Lesson video

Hi everyone, thank you for joining me.

My name is Ms Jeremy, and today's lesson is focused on adding and subtracting using multiples.

So find yourself a nice quiet space and when you're ready press play to begin your lesson.

So let's begin by looking at our lesson agenda.

We're going to start with some part-whole modelling, and then we're going to look at the using derived facts and the making 10 strategy to help us with addition and subtraction.

We'll looking a little bit of some word problems and look at how we can derive information from our known facts.

And then we'll finish off with our independent task and quiz at the end of the lesson.

So for today's lesson, you will need a pencil and some paper and a nice quiet space.

Feel free to pause the video now to find these resources, and once you're ready, press play to begin the lesson.

So let's begin by looking at some part-whole models.

So as you can see on the screen, we've got two different part-whole models here.

And what I would like to know is what equations could these part-whole models represent.

So we'll look at the first one first, which is fairly simple.

You can see that we've just used ones counters for our part-whole model, and we've got two parts each with a different set of ones counters in.

So I can see in the first part here, I've got three ones counters.

So write the number three here, and I've got four ones counters in the second one.

So of course I know that my whole must be equal to seven.

So I've got seven ones counters in my final one.

And I'm going to just draw those in one, two, three, four, five, six, seven.

So let's think about the equations that we can represent using these part-whole models.

Well the first one, is fairly straightforward.

I'm just going to add together my parts, three plus four is equal to seven, nice and simple.

The next equation that we can represent using this part-whole model here, is using the commutative law.

So reminding ourselves that commutative law talks about swapping numbers around in an equation, if we're looking at an addition equation.

So in this case, instead of three plus four, we could do four plus three equals seven, exactly the same.

And then let's think about some subtraction equations that we could also derive from this part-whole model.

Well, if I take my whole to start with, and I start with seven and I subtract three, that's equal to four.

And similarly, if I start with seven and I subtract four, that's equal to three.

So there are four different equations we can derive just from this one part-whole model.

So now it's your turn.

Have a look at the part-whole model on the right of the screen.

This time, we've got place value counters that are equivalent to a value of 100,000.

First of all, can you work out what the equations are that we could represent using these part-whole models, start with your addition equations, and then move on to your subtraction equations.

You should be able to find four equations, just like we did with the previous part-whole model.

I'm going to give you 10 seconds to come up with your four equations.

If you'd like a little bit more time, press pause now, and then restart when you're ready.

Okay, let's have a look together.

So I can see here that I've got exactly the same number of place value counters as I did for my first place part-whole model, but actually they have a different value this time.

So this time, I've got a hundred thousands, which means in this box here, in this part I've got 300,000 and in the box below, in the other part I've got 400,000.

So 300,000 plus 400,000 is equal to? Well I know that three plus four is equal to seven, 300,000 plus 400,000 must be equal to 700,000.

I've used my known facts to derive information.

That's my first equation.

The next equation is going to use the same idea as my first part-whole model.

I'm going to use that commutative law.

I'm going to swap those numbers around.

So instead of 300,000 plus 400,000, I'm going to say, 400,000 plus 300,000 is equal to 700,000.

Then in exactly the same way as we've done with our first part-whole model, we can do 700,000 minus 300,000 is equal to 400,000 and then 700,000 minus 400,000 is equal to 300,000.

So you can see here that actually, if I knew this information over here, I could actually help, use that to help me derive this information over here.

And that's what we're going to be looking at today.

We're going to be looking at using our known facts, those facts that we know really, really easily to help us derive and to help us to calculate much harder questions later on.

So let's use this idea of derived facts to help us with the following question.

It says, can we solve this by deriving information from known facts? So I've got an equation here.

It says 15,000 minus 7,000.

There's lots of ways we could solve this, but actually I'd like to use a known facts that I have to help me answer this question.

When I'm looking at the main digits at the front of my numbers, I can see the main digits are 15 and seven.

And I'm wondering, if I want to calculate 15 subtract seven, potentially that might help me with working out 15,000 subtract 7,000.

So I know that 15 and subtract seven is equal to eight, and I know that the equation I'm originally looking at, so 15,000 subtract 7,000.

Well in this case, each of my integers in my equation have been multiplied by 1000.

So therefore, if I can do you do that for my original equation, I can do that for my answer as well.

So if I multiply my eight by 1000, therefore I can see that my answer would be 8,000.

