We included HMH Into Math Grade 4 Answer Key PDF Module 8 Lesson 2 Estimate Products to make students experts in learning maths.
HMH Into Math Grade 4 Module 8 Lesson 2 Answer Key Estimate Products
I Can estimate products using a variety of methods and predict how the estimated product will relate to the actual product.
Spark Your Learning
Mr. Adkins has this problem on the board for morning work. Use the problem to answer the following questions:
What might the unknown numbers be?
How many different answers can you find?
Answer:
The best digits for the product is 10 x 25
So, 10 x 25 = 250
There are 4 different answers to find 250 and they are,
10 x 25 = 250
1 x 250 = 250
2 x 125 = 250
5 x 50 = 250.
Show your thinking.
Turn and Talk How did you decide which numbers might solve the problem?
Build Understanding
1. For all of the fourth-grade science centers, Mr. Adkins made 11 discovery boxes with 23 small objects in each box. About how many objects did he have to gather for the discovery boxes?
A. What is an estimate?
____________________________
____________________________
Answer:
An estimate is defined as an approximate calculation of the value, number, quantity, or extent of something
B. How can you use rounding to determine a reasonable estimate for the number of objects Mr. Adkins gathered?
____________________________
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Answer:
For finding the number of objects, we should find the product of 11 x 23
11 is near to 10
23 is near to 25
So, 11 x 23 = 10 x 25 = 250.
C. How can you use basic facts to find the estimate?
____________________________
____________________________
Answer:
From the given data,
For all of the fourth-grade science centers, Mr. Adkins made 11 discovery boxes with 23 small objects in each box.
This means we should find the product of the number of boxes and the number of small objects in each box.
D. Mr. Adkins had to gather about ___ objects for the discovery boxes.
Answer:
Therefore, an estimate of the number of objects he has to gather for the discovery boxes is approximately equal to 250.
E. How do the rounded numbers compare to the factors? How will this affect your estimate?
____________________________
____________________________
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Answer:
The numbers are rounded to the nearest tens or hundreds or thousands depending on the number or rounded to the multiples of 5.
It will affect the estimate as the product may be greater or lesser than the original value but it is approximately equal to the original value.
Turn and Talk How can an overestimate and an underestimate affect a real-life situation?
Step It Out
2. Mr. Adkins challenges his students to spend 45 minutes without electronics on each school day in November. How many minutes will each student be electronics-free in November?
Use front-end estimation to estimate the product.
A. In what place value is the front digit in each number? ___
Answer:
In each number, the front digit has the place value of Ten and the place is called Ten’s digit.
B. Circle the tens. Then write the estimated factors changing all of the other digits to zero.
Answer:
19 is near to 20
45 is near to 40.
C. Find the product of the estimated factors.
___ × ___ = ___
Answer:
product of estimated factors is 19 x 45
So,
20 x 40 = 800.
Use rounding to estimate the same product.
D. Round each factor to the nearest ten.
_____ × _____
Answer:
19 is near to 20
45 is near to 40.
So,
20 x 40 = 800
E. Find the product of the rounded factors.
___ × ___ = ___
Answer:
So,
20 x 40 = 800
F. Compare the estimates. Which estimate is more reasonable? Why?
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Answer:
The answer is the same in both estimates.
G. Each student will be electronics-free for about __________ minutes in November.
Answer:
Each student will be electronics-free for about 855 minutes in November.
Turn and Talk Why can there be more than one estimate for any problem?
Step It Out
3. Mr. Adkin’s students each make 8 origami animals. There are 27 students in his class. How can you use compatible numbers to estimate the number of origami animals the students make?
A. Write compatible numbers for 27 and 8.
Answer:
27 is near to 30
8 is near to 10
B. Find the product of the compatible numbers.
Answer:
So, 30 x 10 = 300.
Connect to Vocabulary
Compatible numbers are numbers that are easy to compute mentally.
C. The students make about ___ origami animals.
Answer:
The students make about 300 origami animals.
D. How will this estimate compare with the actual product? How do you know?
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Answer:
The estimate gives the approximate value to the actual product. This product may be higher or lower than the original product but it is the best-approximated value for the product.
Check Understanding Math Board
Estimate the product 37 × 24 using each method.
Question 1.
front-end estimation
____________
Answer:
Given,
37 x 24
So, 40 x 20 = 800
Therefore, 37 x 24 approximately equals 800.
Question 2.
rounding
____________
Answer:
Given,
37 x 24
So, 37 is near to 40
24 is near to 25
So, 40 x 25 = 1000
Therefore, 37 x 24 approximately equals 1,000.
Question 3.
compatible numbers
____________
Answer:
Given,
37 x 24
37 is near to 40
24 is near to 20
So, 40 x 20 = 800
Therefore, 37 x 24 approximately equals 800.
Question 4.
Which method for estimating would be most reasonable if you wanted to make sure you had 37 craft materials for each of the 24 students in art class? Why?
Answer:
Estimating by rounding the digits to the nearest tens or multiples of five. Because it gives approximate answers.
Given,
You had 37 craft materials for each of the 24 students in the art class.
