Lesson video

Hello, my name's Mrs. Cornwell and I'm going to be helping you with your learning today.

I'm really looking forward to working with you.

We're going to use lots of the things we already know to help us with some new learning, and I know you're going to do really well.

So let's get started.

Welcome to today's lesson which is called "I can find the missing addend in an equation." And it comes from the unit Additive Structures, Addition and Subtraction.

So in today's lesson we're going to be looking at different strategies we can use to find missing addends in equations.

We're going to be thinking about how we can use our subitizing skills to help us, and also how patterns in numbers can be really useful for our learning as well.

So let's get started.

So our words that will be important in today's lesson, our keywords are sum.

So my turn, sum.

Your turn.

And addend.

My turn, addend.

Your turn.

And equation, my turn.

Equation, your turn.

Well done.

So in the first part of today's lesson, we're going to use subitizing to find a missing addend, so let's see how we're going to do that.

And in this lesson, you will meet Jun and you will also meet Izzy.

They will help us with our learning today.

So let's play a game.

I'm going to show you a whole group and then hide it.

Use your subitizing skills and your number sense to help you find the missing number.

So remember, don't count.

You're not trying to count all of the objects because you won't have time.

Remember, don't count.

See the amount.

Are you ready? How many teddies did you see? So that was very quick, wasn't it? Keep it in your head.

Don't say it yet.

But think about how many teddies you saw there.

So sometimes we can use the way numbers are arranged to help us see and imagine the amount.

And Izzy's saying that the way those teddies are arranged remind her of something.

Wonder if they remind you of anything.

That's right.

They look like the arrangement of the spots on a die, don't they? We can use the parts in the whole to help us see the numbers without counting.

Look at the objects again.

Close your eyes.

Can you still see the teddies in your head? How many are there? And how do you know? Open your eyes.

That's right, there are five teddies there, aren't they? How did you see the teddies? How did you imagine them to help you see that there were five teddies? Izzy's saying, "I saw a four and a one." I saw that too.

I looked and I saw the four round the outside and the one in the middle.

She says, "I also saw a three and a two." You may have seen three at the top and two at the bottom.

So there's lots of different ways you could have seen those five teddies.

Let's use our number sense to help us play a different game.

I will show you the whole group and only hide part of the group.

Try to imagine the whole group to help you find the missing part.

Are you ready? So there's Izzy saying, how many teddies are hiding? And how do you know? That's right.

There were five teddies in the whole group and we can see four.

We know four and one is equal to five, so there must be one teddy hiding.

Right, let's try again.

So this time, how many teddies are hiding? There are five teddies in the whole group.

Hmm, think about how many we can see.

And then think about how you know how many are missing.

We can see two.

Two and three is equal to five, so there must be three teddies hiding.

Well done if you spotted that.

There are five teddies in the whole group again.

How many teddies are hiding? We can see three.

Three and two is equal to five, so there must be two teddies hiding.

We can represent this as an equation.

So there we can see an addition equation there, can't we? Which part of the equation will represent the whole group, do you think? Let's use our stem centres to help us.

Five is the whole, three is a part, and two is apart.

So the addends combine to make the sum, so five must be the sum.

That's right, so there it is.

Three is an addend and the missing part is an addend, so where will we write those? Can write three there, can't you? And then two must be the missing addend that goes in the other part of the equation.

Well done.

And there we can see our two teddies there that were hiding, can't we? This time, it's a little bit different because there are six in the whole group.

Can you see them there, six pebbles? How many are hiding? So think about we've got six and some are hiding behind the block there.

So let's think about how we'll represent this as an equation.

So think about how many are hiding and what we can already see.

We know there are six in the whole group, six is a sum.

That's where that goes.

Which addend can we see? We can see four stones, can't we? Four is part of the whole group.

It is an addend.

So we can write that there, can't we? And then the missing addend is? That's right, it was two, wasn't it? So we can write that in the other part of the equation there.

Well done with that.

That was excellent.

What does the six represent then in our equation there? That's right, the six represents the whole group of stones, doesn't it, that we started with.

What does the four represent? That's right, the four represents the four stones or pebbles that we could see.

And what does the two represent? The two represents the two stones we could not see.

It was the missing addend, wasn't it? Okay, how many are hiding this time? So we still got six in our whole group, haven't we? So use that to help you.

Try and imagine those pebbles.

There are six in the whole group.

Six is the sum.

That's right, so we write that there, don't we? The sum is equal to the two addends.

Which addend can we see? That's right, we can see one stone.

One is part of the whole group.

It is an addend and there it is.

So what's the missing addend, do you think then? That's right, it's five, isn't it? So we know that five plus one is equal to six, so five must be the missing addend.

Well done.

What does each number in this equation represent? The six represents the six stones in the whole group, doesn't it? The one represents the one stone we could see, and the five represents the five stones that were hidden, that we couldn't see, the missing addend.

So here's our group of stones or pebbles again.

We know there are six in the whole group.

Six is the sum.

There, we can see it in the equation there, can't we? Which addend can we see? We can see three pebbles.

Three is part of the whole group.

It is an addend and we can see that in the equation there, can't we? Six is equal to three plus.

And the missing addend is? That's right, it was three, wasn't it? There we can see it in the equation as well there.

So what does each numeral in our equation represent? So the six represents the six stones in the whole group, doesn't it? And then we can see the three represents the three stones we could see.

And this three, the missing addend represents the three stones we could not see.

So now it's time to check your understanding.

Use the pictures to fill in the missing addends.

Okay, so you can see the first picture there has a tens frame.

Look carefully at it.

And then we've hidden a part.

So I'll pause the video, you pause the video while we try and work out how many are missing, how many are hiding.

Okay, and let's see, how many did you think were hiding? That's right, it was two.

We know that on a tens frame, there are 10 counters, and eight plus two is equal to 10.

Okay, let's look at the group of pebbles here now then.

So look carefully at them.

Try and imagine them, and then I'm going to hide some.

Okay, and then pause the video while you try and think what the missing addend is.

Okay, what did you think? Two plus mm is equal to six.

That's right, it was four, wasn't it? Well done.

Okay, and now look at the teddies at the bottom here and try and imagine them, okay, and then we're going to hide some.

So imagine the whole group, and now we've hidden some, haven't we? We can still see three teddies.

Pause the video while you think about what that missing addend is.

And what did you think? Three plus four is equal to seven.

That's right, there were four teddies that were hiding.

Well done, that was excellent.

Jun represents the equation in a part-part-whole model like this.

Okay, so you can see his part-part-whole model, and he's partitioned six into three and another three, and there's a picture of the pebbles to remind us.

"Oops," says Jun, "My part-part-whole model went a bit wrong.

I drew rectangles instead of circles.

This reminds me of something else that shows parts and wholes." I wonder what he could be thinking of.

Izzy thinks it looks like a bar model.

It does look a bit like a bar model, doesn't it? So if you look at here, so there six is the whole, three is a part, and three is a part.

What's the same and what's different then when you look at a part-part-whole model and a bar model? Jun notices that they both show the same whole, don't they, partitioned into the same parts? The parts of the part-part-whole model can be drawn to any size though, so this is the bit that's different.

But the combined parts of the bar model have to be the same length as the whole.

So you can see that the three and the three in the bar model, when you put them together, they're the same length as the six bar, aren't they? And so let's have a look at this bar model.

Do you think that's okay to draw it like that? No, it isn't, is it? Because the two threes there when you combine them are not the same length as the six.

They're shorter, aren't they? What about this one then? No, you're right, that can't be right either.

You can't draw it like that because this time, the two threes when you put them together and combine them are longer than the six, aren't they? And they have to be the same length in a bar model.

Well done if you spotted that.

And there we go, just telling us that that's not right.

So a tens frame has space for 10 counters, doesn't it? How many counters are hidden? Write the missing addend in the equation.

So think about how many we can see there.

Okay, and let's have a look.

So it says five plus something is equal to 10, and we can see five counters, can't we? So what do we think the missing addend is? That's right, we know five plus five is equal to 10, don't we? Explain where we will write it in the bar model, so let's have a think about that then.

So what is the whole amount and where are the parts? So we've got 10 is our whole amount.

That's the sum, isn't it? And then five is the addend we can see, those five red counters.

And the missing addend is five, isn't it? That's right, there they are.

Well done.

