Grade 8 Math

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Grade 8 Math, Alberta Curriculum Alberta Program Overview Specific Units	Shortcuts Divisibility, Quick Rules Equations, Linear Fractions Geometry Probability Ratios, Rates, Proportions & Percents Squares & Exponents Square Roots	Symmetry Volumes Jump to: Competitions Exams Answers to Waterloo Math Circle Presentations	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.

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Books

Is it too soon to learn Chemistry in grade 8?
Get ahead in STEM and be ready for high school. No previous knowledge required (check out a sample here):

Additional Resources

	Self Guiding Lessons or 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	https://wodb.ca/
	Self Grading Chapter Based Quizzes	Mathematics 8 Making Connections (McGraw - Hill Ryerson)
	Online Course, numerous practice sheets	Grade 8 Math Course Outline
	Nelson's Math Focus 8, online practice	https://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	https://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

(Back to Shortcuts...)

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 (Back to Shortcuts...)	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 (Back to Shortcuts...)
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	Learn how to code with the latest Scratch 3.0 from MIT: Click here to check for scheduled free book downloads on Amazon Kindle.


Practice: Make sure you know how to work with negative numbers	https://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	https://highered.mheducation.com/sites/0070917612/student_view0/chapter12/study_quiz.html

Worksheet	McGraw-Hill Global Education: https://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	https://highered.mheducation.com/sites/0070917612/student_view0/chapter4/study_quiz.html https://highered.mheducation.com/sites/0070973350/student_view0/chapter5/study_quiz.html
Probability Lecture (see examples)	https://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


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 & Percents (Back to Shortcuts...)
Practice on Khan Academy (self grading exercises)	Finding percents Converting decimals to percents Converting percents to decimals Converting percents and fractions Percent word problems
Decimals and Percents Worksheets on Wired Math	https://cemc2.math.uwaterloo.ca/wired_math/English/lessons/grade8/NSN_DECI_Gr8.pdf (answers here)
Ratios Quiz	https://www.mathopolis.com/questions/q.php?id=5040
Quizzes, Videos, Games on Ratios	https://www.mrfischer.ca/rates-ratios-and-percents/


Squares & Exponents (Back to Shortcuts...)
What is an Exponent n?	The exponent n means some number a to the power of n: aⁿ = aa... *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	https://highered.mheducation.com/sites/0070917612/student_view0/chapter7/study_quiz.html Evaluate radical expressions (grade 8)


Square Roots (Back to Shortcuts...)
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) https://www.learnalberta.ca/content/memg/Division03/Symmetric/index.html
see also	Take a different approach to math: learn about fractals, menger cubes, logic with Venn Diagrams, Fibonacci, Golden Ratio and much more. The book includes self-grading online quizzes to test your knowledge. This book is used as enrichment in the classroom, gifted programs, math clubs, and home learning. Click here to download a few worksheets.

Fractions (Back to Shortcuts...)
Learning Materials	https://www.edugains.ca/resources/LearningMaterials/TIPS/TIPS_Grade%208/Unit5_FractionsPercents.pdf Circle Model and Fraction Names: https://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 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

Self Grading Quiz	https://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	https://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 https://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: https://www.math-aids.com/Fractions/ Comparing Fractions and Decimals: https://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 (Back to Shortcuts...)	McGraw-Hill Global Education:
Self Grading Quiz	https://highered.mheducation.com/sites/0070917612/student_view0/chapter2/study_quiz.html https://highered.mheducation.com/sites/0070917612/student_view0/chapter13/study_quiz.html
Worksheets	https://highered.mheducation.com/sites/007092242x/student_view0/get_ready_for_grade_9.html (Choose Area and Perimeter....) https://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)