Lesson video

Hi, my name is Mr. Tazzyman and I'm looking forward to learning with you today.

This lesson is from the unit, "All About Equivalence and Compensation with Addition." It'll give you some extra hints and tips on how to face addition problems and solve them mentally rather than jumping straight to a written method.

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

By the end, we want you to be able to say, "I can use balanced equations to calculate redistribution." Here's the key words that you are going to be hearing during the lesson.

I'd like you to say them back to me.

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

Ready? My turn, whole.

Your turn.

My turn, part.

Your turn.

My turn, equation.

Your turn.

My turn, expression.

Your turn.

Okay.

Here are the definitions for those words then.

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

The part is a piece or section of the whole.

You can see a bar model at the bottom there showing that relationship.

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 at the bottom there there's an expression example, four plus seven, and actually that shows us an equation as well because it's followed by an equal symbol with the number 11.

Here's the outline then for today's lesson on using balanced equations to calculate redistribution.

To begin with, we're gonna look at balancing equations.

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

So we'll start, where we always start, at the beginning.

Here's Izzy and Aisha.

They're gonna help us in today's maths lesson by giving us some prompts and discussing some of the maths.

Hi Izzy.

Hi Aisha.

Aisha and Izzy have a set of balance scales.

"I'm gonna roll up a whole pack of plasticine and put it on my side." "I'll do the same," says Izzy.

What do you notice? The scales are balanced.

Each side has the same mass of plasticine.

Aisha splits hers up into two equal parts.

What do you notice? Each side is still equal because the scales are balanced.

"Your two parts are equal to my whole." Izzy now splits her whole up too.

"I have two equal parts as well now." "Each side is still equal.

The scales balance." Aisha splits one of her parts up further, so she has three unequal parts.

"Our sides are made of a different number of parts." "But we know that they add together to make equal wholes." "Yes, because the scales are balanced.

We don't know the value of the parts." Okay, let's check your understanding so far.

Label the base of the scales with the correct symbol, less than, greater than, or equals to describe the relationship between the two sides.

Pause the video here and have a go.

I'll be back shortly.

Welcome back.

They were the symbols that you should have thought of.

On the first set of scales, they were equal because we could see that both sides were balanced.

Then we had the second set of scales was greater than, and the scales at the bottom were less than.

Izzy replaces her plasticine with a 500 gramme weight.

What do you notice? "The scales are still balanced, so we know that each side is still equal to the other." "So both sides are worth 500 grammes, but mine has one part, whereas yours has three parts." Aisha replaces one of her parts.

"Now my side has three parts.

One part is 50 grammes and the other two are unknowns." "Can you squish your plasticine parts together?" Aisha squishes two parts together to make two parts in total.

"I think I know the mass of the plasticine part." "Me too," says Izzy.

What do you think? Do you think you know what the plasticine part might be? What's the mass? "The scales are balanced.

So I know your side is 500 grammes in total." "Yes, that's right.

One of my parts is 50 grammes, so the other part must be 450 grammes." "Yes, because 450 added to 50 is equal to 500." Okay, your turn.

Look at the scales below.

What's the mass of the plasticine and how do you know? Pause the video here and have a go.

Welcome back.

"Because the scales are balanced, we know both sides are equal to 500 grammes.

I know that 100 plus 400 is equal to 500, so I know the plasticine is 400 grammes." There it is, 400 grammes.

Okay.

Aisha replaces her plasticine part with weights.

450 grammes worth.

"Now we have values for each part.

We can write this as an equation." What do you think? What would that look like if it were written as an equation? "Okay, each side is an expression.

My expression is just the whole." 500 grammes.

"My expression is made up of two parts." 450 grammes plus 50 grammes.

"This is the equation then." 450 grammes plus 50 grammes is equal to 500 grammes.

"What happens if I swap weights between parts?" Aisha redistributes a 50 gramme weight to the second part.

"The scales are still balanced, so it is still a balanced equation." "Yes, but my parts are different now, so my expression will have changed." "Okay, put the weights back and then jot down the change." Aisha re-does the distribution with a written equation.

"Here's the equation at first.

I subtract 50 grammes from one part, so I need to add 50 grammes to the other part." Can you see? She's used brackets to separate the two terms in the expression here.

