Lesson video

Hello, my name is Mr. Tazzyman, and I'm really excited to be working with you on this lesson today.

If you are ready, let's get started.

Here is the outcome for today's lesson.

By the end of it, we want you to be able to say, "I can use addition and subtraction to solve problems involving bar charts, pictograms, and tables." These are some of the keywords that you are going to see throughout the slides.

I'm gonna get you to practise saying them.

I'll say my turn and say the word, and then I'll say your turn, and I want you to say them back to me.

My turn, bar chart.

Your turn.

My turn, pictogram.

Your turn.

My turn, table.

Your turn.

Okay, let's see what these words mean.

A bar chart uses rectangular bars to show different values.

A pictogram is a graph that uses pictures to represent information.

A table has information arranged in rows and columns.

Here's the outline for our lesson on solving problem using scaled bar charts, pictograms, and tables.

The first part of the lesson is going to be all about problem solving with bar charts and pictograms, and the second part of the lesson will be about problem solving with tables.

Let's get started.

We've got a couple of people to meet, Lucas and Izzy.

They're going to help us throughout this lesson by discussing some of the prompts, giving us some of the answers, and hopefully, deepening our thinking mathematically.

Look at this bar chart.

It says, "Bar chart showing the average mass of some bear species." We've got the black bear, grizzly bear, panda bear, polar bear, and sun bear.

And on the Y-axis, you can see we've got their mass in kilogrammes.

Izzy says, "Let's look at each bar and write down its value." That's always a really good place to start when you are reading bar charts.

Lucas says, "Great idea.

We can place a ruler horizontally from the top of each bar to the axis to help." You can see the ruler there has been placed towards the top of the black bar representing the black bear.

It meets the axis at 350.

390 for the grizzly bear.

120 for the panda.

600 for the polar bear.

And 50 for the sun bear.

Poor little sun bear.

How much heavier is a grizzly than a black bear? Izzy wants to know the calculation that we are using for this.

It's a really good place to start.

Lucas says, "I think it's 390 kilogrammes subtract 350 kilogrammes." Lucas writes the equation and draws a number line to help.

He thinks, "Finding the difference will be my strategy because the numbers are close together.

I will start on 390 and count back in 10s." Here we go.

He says, "I end up on 350 having counted back 4 lots of 10 in total.

4 lots of 10 makes 40, so I counted back 40.

The difference between 390 and 350 is 40." So the answer is 40 kilogrammes.

Then he says, "I think I can also count forwards to find the difference, and the result will be the same.

I was right.

I counted on 4 lots of 10, which is 40." Then he says, "I don't even think I needed to count.

I know that the difference between 5 and 9 is 4.

So I also know that the difference between 50 and 90 is 40 even quicker." Well done, Lucas.

Your turn.

Just to check that you've understood what we've just learned about.

You've got the same bar chart here, but the question is, how much heavier is a polar bear than a sun bear? Pause the video and have a go, and I'll be back in a moment with the answer.

Welcome back.

Shall we see how you got on? So you might have recognised that the equation was 600 kilogrammes subtract 50 kilogrammes.

You might have used the number line to clarify your thinking.

And Lucas says, "This time we can count back using the subtrahend.

We can count back 5 lots of 10, which is 50." He ends on 550.

So that gives the answer 550 kilogrammes.

Lucas points out, "You might have completed it with one step." Some of you may have been able to just use one leap of 50 to get to 550.

Well done if you did.

That's even more efficient.

What is the combined mass of a grizzly and black bear? Izzy says, "Let's think about forming an equation again." Lucas says, "Well, combined means we need to add." Izzy replies, "Okay, addition then.

So it must be 350 kilogrammes plus 390 kilogrammes." Izzy writes the equation down, and she decides on an efficient strategy for this addition.

I wonder what she'll choose.

She says, "I'm going to use redistribution because one of the addends is close to a hundreds boundary.

First, I will identify the addend that is closest to a boundary, usually a hundred." So she's identified that 390 is close to a hundreds boundary, it's close to 400.

"Then," she says, "I'll take 10 from the first addend and redistribute it to the second to make an easier calculation." You can see, she's now created 340 plus 400.

That's nice and easy to solve.

She says, "Lastly, I'll add together the redistributed addends to find the sum." 740.

So the answer is 740 kilogrammes.

Well done, Izzy.

Your turn now to check that you've understood that.

The question you've got is, what is the joint mass of a grizzly and panda bear? Pause the video, have a go, and I'll be back with the answer in a moment.

Welcome back.

Let's see what the answer was.

So the equation was 390 kilogrammes plus 120 kilogrammes, is equal to, we don't know yet.

It's an unknown to be worked out.

