Grade 8 Math Unit 1

Grade 8 Math Unit 1 Integers (with answers) Name: _________________________ Date: __________________________ Homeroom: ___________ Student: ❏ correctly identifies the operation required to solve a problem involving integers. ❏ correctly models the process for multiplying two integers. ❏ correctly models the process for dividing two integers. ❏ correctly applies a rule for determining the sign of the product and quotient of

two integers. ❏ correctly solves a problem involving the division of integers (2-digit by 1-digit

without technology). ❏ correctly solves a problem involving the division of integers (2-digit by 1-digit

with technology). ❏ correctly applies order of operations.

Unit 1 - Integers 1

Unit 1 - Integers 2

Review Notes How can we show zero with integers? Subtract integers on a number line

Review

Unit 1 - Integers 3

1) Complete each equation.

(-8) + = 0 = 8

(-5) + = (0) = 5

+ (+6) = 0 =(-6)

+ (-15) = 0 = 15

2) Calculate the sum.

(+2) + (-7) + (+7) = = 2

(-8) + (+12) + (-12) = = (-8) 3) Draw a picture to show each answer.

Unit 1 - Integers 4

(-4) + (+10) = x x = 6 (-10) - (+5) = x x = (-15)

(+8) + (-6) = x x = 2 (-5) + (+12) = x x = 7

(-9) + (-3) = x x = (-12) (-7) - (+4) = x x = (-11)

4) Determine the number described below. The number that is 7 more than -9 = (-2)

The number that is 10 more than -8 = 2

The number that is 2 more than -6 = (-4)

The number that is 10 less than 6 = (-4)

The number that is 5 less than -4 = (-9)

The number that is 2 less than -4 = (-6)

Lesson 1.1 - Integer Multiplication

Unit 1 - Integers 5

Key words, definitions, formulas

Summary: Lesson 1.1 - Integer Multiplication 1) Calculate and explain or draw a picture to show why you are correct.

Unit 1 - Integers 6

(-3)(4) =

(-12)

-5(-5) =

25

5(-2) =

(-10)

(-5)(-2) =

10

(-2)(10) =

(-20)

(-10)(-2) =

20

What do you notice when you multiply a negative number and a positive number? What do you notice when you multiply a negative number with a negative number? 2) Complete the equations.

6 x = (-3) x 4 x (-3) = 5 x = (-2) = 5 = (-3)

Unit 1 - Integers 7

x 4 = (-6) x x (-2) = (-6) x = (-6) = 4 = (-6) = (-2) 3) A deck of cards has two cards each of the integers from -5 to 5.

Suppose you are dealt two cards from the deck and multiply the numbers

on those cards.

Which two cards would give you the greatest product? 5 & 5 or (-5) & (-5) Which two cards would give you the least product?

(-5) & 5 4) Write (-16) as a product of two integers in as many different ways as possible? (-4)(4), (-8)(2), (16)(-1) Write 16 as a product of two integers in as many different ways as possible? (-4)(-4), (-8)(-2), (16)(1)

Unit 1 - Integers 8

5) Replace the with <, >, or = to make each statement true.

(-1)(-2) (-4) >

(-2) (+3)(-1) >

(+4)(-5) (-20) =

(-2)(-6) (+11) >

(-2)(-4) (+7) >

6) Kelvin has 50 rare coins. The value of each coin went down by $2 today. Write the total change of Kelvin’s coins as an integer calculation. 50(-2) = (-100) 8) How can you predict the sign of each product without actually calculating it?

(-3) x (-2) x 4 = 4 x (-5) x 6 = Positive negative

Unit 1 - Integers 9

9) Each pattern is based on multiplying integers. Complete each pattern and write a rule for the pattern. 1, (-3), 9, (-27), 81, ____, ____, ____ (-3), 6, (-12), ____, ____, ____

Times (-3) each time Times (-2) each time Lesson 1.2 - More Integer Multiplication Key words, definitions, formulas

Unit 1 - Integers 10

Summary: Lesson 1.2 - More Integer Multiplication 1) Write an integer multiplication sentence for each description.

Jenna babysat for 3 hours, earning $5 per hour. 3(5)

The temperature fell 2℃ a day for 6 days. 6(-2)

2) Multiply.

0 x (-30) = x

x = 0

x = (-15)(4)

x = -60

7 (-20) = x

x = -140


(-4)(-20) = x

x = 80

x = (-6)(-30)

x = 180

x = (-20)(-50)

x = 1000

3) Each pattern is based on multiplication. Fill in the next three terms and explain the pattern rule.

-20, 100, -500, _____, _____, _____

Pattern rule: multiply by -5

5, -50, 500, _____, _____, _____

Pattern rule: multiply by -10

4) Multiply.

(-5) x (3) x (-8) = (-10) x 2 x (-5) x (-6) = = 120 = (-600)


Grade 7 Review 22 = x - 11 x = 33

2x + 3 = 15 x = 6

7 = x4

x = 28

What is the least common multiple (LCM) of 10 and 12? 60

What is the GCF of 15 and 25? 5

+ 612

712

2 + 53 3

10

- 43

53

10% of 40 4


57 x 0.4 22.8

12 + 0.8 x 3 14.4

7% of $49.98 $3.50

Calculate the circumference. (C = πd)

37.68 m

Calculate the area.

21m2

Simplify.

84


Mid-Chapter Review 1) 1) Calculate and explain or draw a picture to show why you are correct.

