We included HMH Into Math Grade 4 Answer Key PDF Module 4 Lesson 4 Estimate Quotients Using Compatible Numbers to make students experts in learning maths.
HMH Into Math Grade 4 Module 4 Lesson 4 Answer Key Estimate Quotients Using Compatible Numbers
I Can estimate the quotient of a division problem involving a 1-digit divisor using compatible numbers.
Spark Your Learning
Myra has a part-time job as a lifeguard at Lazy Daze Summer Camp. She works 78 hours over 4 weeks. Myra estimates how many hours she works each week.
80 ÷ 4 = 20
Myra says she works about 20 hours each week.
Do you agree? Show your thinking.
Turn and Talk How did Myra change the numbers in the problem to estimate?
Explanation:
Yes, Myra changed the numbers for estimating
Build Understanding
1. Lazy Daze Summer Camp will host 624 campers during 3 sessions. About how many campers will attend each session?
Show how you can estimate the quotient 624 ÷ 3.
A. Circle a number on the number line that is close to 624 that is easier to divide by 3.
B. How can you use basic facts to find compatible numbers for dividing 624 by 3?
___ ÷ 3 = 1, so 300 divides easily by 3.
___ ÷ 3 = 2, so 600 divides easily by 3.
___ ÷ 3 = 3, so 900 divides easily by 3.
___ ÷ 3 = 4, so 1,200 divides easily by 3.
Answer:
3 ÷ 3 = 1, so 300 divides easily by 3.
6 ÷ 3 = 2, so 600 divides easily by 3.
9 ÷ 3 = 3, so 900 divides easily by 3.
12 ÷ 3 = 4, so 1,200 divides easily by 3.
Connect to Vocabulary
Compatible numbers are numbers that are easy to compute mentally and are close to the exact numbers in the problem.
C. Which compatible number for 3 will you use? Explain.
D. Choose the compatible number for 3 that is closest to 624. How can you use a basic fact and place value to divide your chosen compatible numbers?
About ___ campers will attend each session.
Explanation:
624 ÷ 3 = 208
Turn and Talk How do you know that your estimate for the quotient 624 ÷ 3 is reasonable?
Step It Out
2. Shannon has 1,880 energy bars to make welcome packets for campers. She puts 4 energy bars in each packet. Shannon says that she can make 470 welcome packets, is this reasonable?
Estimate 1,880 ÷ 4.
A. Find two compatible numbers for 4 that 1,880 is between.
16 ÷ 4 = 4, so ___ divides easily by 4.
20 ÷ 4 = 5, so ___ divides easily by 4.
Answer:
16 ÷ 4 = 4, so 16 divides easily by 4.
20 ÷ 4 = 5, so 20 divides easily by 4.
B. Use those two numbers to estimate two quotients that the exact quotient is between.
The quotient 1,880 ÷ 4 is between ___ and ____
Answer:
The quotient 1,880 ÷ 4 is between 4 and 5.
Turn and Talk How do your estimates show that Shannon’s exact answer is reasonable?
1880 ÷ 4 = 470
470 is in between 4 and 5
so, Shannon’s exact answer is reasonable
Check Understanding Math Board
Question 1.
Lazy Daze Summer Camp has tents that each fit 5 campers. The camp director says they need 78 tents for 290 campers. Is this reasonable? Use estimation to justify your answer.
Answer:
No, it is not reasonable
Explanation:
78 is rounded to 80
80 x 3 = 240
80 x 4 = 320
80 x 5 = 400
The campers is in between 240 to 320
that means each tent occupy only 3 or 4
Question 2.
Use compatible numbers to estimate the quotient. 1,765 ÷ 6 ___________
Answer:
1,765 ÷ 6 = 300
Explanation:
1765 is rounded to 1800
6 x 3 = 18
1800 ÷ 6 = 300
On Your Own
Construct Arguments Determine if the answer is reasonable. Explain.
Question 3.
Jenna marks her calendar to show how many days until summer camp starts. Jenna says that the camp starts in 13 weeks.
Answer:
147 days
Explanation:
A week has 7 days
13 x 7 = 91 days
No her estimation is wrong.
Question 4.
Each flashlight costs $8. The director of Lazy Daze Camp says that $4,480 will buy enough flashlights for 560 campers.
Answer:
Yes, he is correct.
Explanation:
Each flashlight costs $8.
The director of Lazy Daze Camp says that $4,480 will buy enough flashlights for 560 campers.
4480 ÷ 560 = 8
Use compatible numbers to estimate the quotient.
Question 5.
33 ÷ 3
___
Answer:
33 ÷ 3 = 11
Explanation:
3 x 1 = 3
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally.
Question 6.
352 ÷ 7
___________
Answer:
352 ÷ 7 = 50
Explanation:
352 is rounded to 350
7 x 5 = 35
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally.
Question 7.
8,214 ÷ 9
___________
Answer:
8,214 ÷ 9 = 900
Explanation:
8214 is rounded to 8100
9 x 9 = 81
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally.
Find two estimates that the quotient is between.
Question 8.
510 ÷ 6
The quotient is between ___ and ____
Answer:
510 ÷ 6 = 85
Explanation:
The quotient is between 80 and 90
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally.
Question 9.
2,945 ÷ 6
The quotient is between ___ and ____
Answer:
2,940 ÷ 6 = 490
Explanation:
2945 is rounded to 2940
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally.
I’m in a Learning Mindset!
How do I help my partner understand using compatible numbers to estimate quotients?
____________________________________
Explanation:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers. The numbers 500 and 300 are compatible for addition, since the sum of 800 can be easily calculated mentally.