Izzy says, "We can use redistribution here." She identifies that 390 needs 10 added to it to make 400, but if we've added 10 for one addend, we need to subtract 10 from the other addend, giving us a final calculation of 400 plus 110, which is 510 kilogrammes.

Did you get it? I hope so.

Now we're gonna move on to looking at pictograms. Izzy and Lucas write a quiz for their friends.

They gave 10 points for each correct answer and five points if a clue was needed.

Below is a pictogram of the scores.

You can see that you've got all of the contestants on the left-hand side.

Sam, Jun, Andeep, Alex.

To the right of the pictogram, you can see that we've got a key.

It tells us that one complete emoji is 10 points, half an emoji is five points.

Lucas says, "I'm going to label the value of each row.

I'll count in 10s and then add on any 5s." What a great idea.

It's always worthwhile understanding the data before you start answering questions about it.

You ready to count? 10, 20, 30, 40, 50, 60, 70, 80, 90, plus 5 because it's a half emoji, gives us 95.

He does the same for all the other rows.

He counts and adds on 5 if there's a half emoji.

Jun gets 30, Andeep gets 95, and Alex gets 45.

Izzy says, "Sam and Andeep went together.

They were a sensational team." She says, "I am going to work out their total score, which will be 95 plus 95." Izzy begins by choosing an addition strategy.

She says, "I'm going to use adjustment because I can transform these addends into an easy addition and then adjust the sum at the end.

First, to make an easier addition, I will adjust both addends by adding 5 to each.

This gives me 100 plus 100, which is much easier to solve.

It's 200.

Lastly, I would adjust the sum by subtracting 10, which is the inverse of adding 2 lots of 5.

They scored 190 points.

What a fantastic total." Your turn to have a look at something to check you've understood.

Lucas uses adjustment but gets a different answer.

He calculates the total score as 195 points.

Can you spot Lucas' mistake in the jottings below? Have a good look at those jottings and see if you can see where there's a mistake.

Pause the video and I'll be back in a moment to show you.

Welcome back.

Did you spot the mistake? Well, here's Lucas telling us.

He says, "Oh no, I forgot that I'd adjusted both addends, so I only adjusted the sum by 5 when it should have been 2 lots of 5." You can see, he's crossed the 5 out and written 10.

The actual answer would've been 190 points just as Izzy showed us previously.

Okay, it's practise time.

Here's what I'd like you to do.

We've got some more friends playing the quiz, so there's a new pictogram that you can see on your screen.

Number one, I'd like you to calculate the number of points each contestant has scored.

And for number two, Laura and Aisha were on the same team.

What did they score in total? Use an efficient addition strategy.

For number three, Sofia and Jacob were on the same team.

What did they score in total? Use an efficient strategy.

For number four, how many more points did the winning pair score altogether? Use an efficient strategy.

And lastly, number five says the bar chart shows a number of pages read in a month by some of the children.

Use the bar chart to answer the question from Izzy, and Izzy's question is, "How many more pages did Jun read compare to Lucas?" Okay, pause the video here, have a really good go at these practise questions, and I'll be back in a little while for some feedback.

Good luck.

Welcome back.

We'll start with number one, shall we? The number of points each contestants scored.

Lucas says, "We counted in 10s for each full emoji and then added on any half emojis as 5.

Laura got 100, Jacob got 30, Aisha got 95, and Sofia got 45.

Number two, Laura and Aisha were on the same team.

What did they score in total? Use an efficient addition strategy.

Izzy says, "We needed to add together 100 and 95, so we used adjustment." 95 plus 100.

We added 5 to 95 to give us 100 plus 100, which meant 200, then we subtracted 5 to give us 195.

This is one way of doing it.

It might be that you just combined the two anyway, which could've been more efficient.

Number three, Sofia and Jacob were on the same team.

What did they score in total? Use an efficient strategy.

Lucas says, "We needed to add together 45 and 30, so we counted on in 10s." They got an answer of 75.

Number four, how many more points did the winning pair score altogether? Use an efficient strategy.

Laura and Aisha won with 195 compared to 75 for Sofia and Jacob.

We needed to calculate the difference between 195 and 75.

We found the difference by partitioning 75 and subtracting.

And there's the number line to show what they did.

They started on 195 and subtracted 70 to get to 125, then they subtracted 5 more and ended with 120, so they won by 120 points.

The winning team scored 120 more points.

And number five, our question was how many more pages did Jun read compared to Lucas? So the equation was 290 pages subtract 210 pages.

There's a number line to clarify your thinking, and then you might have recognised that you could make just one big jump of plus 80.

So the difference was 80.

I hope you managed to get those.

Okay, we finished the first part.

It's time to move on to looking at problem solving with tables instead.

The children play a netball game.

Each turn lasts 15 minutes, and the aim is to score as many times as they can.

Every time they score, they get 10 points.

