Lesson video

Hi, I'm Mr. Tazzyman, and today I'm going to be teaching you a lesson from a unit that is all about understanding equivalence and how you can use it with calculations involving addition and subtraction.

So make sure that you are ready to learn so we can get started quickly.

Here we go.

Here's the outcome for the lesson then.

By the end, we want you to be able to say, I can use knowledge of balancing equations to solve problems. The key word today is expression.

Repeat that back to me.

Okay, let's see what it means.

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.

Here's the outline then for the lesson today.

We're looking at missing symbols and numbers first, before going on to solving problems involving data.

Let's start with missing symbols and numbers.

Here are three friends that are gonna help us along the way.

Aisha, Izzy, and Alex.

Hello, you three.

They're gonna be discussing some of the maths prompts on screen, so listen carefully so that they can help you by going through their own thinking.

Alex and Izzy have been set a challenge to fill in the missing symbol between the pairs of expressions, 48.

26 plus 51.

74 and 36.

19 plus 62.

78.

28.

52 plus 12.

83, compared to 79.

72 subtract 40.

08.

108.

2 subtract 11.

8, compared to 219.

2 subtract 118.

8.

Izzy says, "We can use the equal symbol "or inequality symbols, less than or greater than." Alex says, "These numbers all look very different.

"Shall we work out the value of each expression?" I think we can use rounding and estimation to help us here.

They start by looking at the first pair of expressions.

I'm gonna look at the whole number parts and do some mental calculations.

48 plus 51 is equal to 99 and with the decimal part, hang on, that is equal to 100.

So she's noticed that the two decimal parts of the add-ins in the first expression are actually decimal compliments to one.

36 plus 62 is equal to 98, and the decimal parts won't total two.

So it must be less.

Great reasoning and actually much quicker than using any kind of a written method to calculate the actual value of each expression carefully.

You don't always need to do that.

Sometimes math is just about reasoning rather than precision.

They put greater than in between because they know that that's the symbol that should go in there.

They notice that the next pair has one addition and one subtraction expression.

Did you notice that? Okay, 28 plus 12 is equal to 40 and it will be a bit more with the decimal parts.

Again, they're not being totally precise, but they are using reasoning.

Izzy says, "79.

72, I'm going to round 80 "and 80 subtract 40 equals 40.

"I think we need to think about the decimals." Hmm, I think Izzy's right? Hmm, the decimal parts of the addition expression total more than one.

I wonder how Alex knows that.

Well, if you look at the tenths, you can see you've got an eight and a five.

Those two added together will exceed 10, so that means that they know the total of those decimal parts will exceed one.

I rounded up to 80, but I'm only subtracting a tiny bit more than 40.

I think the addition expression has a greater value.

I agree, the subtraction expression is less.

Again, some great reasoning from these two without having to resort to using a written method straight away.

Your turn.

Let's check your understanding.

What reasoning and rounding can you use to fill in the missing symbol in this pair of expressions? Is it less than, equals or greater than? Pause the video here and give that a go.

Welcome back.

Let's see how you got on.

Izzy says, "I can round the first expression "and estimate that 108 subtract 12 is just less than 100." Alex says, "If I round 219 subtract 119 is equal to 100, "the way I have rounded means the difference "will be just over 100." So the answer was less than, how did you get on? Did you get that? Hmm, okay, let's move on.

This time, there is a missing number to fill in to make this statement correct.

What is the smallest value that the missing number can have? 8.

13 plus 0.

59 is less than 6.

54 plus, well there's some missing digits there, we've got the ones column, the tenths column, and the hundredths column to fill in.

Izzy says, "I think we need to be accurate here, "but mental strategies will work." So she then goes on to say 8.

13 plus 0.

59 will be less than nine, so we can add the decimal parts.

So 13 plus 59 equals 72 hundredths.

8.

13 plus 0.

59 is equal to 8.

72.

6.

