Lesson video

Hello, everyone.

Welcome back to another math lesson with me, Mrs. Pochciol.

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

So let's get started.

This lesson is called add three addends efficiently and it comes from the unit calculating within 20.

By the end of this lesson, you should be able to add three addends efficiently.

Let's have a look at this lesson's keywords.

Addends, efficient, and strategy.

Let's practise them.

My turn addends, your turn.

My turn efficient, your turn.

My turn strategy, your turn.

Well done.

Now that we can say them, let's use them.

Let's have a look at this lessons outline.

In the first part of our learning, we're going to explore efficient ways to add three addends.

And in the second part of our learning, we're going to use efficient strategies to solve three addend problems. Let's get started with the first part.

Exploring efficient ways to add three addends.

In this lesson, we're going to meet Laura, Aisha, and Andeep.

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

Are you ready, guys? Let's get started.

The children are helping Mr. Acorn clear out the PE cupboard.

Andeep sorts the basketballs, Laura sorts the footballs, and Aisha sorts the tennis balls.

Laura has four footballs, Aisha collects five tennis balls, and Andeep has one basketball.

They calculate how many balls there are together.

Laura and Andeep use a 10 frame to help them to find out how many balls are in the cupboard altogether.

Laura records the equation 4 + 5 + 1.

The 4 represents the four footballs, the 5 represents the five tennis balls, and the 1 represents the one basketball.

4 and 5 is equal to 9 and 1 more is 10.

So Laura found that the sum was 10.

There were 10 balls in the cupboard altogether.

Andeep said that he added the addends in a different way to make it easier for him.

He knew that 4 and 1 combined to make 5 and that 5 and 5 combined to make 10.

So he also got the sum of 10.

Andeep shows Laura the strategy he used to help her understand it.

First, he added 4 and 1, which is 5.

Then he added 5 and 5, which we know is equal to 10.

There's his strategy in one equation.

Laura now has a go at representing her strategy in the same way.

First, Laura added 4 and 5, which is 9.

She then adds 9 and 1, which we know is equal to 10.

Can you see Laura's strategy there? She added 4 and 5, which was 9 and then added the 1 which is 10.

All of the parts of our equation are equal because we know 4 plus 5 plus 1 is equal to 10, 9 plus 1 is also equal to 10, and then we have equals 10 at the end.

They now look at a new problem.

What strategy could they use to help solve this equation? Remember to look at the facts that we already know to help us.

Here, Laura has spotted that adding 1 is one more, so one more than 7 is 8.

And she knows that 8 plus 2 is equal to 10.

Whereas Andeep did it slightly different.

He knows that 2 plus 1 is equal to 3 and 3 plus 7 is equal to 10.

They both added different addends first.

But even though they calculated differently, both strategies led them to the number pair to 10 to find the sum of 10.

Laura and Andeep now represent their strategies as an equation.

Laura first added the 7 and 1, which is 8, we then added 2 which is 10.

Andeep added the 2 and the 1 first, which is 3.

He then added this to 7, which is equal to 10.

Hmm, two different strategies but the same result at the end.

Which strategy do you think you would've chosen? Right, over to you then.

Can you find the missing parts of these equations to make them correct? You can see that the sums are all missing.

But also the second expression in the equation has a missing number.

Can you work out which two addends have been combined to find the sum? Pause this video.

Have a go at A, B, and C and come on back when you've got an answer to see how you've got on.

Welcome back.

I hope you had fun finding those missing numbers there.

Let's see how we got on.

Let's have a look at A first.

We can see that five is in the second expression, so one and three must have been combined, which we know 3 and 1 combine to make 4.

And we know that 4 plus 5 is equal to 9.

so 9 must have been the sum and 4, the missing number.

Let's have a look at B.

We can see that 3 is in the first expression and the second expression, so we must have combined one and five.

1 and 5 is equal to 6 and 6 plus 3 is equal to 9.

Hmm.

