Mars Percent – Schreuder Academy

Math Assessment Reasoning and Strategies for Percent.

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1. 1/2 = ...%

Can’t do it yet, guesses

50% | I just know it, we have learned that

50% | Connects % with 100: 50 is half of 100 or 100% is 'everything' (the total, the whole) and half of 100% is 50%

Additional observations:

2. 50% = 0.5, 25% = ...

Can’t do it yet, guesses

half, less | Ask: Can you say that as a fraction or a decimal? Score at that answer below

2500 | Change the decimal dot 2 places

1/4 | I just know it, we have learned that. Ask: Can you explain why? "I just learned that" If explained score at one of answers below

0.25 | Change the decimal dot two places to the left. Ask: Can you explain why? "I just learned that" If explained score at that answer below

0.25 | 25% is 25 hundredths, that is 0.25

1/4 | 25% is half of 50%, 0.5 = 1/2, half of 1/2 = 1/4

0.25 | 25% is half of 50% and 0.25 is half of 0.5

Additional observations:

3. 50% of 60

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

10 | 60 - 50 = 10

30 written | can only do it on paper, check answer needed to guess more accurately

30 | imagines algorithm 50 / 100 x 60 = 30

30 | 50% is half of 100%, half of 60 = 30

Additional observations:

4. 25% of 48

? | Can’t do it yet, guesses

23 | 48 - 25 = 23

12 | can't do it mentally give pen and paper and check the answer

12 | imagines algorithm 25 / 100 x 48 = 12

12 | Use a model (double number line, ratio table) and connect 48 with 100% and see that 25% connects with 12

12 | I know 25% = 1/4 and 1/4 of 48 = 12 or 48 divided by 4 = 12

Additional observations:

5. 0.3 = ... %

? | Can’t do it yet, guesses

0.00003 | Change the decimal dot two places

3% | The percent number is always larger than the decimal or other incorrect reason, write given reason in comment

30 % | Move decimal dot 2 places to the right. Ask: Can you explain why? "I just learned that" If explained score at one of answers below

30 % | Move decimal dot 2 places to the right. Ask: Can you explain why? "% means divide by 100, so without % is multiply with 100: dot 2 decimal spaces to the right makes the number 100x larger"

30 % | Move decimal dot 2 places to the right. % means divide by 100 so to compensate for that you need to multiply by 100: 2 places.

30 % | Use a model (double number line, ratio table) and connect 1 with 100% and see that 0.3 connects with 30%

30 % | 0.3 = 3/10 = 30/100 and hundredths are percent

Additional observations:

6. 9% = ... as a decimal

? | Can’t do it yet, guesses

0.9, 0.90 | write given reason in comment

0.09 | I move the decimal dot 2 places to the left. Ask: Can you explain why? "I just learned that"

0.09 | I move the decimal dot 2 places to the left. Ask: Can you explain why? "% means divide by 100, so taking % off is multiply with 100: 2 decimal spaces"

0.09 | I use a model (double number line, ratio table) and connect 1 with 100%, and see that 9% connects with 0.09

0.09 | 9% is 9/100 or 9 in the hundredths place

Additional observations:

7. 200% of 300

? | Can’t do it yet, guesses

100 | 300 - 200 = 100

600 | 200 / 100 x 300 = 600

600 | I use a model (double number line, ratio table) and connect 300 with 100%, and see that 200% connects with 600

600 | if 100% = 300 then 200% is double or twice that so 600

Additional observations:

8. 10% of which number = 50?

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

40 | 50 - 10

5 | 10% = divide by 10, 50 ÷ 10 = 5

500 written | of means the total, = means the part, I need to calculate the total but can't do it mentally, give pen and paper and check

500 | I use a model (double number line, ratio table) and connect 50 with 10%, and see that 100% connects with 500

500 | 10% = 1/10, 1/10 of 500 = 50 or 100% is 10 x 10% and 10x50 = 500

500 | 10% = 1/10, if 1/10 = 50 then 10/10 = 500

Additional observations:

9. 45 is what % of 15?