54 plus what we're about to put in is more than 8.

72.

I can visualise this on a number line.

So he's written out 6.

54 and 8.

72 on a number line.

He's added two to get to 8.

54.

He's added 0.

18 to get from 8.

54 to 8.

72.

2.

18 would make the expressions equal, so to be greater, it would have to be 2.

19.

That's the lowest value that you could put into those missing digits.

Alright, your turn.

Would you use reasoning and mental strategies to work out the missing value or would you use written methods? So here we're not necessarily interested in getting the answer completely correct.

We're interested in what strategies you would use.

Pause the video and think carefully.

Welcome back.

Aisha says, "We do need to be accurate here, "and I think written methods would be the best approach.

"I could estimate the sum of the first expression "is 57 plus 29 equals 86, "but this doesn't help give a precise answer." Okay, it's time for your first practise task.

Use each expression once to make the following statements correct.

Is there more than one way to do it? So you've got some empty boxes there, and in between the first two empty boxes, there's a less than symbol.

In the middle there's an equals, and in the bottom one there's a greater than symbol and you've got six expressions below to put into those boxes.

For number two, you've got to calculate the missing values and decide if you can reason or whether you need to use a written method.

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

Good luck.

Welcome back.

It's time for feedback, so be ready to mark.

Here are the answers for number one.

89,400 subtract 32,600 is less than 40,900 plus 16,800.

28,200 plus 32,500 is equal to 92,350 subtract 31,650.

And 63,750 subtract 27,890 is more than 58,490, subtract 22,730.

There are only two equivalent expressions.

The other four can be used in other combinations, so these are the ones that we've suggested, but you can swap some of them around just not the ones in the middle because those form part of an equation.

Here's number two then.

The missing values were 2A, 57 pounds, 86 pence, 2B, four pounds 15 pence, 2C, 11.

51, and 2D 14,127.

The first one you to use a written method for to be most efficient.

For B, you could use reasoning.

The first addend in the second expression had increased by 10 pence.

That meant that the missing number needed to also be increased by 10 pence, meaning that it was four pounds, 15 pence.

For the third one for C, you needed to use reasoning, 16.

99 rounds to 17, and for D, you needed to use a written method.

Okay, pause the video here if you need extra time to mark those.

Okay, then let's move to the second part of the lesson to solve problems involving data.

This graph shows the monthly high and low temperatures in Calgary, Canada.

Izzy says, "What do you notice about the graph?" There are some negative temperatures.

You can see those ones there.

"I noticed that it gets cold in Calgary.", says Izzy.

Certainly does.

There was only one bar for October.

In some months, the high and low are both negative, and in others they are both positive.

Okay, time to check your understanding.

The graph shows the monthly high and low temperatures in Calgary, Canada.

Izzy says, "Why is there only one bar for October?" And you can see a little green box has been drawn around the bar in October, but why is there only one? There's two in all the others.

Pause the video and think.

Welcome back.

Alex replies, "The low temperature for October "is zero degrees centigrade." That's why there isn't a bar because it's zero.

Is the difference between maximum temperatures of April and May the same as the difference between September and October.

You can see a green box between the maximum temperatures of April and May, and there's a purple box that's been drawn around the maximum temperatures in September and October.

"I'm gonna write an equation for April and May." says Izzy.

16 subtract 11 is equal to five, so the difference in temperature between April and May is five degrees.

"I'm gonna write an equation "for September and October." says Alex.

16 takeaway 11 is equal to five.

Five degrees difference.

Sound familiar? The answer's the same, but my temperature rose and yours dropped.

The change in temperature is five degrees centigrade each time.

One answer represents a five degree decrease and the other one represents a five degree increase.

The answer to the question is yes, the differences are the same.

Different when comparing a change in two values is expressed as a positive value, so five in this case.

Here's a new table of data.

The title is Monthly Rainfall in Manchester and Sydney.

And Aisha says, "What do you notice about the table?" Hmm, have a good look at it.

