Table of Contents
1. Number Sense …………………………………………………………… 4
a. Introduction to Number Sense …………………………………………4
b. Rates & Ratios ……………………………………………………………4
c. Exponents …………………………………………………………………5
d. Perfect Squares & Square-roots ………………………………………… 5
e. Scientific Notation ……………………………………………………….. 6
f. Number Sets & Set Notation …………………………………………….. 7
2. Polynomials and Factoring ………………………………………… 9
a. Introduction to Polynomials & Factoring ……………………………… 9
b. Like Terms ……………………………………………………………….. 9
c. Monomials, Binomials & Trinomials …………………………………… 9
3. Equations and Inequalities ………………………………………… 11
a. Introduction to Equations & Inequalities ……………………………… 11
b. Simple vs. Multi-Step Equations ………………………………………… 11
c. Fractional Equations ……………………………………………………… 11
d. Inequalities ………………………………………………………………… 12
4. Linear Relations …………………………………………………………… 14
a. Introduction to Linear Relations …………………………………………… 14
b. ROCs, Direct and Partial Variations ………………………………………… 14
c. Linear Relation Equations …………………………………………………… 15
d. Slope …………………………………………………………………………… 15
e. Intercept Graphing …………………………………………………………… 15
f. First Differences ……………………………………………………………… 17
g. Perpendicular & Parallel Lines ……………………………………………… 17
5. Geometry ……………………………………………………………………… 18
a. Introduction to Geometry …………………………………………………… 18
b. Triangle Review ……………………………………………………………… 18
c. Interior Angles ………………………………………………………………… 19
d. Exterior Angles ……………………………………………………………… 19
e. Angle Relationships …………………………………………………………… 20
f. Angles in Polygons …………………………………………………………… 21
g. The Pythagorean Theorem …………………………………………………… 22
h. Unit Conversions & Converting Measurements …………………………….. 23
i. Composite Shapes …………………………………………………………… 24
,2
j. Volume ………………………………………………………………………… 25
i. Prisms & Cylinders …………………………………………………… 25
ii. Pyramids & Cones …………………………………………………… 26
6. Finance ………………………………………………………………………… 28
a. Introduction to Financial Literacy …………………………………………… 28
b. Down Payments & Interest …………………………………………………… 28
c. Appreciation & Depreciation ………………………………………………… 29
d. Taxes …………………………………………………………………………… 29
7. Data Management ……………………………………………………………… 32
a. Introduction to Data Management …………………………………………… 32
b. Describing Data ……………………………………………………………… 32
c. Box Plots ……………………………………………………………………… 33
d. The Line of Best Fit …………………………………………………………… 34
,3
Number Sense
Introduction to Number Sense
Number sense is considered to be the basis of intuition and flexible thinking in
math. It consists of many subcategories that all contribute to the main purpose of
creating a sense of numbers that will be used in some form in your everyday life.
Rates & Ratios
A rate compares quantities that are measured in different units, and commonly
expressed through ratios, fractions, and percentages. A unit rate is a rate where the
denominator is always 1 -- a rate that means has a certain amount of something to 1
as an individual amount of something else.
A ratio is a comparison of two or more quantities
measured in the same units. A ratio is either
expressed as a common ratio (e.g. 4 : 11) or as a
4
fraction (e.g. 11
).
Ratios can be simplified just like fractions -- for
example, if an original ratio is 25 : 5, a simplified
and more convenient version would be 5 : 1. The
5
fraction form would be 1
or simply 5.
Here are some practice questions for rates and
ratios:
1. Simplify the following:
a. 24 : 4 = 6 : 1
b. 81 : 27 = 3 : 1
c. 10 : 25 : 45 = 2 : 5 : 9
2. Calculate the unit rate for the following scenarios:
a. Lola read 400 words in 16 minutes.
Unit rate = 25 words/minute
b. Jennifer’s bus drove 32 km in 4 hours.
Unit rate = 8 km/hour
c. Karan made $225 for every 5 hours she worked.
Unit rate = $45/hour
, 4
Exponents
𝑥
An exponent is a mathematical operation that is expressed by the expression, 𝑏 .
The equation is solved by taking the base number (b) and multiplying it as many
times as the value of the exponent (x). Use the diagram below to identify both the
base and exponent.
An example of an exponent is 74 (“seven to the
power of four” or “seven to the four”) and
would be solved by multiplying 7 by itself four
times. This would be written out as:
74 = 7 x 7 x 7 x 7 = 2,401.
Practice working with exponents:
1. Solve the following exponential
expressions:
a. 63 = 6 x 6 x 6 = 216
b. 25 = 2 x 2 x 2 x 2 x 2 = 32
c. 46 = 4 x 4 x 4 x 4 x 4 x 4 = 4096
Perfect Squares & Square-roots
A perfect square is the result of multiplying a whole number by itself.
An example of an exponent is 42, which would be referred to as either “four to the
power of two”, “four to the two”, or most simply, “four squared”. If the exponent to
any base number is 2, the base number is simply “squared”, meaning that it is
multiplied by itself twice. This would be written out as:
42 = 4 x 4 = 16, therefore four squared is equal to 16.
The square-root of a number is what you multiply by itself to get the perfect square.
For example, the square root of 225 is 15, because 152 or 15 squared = 225. This
would be written as 225 = 15.
Practice working with perfect squares and square-roots.