37 is near to 40
24 is near to 25
So, 40 x 25 = 1,000
Therefore, 37 x 24 approximately equals 1,000.
On Your Own
Question 5.
Use Structure Mrs. Hernandez is shopping for a new cell phone plan. She knows that she sends about 28 texts each day. The greatest number of days in any month is 31. How can she use estimation to help her decide which cell phone plan would be best for her?
Answer:
Given,
Mrs. Hernandez is shopping for a new cell phone plan.
She knows that she sends about 28 texts each day.
The greatest number of days in any month is 31.
31 is near to 30.
For a basic cell phone plan, 600/30 = 20
For an extra cell phone plan, 800/30 = 26.7
For a supreme cell phone plan, 1,000/30 = 33.3
So, 20 < 28 ; 26.7 < 28 ; 33.3 > 28.
Therefore, by estimation, the Supreme cell phone plan is best for Mrs. Hernandez .
Question 6.
Reason Bella decides to read for 45 minutes each day for 22 days. What is an estimate for the number of minutes Bella will read?
Answer:
Given,
Bella decides to read for 45 minutes each day for 22 days.
22 is near to 20.
So, 45 x 20 = 900
Therefore, 45 x 22 approximately equals 900.
Question 7.
Critique Reasoning Ian wants to save $425 to buy a new video game system. He earns $15 each week for chores he does around his home. He estimates that if he saves his money for 24 weeks, he will have enough to buy the game system. Do you agree with Ian? Why or why not?
Answer:
Given,
Ian wants to save $425 to buy a new video game system.
He earns $15 each week for chores he does around his home.
He estimates that if he saves his money for 24 weeks, he will have enough to buy the game system.
So, $15 x 24 = $360.
Therefore, He will not have enough to buy the game system. Because he needs $425 ( $425 > $360 ).
Hence, I won’t agree with Ian.
Estimate the product. Choose a method.
Question 8.
86 × 43
Answer:
86 is near to 85
43 is near to 40
So, 85 x 40 = 3,400
Therefore, 86 x 43 approximately equals 3,400.
Question 9.
32 × 71
Answer:
32 is near to 30
71 is near to 70
So, 30 x 70 = 2,100
Therefore, 32 x 71 approximately equals 2,100.
Question 10.
33 × $46
Answer:
33 is near to 30
46 is near to 45
So, 30 x 45 = 1,350
Therefore, 33 x $46 approximately equals 1,350.
Question 11.
11 × 27
Answer:
11 is near to 10
27 is near to 25
So, 10 x 25 = 250
Therefore, 11 x 27 is near to 297
Therefore, 11 x 27 = 297.
Question 12.
$72 × 25
Answer:
72 is near to 70
So, 70 x 25 = 1,750
Therefore, 72 x 25 approximately equals 1,750.
Question 13.
56 × 65
Answer:
56 is near to 55
So, 55 x 65 = 3,575
Therefore, 56 x 65 approximately equals 3,575.
On Your Own
Question 14.
Reason A local bakery needs muffin wrappers for 28 batches of muffins. There are 24 muffins in each batch. About how many muffin wrappers will the bakery need? Explain how you can estimate to solve the problem.
Answer:
Given,
A local bakery needs muffin wrappers for 28 batches of muffins.
There are 24 muffins in each batch.
number of muffins = 28 x 24 = 672
Therefore, total number of muffins = 672
By estimation,
28 is near to 30
24 is near to 25
So, 30 x 25 = 750
Therefore 28 x 24 approximately equals 750.
Question 15.
Melinda quickly enters 49 × 13 into her calculator. The display shows a product. How can Melinda use estimation to check that this product is correct?
Answer:
Given,
Melinda quickly enters 49 × 13 into her calculator.
49 is near to 50
13 is near to 15
So, 50 x 15 = 750
Therefore, 49 x 13 approximately equals 750.
Estimate the product. Choose a method.
Question 16.
86 × 42
__________
Answer:
86 is near to 85
42 is near to 40
So, 85 x 40 = 3,400
Therefore, 86 x 42 approximately equals 3,400.
Question 17.
31 × 23
__________
Answer:
31 is near to 30
23 is near to 20
So, 30 x 20 = 600
Therefore, 31 x 23 approximately equals 600.
Question 18.
78 × 77
__________
Answer:
78 is near to 80
77 is near to 80
So, 80 x 80 = 6400
Therefore, 78 x 77 = 6,400.
Question 19.
91 × 15
__________
Answer:
91 is near to 90
So, 90 x 15 = 1,350
Therefore, 91 x 15 approximately equals 1,350.
Question 20.
25 × 51
__________
Answer:
51 is near to 50
So, 25 x 50 = 1,250
Therefore, 25 x 51 approximately equals 1,250.
Question 21.
68 × 41
__________
Answer:
68 is near to 70.
41 is near to 40
So, 70 x 40 = 2800
Therefore, 68 x 41 approximately equals 2,800.
I’m in a Learning Mindset!
What did I learn from estimating products that I can use in the future?
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Answer:
An estimate can help you know how much you will spend without actually adding those numbers exactly. So, you can find an estimate to an exact answer quickly. It is often helpful to estimate answers before calculating them.