Subtraction Strategy Notebook
2nd Grade
MCC2.OA.2, MCC2.NBT.5, MCC2.NBT.7, and MCC2.NBT.8
This strategy notebook is designed to be a reference for teachers when they are teaching the strategy standards in whole group.
Sketching (Important)
This is a great strategy to being with. It allows students to draw base ten blocks to help them solve the problem. It helps them understanding regrouping as well.
Example: 64 – 28
1. I start with 64.
2. Then I have to take away 28 so I begin with taking 8 ones away. Oh no! I don’t have eight ones to take away? I will turn one ten into ten ones, then I can take eight away..
3. That leaves me with 5 tens and 6 ones. But I’m not done! I still have to take 2 tens away!
4. That leaves me with 36.
Adding Up (Important)
(Standard: 2.OA.2, 2.NBT.5, 2.NBT.7, 2.NBT.8)
In this strategy, students build on their strength with addition by adding up from the number being subtracted (subtrahend) to the whole (minuend). The larger the jumps, the more efficient the strategy will be. When students think about how much more they need to add up to reach the whole, they can build upon their knowledge of basic facts, doubles, making ten, and counting on.
84 - 5684 - 56
56 + 4 = 60
60 + 20 = 80
80 + 4 = 84
4 + 20 + 4 = 28 / This student used an open number line to record his thinking as he added up to get to 84.
This student first added up to make a ten, next added 2 groups of ten, and then 4 more to get to 84.
The student found that the total difference was 28.
Other examples of adding up:
17 – 9 Strategy 1:
This student used an open number line to record his thinking as he added up by counting each number to 17.
Strategy 2: 9 + 1 = 10 This student added up to get to 10 and
10 + 7 = 17 then added 7 more to get to 17.
1 + 7 = 8 The student found that the total
difference was 8.
Strategy 3: 9 + 8 = 17 This student used a known fact and
efficiently added up to the whole.
30 – 12 Strategy 1:
This student used an open number line as he added 8 to 20 and then added 10 more to get to 30.
Strategy 2: 12 + 3 = 15 This student added up to get to 15
15 + 15 = 30 and then used doubles to get 30.
3 + 15 = 18 The student found that the total
difference was 18.
64 – 25 Strategy 1:
This student used an open number line and added 5 to get to the nearest 10, then added 30 to get to 60, and finally added 4 to get to 64. The difference is 39.
Strategy 2: This student used a 99
chart.
25 + 10 = 35
35 + 10 = 45
45 + 10 = 55
55 + 10 = 65
65 – 1 = 64
10 + 10 + 10 +10 – 1 = 39
The difference is 39.
Strategy 3: 25 + 5 = 30 This student added 5 to get to the
30 + 30 = 60 nearest 10, then used doubles to get to
60 + 4 = 64 60, and finally added 4 to get to 64.
5 + 30 + 4 = 39 The difference is 39.
Strategy 4: 25 + 25 = 50 This student used doubles to get to 50,
50 + 10 = 60 then added 10 to get to 60, and finally
60 + 4 = 64 added 4 to get to 64.
25 + 10 + 4 = 39 The difference is 39.
100 – 24 Strategy 1: This student used a
hundred chart.
24 + 6 = 30
30 + 10 = 40
40 + 10 = 50
50 + 10 = 60
60 + 10 = 70
70 + 10 = 80
80 + 10 = 90
90 + 10 = 100
The student found the difference to be 76.
6 + 10 + 10 + 10 + 10 + 10 + 10 + 10 = 76
Strategy 2:
This student used an open number line to add up to 30 and then add 70 more to get to 100.
Strategy 3: 24 + 6 = 30 This student added up to get to the
30 + 20 = 50 nearest 10, then added 20 to get to
50 + 50 = 100 the landmark number 50, and then used
doubles to get to 100.
6 + 20 + 50 = 76 The total difference is 76.
Strategy 4: 24 + 70 = 94 This student added the friendly number
94 + 6 = 100 70 and then added 6 more.
70 + 6 =76 The total difference is 76.
Strategy 4: 24 + 1 = 25 This student added 1 to get to the
25 + 75 = 100 landmark number 25 and then added
75 to get to 100.
1 + 75 = 76 The total difference is 76.
Removal
(Standard: 2.OA.2, 2.NBT.5, 2.NBT.7, 2.NBT.8)
In this strategy, students start with the whole and remove the subtrahend, the number being subtracted, in parts. To effectively use this strategy, students must be able to easily decompose numbers into easy-to-remove parts. Some students will need to begin by counting back by ones to get to the subtrahend. Others will be able to decompose the subtrahend and effectively remove it in pieces.
