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Hello, everyone.

This lesson is on addition of directed numbers.

Hello? I'm still around.

We can represent directed numbers using counters.

These examples, the yellow counters represent positive numbers, and the red counters represent negative numbers.

What is the value of the first example? The value of the first example is 0.

When we have 1 positive an 1 negative, that value equal to 0.

We can call these a zero pair.

How many zero pairs do you see in the second example? There are 2 but there is an extra positive counter.

The value of the second example is 1.

In the last example, I have 3 positive counters and 4 negative counters.

What is the total value of this set of counters? It is -1.

If we were to pair up our positive and negative counters, we would find that there are 3 zero pairs and 1 extra negative counter.

Using counters, let's calculate 3 plus 4.

Here, I have 3 plus 4.

All those counts counters are positive.

My solution is 7.

Now, let's calculate 3 plus -4.

Altogether, I have 7 negative counters.

Our solution is -7.

Using counters, let's calculate 3 plus -4.

Here, I have 3 positive counters.

Here, I have 4 negative counters.

We can align these counters like so.

Remember, each negative and positive counter equal 0.

That just leaves me with an answer of -1.

Let's have a look at this example.

Calculate -3 plus 4.

I have 3 negative counters and 4 positive counters.

Pair up the negative and positive counters.

That leaves me with an answer of 1.

If you don't have any counters, you can just make a drawing.

Here are some questions for you to try.

Pause the video and return to look at your answers.

Here are the solutions to question number one.

One useful thing you can do, if you look at question one b, instead of writing 9 plus -3, where the negative and positive sign sit together, we could rewrite that as just being 9 subtract 3.

Far easier to get your head around.

Work out the missing number.

7 plus a missing number is equal to -2.

Let's use counters to help us with this problem.

7 positive counters is equal to 2 counters.

That means I can pair up my positive counters with negative counters.

How many negative counters do I have altogether? I have 9, 7 plus -9 is equal to -2.

Here are some questions for you to try.

Pause the video and when you finish, return to look at your answers.

Here are the solutions to question number two.

You could write two b to look like this.

Hopefully, this version is simpler.

Here are some questions for you to try.

Pause the video and when you finish, return to look at your answers.

Here are the solutions to question number three.

Now, if you've never seen a part whole model before, it's just a visual way of showing an equation.

We can use counters to help us with algebra problems. Simplify 5x plus -7x by collecting like terms. Here I have 5X, and here I have -7x.

If I find my zero pairs, I see that I have -2 counters remaining.

Those counters represent the value of x.

So 5x plus -7x is equal to -2x.

Pause video here and return to look at your answers.

Here's the solutions to question four and five.

In question four, a, b and c, you need to collect all the like terms together to make it far easier problem.