Question

family note today students learned to express solutions to multistep number stories using correct units and single number models. have your child explain the steps for solving each of the problems below, and then help him or her write these steps as a single number model, including a letter for the unknown quantity.
solve. record a long number model with a letter for the unknown quantity and write the answer with the correct unit.
1 guillermo hires two painters to paint the walls of his living room. the painters each make $42 an hour for an 8-hour workday. if the work takes 3 days, how much will guillermo pay the painters?
number model with unknown: ________
estimate: ________
answer (with unit): ________
2 blaine is on vacation in new york city and wants to collect magnets of places he visits to give to all his friends. the times square magnets cost $2 each and come in sets of 4. the statue of liberty magnets cost $3 each and come in sets of 5. if blaine buys 12 sets of each type of magnet, how much will he pay?
number model with unknown: ________
estimate: ________
answer (with unit): ________
practice
3 $45 \div 5 =$ ________
4 $56 \div 8 =$ ________
5 $54 \div 9 =$ ________
6 ________ $\div 9 = 4$
7 ________ $\div 6 = 6$
8 ________ $\div 8 = 3$

Explanation:

Problem 1

Step1: Define unknown total pay

Let $P$ = total pay for painters.

Step2: Calculate daily pay per painter

Daily pay: $42 \times 8 = 336$

Step3: Calculate 2 painters' daily pay

2 painters daily: $336 \times 2 = 672$

Step4: Calculate total pay for 3 days

Total pay: $672 \times 3 = 2016$

Number model:

$P = 42 \times 8 \times 2 \times 3$

Estimate:

Round $42$ to $40$, so $40 \times 8 \times 2 \times 3 = 1920$

Problem 2

Step1: Define unknown total cost

Let $C$ = total cost of magnets.

Step2: Calculate cost per Times Square set

Times Square set cost: $2 \times 4 = 8$

Step3: Calculate cost per Liberty set

Liberty set cost: $3 \times 5 = 15$

Step4: Calculate total cost for 12 sets each

Total cost: $(8 + 15) \times 12 = 276$

Number model:

$C = (2 \times 4 + 3 \times 5) \times 12$

Estimate:

Round $8$ to $10$, $15$ to $15$, so $(10 + 15) \times 12 = 300$

Practice Problems

Step1: Solve basic division 1

$45 \div 5 = 9$

Step2: Solve basic division 2

$56 \div 8 = 7$

Step3: Solve basic division 3

$54 \div 9 = 6$

Step4: Find missing dividend 1

$4 \times 9 = 36$

Step5: Find missing dividend 2

$6 \times 6 = 36$

Step6: Find missing dividend 3

$3 \times 8 = 24$

Answer:

1.
Number model with unknown: $P = 42 \times 8 \times 2 \times 3$
Estimate: $\$1920$