Lesson video

Hello, my name's Mrs. Hopper, and I'm really looking forward to working with you in today's maths lesson.

It's from our unit adding and subtracting ones and tens to and from two-digit numbers.

So we're going to be looking at two-digit numbers, and we're going to be thinking about adding and subtracting and hopefully using our known facts to help us.

So if you're ready, let's make a start.

So in this lesson, we're going to be using efficient strategies to solve addition and subtraction problems, so let's look and see what this is all about.

We've got three key words in our lesson.

We've got strategy, data, and bar chart.

I'm going to take my turn, and then you can have your turn.

So my turn, strategy, your turn.

My turn, data, your turn.

My turn, bar chart, your turn.

Well done.

So I wonder if you've come across those words before.

Two of them are all about the sorts of problems we're going to be solving in the second part, data and bar charts, so collecting information and representing it in a way that we can all see, and strategies are the way that we solve problems. So let's have a look and see what's gonna be in our lesson today.

So in part one, we're going to be using efficient strategies to solve worded problems, finding the best way that we know, using the facts that we know to solve some problems. And in the second part of our lesson, we're going to be using those efficient strategies again, but in the context of statistics, looking at some data and some bar charts.

So let's make a start on part one.

And we've got Alex and Sam helping us in our lesson today.

The children have been playing in the garden.

They measure the sunflowers that they planted earlier in the year.

Have you done some work with them on sunflowers? Let's see how they've grown now.

"Last week," Sam says, "my sunflower is 67 centimetres tall, but it has grown by 8 centimetres." Wow, I wonder if they've had some rain and some sunshine to help their sunflowers grow.

So it's grown another 8 centimetres.

How tall is Sam's sunflower now? Which equation can help us to find out? So we need to find out what is 8 more than 67, so 67 plus 8 is equal to something.

And Alex says, "Which strategy should I use to solve this?" He says, "I know the answer will cross the tens boundary.

So I will bridge 10 to solve this." He spotted that 7 ones and 8 ones is going to be more than 10 ones.

Let's use a number line to help us.

So there's 67, and we've got to add 8.

So we can partition our 8 into 3 and 5, and that will allow us to bridge through the next multiple of 10.

So 67 plus 8 is the same as 67 plus 3 plus 5.

Let's look 67 plus 3.

Well, that's going to take us to 70 because we know that 7 plus 3 is equal to 10.

And then 70 plus 5, well, we're adding 5 ones, so 75.

So 67 plus 8 is equal to 75.

And Alex says, "Your sunflower is 75 centimetres tall." And there we can see the sunflower has grown to 75 centimetres.

Alex's sunflower is 3 centimetres shorter than Sam's sunflower.

how tall is Alex's sunflower? I wonder which equation will help us find out this time.

Well, we've got to subtract 3 centimetres 'cause it's 3 centimetres shorter.

So 75 subtract 3 is equal to something.

And Sam says, "Which strategy should I use to solve this?" What would you do? She said, "Well, 75 is equal to 7 tens and 5 ones and I must subtract 3 ones, so I can use my known facts." Are we're going to bridge 10 this time? Well, we're not, are we? Because we've got 5 ones in our 75, and we're only subtracting 3 ones.

So 70 can be partitioned into 70 plus 5.

5 subtract 3 is equal to 2.

So 75 subtract 3 must be equal to 72.

Alex's sunflower is 72 centimetres tall.

There we go, just a bit shorter than Sam's.

3 centimetres shorter to be exact.

The children each have a packet of seeds.

When they weigh the packets, their total mass is 96 grammes, and we can see that there on the scale.

Alex knows that his packet has a mass of 50 grammes.

So what is the mass of Sam's packet? Which equation should be right to find out? While we know that the whole mass, the total is 96, and we know that one part of that is Alex's seeds with a mass of 50 grammes.

So to find the other part, we must subtract the known part from the whole, so 96 subtract 50.