If they hit the rim, they get five points.

Each child has two goes at it.

The children record the scores from their two goes into a table.

You can see the table there below.

You've got Izzy, Jacob, Aisha, and Sofia, and you've got the scores on their first go and the scores on their second go.

Izzy says, "So what did I score overall from both my turns?" Lucas says, "We will have to add together both your scores.

340 plus 270 is equal to.

We don't know yet.

It's an unknown.

Izzy decides to use partitioning.

She says, "Both addends have placeholders, but neither is close to a hundred boundaries so I will use partitioning." Good reasoning Izzy.

Izzy decides to use partitioning, and you can see there that she partitions both the numbers, then she writes them down in separate place value groups.

She says, "Then I'll recombine the groups, but I'll need to use bridging for the 10s." You can see that 40 plus 70 is going to bridge through 100.

She says, "I will partition a second time.

70 could be made 60 plus 10, so that I can make another 100.

Now she's got 500 plus 100 plus 10.

She says, "Now I can get the final sum which is 610.

I'm pleased with that score." As you should be, Izzy.

Well done.

Your turn to have a go.

Calculate how many points Aisha scored altogether.

Pause the video here, have a go, and I'll be back in a moment to give you the answer.

Welcome back.

Shall we see how you did? So we were looking at adding 260 and 330.

We might have chosen to use partitioning for this.

We've got our four place value groups written out as separate addends.

We then combined the 100s and combined the 10s.

How did you get on? Well, I hope.

Lucas and Izzy look at the table again.

Izzy says "Aisha really improved.

How much better was her second go?" Lucas says, "We can work it out using subtraction." Lucas calculates Aisha's improvement.

We've circled her numbers on the table.

Lucas says, "I am going to partition and bridge to calculate the difference between Aisha's first go and second go.

Aisha's second go was greatest, so that will be my minuend and her first go my subtrahend.

I'm gonna partition 260 into 200 and 60, and I'll use a number line to help." So he starts with 330, and says, "First, I'll subtract 200," and gets to 130.

"Next, I'll subtract 60, but this will involve bridging.

I know.

I'll partition 60 into 30 and 30." So he does just that.

"I'll subtract 30 to get to 100, which is an easier number to work from.

Now, I'll subtract the leftover 30 to make 70, which is how many points are you should improved by." Izzy calculates Aisha's improvement differently.

She says, "I'm still going to partition and bridge, but I will count on from the subtrahend.

I think it's more efficient." She draws out her number line "Firstly," she says, "I will add on 40 to get to the next hundreds boundary of 300.

Then, I will add on another 30 to get to 330.

Altogether, I added on 70 which is the difference, and shows how much Aisha improved by." Your turn to check your understanding.

Calculate how much Jacob improved by.

Pause the video here, have a go, and I'll be back in a little while to give you the answer.

Welcome back.

Shall we see how you got on? Izzy says, "We chose to partition and bridge counting back because the minuend and subtrahend were more than 100 away from each other." You can see here that they've written out the equation.

350 subtract 170, but they've partitioned 170 into 100 and 70.

They've drawn it all out on a number line.

Their first step was to take away 100, then they took away 50 and then they took away 20.

Those last two jumps were 70 partitioned again in order to bridge through 200.

They finished on 180, and that was the answer.

Did you get it? I hope so.

Now it's time for your practise.

Some more children play the netball game.

For number one, I want you to calculate the total number of points scored by each contestant.

You've got Jun, Sam, Alex, and Andeep.

For number two, I'd like you to calculate the improvement that each child made on their second go.

Pause the video here, have a go at those, and I'll be back in a little while to give you some feedback.

Good luck.

Welcome back.

We'll start with number one.

Calculating the total number of points scored by each contestant.

Izzy says, "We use partitioning and bridging to calculate these.

For Sam, we had to partition twice." Here are the total scores.

Jun got 390.

Sam got 550.

Alex got 680.

And Andeep got 550.

How did you get on? I hope you got them.

Okay, let's move on to looking at number two.

Calculate the improvement that each child made on their second go.

And Lucas says, "We used counting on or back for Jun and Alex, and then partitioning for Sam and Andeep." And here were their improvements.

Jun improved by 70.

Sam got 210.

Alex got 60 more.

And Andeep got 130 more.

I hope you enjoyed that lesson today.

Here's a summary of all the things that we have learned about.

Pictograms, bar charts, and tables contain information that is needed for addition and subtraction.

It is helpful to work out missing values at first so that the data can be understood.

Partitioning with bridging, adjustment, redistribution and counting on our back are very useful strategies to solve problems involving pictograms, bar charts, and tables.

My name is Mr. Tazzyman.

I've really enjoyed working with you today, and I hope to see you again soon in another math lesson.

Goodbye.