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Math Assessment Reasoning and Strategies for Addition and Subtraction

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1. 3+5

can't do it or guesses

Counts all 1, 2, 3, .... 8 out loud or counting on fingers.

Count on by one's or uses fingers (starting with 3, saying 4, 5, 6, 7, 8)

Count on by one's or uses fingers (starting with 5, saying 6, 7, 8)

Holds up one hand with three fingers and the other hand with five fingers and sees it is eight without counting

Just knows it

.Imagines the column algorithm

Additional observations:

2. 6+7

can't do it or guesses

Counts all 1, 2, 3, ....13 out loud or counting on fingers.

Counts on out loud by one's or uses fingers starting with the 6, saying 7, 8, ......, 13 )

split 7 in 4 and 3, uses 10 as a stepping stone: 6+4=10 10+3=13

Uses a doubles and near doubles strategy: "I know double 6 is 12 so 6+7 is one more so 13". Or " I know double 7 is 14 so 6+7 is one less than 14"

Just knows it

Imagines the column algorithm then counts up or adds

Additional observations:

3. 9+8

can't do it or guesses

Counts all 1, 2, 3, ....17 out loud or counting on fingers.

Counts on by one's out loud or uses fingers, starting with 9, saying 10, 11, .... , 17

Split 8 in 1 and 7 and uses 10 as 'stepping stone' 9+1=10 and 10+7=17

Reasoning using doubles: double 9 is 18 so 9+8 is one less so 17. Or double 8 is 16 and one more is 17

Uses a tens number: "10 plus 8 is 18 so 9 plus 8 is 17"

Just knows it

Imagines the column algorithm then counts up or adds

Additional observations:

4. 35+?=100

can't do it or guesses

Thinks the answer is 75. Write a comment which scaffolding the student needs to be able to correct the answer

Answers 65, but can't explain

Imagines the column algorithm (or draws it in the air) 100-35 and mentions how to regroup and answers 65

Uses a mixed strategy of counting up from 35 by ones and tens: Counts on 5 by 1 to 40 and by 6 ten's to 100 and answers 65

Uses 5 and 10 numbers to count up from 35: 35+5=40....40+60=100.....5+60=65...so 35+65=100

Uses a partitioning and place value strategy: " I know 30+70=100 so 35+65=100"

For 100 - 35 separates ones and tens:"100-5=95, 95-30=65"

Uses a flexible numbers and benchmark strategy: "I know that 100-30=70, when you subtract 35, you subtract 5 more, so the answer is 65"

Uses appropriate benchmarks and knows how to compensate for the difference between benchmark and numbers in the question

Additional observations:

5. 105+987

can't do it or does not answer at all

guesses or estimates below 1,000

guesses or estimates over 1,000

Imagines the column algorithm starting with 5+7 = 12 and regroups the ten +80 = 90, then adds 900+100 and answers 1092

Answers 1092 but can't explain

Splits according to place value : 900+100 = 1,000; 80 (or 80+00=80), 5+7=12, then 1000+80+12=1092 or 80=12 = 92 + 1,000 = 1,092

Rounds 105 to 100 and adds 987+100=1087, then adds 5, so 1092.

Uses the benchmark 1,000 for 987, adds 105 and subtracts 13 from 1,105 = 1,092

Additional observations:

6. How would you add up these amounts: $7.25 plus $4.50 plus $3.75 plus $6.50

If too difficult can you estimate the total?

If not possible mentally please provide pen and paper.

doesn't know, guesses

Adds the whole dollars in the order provided; 7+4+3+6, adds numbers one by one so 7+4=11, plus 3 is 14, plus 6 is 20, and thinks total is $20. Write a comment which scaffolding the student needs to be able to correct the answer

add the whole dollars using 10 as a benchmark; 7+3=10 and 4+6=10 so the total is $20

Needs to write down the column algorithm per two amounts in the order given and gets $22

Splits dollars and pennies, adds $0.25 + $0.75=$1 and $0.50 + $0.50=$1, then adds $7+$3=$10 and $4+$6=$10 and answers $22