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

30 % | 45 - 15 = 30

3 % | 3 x 15 = 45

33 or 33.3 % | 15 = 1/3 of 45 and 1/3 = 33%

300 % written | of means the total, = means the part, I need to calculate the % but can't do it mentally, give pen and paper and check

300 % | I use a model (double number line, ratio table) and connect 50 with 10%, and see that 100% connects with 500

300 % | 15 is 100%, 45 = 3 times 15, so 3 x 100% = 300%

Additional observations:

10. Sale $60 - 20% =

? | Can’t do it yet, guesses

40 | 60 - 20 = 40

3 | 60 ÷ 20 = 3

33 or 33.3 | 1/3 of 60 = 20, 1/3 = 33%

48 | 1 % of 60 = 0.60; 10% of 60 = 6; 20% of 60 = 12; $60 - $12 = $48

48 | 20% off means I have to pay 80%. I use a double number line and connect $60 with 100%, and see that 80% connects with 48

48 | 20% = 1/5; 1/5 of 60 = 12 or 60 ÷ 5 = 12; $60 - $12 = $48

Additional observations:

11. Price was $150 now $135 is what % off?

? | Can’t do it yet, guesses

15 % | 150 - 135 = 15

10 % | 1% of 150 = 1.50 and 10 x $1.50 = $15 or 10% of 150 = $15 off

10 % | I use a double number line and connect $150 with 100%, and see that $135 connects with 90%, so 10% is taken off

Additional observations:

12. 70% = 280, 35% = ...

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

35 | 35 is half of 70.

50 | 35 is half of 70. 1/2 = 50%

? written 140 | can't do it mentally, give pen and paper, check only if the answer = 140 and write in comments

140 | 70% = 280 so 1% = 280 ÷ 70 = 4, 35% = 35 x 4 = 140 mentally

140 | I use a model (double number line, ratio table) and connect 280 with 70%, and see that 35% connects with 140

140 | half of 70% = 35%, half of 280 = 140

140 | Numbers and percentages are proportions 70 goes in 280 4 times, 4 x 35 = 140

Additional observations:

13. estimate 12.8% of 81,300

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

? | Observation: tries to calculate instead of estimate, does not round. Ask about thinking and write in comments

? | 12.8% rounds so 13% and 81,300 already has zeros at the end so it can't be rounded, can't estimate

? | Thinks you can only round one of the numbers either the 12.8% or the 81,300, can't estimate

? | Knows you may round both numbers 12.8% to 10%, 13%, or 15% and 81,300 to 81,000 or 80,000, but can't estimate

? written answer > 10,000 | 12.8% rounds to 13% and 81,300 has zeros in the end so it is rounded already. It is 0.13 x 81,300 but can't do it mentally. Ask: does rounding it further before you estimate help you? give pen and paper, check answer and write in comments

8130 | 12.8% rounds to 10% = 1/10 or divide by 10. 81,300 ÷ 10= 8,130. Ask: how can you give a more rounded answer?

8100 | 12.8% rounds to 10% = 1/10 or divide by 10. 81,300 rounds to 81,000. 1/10 of 81,000 = 8,100

10000 | 12.8% rounds to 13%, 81,300 rounds to 80,000, 1% = 800, 13 x 8 = 104, 13 x 800 = close to 10,000

10000 | 12.8% is close to 10%, 81,300 rounds to 80,000. Use a model (double number, ratio table) line and connect 80,000 with 100%, and see that 10% connects with 10,000

10000 | 12.8% is close to 12.5% or 1/8 (because 25% = 1/4 and 12.5 is half of 25); 81,300 rounds to 81,300 or 80,000. 1/8 of 80,000 = 10,000

Additional observations:

14. estimate 4 is what % of 0.389?

? | Can’t do it yet, guesses

? | Observation: tries to calculate instead of estimate, does not round; ask about thinking and write in comments

10 % | 0.389 rounds to 0.4 that is one tenth of 4 so 10%

1000 % written | 0.389 rounds to 0.4 that is 100%, 4 is larger than 0.4 so more than 100%, but can't do it mentally: give pen and paper, check answer and write in comments

1000 % | 0.389 rounds to 0.4, use a model (double number line, ratio table) and connect 0.4 with 100%, and see that 4 connects with 1000%

1000 % | 0.389 rounds to 0.4, 4 is 10 x 0.4, 10 x 100% = 1000%

Additional observations:

15. from 45 to 36 is what % decrease?

? | Can’t do it yet, guesses

9 % | 45 - 36 = 9

20% written | Can't do it mentally, give pen and paper check answer and write in comments

20 % | Use a model (double number line, ratio table) and connect 45 with 100%, and see that $36 connects with 80%, so 20% is taken off

20 % | 45 - 36 = 9. 1% of 45 = 0.45, 2% = 0.90 so 20% = 9, 9 less is 20% decrease

20 % | 45 - 36 = 9, 9 = 1/5 of 45, 1/5 less = 20% decrease

Additional observations: