We included HMH Into Math Grade 5 Answer Key PDF Module 14 Lesson 3 Assess Reasonableness of Sums and Differences to make students experts in learning maths.
HMH Into Math Grade 5 Module 14 Lesson 3 Answer Key Assess Reasonableness of Sums and Differences
I Can use benchmarks or rounding to check the reasonableness of decimal sums and differences.
Spark Your Learning
Mr. Gilbert downloads two files onto his computer. The table shows the sizes of the two files. He says that he downloads about 2 megabytes of data.
Is Mr. Gilbert’s statement reasonable? Justify your answer using a visual model.
Answer:
No Mr.Gilbert’s statement is not reasonable,
Its More than 3 megabytes,
Explanation:
Given Mr. Gilbert downloads two files onto his computer.
File 1 – 1.27 megabytes and File 2 – 1.79 megabytes .
He says that he downloads about 2 megabytes of data.
But Mr.Gilbert is not reasonable as he says he downloaded about
2 megabytes but it is more than 3 megabytes,
Justified my answer using a visual model above which is
3.06 megabytes not 2 megabytes.
Turn and Talk How can you use rounding to check that an answer is reasonable?
Answer:
1.27 megabytes as 1 megabytes and
1.79 megabytes as 2 megabytes,
answer is not reasonable its not 2 megabytes
it is 1 + 2 = 3 megabytes,
Explanation:
Used rounding to check my answer as
1.27 megabytes rounded as 1 megabytes and
1.79 megabytes rounded as 2 megabytes,
answer is not reasonable its not 2 megabytes
it is 1 + 2 = 3 megabytes.
Build Understanding
Question 1.
The table shows the sizes of two different video files. Ms. Lee says that she uses 0.22 gigabyte more for video file A than for video file B, and that she uses a total of 0.96 gigabyte for both video files.
A. Locate points on the number line to show the size of each video file.
Answer:
Explanation:
Located points on the number line and
shown the size of each video files as
File A – 0.74 gigabyte and File B – 0.52 gigabyte above.
B. Which benchmarks on the number line can you use to estimate the size of each video file? How do you know?
Answer:
File A – 0.75,
File B – 0.50,
Explanation:
Benchmarks on the number line I can use to
estimate the size of each video as File A – 0.75 and
File B – 0.50, Because as File A is 0.74 gigabyte which is
nearer to 0.75 and File B is 0.52 gigabyte is nearer to
0.50 on the number line.
C. Is Ms. Lee’s statement that she uses 0.22 gigabyte more for video file A than for video file B reasonable? Explain how you know.
Answer:
Yes, Ms.Lee’s statement is reasonable,
Explanation:
Given video-File A is 0.74 gigabyte and video-File B is 0.52 gigabyte,
Ms.Lee’s statement is that she uses 0.22 gigabyte more for video file A
than for video file B , Yes she is reasonable because she is correct as
File A is 0.74 gigabyte – 0.52 gigabyte = 0.22 gigabyte more than File B.
D. Is Ms. Lee’s statement that she uses a total of 0.96 gigabyte for both video files reasonable? Explain how you know.
Answer:
No, Ms.Lee’s statement that she uses a total of 0.96 gigabyte for
both video files is not reasonable,
Explanation:
Ms.Lee’s statement that she uses a total of 0.96 gigabyte for
both video files is not reasonable as File A – 0.74 gigabyte and
File B – 0.52 gigabyte but if we add we get total
0.74 gigabyte + 0.52 gigabyte = 1.26 gigabyte which is not
0.96 gigabyte theerfore Ms.Lee’s statement is not reasonable.
Turn and Talk How do these benchmarks compare to the benchmarks used in fractions?
Answer:
By comparing less than or greater than or equal,
Explanation:
A benchmark is a reference number that can be used to compare two fractions.
If one fraction is less than the benchmark and a second fraction is
greater, the first fraction is less than the second.
Step It Out
Question 2.
The table shows a cellular phone provider’s monthly charges for voice and data services. What is the difference in cost of voice and data services? Mr. Sanchez says that the difference is $23.23. is his answer reasonable?
A. Estimate the difference in cost by rounding each cost to the nearest ten dollars. Write an equation to support your answer.
Answer:
Voice Services – $10.00,
Data Services – $40.00,
Equation: d = $40.00 – $10.00,
Explanation:
Estimated the difference in cost by rounding each cost to the nearest ten dollars.
