Lesson video

Hello, my name is Mr. Tazzyman and I'm gonna be teaching you today's lesson from the unit that's all about equivalence, compensation, and addition.

I hope that with some of the learning that you experience today, you'll have a better understanding of some of the underlying structures for addition problems that you face in maths.

Here's the outcome for today's lesson then.

By the end we want you to be able to say, "I can solve addition calculations with missing parts." These are the key words that you are going to be hearing during the lesson, and it's important that you know how to say them, and then later on, that you understand them fully as well.

I'm gonna say them, and I want you to repeat them back to me.

So I'll say, "My turn," say the word, and then I'll say, "Your turn," and you say it back.

Ready? Okay.

My turn, equation.

Your turn.

My turn, unknown.

Your turn.

My turn, whole.

Your turn.

My turn, part.

Your turn.

Here's what each of those words means then.

An equation is used to show that one number, calculation, or expression is equal to another.

An unknown is a quantity that has a set value, but it is represented by a symbol or letter, and in this lesson it's often represented by an empty box.

You can see the example below.

The unknown is an empty box there.

It says something plus 7 is equal to 11.

The whole is all the parts or everything, the total amount.

A part is a piece or section of the whole, and that bar model there shows the relationship between those two key words.

So here's the lesson outline, solve edition calculations with missing parts.

Firstly, we're gonna look at changing the whole, but keeping the balance.

Then we're gonna look at decimal fractions and larger numbers.

Let's get started with the first one.

In this lesson, you will meet Jun and Laura.

They're gonna help us out with some of the maths conversations that you're gonna have, and they'll give us some hints, tips, and prompts as well.

Laura and Jun have a set of balance scales.

"I'm gonna roll up a whole pack of plasticine and put it on my side," says Laura.

"I'll do the same." What do you notice? "The scales are balanced.

They have equal value." "Each side has the same mass of plasticine." "This is an equation." Laura replaces her plasticine with a weight.

"I will replace my plasticine with a weight of 500 grammes." What do you notice? "It still balances, so my plasticine must also have a mass of 500 grammes." Jun separates his plasticine into two unequal parts.

"There is still balance." "The two parts still have a combined mass of 500 grammes." Jun replaces one unequal part with weights.

"The scales are still balanced, so now we have one unknown part." Jun calculates the unknown, 'cause Laura is saying, "What is the unknown?" Well, what do you think before we see his calculation? How could you work out what the mass of that ball of plasticine is? "We can use the inverse here.

I'll write it as an equation." 500 grammes is equal to something grammes plus 200 grammes.

"The unknown is 300 grammes." "You must be correct because there is balance." And he's put those weights in place of the plasticine ball.

Okay, your turn to check your understanding so far.

Write an equation for the balance scales and calculate the unknown.

Pause the video here and have a go at that.

Welcome back.

You might have written an equation that looked like this.

250 grammes is equal to something grammes plus 150 grammes.

So the answer was 100 grammes.

Laura adds more mass to her side.

"It's imbalanced now." "I'll add some more plasticine to make it balance." "Now it's balanced again." "What's the mass of my first part then?" "I'll turn it into an equation to work it out." "Before I added weight, the equation was 500 grammes equals 300 grammes plus 200 grammes.

Then I increased my side by 100 grammes.

One of your parts remained the same." So they've left 200 grammes there, but they've put an unknown the other side of it.

"So the other part must have increased by 100 grammes because the scales remain balanced." So it's worth 400 grammes." Laura and Jun tidy away the balance scales.

Laura writes Jun a challenge to find an unknown using a complete equation as a clue.

"Here is your clue equation to work from." 41 plus 34 is equal to 75.

Use it to find the unknown part here.

41 plus an unknown is equal to 79.

"I like this challenge.

I'll draw a part-part-whole model to help." So he's got two parts there that he knows already.

This is his known equation.

41 plus 34 is equal to 75.

"I'm going to look and see how much the whole increased by." It increased by 4.

"Now to check the first part.

No change.

So the second part must have also increased by 4." "How do you know?" "Because it is an equation, it's balanced.

The unknown is 38." Let's check your understanding now.

You've got to find an unknown using a complete equation as a clue.

That complete equation is 36 plus 51 is equal to 87.

Underneath, you can see we've got an unknown plus 51 is equal to 90.

