Mars Decimals – Schreuder Academy

Math Assessment Reasoning and Strategies for Decimals.

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1. 15 + 2.4

? | Can’t do it yet, guesses

39 or 3.9 | Apparently adds without aligning the decimal dot. Ask: One of the numbers has a decimal dot, is there a hidden decimal dot for the other number? If answer is yes, ask: Where is it?

17.4 | 15 + 2 = 17, 17 + 0.4 = 17.4, if says ‘17 point 4’ ask how do you say the complete name? Make a comment when does not know it reads 17 and 4 tenths

17.4 | Aligns decimal dot to add 5+2, knows they are both in the same ones/units column

Additional observations:

2. 20.8 + 0.20

? | Can’t do it yet, guesses

22.8 or 2.28 | If answers ‘22 point 8’ or '2 point 28', ask how does that number read completely? Make a comment when does not know it reads 22 and 8 tenths

21 | Imagines the column addition with decimals aligned, may add a zero to make 20.80

21 | 8 tenths + 2 tenths = 10 tenths = 1, 20 + 1 = 21

Additional observations:

3. 27.5 - 2.05

? | Can’t do it yet, guesses, mistake in written work

7 | Apparently subtracts without aligning the decimal dots. Ask: how do you know and if self corrects score that answer

25 | 27- 2 = 25, subtracts 5 hundredths from 5 tenths and thinks it is .0

25.45 written | Says you need to align the decimal dots but can’t do it mentally: give paper and check answer.

25.45 | Mentally adds a zero to make 27.50 or just imagines the column subtraction

25.45 | 27 - 2 = 25, 5 tenths = 50 hundredths - 5 hundredths = 45 hundredths, so 25.45

Additional observations:

4. What is more 12.3 or 12.13

? | Can’t do it yet, guesses

12.13 | 13 is more than 3, 12.13 has more decimals, it is a longer number. Ask: can you name the decimals in the number ‘12 point 13’? Make a comment when does not know it reads 12 and 13 hundredths

12.3 | Adds a zero to 12.3, 12.30 is more than 12.13

12.3 | Finds the first digit that is different: 3 in the tenths place is more than 1 in the tenths place

12.3 | 12.13 rounds to 12.1 and that is less than 12.3

12.3 | 3 tenths is 30 hundredths and that is more than 13 hundredths

Additional observations:

5. What is more 0.23 or 0.046

? | Can’t do it yet, guesses

0.046 | It is longer, 0.23 has only 2 decimals and 0.046 has 3

0.046 | 46 is double 23, 46 is more than 23

0.046 | Looks at the first digit (that is not zero) after the dot: 4 is more than 2

0.23 | Adds a zero to 0.23, 0.230 is more than 0.046

0.23 | Uses place value: the 2 is in the tenths place, the 4 is in the hundredths place, a number in a column to the right is 10 times smaller, or other correct base ten explanation

Additional observations:

6. 0.85 + … = 1

? | Can’t do it yet, guesses, mistake in written work

1.85 | Apparently adds, possibly misread the question. Ask: how do you know, if self-corrects score that answer

0.25 | Adds 2 zeros to make 1.00, then subtract 0.85 = 0.25

0.15 written | I need to subtract 1 - 0.85 but can’t do it mentally, give pen and paper, check answer, write comment

0.15 | Adds 2 zeros to make 1.00, then imagine the column subtraction with 0.85 = 0.15

0.15 | 85 + 15 = 100 so 0.85 + 0.15 = 1

Additional observations:

7. ½ = 0.5, ⅖ = ... as decimal

? | Can’t do it yet, guesses

0.2 | The numerator of the fraction becomes the decimal

0.5 | The denominator of the fraction becomes the decimal

0.25 | 2/5 = 0.25 using both fraction numbers as decimals

0.1 or 0.10 | 2 x 5 = 10 so one tenths or 0.10

0.4 | 2/5 = 4/10 so a 4 in the tenths place

Additional observations:

8. What is more ⅗ or 0.53

? | Can’t do it yet, guesses

0.53 | 0.53 has 2 decimals, it is a long(er) number

0.53 | 0.53 is more than 0.50

0.53 | 3/5 = 0.35 so 0.53 is more

3/5 | 3/5 = 3.5 that is more than 0.53 or other incorrect explanation

3/5 | 3/5 = 6/10 or 0.6 so more than 0.53

Additional observations:

9. $ 10 - 75 c.

? | Can’t do it yet, guesses, mistake in written work

35 c. | 100 - 75 = 35 makes mistakes in place value and with regrouping

25 c. | 100 - 75 = 25 makes mistake in place value

935 c. | Changes to cents: 1000 c. - 75 c. mistake with regrouping

9.35 | Changes to dollars $10 - $ 0.75, mistake with regrouping

$9.25 written | Can't do it mentally, give pen and paper, check answer

925 c. | Changes to cents: 1000 c. - 75 c.

