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Two--Step Problems
1. Directions: Write the correct answer above each box.
Spring School District had 426 third graders enrolled in 2011. In 2012, 87 more third graders enrolled
than in 2011. In 2013, 45 more third graders enrolled than in 2012.
Samantha estimated the number of third graders expected to enroll in 2013 by rounding all the numbers to the
nearest ten.
Warren estimated the number of third graders expected to enroll in 2013 by rounding all the numbers to the
nearest hundred.
The student with the estimate closest to the actual answer has the most reasonable estimate.
Use the information about how each student rounded to complete the following
sentences.
Samantha had the
Warren had the
reasonable estimate.
reasonable estimate.
2. Use rounding and adjusting to solve the following problem:
In one year, Susan bought 39 shirts, 44 jeans, and 81 socks at the store. How many pieces of clothes did she buy
total?
A. 125 pieces of clothes
B. 120 pieces of clothes
C. 83 pieces of clothes
D. 164 pieces of clothes
3. Jerry was racing with his friends. He ran 14 feet forward, then he ran 6 feet backward. Finally, he ran 10 feet
forward again. How many feet did Jerry end up away from where he started?
A. 16
B. 18
C. 24
D. 30
4. Directions: Write the correct answer below the box. Use numerals instead of words.
Ryan earned $528 shoveling driveways in the winter and $374 mowing lawns in the spring. He used $216 of the
money he earned to buy a new bicycle. How much does Ryan have now?
Ryan has $
now.
6. The staircase in Eric's house has 9 steps. He has 4 toys on each step. If he has cleaned up 8 toys, how many toys
are left on the steps?
A. 21
B. 44
C. 28
D. 5
7. Crystal baked 29 cookies and ate 14 of them. With the rest, she then put the same number of cookies into 5 bags
for a bake sale. How many cookies did Crystal put in each bag?
A. 17
B. 14
C. 5
D. 3
8. There are 30 girls over for Georgann's birthday sleepover. There are 10 girls that have to leave before it's time to
go to sleep. If the other girls are being split up into each of the 4 rooms of the house, how many girls will be in each
room?
A. 26
B. 40
C. 6
D. 5
9. Carla had 18 dolls in her collection. Her grandmother gave her 3 more dolls. Carla gave her sister 4 of the dolls.
How many dolls does Carla have now?
A. 17
B. 20
C. 25
D. 19
10. Devon has 173 large white balloons and 57 small white balloons. He gave 46 white balloons to Travis.
Which equation below can be used to find how many white balloons, w, Devon has now?
A. 173 -- 57 + 46 = w
B. 173 + 57 + 46 = w
C. 173 + 57 -- 46 = w
D. 173 -- 57 -- 46 = w
Answers
1. ---2. D
3. B
4. ---5. ---6. C
7. D
8. D
9. A
10. C
Explanations
1.
Start by finding the exact enrollment by adding.
Now, find the estimated answer found by each student.
Samantha rounded to the nearest ten before adding.
Warren rounds to the nearest hundred before adding.
Using this information, the correctly completed sentences are shown below.
Samantha rounded to the nearest ten. This means that she made the smallest change to the value of the
number. Samantha has the most reasonable estimate.
Warren rounded to the nearest hundred. This means that he made a larger change to the value of the number than
Samantha. Warren has the least reasonable estimate.
2. First, round the numbers up or down.
Round 39 up to 40 because 9 is greater than or equal to 5.
Round 44 down to 40 because 4 is less than 5.
Round 81 down to 80 because 1 is less than 5.
The estimate is equal to 40 + 40 + 80 = 160.
Next, adjust the estimate by how much the rounding affected the original values. Thirty-nine was rounded up by one (+1).
Eighty--four was rounded down by four (--4).
Eighty--one was rounded down by one (--1).
To get the total amount that the estimate was affected, do the opposite of each rounding to the estimate.
The opposite of (+1) is (--1), so subtract 1 from the estimate.
160 -- 1 = 159
The opposite of (--4) is (+4), so add 4 to the new estimate above.
159 + 4 = 163
The opposite of (--1) is (+1), so add 1 to the new estimate above.
163 + 1 = 164
So, Susan bought 164 pieces of clothes.
3. To calculate how many feet Jerry is away from where he started, take the distance he ran forward, subtract the
distance he ran backward, and then add the distance he ran forward again.
14 -- 6
=8
8 + 10 = 18
4.
First, find how much Ryan earned by adding his earnings from shoveling driveways and mowing lawns.
Then, subtract the amount he spent on the bicycle.
So, Ryan has $686 now.
5.
First, subtract 3 from 31 because Yvonne set aside 3 of the 31 cookies.
Then, divide that answer, 28, by 7 because she split the cookies evenly into 7 bags.
So, Yvonne put 4 cookies into each bag.
6. First, find the total number of toys on the steps.
9 × 4 = 36
Then, subtract the toys that he has already cleaned up from the total number of toys.
36 -- 8 = 28
So, there are 28 toys left on the steps.
7. First, calculate the number of cookies Crystal had left after eating 14 cookies.
29 -- 14 = 15
Then, divide the left over cookies by the number of bags she will be putting them in.
15 ÷ 5 = 3
Crystal put 3 cookies in each bag.
8. First, find how many girls are left after the 10 girls leave.
30 -- 10 = 20
Then, find how many girls will be in each room for the sleepover.
20 ÷ 4 = 5
There will be 5 girls in each room.
9. First, add the number of dolls Carla has to the number her grandmother gave her.
18 + 3 = 21 dolls
Then, subtract the dolls Carla gave away.
21 -- 4 = 17 dolls
10.
To find which equation shows how many white balloons Devon has now, start by finding the expression that shows
how many white balloons he had in all.
Devon had 173 large white balloons and 57 small white balloons. Add, 173 + 57, using the number line below.
Count forward 2 and then count by 5s, 55 more.
Next, subtract the number of white balloons Devon gave to Travis.
173 + 57 -- 46
So, the equation that can be used to find how many white balloons Devon has now is shown below.
173 + 57 -- 46 = w