Mrs. Pilon's Math Page



Here is a copy of the Grade Eight Math Review notes.

Silverwood Heights School
May 14, 2007

Dear Parents and Grade 8 Students:

Sometime between May 28 and June 8, all Grade 8 students in Saskatchewan will write the Provincial Math Assessment. It will be administered in two 90-minute sessions.  This is an important assessment, because it is based completely upon the skills and objectives set out for Grade 8 students in the provincial curriculum guide.  It also gives an indication of how well students have mastered elementary school math concepts as they prepare to enter Grade Nine.  Because of the comprehensive nature of this test, I intend to incorporate students’ results into the Grade 8 Final Math mark.  Students who perform well on this test will be exempted from writing the classroom Math Final in mid-June.

There are five components to the PMA.  First, there is a Student Questionnaire.  Next, there is a page containing four questions that students must solve using their calculators.  As well, there is a computation page where students are not permitted to use calculators and must show all of their work.  The fourth component is a multiple-choice booklet, containing 40 questions, where students shade in the circle beside the letter that represents the best answer.  Finally, there is a Math Challenges booklet where students demonstrate their problem-solving skills by attempting to solve three multi-question problems.  Students may not use a calculator for the first challenge, but calculators are allowed for Challenges Two and Three.

Students will require the following materials:  a calculator; a ruler; a protractor; a compass; a pencil and an eraser.  A formula sheet is included, so students do not have to memorize formulae for calculating perimeter/circumference, area, volume (rectangular prisms and cylinders), Pythagorean Theorem, probability, odds, or scale.  They do, however, need to understand how and when to use these formulae.  Use of a calculator is allowed (encouraged) for questions that involve formulae.

In order to help students prepare, I will give a general outline of the types of concepts that will be tested.  Although we will review some of the types of questions on the test, I highly recommend that students study these concepts and practice the related skills as part of their homework.  Students are welcome to sign out a Minds on Math textbook (useful because answers are provided at the back of the book) for home study.


A.  Content that MAY be covered in the 40-question multiple-choice booklet:

1)  Data Management:  five questions, which may include reading and interpreting graphs of different types (including circle graphs and the relationship between percents and degrees), knowledge of specialized terms like mean, median, mode, extremes; percentile; quartile; understanding of different ways to collect and display data (survey, sample, tally, stem-and-leaf plot, box-and-whisker plot, etc.); calculation of probability and odds; probable outcomes.

2)  Numbers and Operations:  16 questions, which may include reading and comparing integers; noticing patterns; reading and understanding decimals to three places; reading and understanding whole numbers to the trillions place; exponents; order of operations (BEDMAS); decimal notation; expanded notation; exponential notation; square roots; using number lines and/or traditional algorithms when adding, subtracting, multiplying and dividing using whole numbers, fractions, decimals and integers; improper fractions; mixed fractions; knowing vocabulary associated with numbers and operations (base; power; squared; cubed; expression; equation; simplify; product; quotient; difference; total and many others)

3)  Ratio, Proportion and Percent:  four questions, possibly including use of equivalent ratios and rates; fraction form; decimal form; percents, including those greater than 100% and less than 1%; finding the missing term in a proportion; reading charts and tables; scale drawings.  Know how to convert between fractions, decimals and percents, and vice versa.

4)  Geometry and Measurement:  11 questions, possibly including properties of congruency of polygons (angles and sides); naming of triangles, quadrilaterals etc.; degrees in a triangle or quadrilateral; scale; length; width; height; perimeter; circumference; area; volume; capacity; mass; metric conversions (memorize the chart!); Pythagorean theorem used to determine right triangles; using the provided formula sheet to help you solve problems using area and perimeter of combination figures; translation, rotation and reflection.

5)  Algebra:  four questions, possibly including calculation of open expressions that include one or two variables replaced by fractions, decimals or whole numbers; coordinate graphing; functions; ordered pairs; finding unit price; writing and solving equations with one variable; general vocabulary like variable, constant, expression, equation, like terms quadrant, coordinate, ordered pairs, etc.

B.  Four Computation Exercises (NO calculator allowed) may include the following: adding, subtracting, multiplying and dividing using whole numbers, fractions, decimals or integers; order of operations.  You must SHOW YOUR WORK.

C. Four Calculator Exercises may include the following: order of operations; conversions between fractions, decimals and percents; comparing and ordering fractions; solving exponents; know the various ways of writing multiplication or division.

