Download Grade 7 Chapter 3 Problem Solving Assessment

NAME
DATE
PERIOD
SCORE
Chapter 3 Test
1.
2.
Write the numerical expressions in order from least to
greatest value. 7.NS.3
<
<
<
<
5(–1)
|–6| + |–5|
4
–3
|3| – |–2|
<
Someone at Oakwood Middle School knocked over all the math cards in
one classroom. Help clean up by sorting the numerical expressions cards
into the category that correctly describes whether the numerical value of
the expression is an integer or a non-integer. 7.NS.3
3+5
_
–6
_
2
2
|–15|
15
_
–|7|
3
Integers
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
–10(–2)
0.7
9–5
_
8
|–8| – 2
Non-integers
3.
Does |–13 + 2| equal |10 + 1|? If so, explain why. If not, state what each
absolute value equals. 7.NS.3
4.
The level of water in the lake rose this year. The number of inches
that the level of water went up can be represented by the expression
|–3 + 2| + |–2| + |–2 + (–1)|. Place a point on the number line to show
how many inches the water rose in all. 7.NS.3
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1
2 3 4 5 6 7
8 9 10
Course 2 • Chapter 3 • Integers
65
5.
Dedrick created a rectangular sandbox in his backyard. The
length of the sandbox y in yards is represented by the numerical
expression –5 + 9 + (–1). The width of the sandbox x in yards
is represented by the numerical expression 8 + (–9) + 3. The
point on the graph represents the bottom left corner of the
sandbox. Draw a rectangle that represents the sandbox. Each
grid line represents 1 yard. 7.NS.1, 7.NS.1b, 7.NS.1d
10
9
8
7
6
5
4
3
2
1
O
6.
y
x
1 2 3 4 5 6 7 8 9 10
Select all of the scenarios or expressions that have a value
of 0. 7.NS.1, 7.NS.1a, 7.NS.1b
The temperature outside was –12 degrees Fahrenheit. The temperature
increased 12 degrees. What is the temperature now?
8 + (–8)
–5 + (–5)
The diver was swimming at –20 feet. He came up 20 feet. What is
the diver’s elevation now?
A company had a net profit of –$2,000 last year. This year, the
company has a net profit of $2,000. How much did the company’s
net profit increase this year from last year?
7.
Part A: Write an addition expression to represent the distances the hiker
climbed up and down during the day.
Part B: What was the elevation of the hiker by the end of the climb in
relation to where he started hiking?
66
Course 2 • Chapter 3 • Integers
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
In one day, a hiker climbed up a mountain a vertical distance of 100 feet,
down a vertical distance of 23 feet, up a vertical distance of 25 feet, and
down a vertical distance of 36 feet. 7.EE.3
8.
Daisha had to simplify the expression
and list the properties that she used to
simplify the expression. The table shows
her first two steps. 7.NS.1, 7.NS.1d
–10 + 12 + 10
= 12 + (–10) + 10
Commutative Property (+)
= 12 + (–10 + 10)
Associative Property (+)
Part A: How did Daisha use the Commutative Property?
Part B: Complete Daisha’s work by simplifying the expression. List the
properties you use.
9.
The number line models a subtraction sentence.
Select whether the situations can be modeled by
the subtraction sentence. 7.NS.1, 7.NS.3
Yes
-6 -5 -4 -3 -2 -1 0 1
2 3 4 5 6
No
A porpoise jumps 2 feet above sea level and then dives down 6 feet.
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
The temperature is at 2 degrees Fahrenheit and then drops 4 degrees.
Belinda has $2 but owes Kimberly $6.
The Tigers were 2 points in the lead, but then the other team scored 6 points.
Henry had 2 puppies and then bought 6 more.
Martin was 2 feet tall when he was 4 months old. He grew 4 feet by the time
he was 17 years old.
10. In his lifetime, Jermain has visited places that have been as high as
8,750 feet above sea level and as low as –98 feet. 7.NS.3, 7.EE.3
Part A: Write a subtraction expression that represents the difference
between the elevation of the highest and the lowest places that Jermain
has visited.
Part B: What is the difference between the elevation of the highest and
the lowest places that Jermain has visited?