Laura knew that the sum would still be nine because the addends haven't changed so they they must equal to the same sum.

Let's have a look at C.

We can see that one is in the second expression, so five and three must have been combined this time.

5 and 3 is equal to 8 and 8 and 1 is equal to 9.

Well done to you if you've got all of those missing numbers.

Let's have a go at another one.

What strategy would help us to solve this equation? Represent your thinking in a new equation.

So you can see that we have got 2 + 6 + 2.

What strategy would you use to combine those three addends and can you find the sum at the end? Pause this video.

Represent your thinking with this new equation and come on back to see how Laura and Andeep tackled this question.

Welcome back.

Let's see how Andeep would've tackled this question.

Andeep can see that we have two addends that are the same, so we know that that's a double.

This is double 2, which is 4 and we know that 4 plus 6 is equal to 10.

Did you use the same strategy as Andeep? Remember, an efficient ways to look for facts that we already know, so spotting a double is always going to be efficient.

Laura used the same strategy but she recorded the equation as 2 + 6 + 2 = 6 + 4 = 10.

Is that correct? Yes, good spot Andeep.

All Laura has done is swapped around the four and the six in the second expression, but the sum is still the same and her equation is still correct.

Well done to Laura and Andeep and well done to you if you spotted that strategy.

Over to you then with task A.

Can you complete the equations explaining what strategy you use to solve them? So A, we have 3 + 3 + 4, B, we have 2 + 5 + 3, and C, we have 2 + 1 + 7.

Pause this video.

Have a go at explaining your strategies and showing the equation and come on back once you're ready to see how you got on.

Welcome back.

I hope you enjoyed exploring those strategies there.

Did you find more than one strategy that you could have used? Let's have a look at how Laura chose to solve these problems. A, she can see that there is double 3, which we already know is 6.

6 add 4 is equal to 10.

Remember those doubles are nice, easy ones to add first because we know those facts already.

B, how did you solve that one then Laura? She knows that 2 add 3 is equal to 5.

5 add 5 is equal to 10.

Well done, Laura.

Again, a number pair to five.

We already know those so we might as well use them.

And C, Laura knew that 2 add 1 is equal to 3 and 3 add 7 is equal to 10.

Well done, Laura, and well done to you if you used any of those strategies.

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

Using efficient strategies to solve three addend problems. Andeep and Laura now sort out the beanbags.

There are 5 red beanbags.

There are 2 yellow beanbag and there is 1 blue beanbag.

How many beanbags are there all together? Hmm, I wonder how we could solve this.

Andeep represents this problem as a part-part-whole model and writes it as an equation.

Andeep first notices 2 and 1 which he knows is 3 and then 5 more, which is 8.

So Andeep started with two and added one and then added five.

So his part-part-whole model and his equation would look like this.

2 + 1 + 5 = 8.

Laura found the sum in a different way.

She also represents her problem as a part-part-whole model and writes it as an equation.

Laura can see 5 and 1 which is 6 and then 2 more which is 8.

So her part-part-whole model and equation would look like this.

5, 1 and 2 is equal to 8 and 5 + 1 + 2 = 8.

Let's have a look at both of the children's strategies.

We can see that when we add three addends, we can change the order of the addends but the sum will remain the same.

Remember, it does not matter which pair of addends we add first.

Laura used a different strategy to Andeep but found the same sum.

Remember, we can change the order of the addends to make an addition more efficient for us.

Andeep found it more efficient to add the addends in this order, 2 + 1 + 5.

Whereas, Laura found it more efficient to add the addends in this order, 5 + 1 + 2.

Both of the expressions sum to eight so we can show that they are equal using an equal sign just like we've done previously.

We can also show that they are both equal to eight like this.

So now we can see 2 + 1 + 5 = to 5 + 1 + 2, which is also equal to 8.

Over to you then.

Can you change the order of these addends to show how you would solve this equation? And then don't forget to complete the sum.

