Addition & Subtraction Strategies
1st Grade:
Addition Strategies
1. Draw all
At the beginning of first grade, it is appropriate for students to draw every part of the problem.
I saw 7 squirrels in a tree. Then 5 more ran up the tree. How many squirrels were in the tree?
12
*Note: If it is a problem about squirrels, they should not draw squirrels, because that takes too long! They may draw circles, squares, dots, or tally marks.
The more students label and organize their work, the better.
7 5
in the tree first ran up
12
When students are ready, we ask them to write one or more equations that go with the story problem:
7+5=12 12-7=5
5+7=12 12-5=7
So an excellent story problem at the beginning of first grade would look like this:
7 5
in the tree first ran up
7+5=12 12-7=5
5+7=12 12-5=7
2. Write about what you did
Some first graders, especially those whose writing skills are solid, may not draw pictures and may instead write about how they solved a problem. They do not HAVE to draw a picture; writing about what they did is fine.
3. Count on
In first grade, we work a lot on “counting on” at the beginning of the year. Some first graders, at the beginning of the year, need to “count all,” which means that if they are adding 7 + 5, they count like this:
“1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.”
Counting on[(] means they remember the first number (keep it in their mind) and count up from there, like this:
8, 9, 10, 11, 12.
To show how they counted on, first graders usually write the numbers they said on their paper, then write some equations for the problem and circle and label their answer:
7 8 9 10 11 12
12 squirrels 7+5=12 12-7=5
5+7=12 12-5=7
Subtraction Strategies
1. Draw all and cross off
There were 13 birds in the garden. 6 flew away. How many birds were still in the garden?
13 – 6 = 7
1 2 3 4 5 6 7 8 9 10 11 12 13 6 + 7 = 13
2. Count backwards
Counting backwards is the equivalent to counting on when adding: you save the first number in your mind and then count down from there.
12, 11, 10, 9, 8, 7
4. Use what you know about numbers
Often this involves using a basic fact the student knows by heart, such as Make-Ten Facts or Doubles. For example, to solve 8 + 5, a student might write:
8 + 5
2 + 3
10
13
Or, to solve 24 + 27, a student might write:
20 + 20 = 40 7 + 4 = 11
40 + 11 = 51
Other examples of this kind of mathematical thinking are:
To solve 25 - 7
I know that 25 – 5 = 20, and 20 – 2 = 18.
OR
I know that 27 – 7 = 20 and 5 is 2 less than 7 so I need to take away 2 more so it will be 18.
We expect by the end of first grade that many students are solving problems using methods like these. Some students will not be able to do this until second grade because their understanding of how numbers work is not strong enough. However, even for these students, we expect that they use these efficient strategies based on math facts for simpler problems.
Third Grade:
The third grade doesn’t teach new strategies for their students to use while adding and subtracting. The strategies that students use for subtraction are regrouping (borrowing), adding on, and separating groups of numbers
Adding on:
14-6=?
Students would count to 14 and find out how many that is or think about what they have to add to 6 to get 14. This is their answer.
Separating Groups of Numbers: This strategy is similar to the end-of-first grade strategy of using what you know about numbers. They break apart the subtrahend and subtract each part one at a time from the minuend.
20-13=20-3-10
or 71-54=(71-4)-50
[(]* Counting on: When adding 2 numbers, being able to save the first total in your mind and count on from there. See description above.