Okay, how many counters are hidden this time? So we know there are 10 counters on the tens frame, don't we? And let's write the missing addend in the equation.

What do you think it would be? That's right, we can see seven, can't we, seven counters, and we know that seven plus three would be equal to 10.

Where will we write that on the bar model then? Let's think about where those parts of the equation will go.

So we've got 10 is the whole amount, so that goes there, doesn't it? Because that is equal to the two parts.

And then we've got seven is the part, the addend we can see.

And three is the addend that we could not see, isn't it? There it is.

Well done.

Could the addend have been written anywhere else, do you think? Hmm, so we can see the equation has been swapped round here, hasn't it? We can see it now says mm plus seven is equal to 10.

That's right, it's still three plus seven is equal to 10, isn't it? But we've just written the addends in a different order.

So there is a 10 on the bar model, the whole amount, and then we can see the seven has been put in that part and the three in that part.

But they still combine to make 10 as the whole amount of the sum, don't they? Well done.

The addends can be written in any order depending on the problem that they represent.

So now it's time to check your understanding again.

Find the missing addend in the equation, then complete the bar model.

So pause the video now while you have a look at that and have a try.

So let's see how we got on.

So we can see six counters on the tens frame, can't we? And if we look at our equation, we can see a six there.

And so we know that six plus mm is equal to 10.

That's right, six plus four is equal to 10.

There must be four counters hiding.

So where will we put those in the bar model? Well, we know the whole amount is 10.

We know six is the part that we could see, so four must be the part that we could not see.

Well done.

That was excellent.

And there's our four counters that were hiding.

Izzy says she thinks the missing addend is eight in this equation, and Jun says, "I know that can't be right." How does Jun know, I wonder? What do we think? It says mm plus one is equal to seven, and Izzy thinks it's eight.

Eight plus one is equal to seven.

That's right, the sum is seven, and an addend cannot be greater than the sum.

The addend must be seven or less.

So Izzy wasn't right, was she? So time to check your understanding again now.

Okay, so which numbers could be a missing addend? And which couldn't be a missing addend? So we've got mm plus mm is equal to seven.

So pause the video now while you think about that.

Okay, and let's see how you got on.

The numbers that are greater than seven could not be addends.

So 8, 9, 10, none of those could be addends because the addends cannot be greater than the sum.

So which numbers could be missing addends then? Well, it must be numbers that are seven and below that could combine to make seven.

Well done.

Excellent work.

Now, Jun and Izzy are comparing their shapes now.

They have found another problem where there's a missing addend.

And if you see the scales, we've got 10 there, haven't we? And it's balanced by two shapes, but we don't know what their value is.

So both sides of the scales must be equal.

10 must be balanced by a square and a triangle.

10 is equal to square plus triangle.

What number could the square, numbers could the square and triangle be? I wonder.

So 10 is equal to the square plus the triangle, and we know that zero plus 10 is equal to 10.

So they could be zero and 10, couldn't they? We know one plus nine is equal to 10, so that could be, they could be that as well.

Two plus eight.

They could also be three plus seven, four plus six, five plus five, six plus four, seven plus three, eight plus two, nine plus one, and 10 plus zero.

So that's all of the possible combinations that could be equal to 10.

How can you be sure that you found all the possible combinations? How did I know that, do you think? That's right, I worked systematically in order, didn't I? I started at zero plus 10, or zero and 10, until I'd found all the numbers that combine to make 10, and that's how I knew I hadn't missed any.

So well done.

So time to check your understanding again.

So 10 is balanced by two circles, so 10 is equal to circle plus circle.

Okay, so what number do you think circle represents and why? So remember, each circle is the same, isn't it? So they will both have the same value.

So pause the video now while you think about what number will be represented by that circle.

Okay, and let's see how you got on.

What number do you think the circle represents? It was five, wasn't it? Each circle represented five.

And why? The circle must equal five because five plus five is equal to 10.

Well done.

Excellent.

So, here's the task for the first part of today's lesson.

There's Jun, okay, and you will see it says you need five cubes and a pot to cover some cubes, and there's Jun with his pot and his cubes.

And then Jun says, "I will look at each equation to see how many to leave outside the pot." So if you look at that first equation there, it says three plus mm is equal to five, so he has to leave three cubes outside the pot and hide the rest.

