Lesson video

Oh hello, everyone.

Today's lesson is about subtracting directed numbers.

Hello, I'm Mr. Lund.

And we're going to use counters to help us subtract directed numbers.

In the first example, I have two positive yellow counters, one negative red counter.

One positive and one negative counter are a zero pair.

That leaves me with just one positive counter.

The value of this set of counters is one.

In the next example, there are two zero pairs, but I have one extra positive that gives me a value of one.

And in the last example, I have four positive counters, three negative counters, that also gives me a total value of one.

Remember, when using counters to represent directed numbers, we are going to use a yellow as a positive counter, and a red as a negative counter.

Placed together, these equals zero.

They are a zero pair.

Calculate three, subtract four.

We're going to use our knowledge of zero pairs to help us work out this sum using counters.

Let's start with three.

We want to subtract four counters.

That seems impossible if we only have three counters.

So let's introduce a zero pair.

The value is still positive three.

But by introducing a zero pair, we can now subtract four positive counters.

By doing that, we are left with an answer of negative one.

Calculate negative three subtract four.

Let's start with negative three counters.

I want to subtract four positive counters, but I can't do that.

Currently I have no positive counters.

However, if I add one, two, three, four, lots of zero pairs, the value of the counters is still negative three.

But now I can subtract four away, leaving me with an answer of negative seven.

So here's where it gets interesting.

Let's calculate three, subtract negative four.

We're going to use counters.

Three positive counters, but I need negative four counters.

So let's use zero pairs.

There we go.

I've created negative four counters.

Remember the value of this set of counters is equal to three still.

But I'm going to subtract negative four counters.

Look what happens.

There see, I end up with an answer of positive seven.

Calculate negative three, subtract negative four.

This time let's start with negative three counters.

We need to subtract negative four counters.

So I need one more negative counter.

There we go.

We can use a zero pairs.

subtracting negative four away, gives me an answer of positive one.

If you don't have counters, you can draw your own diagrams. Pause video here.

Once you finished, come back and view your solutions.

Here are the solutions to question number one.

counters are not the only way of using.

Let's start it.

Here are the solutions to question number one.

counters are not the only way of thinking about directed numbers.

You can also use number lines.

Number lines are a really useful tool in this topic.

You can use them horizontally or vertically.

I quite like the vertical ones.

So how can we work out the missing number here? Negative five, subtract a number is equal to three.

Here's negative five is equal to three.

If I use zero pairs, then I can see there are now eight negative counters.

Negative five, subtract negative eight is equal to three.

If you don't have counters, just use diagrams to help you.

Pause the video here and return to look at your answers.

Here are the solutions for question number two.

You could think about when you see two negative signs sat next to each other, changing it for a positive sign.

In question 2 , blank, negative, negative three, equals eight, can be replaced with blank plus three equals eight.

I think you'll find the one along the bottom in terms of solving looks a lot easier, and probably saves you a lot of brain ache.

Pause the video here and return to look at your answers.

Here's the solutions to question three.

You may never have seen a whole part model before.

It's basically a way of visually showing an equation.

So if you didn't really know what to do there, think of it as a visual way of showing an equation.

We can use counters to help us think about collecting like terms in algebra.

Here I have five X counters, all positive.

I want to subtract negative seven X counters.

So let's use zero pairs again.

There we go.

Let's subtract negative seven X counters away.

That leaves us with an answer of 12 X counters.

Okay, some more questions for you to try, pause the video and return to look at the solutions.

Here are the solutions to questions four and five.

I really like question 4.

sometimes when we have to do sums that involve zeros, it confuses us a little bit.

But just follow the same steps as you have previously.

Well done for getting this far.

And that shows that you're really understanding directed numbers.