We included HMH Into Math Grade 3 Answer Key PDF Module 10 Lesson 6 Model and Solve Two-Step Problems to make students experts in learning maths.
HMH Into Math Grade 3 Module 10 Lesson 6 Answer Key Model and Solve Two-Step Problems
I Can write equations with letters for unknown quantities to solve two-step problems.
Step It Out
Question 1.
Emilio makes two craft stick boxes. He uses 116 craft sticks to make a large box. He uses 46 fewer craft sticks to make a small box. How many craft sticks does Emilio use for both boxes?
A. Write a subtraction equation to model the first step of the problem. Use a letter for the unknown quantity.
Answer:
B. Write an addition equation to model the second step of the problem. Use a letter for the unknown quantity.
Answer:
C. How many craft sticks does Emilio use?
Answer:
Emilio use 186 craft sticks in total
Turn and Talk How do you know which equation to solve first?
Answer:
To find how many sticks used we have to subtract first
then add them to find the total.
Question 2.
Bella buys 3 equal packs of trading cards. Then her friend gives her 5 cards. Now Bella has 26 cards. How many cards are in each pack?
A. Estimate: _____________
Answer:
26 – 5 = 21
21 ÷ 3 = 7
B. Write the numbers from the problem. Use letters for the unknown quantities.
Number of cards Bella has now: _____________
Number of cards her friend gives her: _____________
Number of cards in packs: _____________
Number of packs: _____________
Number of cards in each pack: _____________
Answer:
Number of cards Bella has now: 26
Number of cards her friend gives her: 5
Number of cards in packs: x
Number of packs: 3
Number of cards in each pack: x
C. Write an equation to model the first step of the problem.
Answer:
D. Write an equation to model the second step of the problem.
Answer:
E. How many cards are in each pack?
Answer:
There are 7 cards in each pack.
Turn and Talk How do you know your answer is reasonable?
Answer:
21 + 5 = 26
Explanation:
By this we can say that my answer is reasonable.
Question 3.
Ben collects pennies and dollar coins. He has 75 coins in his collection. He has 6 sheets of pennies.
The number of pennies on each sheet is shown. How many dollar coins does Ben have in his collection?
A. Estimate: ____________
Answer:
75
B. Write an equation to model the first step of the problem.
Answer:
C. Write an equation to model the second step of the problem.
Answer:
D. You can write one equation to model both steps of the problem.
Answer:
E. Show how you can solve the one equation.
Think: Solve the equation from left to right. First, multiply and divide, and then add and subtract.
Answer:
First we have to multiply then we have to subtract
F. How many dollar coins does Ben have in his collection?
Answer:
75 – 54 = 21
21 dollar coins that Ben have in his collection
Turn and Talk How is writing one equation to model the problem like writing two equations to model the problem? How is it different? Explain.
Answer:
In first and second we have did the equations separately
in third we did directly.
Check Understanding
Solve. Write equations to model the problem, and show your work. Use letters for the unknown quantities.
Question 1.
Kai has 65 stamps. He buys 7 more stamps. He uses all the stamps to fill 9 equal pages. How many stamps are on each page? Write two equations to model the problem.
Answer:
8 stamps are on each page.
Explanation:
let n be the total stamps
n = 65 + 7
n = 72
Let t be the stamps shared among 9 pages
t = 72 ÷ 9
t = 8
Question 2.
Nita’s book has 49 pages. She reads 8 pages each day for 5 days. How many pages does she have left to read? Write one equation to model the problem.
Answer:
9 pages left.
Explanation:
let n be the total pages that have read
n = 8 x 5
n = 40
Number of pages in book = 49
Number of pages left be t
t = 49 – 40
t = 9
On Your Own
Question 3.
Critique Reasoning Ed has 8 boxes with 7 rocks in each box. Then he finds 9 more rocks. Ed writes these equations to find how many rocks he has now. Is Ed’s work correct? Explain.
Answer:
No, his equations are not correct.
Explanation:
Ed has 8 boxes with 7 rocks in each box.
8 x 7 = b
b = 56
Let t be the total rocks
56 + 9 = t
t = 65
Question 4.