Sam says, "Which strategy should I use to solve this?" What would you do? What she's subtracting a multiple of 10 there, so she can partition the two-digit number 96, subtract the tens and then recombine with the ones.

So 96 is equal to 9 tens and 6 ones, and I must subtract 5 tens so I can use my known facts.

So there we have 6 ones and 90.

So now, we can see the tens together.

9 tens subtract 5 tens is equal to 4 tens 'cause we know 9 subtract 5 is equal to 4.

So 96 subtract 50 will be equal to 46.

The 4 tens left and the 6 ones.

So she says, "My seeds have a mass of 46 gramme," and there's the mass on her packet of seeds.

Time to check your understanding.

Which of the following problems would you bridge 10 to solve? We sometimes have to bridge 10 but sometimes not.

So have a look at these problems, and which one would you need to bridge 10 to solve? Pause the video, have a look, and when you've decided, we'll get back together for some feedback.

How did you get on? Did you spot that it was B? We will cross the tens boundaries in this, so we can bridge 10.

In the other two problems, we use known facts.

And in fact in the other two problems, we're adding and subtracting multiples of 10, so that we just need to partition, add and subtract our multiples of 10, and then recombine with our ones.

Time for you to do some practise.

Can you circle the correct equation to represent each problem and then use an efficient strategy to solve each one.

Pause the video, have a go at matching and then solving, and then when you're ready, we'll get together for some feedback.

How did you get on? So let's look a day.

My sunflower was 73 centimetres tall.

Last week, it was 5 centimetres shorter.

How tall was it last week? So we're going back in time, we're going to subtract, aren't we? So 73 subtract 5 would give us our answer.

What about B? There were 95 minibeasts in the bug hotel.

Two escaped.

How many minibeasts are there now? So 95 subtract 2.

That's right, two of them had gone away, so we needed to subtract.

And in C, I had 47 seeds in the packet, and I put in 20 more.

How many seeds do I have altogether? So this time we knew two parts, and we were finding a whole, so we needed to combine our parts.

So we needed 47 plus 20 is equal to something.

Now, we need to solve them.

So we had to subtract five from the height of our sunflower to find out how tall it was last week.

73 subtract 5.

So we know that this will cross the tens boundary.

We've got 3 ones, and we're subtracting 5 ones, so we'll need to bridge 10.

So let's partition the number we're subtracting our subtrahend, so we can partition it into 3 plus 2, and then we can do 73 subtract 3 and subtract 2.

Let's look at it on a number line.

73 subtract 3 takes us to our multiple of 10, which is 70, and 70 subtract 2 will take us to 68 because we know that a multiple of 10 subtract 2 will give us a number with an 8 in the ones.

And we are back into the previous decade.

So 73 subtract 5 is equal to 68.

Our sunflower was 68 centimetres tall.

What about B? This was about the 95 minibeasts in the bug hotel and two escaping.

So 95 subtract 2.

Well, 95 is equal to 9 tens and 5 ones, so we can use our known facts.

We're only subtracting 2 ones, 5 ones subtract 1 ones is equal to 3.

So 95 subtract 2 must be equal to 93.

So we can partition and just subtract our ones and then recombine.

There were 93 minibeasts left in the bug hotel.

And what about C? This time we were combining the seeds, 47 seeds and 20 more.

47 is equal to 4 tens and 7 ones we can use known facts.

We are adding 2 more tens.

So 4 plus 2 is equal to 6.

so 40 plus 20 must be equal to 60.

And then we can recombine our ones.

So we can see 40 plus 20 is equal to 60, and then combining with our 7 is 67.

So there are 67 seeds in the packet altogether.

And on into the second part of our lesson, we're going to use efficient strategies in the context of statistics.

Oh, this looks exciting.

The Year Two children have been collecting data about the birds they have seen in their gardens.

I wonder if you've ever collected any data on birds perhaps in your school or maybe birds that you've seen at home.

So this is a bar chart to show the number of birds seen in Year Two.