She's redistributed 50 grammes from the first part to the second part so that the whole was kept the same, 500 grammes.

"Now, my parts look like this." 400 grammes plus 100 grammes is equal to 500 grammes.

Okay, let's check your understanding again, true or false.

If an amount is redistributed from one part to another within an expression, then the equation is still balanced.

Is that true or false? Pause the video and decide.

Welcome back.

That was true, but now let's think about why that might be true.

Here are two justifications for you to choose between.

A says expression and equation are the same thing.

B says the value of the expression doesn't change because redistribution is only occurring within the expression.

Which of those do you think best supports the fact that that statement is true? Pause the video and decide.

Welcome back.

The best justification was B.

The value of the expression doesn't change because redistribution is only occurring within the expression.

For A, expressions and equations are not the same thing.

An equation is where you have an equal sign or more than one equal sign showing that expressions have the same value, that they are equivalent.

Okay, it's time for task A.

The balance scales below are shown before and after a redistribution.

Complete the stem sentences to describe the redistribution shown in the pictures.

So you've got the stem sentence at the bottom there that says, I've subtracted something from one part, so I need to add something to the other part to keep the whole the same.

Here's B, same task.

For number two, using the same images, complete the following three equations showing the redistribution.

And here's B.

And for number three, using the equations below, draw the weights before and after redistribution on the set of scales.

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

Enjoy.

Think carefully.

Watch out because it can be trickier than you think.

Pause the video and I'll be back with some feedback shortly.

Welcome back.

Let's look at number one.

To begin with, I've subtracted 150 grammes from one part, so I need to add 150 grammes to the other part to keep the whole the same.

Let's look at B then.

I've added 150 grammes to one part, so I need to subtract 150 grammes from the other part to keep the whole the same.

Do you have a think about what was the main difference between A and B? It was to do with the direction of redistribution.

Okay, let's move on to number two.

Okay, for number two then, we had 350 grammes plus 150 grammes is equal to 500 grammes.

Then in the brackets we were redistributing 150 grammes.

Then we ended up with 200 grammes plus 300 grammes is equal to 500 grammes.

For B, we started with 100 grammes, plus 400 grammes is equal to 500 grammes.

We redistributed 150 grammes.

We ended up with 250 grammes plus 250 grammes is equal to 500 grammes.

All right, here's number three, then.

This is what you might have drawn.

Don't worry too much about whether the weights look completely accurate or not.

So for the before part, we had two different parts, both totaling 250 grammes.

And then for the after part, we had again had two different parts, but one was worth 350 grammes and the other was worth 150 grammes.

Let's do the second part of the lesson then, larger numbers and decimal fractions in context.

Izzy and Aisha decide to explore balanced equations with some larger numbers that use a seesaw instead of scales.

"Let's put some bags of sand on either side." There they go, two bags of sand.

The seesaw is balanced.

"They have equal mass." Izzy decides to replace her side with weights.

What do you think she should do? "The pack says it's 10 kilogrammes.

How many grammes is that?" "For every one kilogramme, there are 1000 grammes.

That means 10 kilogrammes is equal to 10,000 grammes." "Wow.

I'll need some heavier masses." There they go.

10 masses of one kilogramme each.

They decide to write an equation.

What do you think? What do you think that equation would look like? "But we don't have a value for your side yet." "I think we do.

Your parts total 10,000 grammes and the seesaw is balanced." "I see.

So your bag of sand must be equal to 10,000 grammes." "Exactly.

Let's start with an equal sign for an equation.

My expression is simply 10,000 grammes." "My expression is different.

I'll write it in kilogrammes first.

I've arranged ten one kilo weights into two parts." Five kilogrammes plus five kilogrammes.

"Now I'll convert each part from kilogrammes to grammes." 5,000 grammes plus 5,000 grammes is equal to 10,000 grammes.

Aisha tries a redistribution.

"Let's redistribute, shall we?" says Izzy.

"If I can.

Some heavy lifting required." Did you see that redistribution? "How about that?" "This is still an equation because it's balanced, but the parts in your expression are different now." "Yes, I'll use three equations to show the change." Aisha shows the redistribution using three equations.

5,000 grammes plus 5,000 grammes is equal to 10,000 grammes.

"I subtracted 1000 grammes from one part, so I needed to add 1000 grammes to the other part so that the whole was kept the same, 10,000 grammes.

Now my parts are different, but the whole is the same.

4,000 grammes plus 6,000 grammes is equal to 10,000 grammes." "I'm going to use notation to try a harder one." Izzy starts with Aisha's equation and redistributes again.

"I'll add 500 grammes to one part, so I need to subtract 500 grammes from the other part so that the whole is kept the same." So she's now got 4,500 grammes, plus 5,500 grammes is equal to 10,000 grammes.

"I want to try an even trickier one," says Aisha.

Aisha redistributes a last time.

3,500 grammes plus 6,500 grammes is equal to 10,500 grammes.

"I'll subtract 230 grammes from one part, so I need to add 230 grammes to the other part so that the whole is kept the same.

Now, the parts are different, but the whole is the same." She's ended up with 3,270 grammes plus 6,730 grammes is equal to 10,000 grammes.

Okay, your turn.

Can you spot the mistake in the redistribution below? Have a look closely.

Pause the video and I'll be back to reveal the mistake shortly.

Welcome back.

Did you manage to spot that mistake? Aisha says, "Here, both parts have had amounts subtracted.

The whole will become smaller in this situation." So you can see if you look in the brackets, that 230 has been subtracted from both parts rather than 230 being taken away from one part and redistributed to the other through addition.

So actually the whole will have changed to 9,540 grammes.

Aisha and Izzy investigate redistribution with decimal fractions to see if the whole stays the same.

"Will the equation balance if we use decimal numbers?" What do you think? Do you think it will still balance? "Let's test it by converting our grammes to kilogrammes." Can you convert that? What would you do to change those numbers so that they are showing kilogrammes? "We'll use the last redistribution we did and make the conversions." 3.

5 kilogrammes plus 6.

5 kilogrammes is equal to 10 kilogrammes, so 3.

5 kilogrammes subtract 0.

23 kilogrammes plus 6.

5 kilogrammes plus 0.

23 kilogrammes is equal to 10 kilogrammes.

3.

27 kilogrammes plus 6.

73 kilogrammes is equal to 10 kilogrammes.

Okay, it is time for your second practise task.

You've got to use the equations below to complete the stem sentences, very similar to the first practise task.

Here's A and here's B.

And Aisha says, "What do you notice?" For number two, you've got to fill the missing numbers in the trios of equations below showing redistributions, there's A and B.

Here is C and D.

Okay, pause the video here, have a go at those.

Good luck and I'll be back shortly with some feedback.

Welcome back.

Let's start with number one.

I've subtracted 120 grammes from one part, so I need to add 120 grammes to the other part to keep the whole the same For B, I've subtracted 0.

12 kilogrammes from one part, so I need to add 0.

12 kilogrammes to the other part to keep the whole the same.

And Aisha said, "What do you notice?" Izzy says, "This is the same as the last question, but the measurements are in kilogrammes instead of grammes." Did you notice that? Here's number two, then.

The missing numbers here were 1,900 grammes, 6,500 grammes, 360 grammes, and 6,500 grammes.

On the bottom row, it was 1,540 grammes.

Let's look at B.

Here, we had 4.

6 kilogrammes on the top row, 1.

9 kilogrammes, 0.

36 kilogrammes and 6.

5 kilogrammes on the second row, and we had 6.

5 kilogrammes on the bottom row.

Here's C, 10,100 grammes on the top row, 10,100 grammes, 6,950 grammes and 470 grammes on the middle row, and then 6,480 grammes on the bottom row.

And for D, we had 3.

15 kilogrammes on the top row, 10.

1 kilogrammes on the second row, 6.

95 kilogrammes on the second row, 0.

47 kilogrammes on the second row, and then on the bottom row we had 6.

48 kilogrammes.

That brings us to the end of the lesson then.

Here's a summary of all of our learning, equations show two expressions which have equal value.

Equations are balanced.

They can be represented using a set of balance scales or a seesaw.

If the mass is evenly distributed, then the seesaw or balance scales remain flat.

Amounts can be redistributed between parts of an expression, but the value of the whole remains unchanged.

This is also true for larger numbers and decimal fractions.

My name is Mr. Tazzyman and I've really enjoyed learning with you today.

I hope you have too.

Maybe I'll see you again in another maths lesson in the future.

Bye for now.