$9.25 | Changes to dollars: $10 - $ 0.75

Additional observations:

10. 0.50 x 12

? | Can’t do it yet, guesses, mistake in written work

600 | 5 x 12 = 60 so 50 x 12 = 600

6.00 written | Can't do mentally, give pen and paper, check, write comment

6.0 | 0.50 = 0.5 imagines column multiplication 5 x 12 = 60, then brings in the decimal dot one place

6 | 0.50 is half, half of 12 = 6

Additional observations:

11. 14.6 x 10

? | Can’t do it yet, guesses, mistake in written work

24.6 | Adds instead of multiplies, ask how did you do that and if self-corrects score that answer

140.6 | 14x10 = 140 then adds the .6

14.60 | Multiply by 10 means adding a zero

140.60 | 14x10 = 140 and 6x10 = 60

146.0 written | Can't do mentally, give pen and paper, check, write comment

146 | Multiply by 10 means decimal dot moves 1 place to the right

146 | 14 x 10 = 140 so 14.6 x 10 = 146

146 | All digits become 10 times larger when they are written one column to the left

Additional observations:

12. 245 ÷ 10

? | Can’t do it yet, guesses, mistake in written work

0.245 | Divide by 10 means you have one zero before the number

2.45 | Divide by 10 means you move the decimal one place after the first digit

24.5 written | Can't do mentally, give pen and paper, check, write comment

24.5 | Divide by 10 means decimal dot moves 1 place to the left

24.5 | 10 tens in 100, so 20 tens in 200, and 4 tens in 40, and 5 is half of a ten, so 24.5

24.5 | All digits become 10 times smaller when they are written one column to the right

Additional observations:

13. Estimate 6.85 x 0.49

? | Can’t do it yet, guesses

? | Tries to calculate instead of estimate, does not round; ask about thinking and write comment

? | 6.85 rounds to 6.90, 0.49 rounds to 0.5, can't do it mentally. Ask: Can you round it further and estimate? If so score that answer

0.35 | 6.85 rounds to 7, 0.49 rounds to 0.5, 7 x 0.5 = 0.35

3.5 | 6.85 rounds to 7, 0.49 rounds to 0.5, 7 x 0.5 = 3.5

3.5 or 3 1/2 | 6.85 rounds to 7, 0.49 rounds to 0.5, that is half, half of 7 = 3.5

Additional observations:

14. what is between 0.63 and 0.64

? | Can’t do it yet, guesses

none | 0.63 and 0.64 are right next to each other so there is no number in between

0.63 | 0.630 is in between 0.63 and 0.64 because it is longer

any number from 0.631 to 0.639 | there are 9 possible digits in the hundredths place (actually there is an indefinite number of decimals in between) ask about thinking and write comment

Additional observations:

15. Estimate 28 ÷ 0.65

? | Can’t do it yet, guesses

? | Apparently tries to calculate instead of estimate, does not round; ask about thinking and write comment

4 | 0.65 rounds to 0.7, 28 ÷ 0.7 = 4

0.4 or 0.40 | 0.65 rounds to 0.7, 28 ÷ 7 = 4 so 28 ÷ 0.7 = 0.4

30 | 28 rounds to 30, 0.65 rounds to 1, 30:1 = 30

40 | 0.65 rounds to 0.7, multiply both numbers by 10 and then divide, I know 28 ÷ 7 = 4 so 280 ÷ 7 = 40

40 | 0.65 rounds to 0.7, 28 ÷ 7 = 4 so 28 ÷ 0.7 = 40

Additional observations:

16. Estimate 0.9 ÷ 47

? | Can’t do it yet, guesses

? | Apparently tries to calculate instead of estimate, does not round; ask about thinking and write comment

0.50 | 0.96 rounds to 1; 47 rounds 50; 1 ÷ 50 = 0.50

0.20 | 0.96 rounds to 1; 47 rounds 50; 1 ÷ 50 = 0.20

0.05 | 0.96 rounds to 1; 47 rounds 50; 1 ÷ 50 = 0.05

0.02 | 0.96 rounds to 1; 47 rounds 50; 1 ÷ 50 = 2 ÷ 100 = 0.02

Additional observations:

17. What comes next 4 - 2 - 1 - 0.5 - 0.25 - ?

? | Can’t do it yet, guesses, mistake in written work

? | Ask how the numbers are connected and if doesn’t know score this answer, if says “divide by 2 or half” score next answer

Any answer other than 0.125 or 1/8 | You need to divide by 2, can’t do it mentally: give pen and paper, check, write comment

0.125 written | You need to divide by 2, can’t do it mentally: give pen and paper, check, write comment

0.125 | You need to divide by 2, I know half of 25 is 12.5, so half of 0.25 = 0.125

⅛ = 0.125 | The next number is half and connects with fractions: I know half of a ¼ = ⅛ and I know ⅛ = 0.125

Additional observations: