Practicing the Bridges in Mathematics Grade 4 Home Connections Answer Key Unit 7 Module 4 will help students analyze their level of preparation.
Bridges in Mathematics Grade 4 Home Connections Answer Key Unit 7 Module 4
Bridges in Mathematics Grade 4 Home Connections Unit 7 Module 4 Session 1 Answer Key
Variables & Expressions
Sometimes people use letters to represent unspecified amounts. Such letters are called variables. For example, if you worked for $6 an hour, you would multiply the time you worked by 6 to find out what you earned. If we let t represent the time you worked, we could show the amount of money you earned with this expression.
6 × t
When we say, “evaluate the expression when t = 3,” we mean, “figure out how much money you would make if you worked for 3 hours.” To do this, substitute 3 for t and complete the calculation.
Question 1.
Evaluate the expression 6 × t when:
t = 2
t = 4
t = 5
t = 8
Answer:
6 × t
t = 2
6 × 2 = 12
6 × t
t = 4
6 × 4 = 24
6 × t
t = 5
6 × 5 = 30
6 × t
6 × 8 = 48
Question 2.
How much money would you make if you worked 15 hours and earned $6 per hour?
Answer:
$6 per hour?
15 × 6 = $90
Thus you would make $90 for 15 hours.
Question 3.
Evaluate the following expressions when each variable has the value shown.
4 + b when b = 10
4 + 10 = 14
4 + b when b = 23
Answer:
4 + b when b = 23
4 + 23 = 27
4 + b when b = 103
Answer:
4 + b when b = 103
4 + 103 = 107
(3 × n) – 2 when n = 2
Answer:
(3 × n) – 2 when n = 2
(3 × 2) – 2
6 – 2 = 4
(3 × n) – 2 when n = 4
Answer:
(3 × n) – 2 when n = 4
(3 × 4) – 2
12 – 2 = 10
2 × (k + 12) when k = 7
Answer:
2 × (k + 12) when k = 7
2 × (7 + 12)
2 × 19 = 38
2 × (k + 12) when k = 10
Answer:
2 × (k + 12) when k = 10
2 × (10 + 12)
2 × 22 = 44
Question 4.
Danny is trying to earn money to buy a new bike. His neighbor says he will pay him $4 per hour to help with yard work. His mom says she will give him a $10 bill to add to his savings after he helps his neighbor. Which expression shows how much money Danny will make? (The letter h stands for the number of hours Danny will work for his neighbor.)
4 + h + 10
4 × h + 10 × h
4 × h + 10
14 × h
a. How much money will Danny make if he works for 4 hours with his neighbor? Show all your work.
Answer:
The correct equation is 4 × h + 10
h = 4
(4 × 4) + 10
16 + 10 = $26
b. If Danny wants to earn $34, how many hours will he have to work? Show all your work.
Answer:
(4 × h) + 10 = 34
4h = 34 – 10
4h = 24
h = 24/4
h = 6
Question 5.
CHALLENGE Pick one of the expressions from problem 3 above that does not represent Danny’s situation. Describe a situation where the expression you chose would represent how much money Danny would make.
a. The expression I chose is:
Answer:
b. This expression would show how much money Danny would make if …
Answer:
Bridges in Mathematics Grade 4 Home Connections Unit 7 Module 4 Session 3 Answer Key
Unit 7 Review
Here are some problems about the function machine.
Question 1.
a. Set the function machine’s controls to multiply each input number by 4 and then subtract 2. One has been done for you. (You get to choose and write in the last 4 input numbers yourself.)
Answer:
(3 × 4) – 2
12 – 2 = 10
(4 × 4) – 2
16 – 2 = 14
(10 × 4) – 2
40 – 2 = 38
(2 × 4) – 2
8 – 2 = 6
(6 × 4) – 2
24 – 2 = 22
(24 × 4) – 2
96 – 2 = 94
(5 × 4) – 2
20 – 2 = 18
(6 × 4) – 2
24 – 2 = 22
(11 × 4) – 2
44 – 2 = 42
(7 × 4) – 2
28 – 2 = 26
b. Choose the equation that best represents this rule.
Answer:
Question 2.
a. Now set the machine’s controls to make each output number 5 times as much as the input number. One has been done for you. Choose and write in the last input number yourself.
Answer:
10 × 5 = 50
15 × 5 = 75
20 × 5 = 100
25 × 5 = 125
30 × 5 = 150
35 × 5 = 175
40 × 5 = 200
45 × 5 = 225
50 × 5 = 250
b. Describe 2 different patterns you notice in the output numbers.
Answer:
in × 5 = out
previous output + 25 = output
Question 3.
Solve these multiplication problems.
Answer:
40 × 80 = 3200
By multiplying 80 by 40 we get 3200.
400 × 80 = 32000
By multiplying 80 by 400 we get 32000.
30 × 50 = 1500
By multiplying 30 by 50 we get 1500.
90 × 70 = 6300
By multiplying 90 by 70 we get 6300.
60 × 60 = 3600
By multiplying 60 by 60 we get 3600.
Question 4.
Marco says he can solve 83 × 49 by multiplying 80 × 49 and 3 × 49 and then adding them together.
a. Do you agree or disagree? Explain.
Answer:
83 × 49 = 4067
(80 × 49) + (3 × 49)
3920 + 147 = 4067
Yes, I agree with Marco.
b. Would you solve 83 × 49 with Marco’s strategy or a different strategy? Explain. Then solve the problem and show all your work.
Answer:
You can solve 83 × 49 with Marco’s strategy or standard multiplication strategy.
83 × 49 = 4067
Question 5.
Kaya is sorting the beads in her bead collection. She has a box with 32 different sections. She puts 19 beads in each section. How many beads did Kaya put in her box?
a. Write an equation with a letter to show the number of beads Kaya put in her box.
Answer:
Given,
Kaya is sorting the beads in her bead collection. She has a box with 32 different sections. She puts 19 beads in each section.
32 × 19
b. Solve the problem. Show your work using numbers, sketches, or words.
Answer:
32
×19
608
There are 608 beads in her box.
Question 6.
CHALLENGE Kaya has another box with 46 sections. She puts 18 beads in half of the sections and 21 beads in the other half. How many beads did Kaya put in this box? Show your work.
Answer:
Given,
Kaya has another box with 46 sections. She puts 18 beads in half of the sections and 21 beads in the other half.
46 ÷ 2 = 23 sections
23 × 18 = 414 beads
23 × 21 = 483 beads
702 + 819 = 897 beads
Thus Kaya put 897 beads in this box.