Can you work out what the unknown is? Pause the video and have a go.

Welcome back.

"The whole has increased by 3.

The known part is unchanged.

So the other part has increased by 3 because it's an equation.

The unknown is 39." Laura and Jun look at all of the unknowns they've found so far to look at generalisations.

What do you notice? "If the whole increases and one part stays the same, then the other part also increases." "What about decreases?" says Jun.

"Let's try them." Brilliant from Jun, there.

What a good mathematician to think of another question, another line of inquiry to follow.

Jun now challenges Laura.

47 plus 34 is equal to 81, and an unknown plus 34 is equal to 77.

We can see that the whole has been reduced this time.

"This one features a decrease.

Try it out." "I'll draw a part-part-whole model." She's drawn that complete equation to begin with.

47 plus 34 is equal to 81.

"I'm gonna look and see how much the whole decreased by." Decreased by 4.

So she's written subtract 4 on both the part-part-whole model and on her jottings.

"One part remained the same." That was the 34.

"So the other part, which is the unknown, must have decreased by 4.

The unknown is 43." "It works for decreases too." Laura tries to catch Jun out.

"I've thought of something.

Try this one." What do you notice? Have a go now at working that through in your head.

Look at the whole.

Look at the parts.

What do you notice? Hmm, there's something slightly different to the ones we've already done.

"I noticed that the whole is increased by 6 this time.

I also noticed that the known part has also increased.

It's increased by the same amount, 6.

That means that the other part stays the same to stay balanced.

So the unknown is 32." "I didn't catch you out then," says Laura.

That was a sneaky trick, Laura.

Okay, it's your turn to check your understanding.

Find an unknown using a complete equation as a clue.

We've got 58 plus 17 is equal to 75.

So 56 plus something is equal to 73.

Pause the video here and I'll be back in a moment with some feedback.

Welcome back.

Jun says, "The whole has decreased by 2.

The known part has also decreased by 2.

So the other part remains unchanged because it's an equation.

The unknown is 17." Did you get that? I hope so.

Here's your first task then.

Then match the stem sentences below to the examples that they're describing, and then fill in the blanks and find the unknown parts.

So you can see we've got the stem sentences there on the left.

The whole has decreased by something.

One part has stayed the same, so the other part has decreased by something.

And then we've got the second sentence, which is the whole has increased by something.

One part has stayed the same, so the other part has increased by something.

And on the right you can see that we've got the complete equations and the equations with the unknowns in.

Here's number two, find the unknowns below.

Use the previous equation to help.

So whilst we were learning, we had complete equations to work from, which gave us clues about the unknowns through adjustment.

Well in this task, the complete equations will be the ones that you've just calculated just above.

Okay, pause the video and have a go.

Good luck.

Welcome back.

Let's look at number one to begin with.

You ready to mark? Let's do it.

The top one matched the bottom equation on the right, and the bottom sentence matched the top equations on the right.

The adjustment was adding 9, and that meant that the sentence at the bottom there read the whole has increased by 9.

One part stayed the same, so the other part has increased by 9.

The unknown was 61.

Then for that equation bottom right, the adjustment was taking away 70.

The whole has decreased by 70, one part has stayed the same, so the other part has decreased by 70.

129 was the unknown.

Here's number two then.

We needed to find the unknowns by using the previous equations as a known fact.

A was 13, 8, 59, 59, 107, and 100.

B, 380, 120, 250, 225, 48, and 75.

C, 47, 29, 15, 25, 1,025, and 920.

It's time for the second part of the lesson then.

Decimal fractions and larger numbers.

Laura and Jun use decimal fractions.

"Okay, where do we start then?" They're looking at this pair of equations, 0.

67 plus 0.

56 equals 1.

23.

0.

67 plus an unknown is equal to 2.

24.

"Let's analyse the whole first.

There is a difference of 1.

01.

That means that the whole has increased by 1.

01." "One part remains unchanged." You can see 0.

67 is the same in both equations.

"So the other part will also increase by 1.

01 to keep balance." "0.

56 added to 1.

01 is 1.

57, so that's the unknown." 1.

57.

Laura and Jun, try a new one with decimal fractions.

0.

35 plus 5.

26 is equal to 5.

61.

An unknown plus 3.

26 is equal to 3.

61.