Pause this video and come on back once you've recorded your equation.

Don't forget to explain how you found the sum.

Welcome back.

I hope you enjoyed recording your strategy there.

Was your strategy similar to somebody else's? Shall we see how Andeep solved it? Andeep saw that this equation had a double, so we changed the order of the addends to 3 + 3 + 4.

Double 3 or 3 + 3 = 6.

Then 6 add 4 is equal to 10, so he found that the sum was 10.

You may have used a different strategy to me, but hopefully, you found the same sum.

Over to you then with task B.

Part one is to change the order of these addends to solve the equations.

Which two addends will you add first? Explain your strategy and record the sum at the end of the equation.

1 + 7 + 2 and 3 + 1 + 4.

Part two is to place the digit cards 0, 1, 2, 4, 5, and 6 in the missing squares so that each column and row adds up to nine.

Laura's gonna show you a first attempt just so you understand how to complete this task.

6 and 1 is 7, 7 and 3 is equal to 10.

So that's not right because remember, we are looking for each row and column to add up to nine.

That one didn't work because it was one too many.

Laura, what's your thinking now? She's going to now think about what we need the pair of numbers to combine to equal.

Hmm, that little clue there from Laura might help you to solve this.

So have a go at part one and part two and come on back when you're ready to see how you've got on.

Welcome back.

I hope you enjoyed tackling those two problems there.

Should we see how Laura Andeep got on with them? Let's have a look at A then.

Andeep saw 2 + 1 + 7 because he knows that 2 add 1 is equal to 3 and 3 add 7 is equal to 10.

So he recorded it in that way.

Laura, did you use the same strategy? Oh no, Laura saw it as 7 + 1 + 2 because she knows that 7 add 1 is 8 and 2 more than 8 is 10.

We both found the sum of 10, but it didn't matter which way we solved it.

So which strategy did you choose, Andeep's or Laura's? Let's have a look at B then.

3 + 1 + 4.

How did you solve this one? Laura saw this as 1 + 3 + 4 because she knows that 1 add 3 is equal to 4 and double 4 is 8, so the sum was 8.

Andeep, how did you solve this one? Oh, Andeep used the same strategy but he added them in a different order.

He did 3 add 1 which is equal to 4 and double 4 is 8.

Both of the children noticed the double in the problem and both of them found the sum of eight.

Did you use the same strategy as Laura or Andeep? Let's have a look at part two.

I hope you enjoyed this one.

This one took me a little while to work out.

Let's see if Laura managed to complete it.

We can see that three is in every column, so the other two addends must be equal to six because 6 and 3 is equal to 9.

Ah, a good strategy there, Laura.

I like it.

First, we're going to make pairs to six with the number cards, 1 and 5, 2 and 4, and 0 and 6 because they add up to six.

And remember, we need six to add to three.

Let's put them on the grid.

1, 3, and 5.

2, 3, and 4, and 0, 3, and 6.

Now our columns all add up to nine.

Oh no, but Laura, your rows don't.

Look at the first row, 1, 2, and 0.

That definitely doesn't add up to nine.

If we swap the places of six and zero then that is now correct.

1, 2, and 6 is equal to 9, 3, 3, and 3 is equal to 9, and 5, 4 and 0 is equal to 9.

Well done, Laura.

That's correct.

Did you manage to find a solution to that grid problem? Well done to you if you did.

Let's have a look at what we've learned today.

The order of the addends can be changed to make the addition easier.

3 + 4 + 3 could be changed to 3 + 3 + 4, which we know is equal to 10 because we know that double 3 or 3 plus 3 is 6 and then add 4 is 10.

The sum will be the same whichever pair of addends we add first.

Finding a known fact or double to add first can be more efficient.

Strategies used to be efficient might be different for everyone.

Well done for all of your hard work today.

I hope you've started to realise what makes your maths more efficient.

I can't wait to see you all again soon to continue our maths learning.

See you soon.