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 then.

By the end of the lesson, we want you to be able to say, "I can explain how to balance equations with addition expressions." Here are the key words that you might expect to hear during this lesson.

I'm gonna get you to repeat them back to me.

I'll say my turn, say the word, and then I'll say your turn and you can say it back.

Clear? Okay, let's start then.

My turn.

Unknown.

Your turn.

My turn.

Equation.

Your turn.

My turn.

Expression.

Your turn.

Okay, here's what those words actually mean.

An unknown is a quantity that has a set value, but it is represented by a symbol or letter.

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.

Two or more expressions with the same value can be separated by an equal sign to create an equation.

You can see an example at the bottom.

There's an equation there that reads 4 plus 7 is equal to 11 and 4 plus 7 has been highlighted as an example of an expression.

This is the outline for today's lesson then.

To begin with, we're gonna look at comparing addition expressions.

Then, we're gonna move on to balancing equations with addition expressions.

Here's two people that are gonna help us out, two maths friends.

We've got Sofia and Andeep.

They're gonna help us by discussing some of the prompts that you'll see on screen, giving us some clues, some hints, and some tips, and even revealing some of the answers later on down the line.

Hi, Sofia.

Hi, Andeep.

Okay then, let's get going.

Sofia and Andeep are looking at balanced scales.

You might have seen some of these in school.

"It's balanced.

There's nothing either side." "There's an equal sign because it's balanced." So, that's what an equal sign actually shows us.

That both sides have an equal value.

"We can write this as an equation." What's the equation being shown here by these balanced scales? Hmm.

Nothing on that side.

Nothing on that side.

"We can use zero to represent nothing," says Andeep.

So you've got an equation there, 0 equals 0, makes sense.

Sofia and Andeep each add weights to a side.

There they go.

"It's imbalance now," says Sofia.

What does she mean? "That's why there's a greater than symbol," says Andeep.

You can see that the side that Sofia has put weights on is weighted down further than the side that Andeep has put weights on.

As he says, "That's why there's a greater than symbol." "Let's write out the inequality statement." They can't write an equation, because these two sides are imbalanced.

What's the inequality though? We can use addition expressions to represent each side.

So for Sofia's side, they've written 500 grammes plus 100 grammes, and we know that that is greater than 300 grammes plus 200 grammes.

You can see that on the balance scales.

Andeep adds a hundred gramme weight to the balance scales.

And they balance now.

"Now it balances again," says Sofia.

"We can write an equation using the equal symbol." But what's the equation? What do you think? Will both sides look the same? We know that they have the same value, but will each expression have the same terms? "We have two additional expressions equal in value." 500 grammes plus 100 grammes is equal to 300 grammes plus 300 grammes.

They both are equal, although they look different.

Sofia and Andeep generalised from the equation.

"The value of the expressions on each side of an equal symbol." "Must be the same or the equation isn't balanced." Seems pretty clear.

Okay, let's check your understanding so far.

You need to circle the two expressions that have equal value.

Write an equation and two inequality statements to show your thinking.

Pause the video here and have a go at that.

I'll be back in a little while to reveal the answers.

Good luck.

Welcome back.

What did you think? How did you get on? Well, let's see.

Sofia says these two expressions have the same value of 600 grammes.

She's written that as an equation, 400 grammes plus 200 grammes is equal to 300 grammes plus 300 grammes.

What about the inequalities though? Well, you can match the inequalities by using the expressions that are not equal to one another.

For example, 400 grammes plus 200 grammes is less than 200 grammes plus 500 grammes and 300 grammes plus 300 grammes is less than 200 grammes plus 500 grammes.

Sofia and Andeep look at a missing symbol problem featuring decimal fractions.

How would you solve it? We've got 23.

43 added to 25.

34, a missing symbol in between, and then we've got 35.

28 plus 29.

16.

Sofia says, I'm gonna use column addition to calculate the value of each expression.

"Wait," says Andeep, "I think there's a more efficient way that's quicker.

Let's examine the numbers." That means to look at them closely.

Let's round the numbers in each expression to the nearest whole.

23.

43 rounded to the nearest whole is 23.

25.

34 rounded to the nearest whole is 25.

35.

28 rounded to the nearest whole is 35.

And 29.

16 rounded to the nearest whole is 29.

"Now we can use these to reason with, I know that 23 added to 25 is less than 50.

I know that 35 added to 29 is greater than 50.

The missing symbol is less than." Great reasoning there from Andeep.

But how else could you explain it using the rounded numbers? I think the rounding is a good idea, but it might not be the only way of reasoning to understand that in the middle needs to be a less than symbol.

"I have a different explanation with the same solution," says Sofia.

I wonder how she's managed to reason this.

"Let's compare parts from each expression." So, she's comparing 23 and 35.

"I know that 23 is less than 35.

I know that 25 is less than 29.

