grade 8 math unit 1
TRANSCRIPT
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
Unit 1 - Integers 11
(-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)
Unit 1 - Integers 12
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
Unit 1 - Integers 13
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
Unit 1 - Integers 14
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)
Unit 1 - Integers 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). I spent $10 everyday for 8 days buying donuts. How much did I spend after the 8 days?
Unit 1 - Integers 16
Lesson 1.3 - Integer Division Key words, definitions, formulas
Summary:
Unit 1 - Integers 17
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
Unit 1 - Integers 18
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)
Unit 1 - Integers 19
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
Unit 1 - Integers 20
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
Unit 1 - Integers 21
Lesson 1.4 - Order of Operations
Summary:
Unit 1 - Integers 22
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)
Unit 1 - Integers 23
(-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
Unit 1 - Integers 24
A few more to calculate.
First attempt Second attempt
(-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)
Unit 1 - Integers 25
[(-2) - (-8)] x (-5) = x x = (-30)
35 + (-4) x (-8) -7 = x x = 60
18 x (-3 - [8 x (-5)]) = x x = 666
Unit 1 - Integers 26
Ready for a challenge?
First attempt Second attempt
(−4)(−2)(−6) + (−10)
= (-2)
49 ÷ (−7)1 + (−2)(−3)
= (-1)
(−2 + 4) x 228 ÷ (−4 − 3)
= (-1)
Unit 1 - Integers 27
(−2 + 5)(2)
27 + (−18) ÷ (−2) = 6
(−7)(10) ÷ (2)
(−9) + (−16) − 10 = 1
(−2 + 4)(5 − 6)
[6 + (−38)] ÷ 4(−2) = (-8)
Unit 1 - Integers 28
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)
Unit 1 - Integers 29
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)
Unit 1 - Integers 30
Determine the mean of each group of integers.
10, -8, -16, -6
= (-5)
-21, 9, 15, -30, -3
= (-6)