What do you notice? It is often wetter in Sydney than in Manchester.

Who'd have thought that? The figures seem sort of opposite, so when it is wet in Manchester, it is drier in Sydney.

I'm not sure I want to visit Sydney in June.

I agree, Aisha, unless I take an umbrella with me.

June is winter time in Sydney.

What does this statement represent? 125 plus 95 is greater than 75 plus 95.

Have a look at those numbers.

Where are they in the table? Can you spot them? Izzy's noticed that 125 and 95 are the highest values for Sydney.

"75 and 95," says Aisha, "are the highest values for Manchester." The highest values for Sydney have a greater sum.

The highest values for Manchester have a lower sum.

Okay, let's check your understanding then.

What does this statement represent? Describe it in words relating to the table.

Pause the video and have a go.

Welcome back.

Izzy notes 125 and 55 are the highest and lowest values for Sydney.

95 and 55 are the highest and lowest values for Manchester.

The difference between the highest and lowest values for Sydney is greater than the difference between the highest and lowest values for Manchester.

It's time for your second practise task.

For number one, you need to look at the temperature graph for Calgary.

Which months are being compared in these statements? You've got A, B, and C to complete there.

For number two, you need to write a statement using less than or greater than to compare the temperature differences in A, September and March, B, October and September.

And Aisha says, "Think about what happens "to the difference when a temperature is negative." There's the graph for reference.

For number three, you need to use the monthly rainfall in Manchester and Sydney to write statements to compare the following, A, the difference between the two months with the lowest rainfall in Manchester and Sydney, B, two pairs of two months, which have the same difference in rainfall in Manchester and Sydney, C, a pair of months that have a difference of five millimetres in the rainfall.

Aisha says, "Use less than, equals and greater than "between expressions in your statements." Here's the table for your reference.

Okay, pause the video here.

Enjoy those questions and good luck.

I'll be back in a little while with some feedback.

Okay, then let's do some feedback.

Be ready to mark.

Number one, A, 16 takeaway four is equal to 20 subtract eight.

That was comparing May and June.

For B, we had 23 takeaway 10 is greater than three plus eight.

That was comparing July and November.

And for C we had 22 takeaway nine is less than three plus 14.

That was comparing August and January.

For number two, you were writing these statements.

September and March should have read 16 takeaway four is greater than four plus four.

And then for October and September you should have had a statement that read 11 takeaway zero is less than 16 takeaway four.

Aisha says, "It is four plus four for March "as one temperature is positive and the other is negative." Thanks Aisha.

Okay, let's move on to look at number three then.

So for this, you were looking at using the monthly rainfall in Manchester and Sydney to write statements to compare the following.

The first one, A, was the difference between two months with the lowest rainfall in Manchester and Sydney.

You should have had 55 takeaway 55 is less than 95 takeaway 90.

That was April and May in Manchester and Sydney.

For B, the two pairs of two months, which have the same difference in rainfall in Manchester and Sydney, you should have had 75 subtract 65 is equal to 70 takeaway 60.

That's July in both cities in September in both cities.

Then you could have had 95 subtract 55 and 55 subtract 99.

The difference in April and October is the same, even though one answer will be positive and the other negative.

40 millimetres for both of those.

Then there was C, a pair of months that have a difference of five millimetres in the rainfall in August and September in Manchester and Sydney.

And that statement would've read, or in fact that equation would've read 75 takeaway 70 is equal to 65 subtract 60.

It's time to summarise the lesson then.

You can use knowledge of how addition and subtraction equations can be altered to solve problems. You can form and compare expressions from data presented in tables and graphs.

The expressions can help you to compare the data.

Rounding, estimating and reasoning can be used to solve problems, but sometimes a written method is needed.

My name's Mr. Tazzyman, and I've really enjoyed that lesson.

I hope you did as well.

Maybe I'll see you again soon.

Bye for now.