Lesson video

Hi there.

My name is Mr. Tazzyman, and I'm really looking forward to teaching you the lesson today from the unit that's all about equivalence, compensation, and subtraction.

If you're ready, we can get started.

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

By the end, we want you to be able to say, I can solve subtraction calculations mentally by using known facts.

These are the key words that you're gonna hear today.

I'm gonna say them and I want you to repeat them back to me.

So I'll say my turn, say the word, and then I'll say your turn and you can repeat it.

Ready? My turn.

Minuend.

Your turn.

My turn.

Subtrahend.

Your turn.

My turn.

Partition.

Your turn.

My turn.

Adjust.

Your turn.

Great.

Let's just make sure that we clarify exactly what each of those keywords means.

The minuend is the number being subtracted from, a subtrahend is a number subtracted from another.

You can see them both there at the bottom and an example subtraction equation.

Seven subtract three is equal to four.

In that, the minuend is seven and the subtrahend is three.

Partition is the act of splitting an object or value down into smaller parts.

When you adjust, you make a change to a number.

This is done to make a calculation easier to solve mentally.

This is the outline of today's lesson on solving subtraction calculations mentally by using known facts.

We're gonna begin by using known facts as a mental strategy.

Then we're gonna look at solving problems in context.

Hi Sofia.

Hi Jacob.

These two are gonna help us along the way.

They will be responding to maths prompts, sharing their thinking, and even revealing some hints and tips for you to help you get some of the best out of this lesson.

Okay, are you ready to learn? Let's go for it.

Jacob and Sofia look at a subtraction question.

155 subtract 0.

65 is equal to an unknown.

Ooh, this has decimal fractions.

"I'll use columns here.

I know it well." "Wait, we can be more efficient.

I can use a known fact." One subtract 0.

65 is equal to 0.

35.

You can probably start to see Jacob's thinking here.

If we adjust one part and the other part remains the same, we have to adjust the whole by the same amount.

So you can see what he's done there.

He's looked and he's compared his known fact with the question.

He subtracted 154 to give him his minuend in the known fact.

So, he needs to add 154 to the difference from his known fact in order to give him the difference in the original question.

It's 154.

35.

Jacob and Sofia think about the steps taken.

"I used three main steps here," says Jacob.

Firstly, he looked for the known fact.

There it is.

One subtract 0.

65 is equal to 0.

35.

He probably used his compliments to 100 there as well to help him out.

Two, how does it help? It helps because I can use adjustment.

He took away 154, so he has to use the inverse, which is step three, to add it back.

And he gets 154.

35.

Sofia compares the adjustment method with partitioning.

"Using adjustment is similar to partitioning." She takes 155 and partitions it into 154 and one.

Then, she looks at one subtract 0.

65, which is 0.

35.

She combines 154 and 0.

35 to give her the answer of 154.

35.

A very similar method.

Okay, let's check your understanding so far.

Use the three steps to solve this subtraction equation.

We've got 231 subtract 0.

82, and the three steps are written on the right as prompts for you there.

Pause the video and have a go.

Welcome back.

First, you might have used a known fact like this, one subtract 0.

82 is equal to 0.

18.

Number bonds to 100 were useful here as well.

We know that 82 plus 18 is 100, so 0.

82 plus 0.

18 is equal to one.

The adjustment was 230 because 230 was subtracted to give one.

So that means that the difference needed to be adjusted by adding 230, the inverse.

That gave an answer of 230.

18.

Did you manage to get that? Hopefully.

Jacob and Sofia look at a subtraction question.

25.

42 subtract 0.

18 is equal to an unknown.

"Decimal fractions for both minuend and subtrahend," says Sofia.

"Definitely one for columns here." What do you think Jacob might think to that? "I think we can use two known facts here." Interesting.

"First, I'll use my understanding of unitisation." 42 subtract 18 is equal to 24.

Why do you think he might have picked that out as a known fact? Aha.

He uses that to understand another known fact, 0.

42 subtract 0.

18 is equal to 0.

24.

"Then, I'll use adjustment," he says.

He subtracted 25 from the minuend there, so he needs to add 25 to the difference to get back to the difference in the original question, is 25.

24.

"Wow, that was more efficient," says Sofia.

Sofia compares the adjustment method with partitioning.

"This is similar to partitioning again," she says.

She starts by partitioning 25.

42 into 25 and 0.

42.

Then, she takes a known fact of 42 takeaway 18 is equal to 24, and she uses that to help her find the difference between 0.

