Lesson

## Ideas

In this section you will practice the  addition strategies  we've looked at:

• breaking up numbers and adding the parts

• bridging, or making up to 10

• jumping, using a number line

We also looked at how to use a  vertical algorithm  , writing the numbers down the page and adding them by place value. This strategy can also be really useful if we need to  trade, or regroup  .

### Examples

#### Example 1

Use the number line, to help you find the value of 43 + 12.

Worked Solution
Create a strategy

Start with the bigger number and count to the right as many times as the smaller number.

Apply the idea

Locate where 43 is.

Jump 12 units to the right from 43. 12 is made up of 1 tens and 2 units. So we can jump to the right by 1 tens and then 2 units.

We end up at the number 55. So: 43 + 12 = 55

#### Example 2

Use a strategy to find the sum of 49 + 16

Worked Solution
Create a strategy

We will use the compensation strategy.

Apply the idea

Plot the larger number, 49 on the number line.

We can see that 16 is 4 below 20 on the number line below.

Using the compensation strategy to add 16 to 49 we can add 20 and then take away 4.

So now we can jump to right by 2 tens from 49 to get 49 + 20=69.

And now we subtract 4 by jumping to the left by 4 to get 69 - 4=65.

49 + 16 = 65

#### Example 3

Find the value of 219 + 29.

Worked Solution
Create a strategy

Apply the idea

Write it in a vertical algorithm.\begin{array}{c} & & &2 &1 &9 \\ &+ & & &2 &9 \\ \hline & \\ \hline \end{array}

Add the units value first. So 9 + 9 = 18. Bring down the 8 and carry on 1 to the tens column.\begin{array}{c} & & &2 &\text{}^1 1 &9 \\ &+ & & &2 &9 \\ \hline & & & & &8 \\ \hline \end{array}

So for the tens place we have 1 + 1 + 2 = 4: \begin{array}{c} & & &2 &\text{}^1 1 &9 \\ &+ & & &2 &9 \\ \hline & & & &4 &8 \\ \hline \end{array}

Hundreds place: 2 + 0 = 2

\begin{array}{c} & & &2 &\text{}^1 1 &9 \\ &+ & & &2 &9 \\ \hline & & &2 &4 &8 \\ \hline \end{array}

So 219 + 29 = 248.

Idea summary

When our numbers get bigger, adding down our page is really useful. It helps us keep our digits lined up, and makes it easier if we have to do some regrouping.

### Outcomes

#### MA2-5NA

uses mental and written strategies for addition and subtraction involving two-, three-, four and five-digit numbers