So what I've done there, is I've used a known fact, I knew that 15 minus seven was eight.

I could work out really easily.

And I used that to help me solve a much harder question, 15,000 minus 7,000, because I looked at the links between 15 and seven, and 15,000 and 7,000.

So we can use derived facts to help us calculate equations like this.

There's also another method that we can use.

And it's called the making 10 strategy.

Let me show you how this would work.

Exactly the same equation as before, 15,000 minus 7,000.

But this time we're going to use a counting on strategy to make 10 in order to solve this.

So what I'm going to do, is I'm going to place 15,000 at the end here, and I'm going to place 7,000 here, and I'm going to use an adding on make 10 strategy to help me calculate the answer to this.

So effectively when we are subtracting, we're finding the difference between two numbers.

We can do that by taking away, or we can do that by adding on to find difference.

I'm going to demonstrate the adding on to find difference strategy.

So what am I going to do here is instead of doing one big jump all the way from 7,000 to 15,000, I'm going to do a smaller jump first using my number bonds to 10.

So I know that if I add on three to seven, that gives me 10.

So if I add on 3000, yeah, to 7,000, that would give me 10,000.

So here I've added on 3000.

And that is a make 10 strategy.

Cause that's an easy jump for me to make.

And now I've got a really easy jump to complete to my calculation, and to complete the number line, because I've just got to jump from 10,000 to 15,000.

I know that I have to add on 5,000 there.

So here I've used the make 10 strategy to jump to 10,000 and then to jump up to 15,000, and you can see that the difference is identified here and here, if I add those two numbers together, I also get 8,000 that matches to my previous answer.

So two different strategies you can use to solve questions like this.

You can use known facts to derive information to help you solve a problem like this.

Or you can use the make 10 strategy to help you out as well to find difference between two values.

So, I'd like you to have a go at this one.

I'd like you to use both of those methods, both the derived facts method, and the make 10 strategies method to solve 36,000 plus 5,000.

Have a go now, pause the video to complete your task and then resume it once you're finished.

So let's get started by firstly using the derived facts strategy to help us solve this problem.

So the first thing I'm looking at is the fact that I can use my known fact, 36 plus five to help me answer this.

So I know the 36 plus five is equal to 41.

So therefore when I'm calculating 36,000 plus 5,000, I'm multiplying those values by 1000.

So 36,000 plus 5,000 must be equal to 41,000.

So there I've used a known fact there, six plus five to help me work out a much harder equation, a much harder calculation.

So let's try and use the make 10 strategy.

So this time, we're adding instead of subtracting.

So in order to calculate this, I'm going to start with 36,000 on this side here, because remember we're not finding the difference, we're adding on.

And I want to add on 5,000, but I want to use the make 10 strategy to help me do that.

So I'm going to add on to the next multiple of 10, which is 40000 first.

So I'm going to add, 4,000 on first because I know that 36 plus four is equal to 40.

So 36,000 plus 4,000 must be equal to 40,000.

And then because I've only added 4,000 on, I actually need to add 5,000 on.

I need to add another 1000 to take me all the way up to 41,000, which is my final answer, just that.

So you can see I've used both the derived facts strategy and the make 10 strategy in order to calculate the same answer, 41,000.

And the great thing about these strategies is you can use them interchangeably.

You can choose which one you prefer, or you can use them both because that increases your accuracy.

If you want to solve something using the derived facts strategy first, and then you want to use the make 10 strategy, you can do that.

The other thing to remember is that these are all mental arithmetic strategies.

You can actually do a lot of these in your head.

I'm writing them down to demonstrate how your thought processes might work, but you can actually do a lot of these in your head as you go.

So let's have a look at some more information about derived facts.

And we're going to look at some involving this phrase here.

If I know, then I know.

So, let's start by looking at an example.

The example says this, if I know that 11 equals seven plus four, or using commutative law, seven plus four equals 11, what else do I know? So what I want to do, is to think about all the other facts that I know, all the other facts that I can derive from that known fact.

So I'm going to start off and I'm going to work quite systematically.

I know that 11 equals seven plus four.

So then, I know that if I multiply all those numbers by 10, I know that 110 must be equal to 70 plus 40.

Then, I'm going to start again with my known fact, 11 equals seven plus four.

Let's multiply all those digits by 100 instead.

So that would be 1,100 equal 700 plus 400.

That is another derived fact that I can gain from this known fact.

Let's go back to that known fact, 11 equals seven plus four.