And then he says, "I will hide the rest of the group under the pot and ask my partner to work out the missing addend in the equation.

And then my partner will hide the cubes and I will work out how many are hidden." He will have his turn.

And while you are working, think about what you notice about each pair of equations.

You can see that they're laid out in twos there, aren't they, in pairs.

So see what you notice, if you notice any patterns there.

So pause the video while you try that now.

So you may have done this, so let's see how you got on.

For the first equation, Jun says, my partner could see three cubes, so they knew there must be two under the pot.

They wrote two as the missing addend.

And if you look at the first pair there, you can see that it will be three plus two, or two plus three.

Then the next pair, one plus four, four plus one, and the last pair, zero plus five, and five plus zero.

And Jun's noticed for each pair of equations, he noticed it was the same pair of addends but in a different order, because we know that we can write the addends in any order, can't we, when we're combining them to make the whole.

So well done.

Excellent.

So at the second part of today's lesson is looking at patterns in numbers, and using that to help us find the missing addend.

Sometimes we can spot patterns to help us find missing addends.

Let's use the double-sided counters to explore the number patterns and find the missing addend.

There are no counters with the white side up, and seven counters with the red side up.

We can represent this as zero plus seven is equal to seven.

If we turn over one counter, we can represent it as one plus mm is equal to seven.

What do we think it is? That's right, one plus six is equal to seven.

If we turn over another counter, we can represent it as two plus? That's right, five is equal to seven.

And then if we turn another counter over, we can represent it as three plus four is equal to seven.

That's right.

And then we turn another counter over and we can represent it as four plus three is equal to seven.

That's right.

And then turn another counter over and we will see that five plus, that's right, two is equal to seven.

And then we'll see six plus one is equal to seven, and seven plus zero is equal to seven.

What do you notice about the pattern in the addends there? And Izzy's noticed in each equation, when one addend increases by one, becomes one more, the other addend decreases by one.

That becomes one less, doesn't it? That's right.

So you can see there the first addend has increased by one, and the second addend has decreased by one, but the sum remains the same.

We've still got a whole group of seven counters there, haven't we? Let's use what we can see and the patterns in the numbers to help us find the missing addends here.

And we've got five frogs on a log, haven't we? So there are five frogs on the log.

There are no frogs in the pond.

You can represent this as an equation.

I wonder what equation we will write.

That's right, five is equal to five plus zero.

One frog jumps into the pond.

There it is.

We can represent this as five is equal to four plus? That's right, one.

Another frog jumps into the pond.

We can represent this as five is equal to three plus? That's right, two.

Another frog jumps into the pond.

We can represent this as five is equal to two plus? Three, that's right.

And then another frog jumps into the pond, and we can represent this as five is equal to one plus four.

And then another frog jumps into the pond and we will represent that as five is equal to zero plus? That's right, five.

What do you notice about the equations? That's right, as one addend decreases by one, the other addend increases by one, doesn't it? Well done.

So here we have some birds, and there are no birds on the ground, but there are six birds sitting on a branch.

We can represent this as an equation.

Zero plus six is equal to six, and the six represents the six birds on the branch, doesn't it? If one bird jumps onto the ground, what would the missing addend be now? That's right, it would be five, wouldn't it? Because we've still got five left on there.

What if another bird jumps to the ground? How many will be left on the branch now? What do you think it will be? Can you imagine a bird jumping off the branch and onto the ground? It would be two plus? That's right, it would be two plus four, wouldn't it? What if another bird jumps to the ground? How many will be left on the branch now? So imagine a bird hopping off the branch there onto the ground.

It will be three plus? Three, that's right.

Are we noticing a pattern here? I wonder what the next equation will be.

That's right, it will be four plus something, wouldn't it? So what if another bird jumps to the ground? It would be four plus? That's right, two is equal to six.

And then what if another bird jumps to the ground? How many will be left on the branch? So imagine another bird jumping off and it would be five plus? That's right, one is equal to six.

And then if another bird jumped off, it would be six plus? Zero is equal to six.

Well done.

So did you notice the pattern there again? What do you notice about the addends in the equation? When one addend increases by one, the other addend decreases by one, but the sum remains the same, doesn't it? You're just moving a bird off the branch each time.

