MARS fractions – Schreuder Academy

Math Assessment Reasoning and Strategies for Fractions

How to conduct the assessment in short:

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Name of student assessed

1. What does 3/4 mean?

Doesn't know or guesses

a fraction | Ask: Can you tell more about the fraction? Score most advanced answer

3 = numerator, 4 = denominator | Ask: Can you tell more about numerator and denominator? Score most advanced answer

you get 3 parts/slices | no reference to the denominator, focuses on 3 parts/slices

3 divided by 4 | what you get when 3 pizzas are divided by 4 people

3 out of 4 are colored in | refers to a model: 3 out of 4 are selected but no reference that they are equal parts

one thing cut in four and you have 3 | includes reference to one whole/the total and starts with the denominator: something is divided in 4 equal pieces or 4 equal groups and 3 are counted

Additional observations:

2. What is more 4/10 or 5/10 ?

Can't compare yet, guesses

4/10 | the fraction is bigger when the number is smaller

5/10 | 5 is more than 4

5/10 | 5 is more than 4 and mentions they are both tenths or both have the same denominator

Additional observations:

3. What is more ⅜ or 3/7 ?

Can't compare yet, guesses

⅜ | 8 is more than 7

3/7 | 7 is less than 8, if you divide with 7 you get more than when you divide with 8

3/7 | a smaller denominator means a larger fraction

Additional observations:

4. ½ + ¼

Can’t do it yet, guesses

2/6 or 1/3 | Adds numerators and adds denominators as if there are 2 questions 1+1 and 2 + 4 so 2/6 or simplifies to 1/3

2/8, 3/8, 4/8, 5/8 | Makes same denominators, uses 2x4 = 8 as new denominator, but multiplies the numerators incorrectly

6/8 | Makes same denominators, uses 2x4 = 8 as new denominator, correctly uses equivalent fractions, but does not simplify

3/4 | Makes same denominators, uses 4 as new denominator

3/4 | I know ½ is 2/4 so 2/4 + ¼ = 3/4

Additional observations:

5. 3/8 - 1/4

Can’t do it yet, guesses

2/4 or 1/2 | Subtracts numerators and denominators as if there are 2 questions 3-1 and 8 - 4

4/32 | Makes same denominators, uses 8x4 = 32 as new denominator, does not simplify

other fraction with denominator 32 | Makes same denominator, uses 8x4 = 32 as new denominator, but multiplies the numerators incorrectly

2/16 or 3/24 | Makes same denominators, uses 16 or 24 as new denominator, does not simplify

other fraction with denominator 16 or 24 | Makes same denominators, uses 16 or 24, multiplies the numerators incorrectly

2/8 or 1/4 | Makes same denominators, uses 8, but does not change the numerators

1/8 | Makes same denominators, uses 8, changes numerators correctly

1/8 | I know ¼ = 2/8 so 3/8 - 2/8 = 1/8

Additional observations:

6. What is more 9/10 or 10/9 ?

Can’t do it yet, guesses

9/10 | Any error like 9/10 is a decimal and 10/9 is not a decimal and write in comments

10/9 | can't explain why or says 10 is more than 9 only referring to the numerators

10/9 | 10/9 is an improper fraction, 9/10 is not an improper fraction

10/9 | 10/9 is more than 1, and 9/10 is less than 1

Additional observations:

7. 5/7 + … = 1

Can’t do it yet, guesses

5/7 | Thinks 5/7 + 5/7 = 1 because they are equal

7/5 | Thinks 5/7 + 7/5 = 12/12 = 1, or mentions reciprocal

2/7 | I know 1 = 7/7, so we need 2/7 more

Additional observations:

8. 6 - 1 ¾

Can't do it, guesses

5 ¾ | 6 - 1 = 5 and then I add in the ¾

5 ¼ | 6 - 1 = 5 and then I subtract ¾

Additional observations:

