Lesson video

Hello there.

My name is Mr. Tazzyman and today I'm gonna be teaching you a lesson from the unit that is all about calculating using your knowledge of equivalence with addition and subtraction.

So make sure that you're sat comfortably, you are ready to listen and learn, and then we can begin.

Here's the outcome for the lesson then.

I can explain how to balance equations with addition and subtraction expressions.

These are the key words you might expect to hear, equation and expression.

I'll say them and I want you to repeat them back to me.

Equation.

Repeat that back now.

And then we have expression.

Repeat that back now.

Okay.

This is what they mean.

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

An expression contains one or more values where each value is separated by an operator, such as add or subtract, but an expression does not have an equal sign.

32 subtract 16 is an expression.

This is the outline for the lesson then.

We're gonna start by identifying equivalent addition and subtraction expressions.

Then we're gonna look at correcting equations that are not balanced.

We've got some friends who are gonna join us on this journey.

Aisha, Izzy and Alex.

Hi, you three.

They're gonna be helping us by discussing a lot of the maths, a lot of the learning, and giving us some hints and tips along the way.

Okay then, get yourself comfortable and make sure you're ready to learn.

Here we go.

Without calculating anything, what is the same and what is different about the following equations? 37,000 plus 6,000 is equal to 25,000 plus 18,000.

59,500 subtract 37,000 is equal to 62,000 subtract 39,500.

75,000 subtract 27,000 is equal to 11,000 plus 37,000.

What do you think? Izzy says, "I noticed that 37,000 appears somewhere in all the equations." In two of the equations it's an addend.

In the second equation, it is a subtrahend.

Aisha says, "Each equation has two expressions that are equal to one another.

The first two have either both addition or both subtraction expressions." Alex says, "The last equation has one subtraction expression and one addition expression.

I don't think I've seen an example like that before." Have you? You don't often see those.

Expressions can be equal even if they have different operations.

Okay, it's your turn, let's check your understanding so far.

Match each addition expression to an equal subtraction expression, so you've got a column of additional expressions and a column of subtraction expressions.

Which of those match? Pause the video and have a go.

Welcome back.

Let's look at which of these expressions were equal to the other.

30 plus 50 is equal to 200 subtract 120.

Both have a value of 80.

40 plus 50 is equal to 210 subtract 120.

Both have a value of 90.

50 plus 50 is equal to 220 subtract 120.

Both have a value of 100.

And 60 plus 50 is equal to 230 subtract 120.

Both have a value of 110.

Did you manage to find the correct pairs? I hope so.

We can write these as equations to show the equivalence of the expressions.

You can see them all written there with an equal sign in between.

Are these equations balanced? How could you check? 37,000 plus 6,000 is equal to 25,000 plus 18,000.

59,500 subtract 37,000 is equal to 62,000 subtract 39,500.

And 75,000 subtract 27,000 is equal to 11,000 plus 37,000.

Hmm.

Well, Alex says in the first equation, the values are all thousands and 10 thousands.

"I know that 37 plus six is equal to 43 and 25 plus 18 is equal to 43 as well, so the expressions must be equivalent." Alex has used his understanding of unitization there.

"In the first part of the second equation, I can subtract 37 from 59 and then add the 500." 59 subtract 37 equals 22, so 59,500 subtract 37,000 equals 22,500.

"In the second part of the second equation, I can subtract 40,000 and then add 500.

62,000 subtract 40,000 equals 22,000.

62,000 subtract 39,500 equals 22,500.

That's correct, both the expressions have the same value of 22,500.

In the first part of the second equation, I can subtract 27 from 75.

He's using unitization again.

75 subtract 27 is equal to 48, so 75,000 subtract 27,000 is equal to 48,000.

"In the second part of the second equation, I can add 11 and 37." 11 plus 37 is equal to 48, so 11,000 plus 37,000 is equal to 48,000.

That's correct as well.

These equations are all balanced.

You can use known strategies to calculate when it is not obvious by reasoning.

Okay, it's time for your first practise task.

Check to see if these equations are balanced.

Explain how you know without using column addition and subtraction.

You've got A, B, C, D, and E to have a go at.

Pause the video here, enjoy and good luck.

Welcome back.

It's time for some feedback.

Be ready to mark.

The first one was correct.

The second one was incorrect.

The second addend has increased, so the addition expression is greater.

For the third one, it was correct.

The minuend has been increased by 1000, so they're equivalent again.

For the fourth one, the addition expression is now 1000 less than the subtraction expression.

And on the fifth one, E, the minuend is now 1000 less, so the equation is balanced again.

Okay, pause the video here if you need some more time to catch up with marking or you want to discuss anything that came out of that question.

It's time to move on then.

The second part of this lesson is about correcting equations that are not balanced.

Without completing the calculations, are these expressions equivalent? Is the equation balanced? 80,000 subtract 7,000 is equal to 41,000 plus 33,000.

Is this balanced? Aisha says, "I know that if I subtract 7 from a multiple of 10, I will get a number with 3 in the ones or thousands here." Izzy says the addition expression value will have a 4 in the thousands.

