# Mental Strategies

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Addition and Subtraction of 2, 3 and 4 digit numbers

Addition is when we join numbers together to get one number. The sign for addition is +

Look at this number sentence:7 + 6 = 13

In this example we add seven and six to get one number which is 13. This number is called the sum or the total.

Subtraction is when we take one number away from another number. The sign for subtraction is –

Look at this number sentence: 9 – 2 = 7

In this example we take two away from nine and the answer is seven.

We can add and subtract big and small numbers. Sometimes we can use mental strategies (in your head) to work out answers and sometimes we need to use written methods when the question is a bit tricky. It is important that you are able to solve addition and subtraction problems, whether you work them out mentally or use a written form. Let’s have a look at some mental strategies.

First let’s look at the Jump Strategy.

The jump strategy lets you add or subtract the second number in stages.

Example 1:   26 + 45

We are going to add 45 in two stages. First we will add 40 then we will add 5.
Step 1:        56 + 60 = 116
Step 2:        116 + 3 = 119

Example 2:   56 + 63

We are going to add 56 in two stages. First we will add 50 then we will add 3.
Step 1:        56 + 60 = 116
Step 2:        116 + 3 = 119

Let’s have a look at how we can use the jump strategy to help us subtract.

Example 3:   56 – 27

We are going to take away 27 in two stages.

Step 1:            56 - 20 = 36    (First change 27 to 20 as it is easier to subtract tens)
Step 2:            36 - 7 = 29      (Next, we will take away 7. the units in 27.)

Example 3:   87 – 14

Step 1:          First we will take away 10 then we will take away 4.
87 – 10 = 77
Step 2:          77 – 4 = 69

Now let’s look at the Split Strategy.

The split strategy adds or subtracts numbers by splitting them into their parts and treats each place value column separately.

Here is an example of using the split strategy for addition:

Example 1:     35 + 47

Step 1:            30 + 5 + 40 + 7 (split the numbers using expanded notation))
Step 2:            30 +40 = 70
Step 3:            5 +7 = 12
Step 4:            70 + 12 = 82

Let’s look at one more example for addition.

Example 2:     89 + 36

Step 1:           80 + 9 + 30 + 6
Step 2:           80 + 30 = 110
Step 3:           9 + 6 = 15
Step 4:           110 + 15 = 125

Now let’s look at an example of how we can use the split strategy for subtraction.

Example 3:     76 - 34

Step 1)
Step 2:            70 - 30 = 40
Step 3:             6 - 4 = 2

Example 4:     45 – 21

Step 1:     40 + 5 – 20 + 1
Step 2:     40 – 20 = 20
Step 3:      5 – 1 = 4

Now let’s look at the Compensation Strategy.

This method requires you to add too much and then take away the difference.
Here’s an example of using the compensation strategy.

Example 1:     78 + 36

Step 1: Round 36 to the next multiple of 10 which is 40 (36 + 4 = 40)
Step 2: 78 + 40 =118
Step 3: 118 – 4 += 114 (We added 4 to 36 to make 40, so now we must take the 4 away to get the correct answer.

Example 2:     92 + 49

Step 1: Round 49 to the next multiple of 10 which is 50 (49 + 1 = 50)
Step 2: 92 + 50 = 142
Step 3: 142 – 1 = 141 (We added 1 to 49 to make 50 so now we need to take 1 away to get the correct answer.)

Let’s look at some examples of using the compensation method to subtract.

Example 3:     67 – 37

Step 1: Round 37 to the next multiple of 10 which is 40 (37 + 3 = 40)
Step 2: 67 – 40 = 27
Step 3: 27 + 3 = 30 (We added 3 to 37 to make 40 but because we are completing a subtraction sentence we need to add three to get the correct answer.)

Example 4:     56 – 32

Step 1: Round 32 to the next multiple of 10 which is 40 (32 + 8 = 40)
Step 2: 56 – 40 = 16
Step 3: 16 + 8 = 24 (We added 8 to 32 to make 40 so now we need to add 8 to get the correct answer.)

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