(2)(-5) =

-10

-3(-4) =

12

4(-2) =

-8

(-6)(-4) =

24

2) When playing a game, Joe lost eight points in each of his last three turns.

Use integers to show the change in his score after these three turns. 3(-8) = (-24) 3) Determine the least product you can form using any pair of numbers from this list.

-30, -20, 0, 10, 15 (-30)(15) = (-450)


4) Replace the with <, >, or = to make each statement true.

(-2)(-2) (-4) >

(-20) (+2)(-10) =

(-2)(-5) (7)

>

(-3)(-1) (+4)

<

(0)(-4) (-1)

>

(-3) (-3)(+3) >

5) Create a word problem for 8 x (-10). I spent $10 everyday for 8 days buying donuts. How much did I spend after the 8 days?


Lesson 1.3 - Integer Division Key words, definitions, formulas

Summary:


Lesson 1.3 - Integer Division Steven and Leon researched the highest daily temperature for each month over the past two years for their town. The results are in the table below:

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

Year 1

-8 -3 1 8 20 23 27 29 17 12 -5 -1

Year 2

-6 -7 -3 7 19 22 29 27 12 10 -8 -6

Determine the average highest temperature for each year.

Year 1: 10 degrees

Year 2: 8 degrees 1) Calculate.

(-45) ÷ (-5) = = 9 81 ÷ (-9) = = (-9)

= 00

−8 = (-8)7−56


2) Match each division equation with the related multiplication equation. Write the missing integers. Write the matching

letter below.

(-16) ÷ (-8) = B

A. x (-8) = 16

16 ÷ 8 = C

B. x (-8) = (-16)

(-16) ÷ 8 = D

C. x 8 = 16

16 ÷ (-8) = A

D. x 8 = (-16) 3) Write a multiplication equation for each division equation. Then solve the division. (-72) ÷ (-9) (-9)(8) = (-72)

84 ÷ 7 (7)(12) = 84

66 ÷ (-11) (-11)(-6) = 66

(-800) ÷ 20 (20)(-40) = (-800)


4) Divide.

40 ÷ (-5) = = (-8) (-24) ÷ 6 = = (-4)

= = 8−8−64 = = (-6)

54−9

5) Emma’s scores for the first nine holes of a golf game are given in the table below.

Hole 1 2 3 4 5 6 7 8 9

Score +1 -1 +3 +3 +2 0 0 -1 +2 What is Emma’s mean (average) score per hole? (Remember: to find mean you must add all the numbers then divide by the amount of numbers.) = +1


7) Danny has a small investment. Over seven days, the value of his investment changed as shown below.

-$11, -$24, +$9, +$6, +$8, -$5, +$3

What is the mean change in the value of his investments? = (-$2) 9) Calculate the answer to each equation. x = (-3)(-8) ÷ (-4) = (-6)

x = (7)(-6) ÷ (3)(-7) = 14

= x−4(−6)(6)

= (9)

= x−3(−144) ÷ 12

= 4


Lesson 1.4 - Order of Operations

Summary:


Lesson 1.4 - Order of Operations

G - Grouping symbols - (), []

E - Exponents - x2, x3, x4... M - Multiply of Divide - work from left to right S - Subtract or Add - work from left to right

Find the solution.

First attempt Second attempt

(-9) - (-6) ÷ 6 = x x = (-8)

4 x (-8) - (-5) = x x = (-27)


(-8) x (-3) - (-8) ÷ (-4) = x x = 22

= 1

In each equation below, label the steps you should follow to solve. (-5) + (-6) x (-8) ÷ 2 1) multiply 2) divide 3) add (-8) x 6 ÷ (-2) - [-9 x (-3)] 1) multiply in brackets 2) multiply 3) divide 4) subtract


A few more to calculate.


(-2) + (-3) x (-8 + 4) = x x = 10

(-9) - (-8) x 7 + [6 x (-2)] = x x = 35

7 x [8 - (-2) x (-6)] = x x = (-28)


[(-2) - (-8)] x (-5) = x x = (-30)

35 + (-4) x (-8) -7 = x x = 60

18 x (-3 - [8 x (-5)]) = x x = 666


Ready for a challenge?


(−4)(−2)(−6) + (−10)

= (-2)

49 ÷ (−7)1 + (−2)(−3)

= (-1)

(−2 + 4) x 228 ÷ (−4 − 3)

= (-1)


(−2 + 5)(2)

27 + (−18) ÷ (−2) = 6

(−7)(10) ÷ (2)

(−9) + (−16) − 10 = 1

(−2 + 4)(5 − 6)

[6 + (−38)] ÷ 4(−2) = (-8)


This chart shows the predicted high temperatures in Iqaluit for a week in November. Determine the mean predicted high temperature for the week. Day Predicted high temperature (°C)

Monday -4

Tuesday -4

Wednesday 0

Thursday 1

Friday -1

Saturday -2

Sunday -4 Mean = (-2) Identify the missing operation signs in the equations.

36 (4 1) 2 = 24

-12 4 (-3) = (-24)


Chapter Review

5(-2) =

(-10)

(-2)(8) =

(-16)

6(-10) =

(-60)

(-5)(-5) =

25 = 5−5

−25

= (-4)9

−36

(-12) ÷ 4 x (-7) - (-2) + 10 = = 33

18 x [-3 - (8)(-5)] = = 666

= = (−3 − 4)(−1)54 + 18 ÷ (−2)


Determine the mean of each group of integers.

10, -8, -16, -6

= (-5)

-21, 9, 15, -30, -3

= (-6)

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Grade 8 Math Unit 1