Lesson video

Hello everybody.

Mrs. Popel here, with your maths learning today.

I can't wait to learn lots of new things and hopefully have lots of fun.

So let's get started.

Today's lesson is called Halve Numbers and explain what halving means and it comes from the unit addition and subtraction facts within 10.

By the end of this lesson, you should be able to halve numbers and explain what halving means.

So let's get started.

Let's have a look at this lesson's, key words, half, halving, doubling and inverse.

You may recognise some of these words from any learning that you've done before.

Let's practise saying these words before we start to use them.

My turn, half your turn.

My turn halving your turn.

My turn, doubling your turn.

And my turn, inverse.

Your turn.

Well done.

Let's have a look at our lesson outline.

You can see that our lesson has two parts.

The first part, we are going to halve even numbers within 10.

And the second part of the lesson we are going to use our halving to solve number problems. In this lesson, you are going to meet Sam and Jacob.

They're going to help us with our learning today.

Sam creates a seesaw representation.

She puts three cubes on the left.

The seesaw has to balance.

So how many cubes will she need on the other side of her seesaw? Hmm, I wonder if something is balanced.

It means that it's equal and equal means the same.

Well done if you said three.

If there are three cubes on the left, then that means there must be three cubes on the right also to make the seesaw balance.

Sam and Jacob now discuss this idea using a bar model.

There are three cubes on the left.

If the parts are equal, there must also be three cubes on the right.

Sam places the other three cubes, so that means there are six cubes in total.

Sam then writes an equation to match her bar model, three plus three is equal to six, or Sam says we can say double three is six.

Jacob sees this bar model in a different way.

He writes the equation six, subtract three is equal to three.

Is he correct? Jacob says that he has used the inverse.

Subtraction is the inverse of addition so it can undo the addition.

If we start with the whole and subtract the three that Sam added, we can undo the addition.

So six, subtract that three that Sam has added it leaves us with the three that we started with.

Well done Jacob, a really good spot there.

We can think of subtraction as the inverse of addition.

Subtraction can undo the addition.

So to form the inverse, Jacob started with the whole and subtracted one of the parts which left him with the other parts.

Sam has explained that when we are adding two equal add-ins, we are actually doubling double three is equal to six.

Jacob then wonders if subtraction is the inverse of addition.

What is the inverse of doubling? So in the first one we were adding those two equal parts, but in the second one we were subtracting one of those equal parts.

We can call this halving.

When we subtract an equal part from its double, we call it halving, half of six is equal to three.

Halving is the inverse of doubling.

Halving can undo the doubling.

Let's practise that.

My turn, halving is the inverse of doubling.

Your turn.

My turn, halving can undo doubling.

Your turn.

Let's remember that because that's really gonna help us with the rest of our learning.

Jacob now uses his bar model to practise forming the inverse doubling and halving facts.

He writes the whole as eight.

So what are the two missing parts? We know that double four is eight, so the parts must both be four.

Four plus four is equal to eight or double four is equal to eight.

Jacob now knows that he can subtract one of those equal parts from the double and explain it as eight subtract four is equal to four.

Is there another way that we could describe this? Jacob explains that when we subtract an equal part from its double, we call this halving.

So we could also say half of eight is equal to four, double four is equal to eight.

So Jacob now knows that the inverse would be half, half of eight is equal to four.

Let's have a practise of this.

Sam and Jacob have completed a bar model to show a doubling fact.

What is the doubling fact that's being shown and can you then tell me what the halving fact would also be? Sam has noticed that we've added together one and one and two is the whole, so she can see that double one is two.

Jacob looks for the haling fact.

He knows that the hole is two.

When he halves a number, he subtracts one of the equal parts from its double.

So two, subtract one is equal to one or we can also explain this as half of two is equal to one.

Well done if you've got those correct.

Let's explore halving a little bit more using our 10 frame.

When we half an even number, we subtract one of the equal parts from its double.

So let's start with two.

Two is my whole, let's subtract one of those equal parts.

We can see that two is made up from one blue counter and one red counter.

So let's subtract one of those red counters.

How many does that leave me with? One, well done.

So we know that two subtract one is equal to one or we can say half of two is one.

Let's have a look at another one.

This time my hole is four.

How many counters am I going to subtract and how many will I be left with? I can see that four is made up of two blue counters and two red counters.

So let's subtract two of those red counters and it leaves us with two.

The other equal part.

We can say four subtract two is equal to two or we can say half of four is two.

The next one our whole is six.

I can see that this 10 frame has been made up of three and three.

So let's subtract the three that leads us with three.

So we can say that six subtract three is equal to three or we can say half of six is three.

Have a look at this next one.

What would be our equation and what halving fact can I see? Eight, subtract four is equal to four.

So I know that half of eight is equal to four.

And finally 10 is our whole, we take away the five.

It leaves that other equal part of five.

So we know that half of 10 is equal to five.

Let's practise that learning.

So what would be half of the amount shown on this 10 frame? How many counters can we see as our whole and what would half of them be? Remember halving is subtracting an equal part from its double.

There are four counters in total and we can see this as two and two.

So we know that half of four will be two.

Okay, over to your first task then you are going to need a partner but don't worry if you haven't got a partner, you can still play this on your own.

You are also going to need a set of halving fact cards.

You're going to turn over an expression and if the difference is correct for that expression you shout snap.

If you shout snap first, you'll then explain the fact that you can see.

You might explain this as 10 subtract five is equal to five or you may want to explain this as half of 10 is five.

Once you've explained it, you are the winner of that pair.

The winner of the game is the person with the most pairs at the end of the game.

Pause this video and have a go at this activity.

Welcome back.

Your game might have gone a little bit like this.

