place value
How much smaller is 0.3 than 3? How do you know?
Ten times smaller because 0.3 is one place value to the right and both numbers have the same digit.
Miss Johnson is a science teacher. She has three curriculum textbooks to teach her students science. The first book weighs 2.561 pounds, the second book weighs 2.973, and the third book weighs 2.572. Which book weighs the most. Explain your answer.
The second book. Even though all of the books have the same digit in the ones place, one has a different digit in the tenths place. I compared 0.5 and 0.9 and 0.9 is larger. So the only number with a 9 in the tenths place is 2.973.
Olivia said adding 0.65 + 0.4 will be less than 1. Do you agree or have a different idea? Why?
I have a different idea. 0.64 can be rounded to 0.70 and 0.4 is equivalent to 0.40
0.70 + 0.40 = 1.10
Without doing calculations, what can you conclude about the products of the following equations?
2.5 * 4
2.52 * 4
2.528 * 4
The products will get slightly bigger each time because the number is greater each time by 2 hundredths and then 8 thousandths.
The first answer is 10. The other two answers will be slightly larger than 10
1 / 0.6
1.66666666666666666
(or simply 1.66)
Why does the number 17,682 have a different value than 17,862?
The digits in the hundreds place and tens place are reversed. Even though they are the same digits, the value of those numbers change based on their place in the number. 860 is different from 680.
Gabby said the decimal 6.084 has a greater value than 6.112. Do you agree or have a different idea? Why?
I have a different idea because they have the same value in the ones place, but the two numbers have different values in the tenths place. 1 is greater than 0, so 6.112 is larger.
Where does the decimal go in the answer to 0.56 + 0.62 = 118? How do you know?
1.18
0.56 can be rounded to 0.60 and 0.62 can be rounded to 0.60. 0.6 + 0.6 = 1.20. 1.20 is close to 1.18.
Cate says that the product of 2.96 * 12.6 will be less than 35. Using mental math (no work on paper or on technology) do you agree or have a different idea? Why?
I have a different idea because 2.96 rounds to 3 and I see than 12.6 is close to 12. (Its easier to do in my head because I don't have 13s facts memorized) 3 * 12 = 36. This is greater than 35.
Solve 7 / 0.8
(You may use paper if you want to)
8.75
Is "ten times less" the same thing as "1/10 as much"? Why or why not?
Yes.
"Ten times less" means divide by ten. "1/10 as much" means multiply by 1/10. If you divide by ten, the digits shift down in place value. If you multiply by 1/10 your product is going to be ten times smaller and the digits will shift down in place value.
Jaia said that 426.896 rounded to the nearest tenth is 427. Morgan said that it is 426.9. Who is correct? Why?
Morgan is correct because she looked at the hundredths place and rounded up.
It seems that Jaia doesn't know how to round to the tenths place instead of using the hundredths place to round, she used the tenths place and ended up rounding the ones place.
Anna says that 2.68 - 1.4 is greater than 1. Do you agree or disagree? Why?
I agree. 2.68 - 1 is 1.68. because 1.4 is less than that, the difference/distance between the two numbers is greater than 1.
Rylan says that when you multiply 5.97 * 7.4 the product will be greater than 43. Using Estimation (mental math) do you agree or have a different idea? Why?
You can agree or disagree. I round 5.97 to 6 and 7.4 to 7. 6 * 7 = 42. So less than 43 is reasonable. But 43+ is a reasonable answer and the product IS greater than 43, so Rylan is correct.
As long as students give solid reasoning, they will get this one correct.
The annual bike race is 41.25 miles long. The race organizers want to place 5 water stations close to equal distance apart. The final water station is at the finish line. A water station is not needed at the start line. About how many miles should be between each water station? How do you know?
About 8 miles in between each water station.
41.25 rounds to 40. 40 / 5 is 8.
Why is 500 ten times greater than 50?
The fives are in a different place, so even though the digit (5) is the same, the place is different, so the value changes. A 5 in the hundreds place is worth 500. A 5 in the tens place is only worth 50.
Liam rounded the weight of his bag of supplies to 12.5 pounds. What could be the exact value of his bag to thousandths of a pound?
Any number between 12.450 and 12.549
The number must be read correctly.
Where do the decimals go in the following problems?
0.74 - 0.61 = 13
4.56 - 1.32 = 324
2.14 - 1.95 = 19
0.13
3.24
0.19
Place the decimal point in the factors by looking at the product:
32 * 7 = 22.40
63 * 4 = 2.52
70 * 16 = 11.2
73 * 12 = 8.76
3.2 * 7.0 = 22.40 or 32 * 0.70 = 22.40 or 0.32 * 70 = 22.40
0.63 * 4.0 = 2.52 or 6.3 * .4 = 2.52 or 63. * .04 = 2.52
7.0 * 1.6 = 11.2 or 70 * .16 = 11.2 or 0.70 * 16 = 11.2
7.3 * 1.2 = 8.76 or .73 * 12 = 8.76 or .73 * 12 = 8.76
1.25 can be broken into 1 + 0.25
Solve the following problems and give decimal answers:
1 / 5
0.25 / 5
1.25 / 5
1 / 5 = 0.2
0.25 / 5 = 0.05
1.25 / 5 = 0.2 + 0.05 = 0.25
Read the number 941.34 out loud correctly.
Compare the two 4's and explain what you notice.
Nine hundred forty-one and thirty-four hundredths.
One 4 is in the tens place and has a value of 40. The other 4 is in the hundredths place and has a value of 4/100. The first 4 is 1,000 times greater than the second 4.
My number rounded to the nearer hundredths place is 3.62 What might my number be?
Any number between 3.615 and 3.624
The number must be read correctly.
4.32 - 1.87
(you may solve on paper)
2.45
0.6 * 0.85 = n
(You may solve on paper)
n = 0.51
You divide two numbers and the answer is 2.5
What could those two numbers be?
(you may use paper if you need to)
(Answers can vary greatly)
One possible solution is 10 / 4
another is 5 / 2