These equations are not equivalent.

How could you change the expressions so that the equation is balanced and the expressions are equal? Hmm.

How could you do that? Well, Aisha says we could change either of the expressions.

We could change either value in each expression.

That would give us four ways to correct the equations.

Let's start by changing the subtrahend of the first expression.

And remember, subtrahend is the number that you subtract from the minuend.

They've highlighted 7,000.

That's the subtrahend in that first expression.

We need a 4 in the thousands, so we could subtract 6,000 from 80,000 using our understanding of place value and subtraction there.

Well done, Aisha.

That would work.

Now the equation is balanced.

You can see it there.

80,000 subtract 6,000 equals 41,000 plus 33,000.

Okay, let's check your understanding so far.

How could you change the minuend of the first expression so that the equation is balanced? And remember, the minuend, which has been given a green box around it there, is the number that you subtract from in a subtraction expression.

At the moment, this equation is imbalanced.

How are you gonna change 80,000 to make it balanced? Pause the video and have a go.

Welcome back.

Aisha says we need a 4 in the thousands so we could subtract 7,000 from 81,000.

So she's proposing that the 80,000 becomes 81,000.

"That would work!" Says Izzy.

Now the equation is balanced.

There's the proper equation that works.

81,000 subtract 7,000 equals 41,000 plus 33,000.

Did you manage to figure that out? I hope so.

Okay, let's move on.

We return back to the same problem again.

We've already checked 80,000 and 7,000 and thought about ways to change those.

Izzy says, "Let's change the first addend of the second expression" This time.

The value of the first expression has a 3 in the thousands column.

We could change the first addend to 40,000.

That would work.

Now the equation is balanced.

80,000 subtract 7,000 is equal to 40,000 plus 33,000.

Let's check your understanding again.

How could you change the second addend in the second expression so that the equation is balanced? It's been highlighted there by using a green box.

Pause the video and think about how you could change that.

Welcome back.

Aisha says, "The value of the first expression has a 3 in the thousands column.

We could change the second addend to 32,000.

That would work.

Now the equation is balanced.

80,000, subtract 6,000 is equal to 40,000 plus 32,000.

Okay, have a look at these then.

How could you describe the way we have changed the expressions? We had to increase the difference of the subtraction expression by 1000.

Decreasing the subtrahend increases the difference.

That's a really important thing to remember.

If we make what we are taking away smaller, then the difference actually increases because the minuend and subtrahend are further apart.

Increasing the minuend increases the difference.

Or we had to decrease the sum of the addition expression by 1000.

Decreasing either addend decreases the sum.

Okay, it is time for your second practise task then.

For number one, look at the unbalanced equations from task A.

How many different ways can you correct them? For number two, make balanced equations using the values below.

How many different equations can you make? Pause the video here.

Have a go at those, and I'll be back in a little while with some feedback.

Welcome back.

Here are the equations that you looked at in practise task A, and we knew that B and D were the ones that were in balanced, but how could we have corrected them? Well, for B, here are two different ways.

You could have started by decreasing the addition expression by 1000.

On the example shown on screen, we took the first addend and we decreased it by 1000, going from 56,000 to 55,000.

You could also though have actually started by decreasing the 8,000 to 7,000 instead.

That would've given you two equal expressions and a balanced equation.

Alternatively, you could have looked at the subtraction expression.

In order to make a subtraction expression greater, you need to decrease the size of the subtrahend, which is what the example there has shown.

You could have decreased the subtrahend from 19,000 to 18,000, making the difference 1000 greater.

Alternatively, although it's not shown here, you could have started by increasing the minuend by 1000.

If the minuend is increased, then the difference is increased.

Let's look at D then.

You could here have started by decreasing the addition expression by 1000.

Here it's been shown as decreasing 8,000 to 7,000, the second addend.

But you could as well have decreased 57,000 to 56,000.

Alternatively, if you look to the subtraction expression, then you needed to make sure that that was greater.

We've chosen to increase the minuend by 1000 here.

Alternatively, you could have decided to decrease the subtrahend by 1000 to make the difference 1000 greater.

A and C are the other ways to correct equation B, and C and E are the other ways to correct equation D.

Pause the video here for more time to mark those carefully and accurately and to discuss any things that may have arisen from that feedback.

Let's do number 2 then.

These are the equations we found.

32,600 plus 28,700 is equal to 89,500 subtract 28,200.

Or 28,200 plus 28,700 is equal to 89,400 subtract 32,500.

Did you use some rounding and estimating to help you to select the values to put into the equation? You might well have done.

Might be a good idea now to pause a video and compare with anybody else who's had a go at making some of these equations.

Time to summarise the lesson then.

You can use your knowledge and understanding of addition and subtraction to identify equivalents and to balance equations.

You can reason rather than calculate the value of each expression to know if they are equivalent.

You can apply your understanding of how changing the values within an expression affects its value.

My name is Mr. Tazzyman and I've enjoyed that lesson today.

I hope you did as well.

Maybe I'll see you again soon.

Bye for now.