As Voice Services – $10.00,
Data Services – $40.00,
Let d be the diffrence between voice services and data services,
So the equation to support my answer is d = $40.00 – $10.00.
B. Estimate the difference in cost by rounding each cost to the nearest dollar. Write an equation to support your answer.
Answer:
Voice Services – $10.00,
Data Services – $40.00,
Equation: d = $40.00 – $10.00,
Explanation:
Estimated the difference in cost by rounding each cost to the nearest ten dollars.
As Voice Services – $10.00,
Data Services – $40.00,
Let d be the diffrence between voice services and data services,
So the equation to support my answer is d = $40.00 – $10.00.
C. Is Mr. Sanchez’s answer reasonable? How do you know?
Answer:
Yes, Mr.Sanchez’s answer is reasonable,
Explanation:
Mr. Sanchez says that the difference is $23.23. is his answer reasonable,
Yes his answer is reasonable as the voice services $12.72 and
data services $35.95 has the difference $35.95 – $12.72 = $23.23 which
is equal and matches to what Mr.Sanchez says, So his answer is
reasonable.
Check Understanding
Question 1.
Use the table of cellular phone charges above. Is it reasonable to say that the cost of both services is about $40? Explain.
Answer:
No, The cost of both services is about $40 is not reasonable,
Explanation:
Using the table of cellular phone charges we have voice services
$12.72 and data services $35.95, So the cost of both services is
$12.72 + $35.95 = $48.67 which is not almost about $40 but $50,
therefore it is not resonable to say that the cost of both services is about $40.
Question 2.
Nancy buys 0.12 pound of black beans and 0.81 pound of pinto beans. She says she bought 0.69 pound more pinto beans than black beans. Is her statement reasonable? Explain how you know.
Answer:
Yes, Nancy statement is reasonable,
Explanation:
Given Nancy buys 0.12 pound of black beans and
0.81 pound of pinto beans. She says she bought 0.69 pound
more pinto beans than black beans. Yes her statement is reasonable
because if we see the difference between them it is
0.69 pound – 0.12 pound = 0.69 pound which is same and
matches with what Nancy says she bought 0.69 pound
more pinto beans than black beans.
therefore yes her statement is reasonable.
On Your Own
Question 3.
In professional hockey, the record for the average number of points scored each game by a player is 1.92 points. The fourth best average number of points is 1.39 points. Is it reasonable to say that the difference in the average numbers of points is 0.53 point? Explain.
Answer:
Yes, it is reasonable,
Explanation:
Given in professional hockey, the record for the average number of
points scored each game by a player is 1.92 points. The fourth best
average number of points is 1.39 points. Yes, it reasonable to say that
the difference in the average numbers of points is 0.53 point as
the difference between the average number of points scored each
game by a player and the fourth best average number of points is
1.92 points – 1.39 points = 0.53 points which is same and equal to
what is given so yes it is reasonable.
Question 4.
Construct Arguments Nicole buys the two small pizzas shown. Nicole says that the cost of both pizzas is about $20. Is her answer reasonable? Justify your answer.
Answer:
Yes, Her answer is reasonable,
Explanation:
Given Nicole buys the two small pizzas one is at $6.79 and
other is at $9.29, The total cost is $6.79 + $9.29 = $16.08,
As Nicole says that the cost of both pizzas is about $20 which is
about the same, so yes Nicole answer is reasonable.
Question 5.
Use Tools Carson says that the difference of 0.73 and 0.45 is 0.28. Is Carson’s answer reasonable? Justify your answer using the number line.
Answer:
Yes, Carson’s answer is reasonable,
Explanation:
Given Carson says that the difference of 0.73 and 0.45 is 0.28.
Yes Carson answer is reasonable as 0.73 – 0.45 = 0.28 same which Carson
said, Justified my answer using the number line above.
I’m in a Learning Mindset!
What strategies can I use to assess reasonableness?
Answer:
A reasonable estimate should not exceed the
original numbers in a problem,
Explanation:
We can also check for reasonableness by making numbers more
compatible with each other. This can be done by placing sums into in
times tables we understand, or blocks of ten that are easier to work with.
Rounding numbers, making numbers compatible, properties of
operations are some strategies that are used to check the
reasonableness of answers.