Grade 8 Math Unit 1 Integers

Grade 8 Math Unit 1 Integers 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

Unit 1 - Integers 3

Review 1) Complete each equation.

(-8) + = 0 (-5) + = (0)

+ (+6) = 0 + (-15) = 0

2) Calculate the sum.

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

(-8) + (+12) + (-12) =

Unit 1 - Integers 4

3) Draw a picture to show each answer.

(-4) + (+10) = x x = _____ (-10) - (+5) = x x = _____

(+8) + (-6) = x x = _____ (-5) + (+12) = x x = _____

(-9) + (-3) = x x = _____ (-7) - (+4) = x x = _____

4) Determine the number described below.

The number that is 7 more than -9 The number that is 10 more than -8

The number that is 2 more than -6 The number that is 10 less than 6

The number that is 5 less than -4 The number that is 2 less than -4

Unit 1 - Integers 5

Lesson 1.1 - Integer Multiplication Key words, definitions, formulas

Summary:

Unit 1 - Integers 6

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

(-3)(4) = -5(-5) =

5(-2) = (-5)(-2) =

(-2)(10) = (-10)(-2) =

What do you notice about when you multiply a negative number and a positive number? What do you notice when you multiply a negative number with a negative number?

Unit 1 - Integers 7

2) Complete the equations.

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

x 4 = (-6) x x (-2) = (-6) x 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? Which two cards would give you the least product?

Unit 1 - Integers 8

4) Write (-16) as a product of two integers in as many different ways as possible? Write 16 as a product of two integers in as many different ways as possible?

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)

Unit 1 - Integers 9

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. 8) How can you predict the sign of each product without actually calculating it?

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

Unit 1 - Integers 10

Lesson 1.2 - More Integer Multiplication Key words, definitions, formulas

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. ________________

The temperature fell 2℃ a day for 6 days. _________________

2) Multiply.

0 x (-30) = x

x = ______

x = (-15)(4)

x = ______

7 (-20) = x

x = ______

(-4)(-20) = x

x = ______

x = (-6)(-30)

x = ______

x = (-20)(-50)

x = ______


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

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

Pattern rule: ___________

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

Pattern rule: ___________

4) Multiply.

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


Grade 7 Review 22 = x - 11 2x + 3 = 15

7 = x4

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

What is the GCF of 15 and 25?

+ 612

712

2 + 53 3

10 - 43

53

10% of 40


57 x 0.4 12 + 0.8 x 3

7% of $49.98

Calculate the circumference. (C = πd)

Calculate the area.

Simplify.

84


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

(2)(-5) =

-3(-4) =

4(-2) =

(-6)(-4) =

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) Determine the least product you can form using any pair of numbers from this list.

-30, -20, 0, 10, 15

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).


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: ________________

Year 2: ________________ 1) Calculate.

(-45) ÷ (-5) = 81 ÷ (-9) =

0−8 7

−56


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

Write the matching letter below.

(-16) ÷ (-8) =

A. x (-8) = 16

16 ÷ 8 =

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

(-16) ÷ 8 =

C. x 8 = 16

16 ÷ (-8) =

D. x 8 = (-16)

3) Write a multiplication equation for each division equation. Then solve the division.

(-72) ÷ (-9) 84 ÷ 7

66 ÷ (-11) (-800) ÷ 20


4) Divide.

40 ÷ (-5) = (-24) ÷ 6 =

= −8−64 = 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.)


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? 9) Calculate the answer to each equation.

x = (-3)(-8) ÷ (-4) x = (7)(-6) ÷ (3)(-7)

= x−4(−6)(6)

= x−3(−144) ÷ 12


Lesson 1.4 - Order of Operations Key words, definitions, formulas

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

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


(-8) x (-3) - (-8) ÷ (-4) = x

(−16)

[ −2 − (−18)] x (−1)

In each equation below, label the steps you should follow to solve. (-5) + (-6) x (-8) ÷ 2 (-8) x 6 ÷ (-2) - [-9 x (-3)]


A few more to calculate.


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

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

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


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

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

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


Ready for a challenge?


(−4)(−2)(−6) + (−10)

49 ÷ (−7)1 + (−2)(−3)

(−2 + 4) x 228 ÷ (−4 − 3)


(−2 + 5)(2)

27 + (−18) ÷ (−2)

(−7)(10) ÷ (2)

(−9) + (−16) − 10

(−2 + 4)(5 − 6)

[6 + (−38)] ÷ 4(−2)


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 Identify the missing operation signs in the equations.

36 (4 1) 2 = 24

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


Chapter Review

5(-2) = (-2)(8) = 6(-10) =

(-5)(-5) = −5−25 9

−36

(-12) ÷ 4 x (-7) - (-2) + 10 =

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


= (−3 − 4)(−1)54 + 18 ÷ (−2)

Determine the mean of each group of integers.

10, -8, -16, -6

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

Grade 8 Math Unit 1 Integers

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