Well done if you spotted that pattern.

Okay, so now there are 10 beads on the bead string.

Let's hide some again, and we're going to say how many are hidden each time and fill in the missing addend in the equation.

But we're going to use our number patterns and see if we can spot those patterns to help us.

So there are 10 beads, five red and five white, okay, and we know 10 plus mm is equal to 10.

What will that be? That's right, there's no beads hiding, so it's 10 plus zero is equal to 10.

But now we'll notice that instead of 10 showing, there are nine showing.

There's one less.

So what must happen to the second addend? That's right, it must be one more, mustn't it? The nine plus one must be equal to 10.

Okay, and then this time we can see that instead of nine showing, beads showing, there are eight beads showing, so that has decreased by one.

So what must happen to the other addend? Eight plus? That's right, it must be two beads hiding, because each time we decrease the amount showing by one, we increase the amount hiding by one, don't we? Okay, so let's have a look at the next one.

Seven plus? That's right, it will be seven plus three is equal to 10.

What do we think the next equation may be? That's right, six plus? Four is equal to 10.

And then we've got five plus five is equal to 10.

Excellent.

Four plus six is equal to 10.

And then it will be three plus seven is equal to 10, and two plus eight is equal to 10, and nine plus one is equal to 10.

And then this time we hide all of the beads.

Zero plus 10 is equal to 10.

So well done if you spotted that pattern that could help us.

What did you notice about the addends in the equation? That's right, when one addend increased by one, the other addend decreased by one, but the sum remained the same.

There were still 10 beads, weren't there? So well done.

So now it's time to check your understanding.

Okay, so we've got some equations here and they're following a pattern, aren't they? Okay, so think about what that pattern is, and use that to help you to find those missing addends.

And remember, Izzy's reminding us there, you could use a bead string to help you with that as well, couldn't you? So pause the video while you try that.

Okay, and let's see how you got on.

Did you notice that the first addend was increasing by one each time, it was becoming one more, so what must happen to the second addend? That's right, it would become one less.

So instead of five plus four is equal to nine, we had six plus three is equal to nine, and seven plus two is equal to nine.

Well done if you spotted that.

Okay, so here's the task for the second part of today's lesson.

Use the patterns in numbers to find the missing addends.

You could use double-sided counters to help you, couldn't you, if you wanted to.

So if you look, part A, all of the equations have a sum of eight.

They all have to combine to make eight in the addends.

And part B, all the addends combine to make nine in each equation.

So in each set of equation, think about what you notice about the addends on each side of the equation.

And then when you finish part A, see if you can use the equations in part A to help you solve the equations in part B.

You might spot a pattern to help you.

Okay, so pause the video now while you try that.

Okay, and let's see how you got on.

Okay, so you can see the double-sided counters there.

Okay, you may have used those.

And in this first set of equations here, we've got eight is equal to, and we can see, can't we, that because the second addend is decreasing by one, the first addend we know has to increase by one, doesn't it? So first of all, we know that eight is equal to zero plus eight, but then we can think, right, okay, so the first addend needs to increase by one.

So eight also must be equal to one plus seven, and then two plus six.

And there we are, and we can see that pattern.

This first addend is increasing by one each time, isn't it? And then in part B, we know nine plus zero is equal to nine, but then we can use what we know about numbers to help us.

So we know that nine is one more than eight, so each equation will be one more than it was for eight.

So we can see eight plus zero was equal to eight, so eight plus one must be equal to nine.

And we can see seven plus one was equal to eight, so seven plus two must be equal to nine.

So each addend is one more than it was for when the equations had a sum of eight.

Okay, and then let's have a look, six plus three.

And you can see each time, you could put one more on the addend that you used in the equations that sum to eight made eight.

Okay, so well done if you spotted that pattern, that's excellent.

You've worked really hard.

So let's think about what we've learnt in today's lesson then.

So you can use your number sense and subitizing skills to help you find missing addends.

You can use number patterns to help you find missing addends.

And working systematically in an order can help you to spot those number patterns, can't it? So well done.

You've worked really hard and I've really enjoyed today's lesson.

And hopefully you'll feel much more confident now using your skills that you already have and spotting those patterns to help you find missing addends.

Well done.