Course 2 • Chapter 3 • Integers
67
11.
Select all of the expressions that are equivalent to 8 – 9 + 3. 7.NS.1, 7.NS.1c
8 + (–9) + 3
–4 + 15 – 7
–9 + 8 + 3
–9 – (–12) + (–1)
13 – 6 – 3
8 – (9 + 3)
12. A game in the Math Corner of the classroom provides cards with
missing-addend number sentences. Students are dealt a hand of integer
cards, and they try to make each sentence true using one of those cards.
Write the integer that will make each number sentence true. 7.NS.1
+ 2 = –3
–2 –
– 3 = –2
3+
=1
–5
–4
–3
–2
–1
1
2
3
4
5
= –1
13. Lakeisha was solving the problem at the top of the table.
The table also shows the steps she took in solving the
problem. 7.NS.2, 7.NS.2a, 7.NS.3
Part A: During which step did Lakeisha make her first
mistake?
–10(–11 + 4) + 5(–6)
Step 1
–10(–7) + 5(–6)
Step 2
= –70 + (–30)
Step 3
= –100
Part C: What is the correct answer?
14. Use numbers from the box to build a multiplication expression
that simplifies to a negative product. 7.NS.2, 7.NS.2a
(
68
) (
) (
Course 2 • Chapter 3 • Integers
)
–4
–3
–2
–1
0
1
2
3
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
Part B: What mistake did Lakeisha make?
15. Quincy was simplifying the multiplication expression –13(5)(–4). For the
first step, he used the Associative Property to put brackets around the
5 and the –4, to get –13[(5)(–4)]. He thought it would be easier to multiply
the 5 by the –4 first, since he already knew that product.
Can Quincy multiply the 5 by the –4 first and still get the same product
as he would have if he multiplied the numbers in the order they were
given? If yes, show how the simplified expressions are equivalent. If no,
explain why Quincy cannot do that. 7.NS.2, 7.NS.2a, 7.NS.2c
16. Sana went on a walk from her home. She traveled at 4 feet per second.
Her home represents 0 on the number line. 7.NS.2, 7.NS.2a, 7.EE.3
West
Home
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1
East
2 3 4 5 6 7
8 9 10
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
Part A: Write a multiplication expression that represents Sana’s position
on the number line after walking 2 seconds to the west of her home.
Part B: The numbers on the number line represent feet. Place a point on
the number line showing where Sana is located after walking 2 seconds
to the west of her home. Label the point S.
17. Select all of the numerical expressions that simplify to 4. 7.NS.1, 7.NS.2
–8(2) + (–5)(–4)
–10
_
+ (–3)(–3)
2
–1(2) + (–1)(–2)
–12
_
+3
3
–15
_
–1
–3
Course 2 • Chapter 3 • Integers
69
18. Select whether each situation can be represented by the
–24
expression –4 . 7.NS.2, 7.NS.2b
_
Yes
No
A diver swam down 4 yards every minute. How many minutes did it take her
to dive down 24 yards?
The temperature is dropping 4 degrees every hour. How many degrees will
the temperature drop in 24 hours?
Kylee lost 4 pounds each month. After 24 months, how many pounds did
she lose?
Howard borrows $4 each month. He now owes $24. How many months has
he borrowed money so far?
19. Temperatures in degrees Fahrenheit can be converted to Celsius using
the formula C =
–5F + 160
_
, where C is the temperature in degrees Celsius
–9
and F is the temperature in degrees Fahrenheit. The coldest temperature
ever recorded in Oklahoma is –31 degrees Fahrenheit. What is that
temperature in degrees Celsius? 7.NS.2, 7.NS.2b
-9
-5(-2) + 3
-8(5) + (-11)(-4)
-48
18
+ -6
-8
-81
+ 3(-1)
-9
Write the numbers that are equivalent to each of the expressions next to
the correct sides of the model. 7.NS.3
70
Course 2 • Chapter 3 • Integers
–84
–13
–12
–9
–7
–6
–4
–3
3
4
6
7
9
12
13
84
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
20. Yvonne built a flowerbed in her backyard. The model of the flowerbed has
expressions that represent the lengths in feet of each side of her
flowerbed. The model is not necessarily drawn to scale.