So, we know the missing symbol is less than because both parts in the." "First expression are less than the parts in the second expression." Again, some great reasoning and it shows that you don't always have to jump straight into using a written method to calculate the absolute value.

By examining the numbers, you can actually get to an answer quicker.

Okay, let's check your understanding then.

True or false.

To work out missing inequality symbols, you have to calculate the precise value of each expression.

What do you think? Pause the video and consider this.

Welcome back.

So the answer is false, but why? Well, you can use your understanding of number and reasoning to work out which expression has a greater value.

You don't need to know the exact value, just whether it is greater or smaller.

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

For number one, you are gonna use rounding, estimating, comparing, and reasoning to determine the missing symbol in each of the following inequality statements.

Once you've done it, Andeep wants you to answer his question as well.

He says, "What do you notice?" Here's e and f as well.

Here's number two.

You've got to decide which character you agree with and explain why.

There's another missing symbol problem here.

The first expression reads 39, added to 37.

Then, there's the missing symbol.

Then, we have a second expression of 31 added to 42.

Both of them are additions.

Sofia says, "The missing symbol is greater than because if I compare parts across both expressions, I see that the difference between 39 and 31 is greater than the difference between 37 and 42." Andeep says, "The missing symbol is less than because both parts in the first expression are in the 30s, whereas in the second expression, there is one part in the 30s and one part in the 40s." Hmm.

It takes some unpicking that.

Do have a good read of each of those statements and decide which you think is correct and why.

Okay, pause the video here.

Have a go at those two questions.

Good luck.

Welcome back.

It's time for some feedback then.

We've got a, b, c, and d to begin with.

For a, you ran the numbers to the nearest multiple of 10 and you should find that it is a greater than symbol that's missing.

For b, you can compare the parts to c.

Again, it's a greater than symbol.

If we compare 59, it's more than 57.

If we compare 27 to 25, we can see it's also more than.

So, it's more than overall.

Let's look at c then.

We had some decimal numbers here.

If we round them to the nearest whole number, we can see that it's a greater than symbol in the middle again.

And for d, we can compare the parts to c just like we did on b.

Andeep says, "What do you notice?" Hmm.

Well, c and d feature the same digits but are one-tenth times the size.

You can still use those same reasoning techniques though without having to calculate any of the values of the expressions.

Okay, let's look at c.

Round the numbers to the nearest multiple of 10, and then compare the expressions.

So, we've got 50 added to 30 is more than 40 added to 30.

So, rounding really helped here.

Let's look at d.

For this one, it's useful to compare the parts to C.

52,987 is less than 61,102 and 32,411 is more than 31,979.

So if you compared those parts, although there is a greater than and less than symbol, you can examine the numbers and see that the difference between 52,987 and 61,102 is greater than the difference between 32,411 and 31,979.

Therefore, we have a less than symbol in between them.

So, great reasoning in those.

Here's number two then.

Sofia was correct and Andeep was incorrect.

It should have been a greater than symbol in between those two addition expressions.

Andeep did spot something.

31 is in the 30s and 42 is in the 40s.

However, the ones digit in each of those numbers is relatively low in comparison to the other parts in the first addition expression.

Always remember that the total of the ones is important as well.

Here's the second part of the lesson then, balancing equations with addition expressions.

Sofia and Andeep return to the balance scales.

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

I will replace my plastering with a 500 gramme weight and a 100 gramme weight." What do you notice? "It still balances so my plasticine must also have a mass of 500 grammes plus 100 grammes." Andeep separate his plasticine into two unequal parts.

You can see there're unequal there because of their size.

"There is still balance." "My two parts still have a combined mass equal to 500 grammes plus 100 grammes." Andeep replaces one unequal part with weights.

So, he's put 100 grammes and another 100 grammes on top of one another to replace the second unequal part.

"The scales are still balanced.

So now we have one unknown part." That's the blob of plasticine that's still there.

"Can we write this as an equation?" What's the equation? What do you think? How would you write that out as an equation? The 1st expression has known parts of 500 grammes and 100 grammes.

Let's use the letter p to represent the unknown, the mass of a blob of plasticine." So now, they've got their equation.

You can see Sofia's side has the expression 500 grammes plus 100 grammes, and that is equal to Andeep side, which is the expression p to represent the unknown plasticine, plus 200 grammes.

Sofia and Andeep represent the equation as a Bar Model.

"There's the first expression as a bar." 500 grammes added to 100 grammes And here's the second expression using p for the unknown.

So, we've got p added to 200 grammes.

They then use this to calculate the unknown.

600 grammes is equal to p plus 200 grammes.

Andeep says, "The value of the first expression is 600 grammes because 500 plus 100 is equal to 600." Now, they've got a Bar Model that makes a bit more sense.

"We can use the inverse to help." 600 grammes subtract 200 grammes is equal to p.

"I know that 600 subtract 200 is equal to 400, so p is equal to 400 grammes." They filled in the Bar Model, and they've written that final equation.