1. Solve the following perfect squares:
d. 62 = 6 x 6 = 36
e. 92 =9 x 9 = 81
f. 122 = 12 x 12 = 144
(next page contains the next set of practice questions)
1. Number Sense …………………………………………………………… 4
a. Introduction to Number Sense …………………………………………4
b. Rates & Ratios ……………………………………………………………4
c. Exponents …………………………………………………………………5
d. Perfect Squares & Square-roots ………………………………………… 5
e. Scientific Notation ……………………………………………………….. 6
f. Number Sets & Set Notation …………………………………………….. 7
2. Polynomials and Factoring ………………………………………… 9
a. Introduction to Polynomials & Factoring ……………………………… 9
b. Like Terms ……………………………………………………………….. 9
c. Monomials, Binomials & Trinomials …………………………………… 9
3. Equations and Inequalities ………………………………………… 11
a. Introduction to Equations & Inequalities ……………………………… 11
b. Simple vs. Multi-Step Equations ………………………………………… 11
c. Fractional Equations ……………………………………………………… 11
d. Inequalities ………………………………………………………………… 12
4. Linear Relations …………………………………………………………… 14
a. Introduction to Linear Relations …………………………………………… 14
b. ROCs, Direct and Partial Variations ………………………………………… 14
c. Linear Relation Equations …………………………………………………… 15
d. Slope …………………………………………………………………………… 15
e. Intercept Graphing …………………………………………………………… 15
f. First Differences ……………………………………………………………… 17
g. Perpendicular & Parallel Lines ……………………………………………… 17
5. Geometry ……………………………………………………………………… 18
a. Introduction to Geometry …………………………………………………… 18
b. Triangle Review ……………………………………………………………… 18
c. Interior Angles ………………………………………………………………… 19
d. Exterior Angles ……………………………………………………………… 19
e. Angle Relationships …………………………………………………………… 20
f. Angles in Polygons …………………………………………………………… 21
g. The Pythagorean Theorem …………………………………………………… 22
h. Unit Conversions & Converting Measurements …………………………….. 23
i. Composite Shapes …………………………………………………………… 24
,2
j. Volume ………………………………………………………………………… 25
i. Prisms & Cylinders …………………………………………………… 25
ii. Pyramids & Cones …………………………………………………… 26
6. Finance ………………………………………………………………………… 28
a. Introduction to Financial Literacy …………………………………………… 28
b. Down Payments & Interest …………………………………………………… 28
c. Appreciation & Depreciation ………………………………………………… 29
d. Taxes …………………………………………………………………………… 29
7. Data Management ……………………………………………………………… 32
a. Introduction to Data Management …………………………………………… 32
b. Describing Data ……………………………………………………………… 32
c. Box Plots ……………………………………………………………………… 33
d. The Line of Best Fit …………………………………………………………… 34
,3
Number Sense
Introduction to Number Sense
Number sense is considered to be the basis of intuition and flexible thinking in
math. It consists of many subcategories that all contribute to the main purpose of
creating a sense of numbers that will be used in some form in your everyday life.
Rates & Ratios
A rate compares quantities that are measured in different units, and commonly
expressed through ratios, fractions, and percentages. A unit rate is a rate where the
denominator is always 1 -- a rate that means has a certain amount of something to 1
as an individual amount of something else.
A ratio is a comparison of two or more quantities
measured in the same units. A ratio is either
expressed as a common ratio (e.g. 4 : 11) or as a
4
fraction (e.g. 11
).
Ratios can be simplified just like fractions -- for
example, if an original ratio is 25 : 5, a simplified
and more convenient version would be 5 : 1. The
5
fraction form would be 1
or simply 5.
Here are some practice questions for rates and
ratios:
1. Simplify the following:
a. 24 : 4 = 6 : 1
b. 81 : 27 = 3 : 1
c. 10 : 25 : 45 = 2 : 5 : 9
2. Calculate the unit rate for the following scenarios:
a. Lola read 400 words in 16 minutes.
Unit rate = 25 words/minute
b. Jennifer’s bus drove 32 km in 4 hours.
Unit rate = 8 km/hour
c. Karan made $225 for every 5 hours she worked.
Unit rate = $45/hour
, 4
Exponents
𝑥
An exponent is a mathematical operation that is expressed by the expression, 𝑏 .
The equation is solved by taking the base number (b) and multiplying it as many
times as the value of the exponent (x). Use the diagram below to identify both the
base and exponent.
An example of an exponent is 74 (“seven to the
power of four” or “seven to the four”) and
would be solved by multiplying 7 by itself four
times. This would be written out as:
74 = 7 x 7 x 7 x 7 = 2,401.
Practice working with exponents:
1. Solve the following exponential
expressions:
a. 63 = 6 x 6 x 6 = 216
b. 25 = 2 x 2 x 2 x 2 x 2 = 32
c. 46 = 4 x 4 x 4 x 4 x 4 x 4 = 4096
Perfect Squares & Square-roots
A perfect square is the result of multiplying a whole number by itself.
An example of an exponent is 42, which would be referred to as either “four to the
power of two”, “four to the two”, or most simply, “four squared”. If the exponent to
any base number is 2, the base number is simply “squared”, meaning that it is
multiplied by itself twice. This would be written out as:
42 = 4 x 4 = 16, therefore four squared is equal to 16.
The square-root of a number is what you multiply by itself to get the perfect square.
For example, the square root of 225 is 15, because 152 or 15 squared = 225. This
would be written as 225 = 15.
Practice working with perfect squares and square-roots.
1. Solve the following perfect squares:
d. 62 = 6 x 6 = 36
e. 92 =9 x 9 = 81
f. 122 = 12 x 12 = 144
(next page contains the next set of practice questions)
