Addition and Subtraction Strategies

Mental Math Strategies

Teaching for Mastery of Basic Facts

It is important that most students have mastery of basic facts. It is equally important that they make sense of number combinations as they are learning these facts. Here are some strategies to help with this understanding.

Model adding zero (with younger students) or review it with older students. If a child understands that when you add zero you add nothing, he/she should never get a basic fact with zero wrong. Make sure this understanding is in place.

Adding One (Count up)
Adding one means saying the larger number, then jumping up one number, or counting up one number. This happens every time you add one. It never changes. Never recount the larger number, just say it and count up one.

Example: 6 + 1 = say 6 then 7
44 + 1 = say 44 then 45

Adding Two – Count up Two
Adding two means saying the larger number, then jumping up or counting up twice. Again this is always correct and never changes.

Example: 9 + 2 = say 9 then 10 then 11
45 + 2 say 45 then 46 then 47

Commutative Property:
You also have to teach or review the commutative property. The answer will be the same regardless of the order you add the two numbers. 9 + 2 = 2 + 9 Order doesn’t matter.

The following printable resources can be used to check student understanding of the above strategies. If a child does not get them all right you can check to see which strategy they don’t understand and reteach it.

Adding ten means jumping up ten (think of a hundred’s chart). The ones digit stays the same but the ten’s digit increases by one. Students must understand this. Using a hundreds board to teach this works well to build understanding. Have students actually count up the ten and write down the result. Then affirm with them the pattern and explain why it works every time.

Example: 5 + 10 = 15

10 + 7 = 17
For older students you can relate this to higher numbers:

Example 23 + 10 = 33
48 + 10 = 58

Adding 9 makes sense if students understand adding ten. It sounds more difficult than it actually is.

Remind students of the jump of ten – 5 + 10 = 15. A student would say (in their head) “5 plus 10 = fifteen”
The five and fifteen are naming the same number of ones.

With the nines – a student must count down one in the ones.
A student would say “5 + 9 = fourteen”.
It sounds difficult but once they catch on it is really simple.

Work with lots of examples until the idea is understood:
5 + 10 = fifteen 5 + 9 = fourteen 7 + 10 = 17 7 + 9 = sixteen

This works exactly the same only a child must think 2 less. Using the examples above students would say; 5 + 10 = 15 so 5 +8 = 13, 7 + 10 = 17 so 7 + 8 = 15 (2 less)

Double Numbers
To add double numbers there are a couple of strategies that might help students.

When you add a double you are counting by that number once.
For example: 4 + 4 = think of 4,8 … counting by fours
Practice skip counting by each number in turn:
2-4
3-6
4-8 etc. This gets harder with the higher numbers but skip counting is an important skill for students to have.

Doubles occur everywhere in life.
For example: an egg carton is 6 + 6
two hands are 5 + 5
16 pack of crayons has 8 + 8
two weeks 7 + 7 =
legs on an insect (4 on each side) 4 + 4

Do a variety of activities with double numbers and have students determine and explain which strategies help them remember. Each student should look at each fact and relate to a visual image or counting by strategy that works for them.

Near Doubles
To use the near doubles strategy a student first has to master the doubles. Then, if the double is known, they use that and count up or down one to find the near double.
Example: 4 + 4 = 8 5 + 4 = 9 (count up one)
Or: 4 + 4 = 8 so 4 + 3 = 7 (count down one)

Adding five has a strategy that is helpful but not completely effective as it is a bit tricky. You can decide if it is helpful or not.

To add fives look for the five in both numbers to make a ten then count on the extra digits.

Example: 5 + 7 = (10 + 2) = 12

5 + 8 = 5 + 5 + 3 = 13

Students who can see the five in 8 should have no difficulty. Students who can’t visualize numbers will find this hard. Most students can be taught to do this with some extra work.

The strategies we have discussed should have eliminated the need to memorize most of the facts.