"Let's replace the plasticine with 400 grammes to make sure the equation is balanced," says Sofia.

There are the 400 grammes.

The scales are still balanced.

We found the correct value for the unknown.

Well done you two.

"By finding the value of the unknown, we have balanced the equation." That's what it's called, balancing the equation when you find the value of an unknown.

Okay, your turn.

Write an equation to represent these balance scales using p to represent the unknown.

So, we're just looking for you to write the equation here.

Pause the video and have a go.

Welcome back.

This was the equation then, 200 grammes plus 50 grammes is equal to p plus 100 grammes.

Sofia and Andeep balance another equation, x added to 23,670 is equal to 82,152 plus 5,971.

"The unknown appears in the first expressions and is represented by an x." Sofia has spotted that difference compared to the last equation that they balanced.

"These are larger numbers too," says Andeep.

Let's do a Bar Model again.

"Here's the first expression as a bar including the unknown." So, you can see there the bar's been separated into two parts.

One of them has been labelled x and the other 23,670.

Here's the second bar showing the expression with known parts.

We've got two parts in that bar, 82,152, which is the largest part, and then, 5,971.

How did you know how big to make each part? What do you think? I use my reasoning skills and compared the parts.

You can see 23,670 compared to 5,971.

Looks something like that.

"I knew the expressions were equal so the bars needed equal width." So then she filled in the rest.

"I see! They don't have to be completely precise anyway." Andeep is absolutely correct on that.

The Bar Model is to aid your thinking.

It's a way of modelling the equation.

It's not about being completely accurate and precise, and wasting time trying to do that rather than letting it aid your thinking.

Okay, it's time for you to have a go then.

Represent the equation featuring an unknown using a Bar Model.

And Andeep says, "Remember to compare parts for approximate sizings." Pause the video and have a go.

Good luck.

Welcome back.

Let's see if you drew a Bar Model similar to the one that's about to be revealed.

It might have looked something like this.

The first expression has 10,600 as the larger part, and then 2,680 is the smaller part.

And the second expression has sizings that are a bit closer together.

You've got 5,234 and then x.

How did you get on? Does your Bar Model look similar to this? Okay, let's move on.

Sofia and Andeep continue.

Sofia says, "I think we might need to use columns to calculate the value of the known expression." I agree.

These are larger numbers, so they use columns.

They've written out both of the addends there.

And they've ended up with 88,123.

Now, to use the inverse, we need to find the difference between 88,123 and 23,670.

I think we should use columns again.

So this time, they set out subtraction columns.

(numbers ticking) And they end up with 64,453.

"The value of x was 64,453." "We have balanced the equation." Okay, time for your second practise task.

Look at the image of balance scales below.

A, write an equation to represent these balance scales using p to represent the unknown, b, draw a Bar Model to represent the equation from a, and c, balance the equation by finding the unknown.

For number two, you've got to balance these equations by finding the unknowns.

You can see the unknowns here have been represented using the letter x.

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

Good luck.

Welcome back.

Let's give you some feedback then.

Be ready to mark your questions and answers.

So for the first one, you might have an equation that looked like this.

500 grammes plus 50 grammes is equal to p.

The unknown added to 100 grammes.

Here's the Bar Model.

In that top bar, we've got 500 grammes and 50 grammes as the labels for our parts.

And in the second expression, the second bar, we've got p are unknown and a hundred grammes.

So if we add together the top bar, we've got 550 grammes is equal to p plus 100 grammes.

Now, we can use the inverse.

That gives us 550 grammes subtract 100 grammes is equal to p, so p is equal to 450 grammes.

Okay, pause the video here if you need a bit more time to finish marking that.

Here's number two, then.

You were asked to balance the equations by finding the unknowns.

X was the letter used for the unknown in each.

There were some larger numbers featured here, so you might have needed to use columns.

First of all, you might have wanted to add together the first two parts to give you the value of the first expression, which was 91,065.

We know that that is equal to 68,152 plus x.

Time to use the inverse.

This time, you might have used subtraction columns instead.

So you ended up with 91,065, subtract 68,152.

That gave you an answer of 22,913, and that was the value of x.

The equation was balanced.

Okay, let's look at b, c, and d then.

For b, you should have got 64,750, for c, it was 18.

43, and for d, it was 1,001.

899.

There was some tricky questions there.

If you need more time to mark those carefully and maybe discuss how you got to the answers you did, then pause the video here.

It's time to summarise the lesson then.

Addition expressions are values that are separated by an addition symbol.

If they have a different value, they could be separated by inequality symbols.

If their value is equal, they can be put in an equation separated by an equal symbol.

to balance an equation with addition expressions.

Find the unknown value by calculating the value of the expression with known parts, and then find the difference between that value and the known part in the addition expression featuring an unknown.

My name's Mr. Tazzyman.

I've really enjoyed this lesson today and I hope you have.

I'll see you again soon in another maths lesson.

Bye for now.