"Right, let's get going." "I don't think we need to do much here.

I've noticed something." What has Jun noticed? Look at those.

What can you see? "The whole and the known part have both decreased by 2.

So the unknown is unchanged." "Oh yes.

So the unknown is 0.

35." Okay, your turn.

Find the unknown.

You've got a complete equation above and then you've got one with an unknown below.

Pause the video and have a go.

Welcome back.

We can see that the whole was adjusted by adding 2.

So the first part also needed to be adjusted by adding 2 because the known part remained the same.

That gave 2.

78 as the unknown.

This time Jun and Laura used larger numbers.

23,650 plus 22,400 is equal to 46,050.

Then we have an unknown plus 22,400 is equal to 45,850.

"Starting the same way?" says Jun.

"Yes, analyse the whole first.

There is a difference of 200." So 200 has been subtracted from the whole "One part remains unchanged," 22,400.

"So the other part will also decrease by 200." "23,650 subtract 200 is 23,450, which is our unknown." This time Jun and Laura use larger numbers again.

14,150 plus 65,600 is equal to 79,750.

Then they've got an unknown plus 66,500 is equal to 80,650.

"Not much to do here," says Laura.

What has Laura noticed? "The whole and the part have both increased by 900.

So the unknown is unchanged." It's one of those sneaky ones, again.

"The unknown is 14,150." Time to check your understanding then.

You are gonna find the unknown, and here are some equations with larger numbers for you to be able to do it.

17,920 added to 56,930 equals 74,850.

And then in the second equation we've got 17,120 added to an unknown is equal to 74,050.

Pause the video and have a go.

Welcome back.

The adjustment was subtracting 800.

You could see this from the whole.

But it was also done on the known part as well.

That meant that the unknown remained the same as the part above it in the first equation, 56,930.

All right, time for the second task then.

You are going to match the stem sentences below to the examples that they're describing and then fill in the blanks and find the unknown parts.

This is very similar to the first task.

It's just that this time you've got it with larger numbers and decimal fraction numbers.

For number two, you're gonna find the unknown parts in these pairs of equations.

And for number three, you're gonna find the unknowns below.

Use the previous equation to help.

And Jun's also asked, "What do you notice?" once you've finished.

There's C and D to do as well.

Pause the video here and have a good go at those.

Enjoy.

Welcome back.

Here's the first ones to mark.

You can see the jottings on the right there.

In those first equations, 700 was subtracted from the whole and was subtracted from the first part, giving the unknown a value of 34,050.

And on the second set of equations, we had added 0.

8, giving the unknown a value of 3.

86.

That meant that the top sentence matched the top equation, and the bottom sentence matched the bottom equation.

We had to put the number 700 in the top one and 0.

8 in the bottom ones.

It should have looked something like this.

Okay, here's number two then.

We had to find the unknown parts in these pairs of equations.

So for A, we were subtracting 600 from the whole and from the known part.

That meant that the unknown needed to remain the same at 45,150.

For B, the adjustment was adding 90 to the whole and then we added 90 to give us an unknown of 11,400.

For C, we were subtracting 8,000 from the whole and subtracting 8,000 from the known part, so the unknown remained the same at 31,320.

And for D, we were adding 11,000 to get the new whole, which meant we added 11,000 on to get the unknown of 60,560.

Let's look at three then.

A, first was 82, then 60, 15, 15.

5, 105, and 14.

75.

for B, 8.

2, 6, 1.

5, 1.

55, 10.

5, and 1.

475.

Jun also asked, "What do you notice?" Laura says, "Both 3A and 3B feature the same digits, but the place value has changed.

They're all 1/10th of the size." Okay, here are C and D then.

8.

2 for C to begin with.

Then 6.

72, 6.

72, 3.

72, 11.

54, 103.

72.

D, 38,500.

23,000, 24,050, 15,100, 15,100, 35,100.

That brings us to the end of today's lesson then, and here's a summary of the things that we've learned about.

Using completed equations to find missing parts is a very useful tool when looking at addition calculations.

In an addition with two parts, if the whole has increased or decreased, and one part remains the same, then the other part will have increased or decreased by the same amount to maintain balance.

This knowledge can be used to find missing parts.

I've really enjoyed today.

I hope you have as well.

My name is Mr. Tazzyman.

I hope to see you again soon.

Bye for now.