D.  Three Math Challenges:  If you know the material suggested for the 40-question multiple-choice test, you will be able to do anything required for these challenges.  Take time to read the questions carefully and be sure that you understand what you are being asked to do.

Additional Notes: 
1)  Estimation (or approximation, and including rounding to a specified place) (done without a calculator) is required for many questions.
2)  Read the questions carefully.  Be sure that you understand exactly what you are being asked to do.
3)  Please start reviewing now.  Use your homework review booklets and Minds on Math to help you.  If you run into difficulties, please ask for help.  I am almost always available to help students before school, at noon hour or after school.  Please make arrangements if you need tutorial work.
4)  If you hate writing tests, it is especially important to study carefully.  By the time we do the test, you will have covered everything at least once in class.  If you prepare carefully, even overlearn the material, you will feel much less anxious.
5)  Look over the practice materials very carefully.  Although the questions will be different, the way they are presented give a fairly good indication of what to expect.

You can do it!  Start preparing now!

Mrs. G. Pilon (683-7450 or pilong@spsd.sk.ca)




  Here is a review of the rules for using integers and rational numbers.

Integers
(This is a summary of material from pp. 262-272, 277-279, 283-284, 289-290 of Minds on Math.)

In order to complete some of the following assignments, you may find it helpful to create a number line with both positive and negative values. 

…-5, -4, -3, -2, -1, 0, +1, +2, +3, +4, +5…

Another useful image is a thermometer, where there are temperatures above zero (“plus”) and below zero (“minus”).  Note, however, that you always say POSTIVE and NEGATIVE when working with integers (never plus/minus).

Use parentheses around individual integers to provide clarity.  If you need to use brackets for BEDMAS (Order of Operations) questions, use square brackets [ ].   Most advanced integers users leave out the + sign and just notate the – signs.  It makes your work less cluttered. 

Here are the algorithms for performing basic operations using integers.

1.  Addition. 
a)  If all of the signs are the SAME, add normally and then attach the sign. 
Example:  (-3) + (-10) + (-4) = -17  (Think “ 3 + 10 + 4 = 17; they are all negative, so the final answer will be negative.)

b)  If there is a mixture of positive and negative numbers, look and see which VALUE will be greater.  Then write the sign.  Next, find the difference between the positive and the negative values (notice that “difference” implies subtraction...shhh!)

Example:  (-8) + (+2) = -6  (You can see that the absolute value of 8 is greater than the absolute value of 2, so the answer is going to be negative because 8 is.  The difference between 8 and 2 is 6, so the answer is -6.)

2.  Subtraction is easy if you just remember to ADD THE OPPOSITE.  Remember that negative signs and minus signs look the same; be sure you know which is which.

Example:  (-9) – (-6) = ?  (in this question, there is one minus sign, between the two negative numbers in the parentheses.  Leave the -9 alone.  Change the – sign to +.  Change -6 to +6.  See the instructions in 1(b) about how to add numbers with different signs.

Here goes:   (-9) – (-6) = ?
                     (-9) + (+6) =?  (9 has a greater absolute value than 6 so the answer is going to be                                                                                     negative)
        (-9) + (+6) = (-3)  (find the difference between 9 and 6)

3.  Multiplication and Division:  Start by counting the NEGATIVE SIGNS.  If there is an EVEN number of negative signs (0, 2, 4, …), the final answer will be POSITVE.  If there is an ODD number of negative signs, the answer will be NEGATIVE. 

Example:  (-2) x (-4) = ?  There are two negative signs (an even number), so the answer will be POSITIVE.  Determine the sign, then multiply normally.
                (-2 ) x (-4) = (+8)

          (-15) ÷ (+3) = ?  (There is only one negative number (an odd number), so the answer will be NEGATIVE.  Determine the sign, then divide normally.
          (-15) ÷ (+3) = -5

4.  Remember BEDMAS:  Brackets, Exponents, Division/Multiplication, Addition/Subtraction.

5.  You will notice that fractions and decimals can also be positive or negative.  These are part of the set of RATIONAL NUMBERS 
(integer1 ÷ integer2, where integer2 ≠ 0).
(Remember that a number divided by 0 is undefined). 

Use the usual rules for performing operations with fractions and decimals when dealing with rational numbers.







Here are some useful links that will help you master basic operations.

A + Math

WebMath

Math Operations Games
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Homework