Q: How can you use estimation to check if 58 × 32 = 1,856 makes sense?

I can round 58 to 60, and 32 to 30. 60 × 30 is 1,800, which is close to 1,856. This is how I know my answer makes sense.

Q: You want to calculate 3.4 – 0.8. You represent 3.4 using 3 wholes and 4 tenths. What else do you need to do before you can subtract 8 tenths?

I don’t have enough tenths to subtract 8 tenths, so I need to regroup 1 of the wholes as 10 tenths. Then, I have 2 wholes and 14 tenths. Now I can subtract 8 tenths from 14 tenths. The answer is what remains, 2 wholes and 6 tenths, or 2.6.

Q: What can you do to check if 3.8 × 5.1 = 19.38 makes sense?

I can round 3.8 to 4 and 5.1 to 5. Multiply: 4 × 5 = 20. 20 is close to 19.38, so the answer makes sense.

Question 1

Give the value of each digit in 5.39.

Accepted Answer

5 wholes, 3 tenths, and 9 hundredths

Question 2

What is another way to name 56 hundredths?

Accepted Answer

Every 10 hundredths can be regrouped as 1 tenth. So, 56 hundredths is 5 tenths and 6 hundredths.

Question 3

What is another way to name 48 tenths?

Accepted Answer

Every 10 tenths can be regrouped as 1 whole. So, 48 tenths is 4 wholes and 8 tenths.

Question 4

Describe how to solve 63 &#247 9.

Accepted Answer

If I divide 63 wholes equally among 9 groups, each group has 7 wholes. 63 &#247 9 = 7.

Question 5

How can you use estimation to check if 58 &times; 32 = 1,856 makes sense?

Accepted Answer

I can round 58 to 60, and 32 to 30. 60 &times; 30 is 1,800, which is close to 1,856. This is how I know my answer makes sense.

Question 6

If you are calculating 3.64 &ndash; 2.14, which number should you represent using the fraction square model? What is the second step?

Accepted Answer

The greater number, 3.64. Then, take away blocks that represent 2.14 in total.

Question 7

You want to calculate 3.4 &ndash; 0.8. You represent 3.4 using 3 wholes and 4 tenths. What else do you need to do before you can subtract 8 tenths?

Accepted Answer

I don&rsquo;t have enough tenths to subtract 8 tenths, so I need to regroup 1 of the wholes as 10 tenths. Then, I have 2 wholes and 14 tenths. Now I can subtract 8 tenths from 14 tenths. The answer is what remains, 2 wholes and 6 tenths, or 2.6.

Question 8

How can you use skip counting to multiply 6 &times; 1.4?

Accepted Answer

1.4 means 1 whole and 4 tenths. I need to multiply each number by 6, which is the same as skip counting sixes. 6 &times; 1 = 6. 6 &times; 4 tenths = 24 tenths. 24 tenths is the same as 2 wholes and 4 tenths, so altogether I have 8 wholes and 4 tenths, or 8.4.

Question 9

Mimi multiplies 4 by 2 wholes, 3 tenths, and 7 hundredths and gets 8 wholes, 12 tenths, and 28 hundredths. Is that the final answer?

Accepted Answer

No, Mimi needs to do some regrouping, starting with the smallest place, the hundredths place. 28 hundredths can be regrouped as 2 tenths and 8 hundredths. So, now there are 8 wholes, 12 + 2 = 14 tenths, and 8 hundredths. Next, regroup some of the tenths. 10 tenths can be regrouped as 1 whole, so the final answer is 9 wholes, 4 tenths, and 8 hundredths, or 9.48.

Question 10

What can you do to check if 3.8 &times; 5.1 = 19.38 makes sense?

Accepted Answer

I can round 3.8 to 4 and 5.1 to 5. Multiply: 4 &times; 5 = 20. 20 is close to 19.38, so the answer makes sense.

Solve Problems with Decimals (Using Models)

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