Model with Mathematics Tabitha has 96 stamps. She displays 16 stamps in a frame. She equally fills 8 pages of her stamp collection book with the rest of the stamps. How many stamps are on each page? Write two equations to model and solve the problem. Use letters for the unknown quantities.
Answer:
10 stamps are on each page
Explanation:
Tabitha has 96 stamps. She displays 16 stamps in a frame.
let n be the unknown
96 – 16 = n
n = 80
let t be the stamps
80 ÷ 8 = t
t = 10
Model with Mathematics Solve. Write two equations to model the problem, and show your work. Use letters for the unknown quantities.
Question 5.
The students make 82 show programs on Monday. The students make 139 programs on Tuesday. They need to make 400 programs by Wednesday. How many more programs do the students need to make by Wednesday?
Answer:
179 more programs they need to make by Wednesday
Explanation:
The students make 82 show programs on Monday. The students make 139 programs on Tuesday.
let n be the shows on Monday and Tuesday
n = 82 + 139
n = 221
Let t be the shows remaining to do by Wednesday
t = 400 – 221
t = 179
Question 6.
Ji uses 134 blocks to build one level of a tower. He uses 50 fewer blocks for the next level. How many blocks does he use for the two levels?
Answer:
218 blocks that he use for the two levels
Explanation:
let n be the unknown
n = 134 – 50
n = 84
Let t be the total blocks
t = 134 + 84
t = 218
Question 7.
STEM Metamorphic rock forms when high heat and pressure act on igneous rock or sedimentary rock. Igneous rock forms when magma cools. Sedimentary rock forms when layers of sediments harden into rock over time. Cruz has 4 groups of metamorphic rocks. The number of metamorphic rocks in each group is shown. Cruz also has 8 sedimentary rocks. How many rocks does Cruz have?
Answer:
Cruz have 36 rocks
Explanation:
let n be the unknown
4 x 7 = n
n = 28
Let t be the unknown
t = 28 + 8
t = 36
Question 8.
Open-Ended Write a two-step word problem with an unknown number. Write equations to model the problem. Then solve.
Answer:
Kitty has 25 chains. she uses 5 beads in 4 chains each. How many beads does she have left over
Explanation:
5 x 4 = n
n = 20
t = 25 – 20 = 5
t = 5
Model with Mathematics Solve. Write one equation to model the problem, and show your work. Use a letter for the unknown quantity.
Question 9.
Destiny has 100 photographs. She fills 8 pages with 8 photographs each. How many photographs does she have left over?
Answer:
36 photographs
Explanation:
let n be the unknown
She fills 8 pages with 8 photographs each.
8 x 8 = n
n = 64
100 – 64 = t
t = 36
36 photographs that she have left over
Question 10.
Min Soo has $36. He buys 7 packs of stickers at the craft store. Each pack of stickers costs $4. How much money does Min Soo have left?
Answer:
$8 that Min Soo have left
Explanation:
He buys 7 packs of stickers at the craft store. Each pack of stickers costs $4.
7 x 4 = 28
36 – 28 = 8
Question 11.
Mika sells 16 spools of thin ribbon. She sells 11 fewer spools of wide ribbon. How many spools of ribbon does she sell?
Answer:
21 spools
Explanation:
Mika sells 16 spools of thin ribbon. She sells 11 fewer spools of wide ribbon.
16 – 11 = 5
16 + 5 = 21
21 spools of ribbon that she sell
Question 12.
Hira has $47 saved. She earns $10 by walking the neighbor’s dog. She spends $6 at the dollar movie theater. How much money does Hira have now?
Answer:
$51
Explanation:
Hira has $47 saved. She earns $10 by walking the neighbor’s dog.
47 + 10 = 57
She spends $6 at the dollar movie theater.
57 – 6 = 51
Hira have now $51
Question 13.
There are 6 tables in a classroom. Mr. Wilson opens a package of paper and puts 8 sheets at each table. There are still 12 sheets of paper left in the package. How many sheets of paper were in the package to start?
Answer:
60 sheets
Explanation:
There are 6 tables in a classroom.
Mr. Wilson opens a package of paper and puts 8 sheets at each table.
6 x 8 = 48
There are still 12 sheets of paper left in the package.
48 + 12 = 60
60 sheets of paper were in the package to start