Now let's multiply them by 1000.

So that would be 11,000 equals 7,000 plus 4,000.

Again, another derived fact that I've worked out just from that known fact.

Let's go back to it, 11 equals seven plus four.

Let's multiply that part there, that known fact there by 10,000.

So this time, I've got 110,000 equals 70,000 plus 40,000.

So you can see from just that one known fact, I've actually managed to derive one, two, three, four derived facts from it.

And that shows you that actually whilst we can do, whilst we can calculate derived fact from known facts, we can also do it the other way around.

We can take unknown fact and derive lots of facts from that.

So I'd like you to have a practise of this as well yourself, you've got an example here.

If I know that seven plus 11 is equal to 18, what else do I know? In the same way that I did really systematically, multiplying those digits by 10, 100, 1000 to 10,000, can you pause the video now to complete the task and resume it once you've got all of your derived facts.

Okay, let's have a look at all the derived facts that you might have got.

So the first one you might found multiplied by 10, where 70 plus 110 is equal to 180.

Then you might have decided to multiply by 100.

That would be 700 plus 1,100 is equal to 1,800.

Then you might decide to multiply by 1,000.

7,000 plus 11,000 is equal to 18,000.

And finally, you might have looked at multiplying by 10,000, 70,000 plus 110,000 is equal to 180,000, really systematic.

You could carry on actually, you could keep multiplying that known fact out.

And as long as you're doing the same thing to all of the digits in that equation, your answers will be accurate.

So really handy way of using known facts to help you to derive other equation fact.

Then let's move on to looking at some word problems because we can also use our derived and known facts strategies to help us with problems like this.

Let me read the problems out to you.

It says there are 45,231 people in the stadium and another 30,000 people enter, how many people are there now? So let's underline the information that's really important.

So we know there are 45,231 people and another 30,000 people enter, that suggest we're adding on another 30,000 people.

So the first thing I want to do after I've underlined that information, is to just write an equation to help me represent the calculation that I'm going to be doing here.

So I'm starting with 45,231, and I'm adding on 30,000.

Now for this particular equation, I want you to think about which digits in my original number, 45,231 will be changing in this case.

I'm adding on 30,000 and actually, in this particular case, only one digit is going to change, which one is it and why? I'm going to give you five seconds to work out.

So you might've seen that the only digit that is likely to change in this case, is the digit in the 10 thousands column.

And that's because I'm only adding 30,000.

I'm not adding to any of the other columns in this particular equation.

So I want to use my known facts to help me here.

I know that four plus three is equal to seven.

So 40,000 plus 30,000 must be equal to 70,000.

So my answer's going to be 75,231.

And you can see all the other digits and the rest of the numbers stay exactly the same as the original number, is just that digit in the 10 thousands changes.

So next part of the question says, 4,000 people leave early.

So if they're leaving, it suggests that we're subtracting, how many leftovers? I'm subtracting 4,000, once again, only one digit it's going to change in my original number, which digit will it be? Five seconds to work it out.

Okay.

You might have seen that the digit that we're likely to change, is the digit in the thousands column.

So you can see we're subtracting 4,000 and we're not subtracting anything else.

So it's just the digit in the thousands column that is going to change.

Currently, it is 5,000 and I'm subtracting 4,000.

So five minus four is equal to one.

So 5,000 minus 4,000 is equal to 1000.

So my final answer is 71,231.

And you can see how I use my known and derived facts there to help out with solving that problem.

I could have done that in my head.

So I've just shown you some workings out there, but mental arithmetic is absolutely fine.

You don't need to use the column method when you can use your known and derived facts in that way.

So it's time for your independent task now.

We've got three questions.

Question one has three parts to it.

You're going to start by using derived facts or the make 10 strategy to solve those three equations.

Then you're going to do a complete if I know then I know, and for 15 plus four equals 19, and you've got a word problem to end on that.

Pause the video to complete your task and then resume it once you're finished? Okay.

Let's have a look at some of the answers to the questions.

So you can see the answers to questions one, A, B and C are on the board there.

You can also see the derived facts and the number you can get from that known fact, all written out for you for question two, and the answer to that word problem is written the question number three.

So, if you'd like to today, please ask your parent or carer to share your work on Twitter, tagging @OakNational and #LearnwithOak.

Now it's time to complete the quiz.

Thank you so much for joining me for another math lesson today.

It was great to have you, do join us again soon.

Bye bye.