9. 3 x 2 ½

Doesn't know, guesses

6 ½ | Split 2 and 1/2, 3 x 2 = 6 then adds ½ = 6 ½

7 ½ | Use a decimal: 2 ½ is 2.5 and 3 x 2.5 is 7.5 (because I know 3 x 25 = 75)

7.5 | Split 2 and 1/2, 3 x 2 = 6, 3 x ½ = 1 ½ , then add 6 + 1 ½ = 7 ½

Additional observations:

10. What is more ⅗ or 4/9 ?

Can’t compare it yet, guesses

4/9 | 9 is larger than 5 so 4/9 is larger, or any other error and write in comments

3/5 | Can't explain why

3/5 | Uses benchmarks to compare: ⅗ > ½ and 4/9 < ½

Additional observations:

11. ½ x ¼

Can’t do it yet, guesses

Any answer other than 1/8 | Ask about thinking and write in comments

1/8 | Multiply across, 1x1 / 2x4

1/8 | I know half of a fourth is an eighth, or I visualize it like with cutting a pizza

Additional observations:

12. 3/10 x 4/10

Can’t do it yet, guesses

12/10 or 6/5 | Denominators are the same already, 3x4=12, the denominator does not change

Any answer other than 12/25 | Ask how it was done and write in comments

1.2 | Makes decimals: 0.3 x 0.4 but misplaces decimal dot

0.12 | Makes decimals: 0.3 x 0.4. Ask: Can you say it as a faction?

12/100 or 6/50 | Multiply across: 3x4 / 10x10. Ask: Can you simplify?

3/25 | 3/10 x 4/10 = 12/100 and simplifies completely

Additional observations:

13. 4 ÷ ½

Can’t do it yet, guesses

2 | Half of 4 = 2 (multiplies instead of divides or can't divide by a fraction yet)

8 | Keep - change - flip: 4 x 2 = 8. Ask why that works and write in comments

8 | There are 2 halves in one whole so there are 8 halves in 4 holes

Additional observations:

14. Estimate 9/10 - 9/21

Can’t do it yet, guesses

0/11 | 9-9 = 0 and 21-10 = 11, does not estimate

0/21 | 9-9 = 0 and keep the largest denominator, does not estimate

0/11 | 9-9 = 0 and keep the smallest denominator, does not estimate

½ or close | Estimate using benchmark numbers 9/10 rounds to 1, 9/21 rounds to ½ , 1 - ½ = ½

1/2 or close | Estimate using benchmark (9/10 close to 1) and comparison of the denominators 20 is 2x10 so 9/20 is close to half of 9/10, 1 - ½ = ½

Additional observations:

15. Estimate 7/12 x 14/29

Can’t do it yet, guesses

Answer other than ¼ | Tries to calculate instead of estimate, does not use benchmarks, other error, ask how answer was got and write in comments

close to ¼ | Estimate using benchmark numbers 7/12 is close to ½ , 6/14 is close to ½ , ½ x ½ = ¼

¼ | 7/12 is a bit more than 1/2, 14/29 is a bit less than 1/2, ½ x ½ = ¼

1/4 | Simplify before multiplying across: 7/29 is close to 7/28 or 1/4 and 12/14 is close to 1 so 1 x 1/4

Additional observations:

16. ⅓ is between ½ and ¼ what is another fraction between ½ and ¼

Can’t do it yet, guesses

none | Only 3 is between 2 and 4, there is no other fraction than ⅓ between ½ and ¼,

Equivalent of ⅓ | Any fraction equivalent to ⅓. Ask: Do you know a fraction that is different from 1/3? If yes score at an answer below and write in comments

Decimal between 0.25 and 0.5 | Make decimals 0.25 and 0.5 and find a decimal in between. Ask: Can you name a fraction? If yes score at next answer and write in comments

⅖, 3/7, ⅜ 3/10, 4/10, etc. check | Ask how that answer was found and how you know it is in between ¼ and ½ and write in comments

Additional observations: