Lesson video

Hello there.

My name is Mr. Goldie.

And welcome to today's Math lesson.

And here is our learning outcome.

I can use addition and subtraction to solve problems with multiples of 100.

And here are the keywords for today.

Just one keyword today.

I'm going to say the keyword.

Can you repeat it back? The keyword is multiple.

Let's take a look at what that word means.

A multiple is the result of multiplying a number by another whole number.

Multiples of 100 include 100, 200, 500 and 1,000.

And here's our Lesson Outline.

So in the first part of the lesson, we're going to be answering questions using a bar graph.

And in the second part of the lesson, we're going to be solving problems using a bar graph.

Let's get started.

In this lesson, you will meet Sam and Jacob.

Sam and Jacob have been playing some computer games with some of their friends and they're going to be asking you questions all about the scores the different children scored in some of those games.

The Oak Academy children have been playing "Angry Acorns." "This graph shows the number of points we each scored in the computer game." So you can see there at the top of the graph, there's the title.

"Graph showing number of points scored in 'Angry Acorns.

'" At the bottom of the graph, we've got the names of the children, Aisha, Alex, Andeep, Izzy, Jacob and Sam.

And then up the side of the graph, we've got the points that are scored.

"A player always scores a multiple of 100." Sam and Jacob look at the number of points scored.

Sam says, "I scored halfway between 1,200 and 1,400 points." What multiple of 100 comes between 1,200 and 1,400? "I scored 1,300 points," says Sam.

"I scored exactly 1,000 points," says Jacob.

So you can see the bar showing that Jacob's points ends exactly on 1,000, so he's got exactly 1,000 points.

"It's helpful to write the scores on the graph." That's a really useful strategy when you're answering questions to do with bar graphs, is actually to write the number that each bar shows at the top of the bar.

What did the other players score? Now have a look at the other four children, Aisha, Alex, Andeep and Izzy, how many points did they score? Pause the video and see if you can work out the scores of those four children.

And welcome back.

Let's take a look to see whether you got the right answers.

So first of all, Sam says, "Aisha scored 500 points." Aisha's bar goes all the way up to halfway between 400 and 600 so she scored 500 points.

"Alex scored 300 points." Alex did not score very highly.

Apparently, "Alex had trouble avoiding the acorns." "Andeep scored 700 points." So his bar ends between 600 and 800.

So he must have scored 700 points.

"Izzy scored 1,200 points," altogether, so Izzy did pretty well as well.

So very well done, if you managed to work out the scores of each of those four children.

Which two players scored a total of 1,000 points? "We're looking for two multiples of 100 with a sum of 1,000." Can you spot two multiples of 100 with a sum of 1,000? Jacob says, "I know, 7 + 3 = 10.

So 700 + 300 = 1,000." "Andeep and Alex scored a total of 1,000 points." Which player scored 100 points fewer than another? "We're looking for two multiples of 100 with 100 difference." So can you spot two scores with a difference between the two scores is 100? Jacob says, "1,300 - 1,200 = 100." "Sam scored 100 points more than Izzy." The difference between those two scores is 100 points.

Which player scored 600 points fewer than Sam? "I scored 1,300 points.

I need to calculate 1,300 - 600." So Sam's going to use a number line to help her work out the answer.

She says, "I need to bridge 1,000.

I'll partition 600 into 300 and 300.

1,300 - 300 = 1,000.

1,000 - 300 = 700." So Sam has partitioned 600 into 300 and 300, to help her bridge that 1,000.

And the question is, which player scored 600 points fewer than Sam? What's the answer? The answer is, Andeep.

Andeep scored 700 points.

"Andeep scored 600 fewer points than I did." Now here's one for you to try on your own.

How many points did Izzy and Andeep score in total? "How can you efficiently add the scores together?" So you need to find Izzy and Andeep scores on the bar graph and then you need to add them together to work out their total score.

How much they score altogether? Pause the video and see if you can work out the total.

And welcome back.

Did you manage to get the answer? Let's take a look to see whether it is the correct answer.

Sam says, "You needed to calculate 1,200 + 700." Izzy scored 1,200 points, Andeep scored 700 points.

To get their total score, you'd have to add those two scores together.

Jacob says, "I know 700 + 200 = 900.

1,000 + 200 + 700 = 1,900.

1,200 + 700 = 1,900." "Andeep and Izzy scored 1,900 points in total." Very well done.

That's the answer that you got.

And let's move on to Task A.

The children play "Angry Acorns" again.

So this time they've scored different number of points each.

"Use the graph to answer the questions," says Sam.

"It's helpful to write the scores on the graph," says Jacob.

So once you work the scores out, actually write them on the graph that's gonna help you answer the questions later.

So here are the questions.

Use the graph to answer these questions.

How many more points did Alex score than Andeep? How many more points did Izzy score than Sam? Which two players had 1,000 difference between their scores? Which two players scored a total of 2,000 points? Who scored 800 fewer points in Aisha? Which two players had 400 difference between their scores? So think carefully about each of the questions and how are you going to work out the answer.

Is it an adding question? Is it a subtraction question? Think carefully about the answer.

Is it definitely the right answer? Does it definitely look right? Pause the video and have a go at completing Task A.

And welcome back.

How did you get on? Did you complete all of the questions? Let's take a look to see whether the answers you did get were the right ones.

So the children play "Angry Acorns" again.

"Here are the points that were scored." So they are the points of a score by each of the children.

So Izzy scored 1,100 points.

Andeep scored 500 points.

Jacob scored the most with 1,500 points.

Here are the answers to the questions.

So the first question was, how many more points did Alex score than Andeep? So the calculation you should have done was 600 - 500, that is equal to 100.

Alex scored 100 more points in Andeep.

And you may have spotted there that the easiest way of working out the difference between those two numbers is by counting back from 600 to 500.

There's only 100 difference between those two numbers.

Question B.

How many more points did Izzy score than Sam? So this is a subtraction question as well.

So 1,100, that's Izzy's score.

Subtract 800, that Sam's score is equal to 300.

Izzy score 300 more points than Sam.

You may have used number line to help you work out the answer.

You may have started with 1,100 - 100, that gets you to 1,000.

And then subtract 700 that counts all the way back to 300.

So you can partition 800 into 100 and 700 to help you bridge through that thousands boundary.

But Jacob says, "You could have also counted back from 1,100 to 800 to find the difference." So find the difference between those two numbers is sometimes easier to count back from the larger number to the smaller number.

Let's look at question C.

So which two players had 1,000 difference between their scores? 1,500 - 500 = 1000.

Jacob's and Andeep's scores had a difference of 1,000.

D, which two players scored a total of 2,000 points? You are looking this time for two numbers, two scores that add together to equal 2,000 points.

And in fact, there were two different answers for this one.

I don't know if you've got one of them.

Very well, if you've got both.

So 1,400 + 600 = 2,000.

So Aisha and Alex scored a total of 2,000 points.

And 1,500 + 500 = 2,000.

Jacob and Andeep also scored a total of 2,000 points.

So very well done if you spotted both of those.

Jacob says, "14 +6 = 20.

14 hundreds add six hundreds is equal to 20 hundreds or 2,000." So it's all about using those name facts.

So you might have used number pairs, the total 20 to help you work out the answers.

So question E, who scored 800 fewer points in Aisha? The 1,400 - 800 = 600.

Alex scored 600 points.

So Alex scored 800 fewer points than Aisha.

And again, you may have used number line to help you work out the answer.

You may have partitioned 800 into 400 and 400.

1,400 - 400 = 1,000.

And then 1,000 - 400 = 600.

And then finally question F, which two players had 400 difference between their scores? So 1,500 - 400 = 1,100.

And 1,100 + 400 = 1,500.

There is a difference of 400 between Jacob's and Izzy's scores.

So very well done if you managed to answer some of those questions, and if you managed to answer all of them, brilliant work, very well done indeed.

And let's move on to part two of the lesson.

So part two of the lesson is solving problems using a bar graph.

The Oak Academy children play the game "Quercus." "Quercus" is actually the Latin word for Oak tree.

Latin is the language of the Romans.

So I suppose it makes sense that the Oak Academy children have been playing a game called "Quercus." Sam says, "Every score is a multiple of 100." Jacob says, "We're going to work out who achieved each score using some clues." So you may have spotted on the graph this time the thing that is missing are the names of the children.

So we've got their scores, but we don't know which child scored which number of points.

Clue number one.

Lucas scored 200 more points than Laura.

Wow.

We should be able to use that to help us work out what Lucas scored and what Laura scored.

So Sam says, "We are looking for two scores with a difference of 200 points." Can you spot two scores with a difference of 200 points? 1,400 + 200 = 1,600.

So perhaps Laura scored 1,400 points.

Lucas scored 1,600 points.

Seems to make sense, doesn't it? Oh, hang on a minute.

There were two more numbers with the difference of 200.

So 700 + 200 = 900.

So Lucas could have scored 900 and Laura could have scored 700.

And that's not all, 500 + 200 = 700.

So perhaps Laura scored 500 points and Lucas scored 700.

Could have a bit of a problem here, aren't we? Jacob says, "There are three different possible answers.

Let's come back to this clue later." So they look at clue number two.

Clue number two says Izzy scored 500 fewer points than Laura.

So Laura scored 500 more points than Izzy.

I wonder how they'll work out the answer to this question? Sam says, "We're looking for two scores with a difference of 500 points." Jacob says, "Let's start with 1,600 points." So one of the scores could be 1,600.

"1,100 is 500 less than 1,600." Ah, so perhaps Laura scored 1,600 points and Izzy scored 1,100 points.

That makes a lot of sense.

Sam says, "There isn't a score of 1,100 points so 1,600 cannot be one of the numbers." So it's not correct.

So it's definitely not 1,600 and 1,100, because there isn't a score of 1,100.

Now you might be thinking, well that's a bit of a waste of time, but it's not is it? Because Sam and Jacob now know that 1,600 is not one of the numbers.

Sam says, "Perhaps Laura scored 1,400 points." Now they know that Laura scored 500 more points than Izzy.

Perhaps Laura scored 1,400 points.

"I'll work out 1,400- 500," says Jacob.

"I'll partition 500 into 400 and 100 to help me bridge 1,000." So "1,400 - 400 = 1,000.

1,000 - 100 = 900." Brilliant.

"Laura scored 1,400 points and Izzy scored 900 points." There is a score of 900.

So Sam and Jacob are pretty confident that Laura scored 1,400 points and Izzy scored 900 points.

Because actually if you look at the other numbers, we've got their 900.

500 - 900 is 400.

There is not a score of 400.

And 500 less than 700, which is the other score is 200.

Nobody scored 200 and the lowest score is actually 500.

If Laura scored 500, Izzy would've scored zero points because 500 - 500 = 0.

So the answer must be Laura scored 1,400 points and Izzy scored 900 points.

Brilliant work you two.

So you now know the names of two of the children on the bar graph.

They've worked out which score Laura achieved and which score Izzy achieved.

Very well done.

Clue number three.

So this is one for you to try on your own.

Sofia scored 200 more points than Jun.

So one of those is Sofia's score and one of those is Jun's score.

Which score is which? "Work out how many points Jun and Sofia scored." So have a good look at the bar graph.

Sofia scored 200 more points than Jun, which bar shows Sofia's points, which bar shows Jun's points.

Pause the video, see if you can work out the answer.

And welcome back.

Did you manage to work out the answer? Let's take a look to see whether you were right.

Now, first of all, before we actually look at the correct answer, you may have said, "Ah, 1,600, that's the highest score is 200 more than 1,400.

So perhaps the fear scored 1,600." Bit of a problem with that one isn't there? Because it wasn't Jun that scored 1,400, it was Laura.

And this doesn't say Sofia scored 200 more points in Laura.

It says Sofia scored 200 more points than Jun.

Okay, so 1,600 cannot be one of the scores.

"500 + 200 = 700.

Sofia scored 700 points and Jun scored 500 points." Remember Sofia scored 200 more points than Jun.

So very, very well done, if you worked out that 700 was Sofia's total points and 500 was Jun's total points.

Very well done indeed.

Now there's just one name missing now on our graph, isn't there? So we've got to go back to clue number one.

It should be pretty obvious now who scored the number of points? Clue number one says, Lucas scored 200 more points on Laura.

Now we can go back to clue number one.

"Laura scored 1,400 points." "1,400 + 200 = 1,600.

Lucas scored 1,600 points." So that was the first clue we looked at.

But in fact, we couldn't use that clue first of all, so Lucas is the missing name here.

"That's brilliant.

I think we've worked out each person's score," says Sam.

So very, very well done, Sam and Jacob and well done you too as well for helping them on their way.

And let's move on to Task B.

So Task B, you're gonna be solving a very, very similar problem to the one that Sam and Jacob have just been solving.

You're gonna work out who scored which points.

Sam says, "Use the clues to help you." Jacob says again, "It's helpful to write the scores on the graph." And then you can use those to help you work out the answers to the clues.

And here are the clues.

Aisha scored 400 more points than Sam.

Andeep and Izzy scored a total of 2,000 points.

Jun scored 300 fewer points in Andeep And Jacob scored 100 fewer points than Izzy.

It's quite a tricky problem this one.

And a bit like the problem we just looked at with Sam and Jacob, you may need to think very, very carefully about the order in which you answer the questions.

Sam says, "This is not the suggested order.

You'll need to work out some clues before others." You need to do quite a lot of thinking here.

There's only six names that are missing on the graph, but can you work out the definite which scores each child achieved? Tricky problem, this one, lots of thinking involved.

Bit of trial and improvement and you should be subtracting and adding those multiples of 100.

Try and help you work out the answers.

So very, very best of luck.

Pause the video and have a go at Task B.

And welcome back.

How did you get on? Did you manage to work out the missing names and managed to put a name to each of the scores on the graph? Now let's take a look to see whether you got the right answers.

So here are the answers.

So Sam says, "I scored 1,300 points." Jacob says, "I scored 1,100 points." And you can see the scores of the other children on there as well.

But most importantly, how did we get to those answers? Now you may have used the clues in this order.

You may have solved the problem a different way, but this might be the easiest way to solve the problem.

Start with clue B.

Andeep and Izzy scored a total of 2,000 points.

So we're looking for two numbers that add together to make a sum of 2,000 as only two numbers actually do that.

The numbers are 800 and 1,200.

800 + 1,200 = 2,000.

Izzy and Andeep either scored 800 or 1,200 points.

A bit of a problem here 'cause we don't know which score Andeep achieved and which one Izzy achieved at the moment, do we? So we're gonna have to use another clue to help us work that out.

If we look at clue D.

Clue D says Jacob scored 100 fewer points than Izzy.

Now we know that Izzy scored either 800 points or 1,200, but we don't know which one she achieved.

But Izzy cannot have scored 800 points because nobody scored 700 points.

If Izzy has scored 800 points, that meant that Jacob has scored 700 points, but there is no score of 700 points.

So Izzy must have scored 1,200 points, which means that Jacob scored 1,100 points, and Andeep scored 800 points because remember Izzy and Andeep scored 2,000 points between them.

So you sort of had to use those two clues together.

Very tricky this, isn't it? So Izzy scored 1,200 points, Andeep scored 800 points, Jacob scored 1,100 points.

Now once you've done this bit, the rest is much, much easier because clue C says Jun scored 300 fewer points than Andeep, we know that Andeep scored 800 points.

So 800 - 300 = 500.

So Jun scored 500 points.

Aisha scored 400 more points than Sam.

1,700 - 1,300 = 400.

And 1,300 + 400 = 1,700.

So Aisha scored 1,700 points and Sam scored 1,300 points.

Very, very well done if you managed to solve that problem 'cause it's really quite a difficult problem that one.

And don't worry if you didn't quite get there, 'cause actually solving problems like that are really, really important.

And sometimes they're really, really tricky and we don't always get to the right answer.

But actually, if you've shown real resilience and real perseverance and really had a go at trying to find the answer and you didn't give up, that's a really, really important skill to have.

So very well done if you managed to solve the problem.

Really, really well done if you persevered, even if you didn't solve it, excellent work.

And hopefully you are feeling really confident at solving problems using bar graphs, and adding and subtracting multiples of a hundred to work out different answers.

Excellent work today.

Very well done.

And finally, let's go on to my lesson summary.

So known facts help us to add and subtract multiples of 100.

Unitizing can help us to add and subtract multiples of 100.

Adding and subtracting multiples of 100 can be represented in different ways.