And we've got types of bird, pigeon, magpie, robin, and blackbird, and then along the bottom, we've got like a number line so that we can see how long those bars are and how many of each bird were seen.

So the teachers recorded it on a bar chart.

Let's read the scale and record the data in a table.

So we're going to list the bird and the number that were seen.

So let's start with the blackbird and let's line up the bar with the number line, and we can see that there were 53 blackbird seen.

What about robins? Well, let's line up the bar with the number line, and we can see that there were 28 robins.

What about magpies, those lovely black and white birds? We line up the end of the bar with our number line, and we can see that there were 38 magpies.

And finally pigeons, lots of pigeons.

Line up the end of the bar with the number line, and we can see that there were 63 pigeons seen.

So now, we've taken the data from our bar chart, and we've recorded it in a table.

What information can you gain from the bar chart? What can you say by looking at it? You might want to have a think before we share what we thought.

Well, Alex says, "The bird that was spotted most was the pigeon." We can see that there are more pigeons recorded on the bar chart than any other bird.

And Sam says, "The bird that was spotted least was the robin." Oh, that's a shame.

I do like robins.

I like seeing them in the garden and perhaps when I'm out for a walk as well.

When Alex looks at the bar chart, he notices that there is a difference of 10 between two groups of birds.

Which two groups of birds are they? So which group is 10 more than another? So can we put numbers on the number line that would give us a difference of 10? A jump of 10 from one number to the next, or we could think which group is 10 less than another.

So which would we subtract 10 from to get to the other number? When 10 is added or subtracted, the ones digit does not change.

Ah, that gives us a clue.

Can we see anything there? Well, we've got 28 robins and we've got 38 magpies.

Can you see that the 10 digits have changed but the ones have stayed the same? So we could put those two numbers on our number line, and we could complete the equation.

28 plus 10 is equal to 38.

Or we could think about it with subtraction, 38 subtract 10 is equal to 28, and we can record that with an equation as well.

So the robins and the magpies have a difference of 10.

Can you see another pair that would have a difference of 10 there as well? Maybe you could explore that one as well.

Over to you to check your understanding.

This is a bar chart from the previous week.

So this was a different week when Year Two were counting birds as well.

So on this bar chart, which two groups of birds had a difference of 10 between them? Pause the video, have a go, and when you're ready, we'll get back together for some feedback.

How did you get on? Did you remember that when 10 is added or subtracted, the ones digit does not change? So can you find two totals of birds which have the same ones digit? Ah, yes.

47 is 10 more than 37, and 37 is 10 less than 47.

And we can show that on the number line as an addition or as a subtraction.

So 37 and 47 have a difference of 10.

The tens digits change by one, but the ones digits remain the same, and we can show that in an equation.

37 plus 10 is equal to 47, or 47 subtract 10 is equal to 37.

So the blackbird and the magpie were the two groups of birds that had a difference of 10.

Sam's been counting birds as well, and she gives her data to the teacher, so she can add it to the bar chart.

So we've got some data here, but Sam's got some more to add in.

She saw four blackbirds.

What's the number of blackbirds that have been seen during the week now? Sam says, "There are 53 blackbirds on the bar chart, and I saw 4 blackbirds." So there's 53, but she saw 4 more.

"What equation should I write to solve this," she says.

Can you think? That's right.

It's 53 plus 4.

The total that we have already, plus the four that Sam saw.

She says, "50 is equal to 5 tens and 3 ones, and now I can use my known facts." 3 plus 4 is equal to 7.

So 53 plus 4 must be equal to 57.

We didn't need to bridge through 10 this time, did we? Because 3 plus 4 is less than 10.

Ah, so now we can alter the bar so that it records the total numbers including Sam's blackbirds.

When Sam's data is added, the number of magpies also changes.

There are 38 magpies on the chart now.

When my data is added, it becomes 40.

We can represent this as an equation.

38 plus something is equal to 40, but let's think about it with a bar model as well.