Two subtract one is equal to eight.

No, we know that's not correct.

10 subtract five is equal to five.

Snap.

Well done, Sam.

Now explain it.

Half of 10 is five, correct? That pair is yours.

Let's keep going.

Come on Jacob.

Four subtract two is equal to six, no.

Eight subtract four is equal to four.

Snap.

Well done, Jacob, what does your fact show? Half of eight is four.

Well done Jacob, that pair is yours.

Let's move on to the second part of our learning now.

Using halving to solve number problems. Jacob is using a bar model to represent this halving problem.

Jacob has six cupcakes.

Sam has half the amount of cupcakes that Jacob has.

So how many cupcakes does Sam have? So how are we gonna work out how many cupcakes Sam has and what will our bar model look like? Hmm, let's have a look.

We know that Jacob has six cupcakes, so we can see this as our whole.

Jacob knows that double three is six.

So both of our parts must be equal to three.

That means that three plus three is equal to six.

Now we've completed our bar model.

We can see halving is the inverse of doubling.

So we are going to subtract one of those equal parts from that double and that will leave us with three six.

Subtract three is equal to three.

Half of six is three.

So Sam must have three cupcakes.

Well done.

If you've got that answer correct.

Sam now gives Jacob two missing number problems to solve.

She's given him a doubling equation and a halving equation.

So can we help Jacob complete them? Let's have a look at the 10 frame.

We can see that there are six counters in total, three blue counters and three red counters.

So we can see this as double three or three plus three is equal to six.

So we know that three must be the missing number in that equation.

If we know that three plus three is equal to six, we can now use the inverse to undo that addition.

So six, subtract three will leave us with three.

Well done.

We know that double three is six and that halving is the inverse of doubling.

So half of six must be three.

Now let's have a go at a word problem.

We're going to use our part-part whole model to help us.

Jacob had eight biscuits, he gave four of them to his teacher.

How many biscuits does he have now? What information do we already know? We know that Jacob had eight biscuits altogether, so we know that eight must be our whole.

He gave four of them to his teacher.

So four must be a part.

Four plus something is equal to eight.

So what would be our missing part? Do we know a doubling or a halving fact that would help us to solve this? Yes, Sam, well done.

Double four is equal to eight.

So we know that four must be the missing part.

Four plus four is equal to eight.

Sam has explained that she could also have used her subtraction to find the missing part.

Eight subtract four would be equal to four and we could describe this as half of eight is equal to four over to you.

Here's three for you to have a go at, pause this video and try and find what the missing parts of A, B and C are.

Once you've had a go, come on back to see how you've got on.

Okay, let's have a look.

So I can see that two is our whole and one is a part.

If I subtract one from two, I know that the missing part is one.

Let's have a look at this.

Four is my whole and two is a part.

I can see on this bar model that both of my parts are equal.

So that must mean that two is the missing part from this side.

And finally I can see that my hole is 10.

I know that 10 subtract five will equal five or half of 10 is five.

So the missing part must be five.

Well done if you've got those correct.

Jacob has remembered that when we subtract one of the equal parts from the double, we are halving.

So in A, we can say that half of two is one.

One was our missing part.

In B, half of four is two.

So two is our missing part and in C, half of 10 is five.

So five was our missing part.

Okay, time for you to show off all you've learned today in task B.

So task B part one, you have got two word problems to have a go at.

You might want to use part-part-whole model to help you to solve this.

A Jacob had 10 cards.

He gave half of them to Sam to play with.

How many cards did Sam get? And B, Sam's mom said she could only eat half of her sweets.

Sam had six sweets, so how many did she get to eat? Once you've had a go at those.

Task two is to find some missing numbers to complete the equations.

You can see that you've got some equations, you have got some facts and you've also got part-part-whole models to find the missing parts.

Have a go at both parts of that task and come on back to see how you've got on.

Welcome back, well done for having a go at those tasks.

Now let's see how you did.

So part one, question A, Jacob had 10 cards.

He gave half to Sam to play a game.

So how many cards did some get? We know that Jacob had 10 cards.

So 10 is our whole.

Jacob is using a part-part-whole model here to help him.

We need to subtract an equal part from the whole.

We know that five plus five is equal to 10.

If we subtract five from our whole, it will give us five.

So we know that half of 10 is five.

Sam will get five of Jacob's cards.

Well done if you got that one correct.

B, Sam's mom said she could only eat half of her sweets.

She has six sweets, so how many did she get to eat? Again, we know that six is our whole, we need to subtract an equal part from the whole, which is? Three, because we know that three plus three is equal to six.

If we subtract that equal part from the whole, that will leave us with three.

So half of six is three.

Sam, ate three of her sweets.

Let's have a look at these equations.

Two subtract one is equal to one.

10 subtract five or half of five is equal to five.

Eight subtract four is equal to four.

Now D, does that change any of our working out? No, it does not.

Six subtract three is equal to three.

Now let's look at these facts.

Let's see how quick we can recall these.

Half of six is three, half of eight is four, half of 10 is five, and half of four is two.

Well done.

Let's have a look at I, then.

Ooh, eight is my whole, and I can see that two equal parts add together to make my whole.

We know that half of eight is four, so both parts must be four.

Four plus four is equal to eight.

Well done.

And Jay, we can see that six is our whole and three is a part.

So if we subtract that equal part from our whole, it will leave us with three.

Well done for completing those problems. You've done a great job with those tasks today.

Let's have a look at what we've learned in this lesson.

Halving is the inverse of doubling.

Halving can be used to subtract a number from its double.

Thank you for joining me.

I've really enjoyed our maths learning today and hope you'll come on back to join me again soon.

Goodbye.