Download Operations and Algebraic Thinking STUDY

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UNIT 2: OPERATIONS & ALGEBRAIC THINKING STUDY GUIDE
Directions: Fill in the blanks or bubble in the circle with the correct answer to each question. Feel free to use a scrap
sheet of paper to help you work out the problems. These problems are similar to what you will see on your
test.
1. Which has the same value as 3 x 7?
XXX
O
O
O
O
XXX
7+7+7
X
3+3+3
3+7
3+7+3+7+3+7
XXX
XXX
X
XXX
XXX
X
2. Each package of hot dogs has 8 hot dogs.
If Sally counted the hot dogs in groups of
8, which list shows numbers she could have
named?
O
O
O
O
8, 16, 27, 48
16, 24, 45, 64
8, 18, 24, 40
8, 16, 24, 40
8X1=8
8 X 2 = 16
8 X 3 = 24
8X 4 = 32
8 X 5 = 40
3. What number makes the number sentence
true?
4 x 11 = ___ x 4
O
O
O
O
4
11
7
44
Commutative Property
allows 11 to be the
answer.
21 + 21
24 + 25
14 + 29
25 + 15
Rule: Add 6
23, 29, 35, 41, 47, _53_, _59_, _65_
7. Mr. Sanchez has 42 screwdrivers. He puts an
equal number of screwdrivers in each of 6
drawers. How many screwdrivers are in each
drawer?
O
O
O
O
6
7
8
9
42 ÷ 6 = 7
7 x 6 = 42
8. What is 54 ÷ 6?
O
O
O
O
12
7
8
9
9 x 6 = 54
9. Which math fact can help you find 9 ÷ 9?
4. Which is a way to find 7 x 6?
O
O
O
O
6. What are the next three numbers in the
pattern?
7 x 6 = 42
21 + 21 = 42
5. What number makes both number sentences
true?
9 x ___ = 72
72 ÷ 9 = ___
O 6
O 7
9 x 8 = 72
O 8
72 ÷ 9 = 8
O 9
O
O
O
O
9 + 9 = 18
9x1=9
18 - 9 = 9
9 x 9 = 81
9÷9=1
9x1=9
10. Pablo has 6 balloons. His sister has 3 times
as many balloons. How many balloons does
Pablo's sister have?
O
O
O
O
12
18
24
21
6 x 3 = 18
11. Which number is not a multiple of 8?
O
O
O
O
16
64
27
40
8x1=8
8 x 2 = 16
8 x 3 = 24
8 x 4 = 32
8 x 5 = 40
8 x 6 = 48
8 x 7 = 56
8 x 8 = 64
8 x 9 = 72
8 x 10 = 80
17. Mr. Chen buys boxes of crayons for his
students. The chart shows the different
prices for the boxes of crayons.
Total Number of Boxes
2
4
6
10
12. Which number is a prime number and a
factor of 20?
O
O
O
O
2
3
4
10
2 is a prime number. Its
factors are 1 and 2. AND
2 x 10 = 20
13. Which is not a factor pair of 36?
O
O
O
O
{2, 16}
{3, 12}
{4, 9}
{6, 6}
What is the total price for 6 boxes of
crayons?
Rule:
__$24__
Multiply by 4
18. What rule can be used to find the number of
wheels on 7 tricycles?
16 x 2 = 32, NOT 36.
14. Carly writes this number pattern in chalk on
the sidewalk. Write the next three numbers
in the pattern.
1, 3, 9, 5, 1, 3, 9, 5, 1, 3, _9_, _5_, _1_
15. Lockers in the Green Street School are lined
up in the pattern shown below.
Total Price
$8
$16
?
$40
Number of
Tricycles
Number of
Wheels
O
O
O
O
Add 6
Subtract 2
Multiply by 3
Divide by 3
3
5
7
9
9
15
?
27
3x3=9
5 x 3 = 15
9 x 3 = 27
19. James is measuring the sides of triangles. If
the pattern continues, how many inches will
he measure all around if one side is 6 inches
long? __18 inches__
Rule: x 3
6 x 3 = 18
Write the number that belongs on the blank
locker.
__34__ Rule: Add 5
16. Last month, Ms. Barkley spent $378 on food,
$925 on rent, and $272 on utilities. Which is
the best estimate of the total amount Ms.
Barkley spent on these three things?
O
O
O
O
$1,500
$1,550
$1,600
$1,700
$378 
$400
$925 
$900
+ $272  + $300
$1,575
$1,600
20. Cheryl's car traveled 226 miles on 8 gallons
of gas. She traveled about the same number
of miles with each gallon. Which is the best
estimate for the number of miles she traveled
with each gallon of gas?
O 20 miles
O 30 miles
O 40 miles
O 60 miles
226 ÷ 8 = 28 R2
28 rounds to 30.
SHORT RESPONSE QUESTION
Directions: Read all parts of the short response question before you begin. Write your answers to the short response
question in the space provided. For each short response question, use the grid provided to create any required charts or
graphs. If a question does not require a chart or graph, write your written response over the grid lines.
Kathy is thinking of a number pattern. The first four numbers of her pattern are shown below.
6, 12, 18, 24, _____, _____, _____
A. Write the next three numbers in Kathy's pattern.
B. Write a rule that tells how to write Kathy's number pattern.
21.
A. The next three numbers in Kathy’s pattern are
30, 36, 42. They are all multiples of 6.
B. You can write Kathy’s number pattern by “adding
6” to the previous number to get the next number in
the pattern.
OPEN RESPONSE QUESTION
Directions: Read all parts of each open response question before you begin. Write your answers to the open response
questions in the space provided. For each open response question, use the grid provided to create any required charts or
graphs. If a question does not require a chart or graph, write your written response over the grid lines.
Alice drew three geometric patterns made up of squares. She collected data about her
patterns in the table below.
Rows
Squares
2
3
3
5
4
7
A. If Alice continues her pattern, how many squares would a shape with 6 rows have? Draw the
geometric shape, and explain the number of squares it took to help you create it.
B. What is the rule for this geometric pattern? Explain the pattern in your own words.
22.
A.
A. It took 11 squares to help create the geometric shape
with 6 rows.
B. The numbers in the second row of Alice’s table form
a number sequence. A rule for this sequence is “add 2”
squares to the previous pattern of squares in order to find
the number of squares in the next geometric pattern. To
make the geometric shape with 6 rows, 4 squares had to be
added to the last shape that had 4 rows. Two squares
created 2 more columns, and 2 squares created 2 more
rows.