So we know about 38 magpies, and we know that when Sam's data is added, the bar's going to become 40 magpies.

So what's that part that's missing? 38 plus what is equal to 40? Sam says, "I can use my known facts to reach the next multiple of 10." 8 plus 2 is equal to 10.

So 38 plus 2 must be equal to 40.

So there we go.

She says, "I saw two magpies." Time for you to do some practise now.

Here is a bar chart of birds seen by Year Three.

They compare their data to what they know about Year Four's observations.

So you might need to keep sight of this data when you're working on the questions.

So let's help them to answer the questions on the next slide.

Remember to write the equation you would use to answer each question and use an efficient strategy to solve it.

And here are our questions.

So pause the video, remember to record the equation that you would use and the efficient strategy.

How did you get on? So which groups of birds have a difference of 10? So remembering that when 10 is added or subtracted, the ones digits do not change, but the tens digits will have a difference of one.

So we can see that 36 is 10 more than 26, and 26 is 10 less than 36.

We can show that on the number line.

So the robins and the sparrows have a difference of 10 on the bar chart that you were looking at.

You could also have said 43 is 10 less than 53, and 53 is 10 more than 43.

So they both have a difference of 10.

So the blackbirds and the magpies also have a difference of 10 on the bar chart.

Okay, for B.

This week, Year Three saw 53 magpies, and last week, they saw 7 fewer magpies.

How many magpies did they see last week? So we've got to do 53 subtract 7.

So this will cross the tens boundary.

So our bridge through 10, we can partition our 7 into 3 and 4, so we can bridge through 10.

53 subtract 3 subtract 4.

So 53 subtract 3 is equal to 50 and subtract another 4 is equal to 46.

Year Three saw 46 magpies.

For C, Year Three saw 43 blackbirds, and Year Four saw 6 more blackbirds than Year Three.

How many blackbirds did they see? So we've got to work out, 43 plus 6 is equal to something.

43 is 4 tens and 3 ones.

And I must add 6 ones so I can use my known facts.

I'm not going to bridge through 10 this time.

6 plus 3 is less than 10.

So 43 is 40 plus 3.

My 3 ones plus 6 ones is equal to 9 ones.

And when I recombine that 43 plus 6 is equal to 49, 4 tens and 9 ones.

Year Four saw 49 blackbirds.

So for D, Year Four saw 40 sparrows.

How many more sparrows did they see than Year Three? Just a reminder, Year Three saw 36 sparrows.

So we could think about this as 40 subtract something is equal to 36 or 36 adds something is equal to 40.

36 is 3 tens and 6 ones.

So I must add 4 ones, and I can use my known facts.

6 plus 4 is equal to 10.

So 36 plus 4 is equal to 40.

Year Four saw 4 more sparrows than Year Three.

And for E, Year Three saw 78 pigeons and Year Four saw 20 fewer pigeons than Year Three.

How many pigeons did they see? So it's 78 subtract 20.

So we're subtracting a multiple of 10.

So 78 is 7 tens and 8 ones.

So I'm a subtract 2 tens.

I can use my known facts.

7 tens subtract 2 tens is equal to 5 tens.

And when I recombined with our ones, that makes 58.

So 78 subtract 20 is equal to 58.

So Year Four saw 58 pigeons.

Well done for spotting those equations and using efficient strategies to solve the problems. And we've come to the end of our lesson.

So we've been using efficient strategies to solve problems. What have we learned about? Well, we can use facts we already know to help us solve equations at problems efficiently.

We can partition numbers to bridge 10 to help us to work efficiently.

And when we solve an equation, it's important to choose a strategy that allows you to solve the problem efficiently, so that means by using facts that we know and applying them to find out new facts.

Thank you for all your hard work and your mathematical thinking.

I hope you've enjoyed learning lots of different ways to add and subtract one digit numbers and multiples of 10 from two-digit numbers.

And I hope I get to work with you again soon.

Bye-bye.