites.google.com/site/mathdepartmentspjh/math-8
Waterloo, Grade 8 Math Circle Presentations https://www.cemc.uwaterloo.ca/events/mathcircle_presentations_gr78.html

Volumes

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Formula Sheet for Grade 8

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 Linear

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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,
Khan Academy Topics
  https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-solving-equations
  • Equations with variables on both sides
  • Equations with parentheses
  • Number of solutions to equations
  • Equations word problems
  • Equations & geometry
https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions
  • 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
https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-systems-topic 
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Practice: Make sure you know how to work with negative numbers   http://highered.mheducation.com/sites/0070917612/student_view0/chapter11/study_quiz.html
     
Practice   https://ca.ixl.com/math/grade-8/solve-equations-complete-the-solution
     
Self Grading Quiz   http://highered.mheducation.com/sites/0070917612/student_view0/chapter12/study_quiz.html
     
Worksheet   McGraw-Hill Global Education:
http://highered.mheducation.com/sites/007092242x/student_view0/get_ready_for_grade_9.html (Choose Modeling with equations....)

Probability

(Back to Shortcuts...)

   
Probability Lesson:  
     
Self Grading Quiz   http://highered.mheducation.com/sites/0070917612/student_view0/chapter4/study_quiz.html

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
     
Probability Worksheets   https://ca.edugain.com/math/grade-8/Data-Handling-Probability-Statistics/
     
Experiment with Digital Spinner
(Hands on...)
  https://illuminations.nctm.org/adjustablespinner/
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
     

Testing out the Monty Hall problem

 
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.
https://online.maryville.edu/online-masters-degrees/business-data-analytics/students-guide-to-probability-and-statistics/
     

Ratios, Rates & Proportions

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Practice on Khan Academy
(self grading exercises)
  Finding percents

Converting decimals to percents

Converting percents to decimals

Converting percents and fractions

Percent word problems
     
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.
Exponent Laws Click here to see exponent laws on Pinterest
     
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
Practice, Self Grading Quiz   http://highered.mheducation.com/sites/0070917612/student_view0/chapter7/study_quiz.html
     

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.

Square Root Laws   Click here to see common Square Root Laws.



Practice Square Roots on Khan Academy
(self grading exercises)
  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
     
Practice   https://ca.edugain.com/math/grade-8/Square-and-Square-Roots/
(may require registration, it's free).

Symmetry

(Back to Shortcuts...)

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

Fractions

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Learning Materials   http://www.edugains.ca/resources/LearningMaterials/TIPS/TIPS_Grade%208/Unit5_FractionsPercents.pdf

Circle Model and Fraction Names: 


http://www.aaamath.com/fra.htm

Introduction to Fractions:  https://study.com/academy/topic/sba-math-grade-8-introduction-to-fractions.html#overview

Quizlet Flash Cards on Fractions and other topics

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
     
Self Grading Quiz   http://highered.mheducation.com/sites/0070917612/student_view0/chapter3/study_quiz.html

SBA Math - Grade 8: Introduction to Fractions Chapter Exam
      https://study.com/academy/exam/topic/sba-math-grade-8-introduction-to-fractions.html

Fraction (self-grading) worksheets on Nelson


Worksheets   http://highered.mheducation.com/sites/007092242x/student_view0/get_ready_for_grade_9.html (Choose Fractions....)

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

     
Operations with Fractions, resources   https://sites.google.com/site/mathdepartmentspjh/math-8/unit-3---operations-with-fractions
     

Geometry

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McGraw-Hill Global Education:
Self Grading Quiz http://highered.mheducation.com/sites/0070917612/student_view0/chapter2/study_quiz.html

http://highered.mheducation.com/sites/0070917612/student_view0/chapter13/study_quiz.html
Worksheets http://highered.mheducation.com/sites/007092242x/student_view0/get_ready_for_grade_9.html (Choose Area and Perimeter....)
http://highered.mheducation.com/sites/007092242x/student_view0/get_ready_for_grade_9.html (Choose Surface area and volume....)
     
Geometry on Mathopolis
(scroll down to the Geometry section)

 

Answers to Waterloo Math Circle Presentations

Junior - Grades 7/8 - All Math Circle Presentations

Winter 2010 3D Geometry I

List of Questions

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.

Answer (PDF)

 

 

Get Ready for Grade 9 Worksheets

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

Canadian Math Kangaroo Contest 2018 (select grade page)

 

Additional Resources

Math Games

Wired Math - University of Waterloo

 

Exams

Practice Exam (Burnaby South Grade 8 Honours PRACTICE Math Entrance exam).

Louisiana Depart. of Edi. - Grade 8 Practice Test (w/Answer Key).

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

Nebraska Department of Education, Practice Exam (w/Answer Key)

PDF, Mathematics Test

 

 

 

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