95 – 3295 – (10 + 10 + 10 + 2)
95 – 32
95 – (30 + 2)
95 – 30 = 65
65 – 2 = 63
95 – 32
(10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 1 + 1 + 1 + 1 + 1)
(10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 1 + 1 + 1 + 1 + 1)
10 + 10 + 10 + 10 + 10 + 10 + 1 + 1 + 1 = 63 / This student decomposed the subtrahend into three tens and two ones. An open number line was then used to show how each part was removed.
This student decomposed the subtrahend into place-value components and then removed them.
This student broke 95 into nine tens and five ones.
The student then marked out three tens and two ones for a total of 32.
The student then calculated the remaining numbers for a total of 63.
Examples of removal where the subtrahend, the number that is to be subtracted, can be removed in parts that are the same as the digit in the minuend, the number that is to be subtracted from:
13 – 7 Strategy 1: This student used an open number line
to remove the 3 and then the 4.
Strategy 2: 13 – (3 + 4) This student decomposed the 7 into parts
13 – 3 = 10 that could easily be removed.
10 – 4 = 6
34 – 6 Strategy 1: This student used an open number line
to remove the 4 and then 2 more.
Strategy 2: 34 – (4 + 2) This student decomposed the 6 into parts
34 – 4 = 30 that could easily be removed.
30 – 2 = 28
57 – 37 Strategy 1: This student removed 7 to
and then removed 30.
Strategy 2: This student used an open
number line to remove 7 and
then remove 3 groups of ten.
Strategy 3: 57 – (30 + 7) This student decomposed 37 into
57 – 7 = 50 parts that could easily be
50 – 30 = 20 removed.
225 – 75 Strategy 1:
This student used an open number line to remove 25 to
get to the landmark number 200 and then the student
removed 5 groups of ten.
Strategy 2: 225 – (25 + 25 + 2 5) This student decomposed 75 into
225 – 25 = 200 3 groups of 25 and then removed
200 – 25 = 175 each group.
175 – 25 = 150
Strategy 3: 225 – (25 + 50) This student decomposed the 75 into
225 – 25 = 200 25and 50, removed the 25 to get to 200 – 50 = 150 200, and then removed the 50.
Examples of removal using place-value chunks:
20 – 13 Strategy 1: This student decomposed 13 and then
removed it in chunks.
Strategy 2: 20 – (10 + 3) This student decomposed 13 into its
20 – 10 = 10 place value and then removed it in
10 – 3 = 7 chunks.
58 – 35 Strategy 1: This student removed the 35 in place value chunks.
Strategy 2: This student removed 30
and then removed 5.
Strategy 3: 58 – (30 + 5) This student decomposed the 35
58 – 30 = 28 into its place value and then
28 – 5 = 23 removed it in chunks.
168 – 49 Strategy 1: This student
decomposed 49 and
then removed it in
chunks.
Strategy 2: 168 – (40 + 9) This student broke the 49 into 40
168 – 40 = 128 and 9 and removed the 40. The
128 – 10 = 118 student removed 9 by taking
118 + 1 = 119 away 10 and adding back 1.
Examples of removal using place value chunks and decomposing a single-digit number:
23 - 14 Strategy 1: This student removed the ten
and then removed 3 and 1.
Strategy 2: 23 – (10 + 4) This student broke 14 into a ten and 4
23 – 10 = 13 ones and removed the 10. The student
13 – 3 = 10 then broke the four into a three and
10 – 1 = 9 a one.
41 – 26 Strategy 1: This student removed 2
groups of 10 to make 20 and
then removed 1 and 5 for 6.
Strategy 2: This student used a 99
chart. The student
removed 2 tens and then
removed 1 and 5 for 6.
Strategy 3: 41 – (20 + 6) This student broke 26 into 2 tens
41 – 20 = 21 and 6 ones and removed the 2 tens. 21 – 1 = 20 The student then broke the 6 into a 20 – 5 = 15 one and a five.
365 – 237 Strategy 1:
This student used an open number line to remove 237 in place value chunks. The 7 in the ones place was removed in parts.
Strategy 2: 365 – (200 + 30 + 7) This student removed the 237 in
365 – 100 = 265 place value chunks by removing
265 – 100 = 165 2 groups of 100 and then 165 – 30 = 135 removing 3 groups of 10. Finally, 135 – 5 = 130 the student removed the 7 as a
130 – 2 = 128 group of 5 and 2.
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