Imagines the column algorithm combining $7.25 + $3.75 = $11.00 and then $4.50 + $6.50 =$11.00 and says total is $22.00

First estimates then calculates and checks if the answer makes sense: Estimate total must be more than $20, or close to $21, then calculates mentally for whole dollars and pennies separately, says "total is $22" and mentions that it makes sense because my estimate was $21

Additional observations:

7. 5-2

Can't do it, guesses

Counts back incorrectly

Counts back correctly and says 5, 4, 3 out loud or on fingers and thinks answer is 3

Counts up from the smallest to the largest number out loud, says 3, 4, 5 or on fingers and thinks answer is 3

Just knows it

Additional observations:

8. 9-6

Doesn't know, guesses

Counts back incorrectly and says 9, 8, ..., 4 counting out loud or using fingers and thinks answer is 4

Counts back correctly and says 8, 7, ..., 3 counting out loud or using fingers, and answers 3

Counts up from the smallest to the largest number. Says 7, 8, 9 counting out loud or using fingers and answers 3

Uses a known fact to reason a new fact. Says I know 10 - 6 = 4, so 9 - 4 must be 3

Just knows it

Additional observations:

9. 14-7

Doesn't know, guesses

Counts back incorrectly and says 14, 13, .... , 8 out loud or on fingers and thinks answer is 8

Counts back correctly, says 13, 12, ..... , 7 out loud or on fingers and answers 7

Counts up from smallest number to largest number, says 8, 9,....,14 and answers 7

Imagines the column subtraction, answers 7

Uses a doubles strategy: I know double 7, or 7 plus 7 = 14 so take one 7 away and the other is left over, the answer is 7

Subtracts using 10 as "stepping stone" and splits 7 in 4 and 3, then subtracts 14-4=10 and 10-3=7

Just knows it

Additional observations:

10. 100-27

Doesn't know or guesses

Attempts to count back by ones but gets stuck.

Counts back correctly by tens and ones separately: 100-90-80-79-78-77....73

Imagines the column subtraction with regrouping mentally, answers 73

Separates tens and ones: 100-20=80 and 80-7=73

Uses counting up to find the difference: 27 to 30 is 3 more, 30 to 100 is 70 more together 7+3 are 73

Additional observations:

11. 745-98

Doesn't know it or guesses

Starts counting back by ones

Starts counting back by tens

Can't do it mentally and needs to write the column algorithm, answers 747

Imagines column algorithm with regrouping mentally, answers 747

Uses place value strategy and separates tens and ones: 745-90=655 and 655-8=647

Uses counting up to find the difference: 98 to 100 is 2 more, 100 is 700 is 600, 700-745 is 45 more together 2+600+45 is 647

Uses benchmark 100 for 98: so 745-100=645, then adds back the 2: 645+2=647

Uses a numberline concept to find the difference between 2 numbers; 98 to 100 = 2, 100 to 700 = 600, 600-645 = 45 so total distance on number line is 2+100+15=647

Additional observations:

12. What is the difference between 248 and 365?

Doesn't know it, guesses

Can't do it mentally and needs to write column algorithm with 248 on top

Can't do it mentally and needs to write column algorithm with 365 on top, but subtracts 5 from 8 because you can't subtract 8 from 5

Can't do it mentally and needs to write column algorithm with 365 on top and subtracts correctly: 117

Imagines the column algorithm mentally and says 117

Counts up from smallest number: +2=250, +100=350, +10=360, +5=365, the difference is 2+100+10+5=117

Uses benchmarks 250 for 248 and 360 for 365 and says that difference = 110, then works in the compensations for the actual numbers: 248 is 2 less than 250 so add 2 and 365 is 5 more then 360 so add 5: the difference is 110+2+5=117

Uses a numberline concept to find the difference between 2 numbers; 250 to 350=100 248 to 250 = 2 and 350 to 365=15, total distance on number line is 2+100+15=117

Additional observations:

Category: Uncategorized

MARS Addition | Subtraction (Copy)