42 and 0.

18.

It's 0.

24.

She combines 25 and 0.

24 to give 25.

24.

Okay, your turn.

Use the three steps to solve this subtraction equation.

65.

57 subtract 0.

21.

Pause the video and give it a go.

Welcome back.

Did you start with a known fact like this? 57 subtract 21 is equal to 36.

That means that I know 0.

57 subtract 0.

21 is equal to 0.

36.

I've adjusted by subtracting 65, so I need to add 65 to the difference in order to work out the difference for the initial question, 65.

36.

Did you get that? Hopefully.

Jacob and Sofia look at a subtraction question again.

This time, it's 36.

11 subtract 0.

72.

What do you notice about this subtraction question? "I can tell that this will involve regrouping." "The value of the tenths and hundredths in the subtrahend is greater than in the minuend." "A written method is more efficient here." "This time I agree," says Jacob.

The answer is 35.

39.

Okay, let's check your understanding again.

Why might this calculation be harder to use adjustment with? It's 33.

14 subtract 0.

77.

Give a really clear explanation here.

Pause the video and have a go.

Welcome back.

Let's look at an explanation.

Jacob says, "To use adjustment here, I would have to regroup because the tenths and hundredths are greater in the subtrahend." So you can see the tenths and hundredths column have seven as a digit.

That's greater than one and four which feature in the minuend.

That means that you would have to regroup if you were going to do the subtraction.

Jacob and Sofia look at another subtraction with larger integers.

And there's our prompts on the left just to remind us.

478,000 subtract 28,000.

"Larger numbers," says Sofia.

"We can still make use of known facts here." So Jacob's written down 78,000 subtract 28,000 equals 50,000.

He might well have even used 78 subtract 28 equals 50 there.

He's adjusted by subtracting 400,000 from the minuend.

So, in order to adjust back to the original question, he needs to add 400,000 to the difference, giving him 450,000 in total.

Sofia compares the adjustment method with partitioning.

She shares another possible use of partitioning.

She partitions 478,000 into 400,000 and 78,000.

Then, she looks at 78,000 subtract 28,000.

That gives a difference of 50,000.

If she combines that with 400,000, she gets 450,000.

Very similar method and very, very accurate.

Okay, let's check your understanding again.

Use the three steps to solve this subtraction equation.

282,000 subtract 42,000.

Pause the video here and give it a go.

Welcome back.

You might have started with this known fact, 82,000 subtract 42,000 is equal to 40,000.

Perhaps to get that, you might have used 82 subtract 42 is equal to 40, and then your understanding of place value to change which power of 10 you were using there.

We can see the adjustment was takeaway 200,000, which meant that using the inverse, we had to add 200,000 to the resulting difference to give us our initial difference, which was 240,000.

I hope you managed to get there.

Sofia has to tick the expressions that she thinks she could calculate efficiently mentally using adjustment or partitioning.

So we've got three expressions here, 289,000 subtract 11,000.

62.

64 subtract 0.

87, 119 subtract 0.

78.

What do you think? Which ones of those do you think you could use adjustment or partitioning on? Well, Sofia has ticked the top one and the bottom one and she's gonna explain to us why.

"In both ticked expressions I can use a known fact to help solve them mentally.

The unticked expression will need regrouping, so I would use a written method." Okay, it's time for your first practise task.

For number one, I'd like you to use a known fact and adjustment to solve these mentally using jottings if needed.

You've got a and you've got b.

For number two, below are some addition expressions.

Tick the expressions you think could be solved mentally using adjustment or partitioning.

Write an explanation about your decisions, and that last part's really important for developing your mathematician skills, writing explanations.

We've got 62.

13 subtract 0.

64, 976,000 subtract 16,000.

And 312 subtract 0.

46.

For number three, you've got to complete the following subtraction in two ways.

Firstly, calculate mentally using adjustment or partitioning.

Then, use a written method such as column subtraction.

Which did you find to be more efficient? Okay, I'll be back in a little while to give you some feedback.

So pause the video and enjoy.

Okay then, let's get going with some marking and some feedback.

We'll start with number 1a.

We have 1.

13, 2.

13, 68.

79, 69.

3, 450.

38, 451.

33.

Now let's move on to b.

50,000, 350,000, 1,350,000, 56,000, 456,000, 1,456,000.

Here's number two, then.

We ticked the middle and the bottom one.

We've got an explanation coming from Sofia as well.

"The two ticked expressions can use known facts." You can see them listed there.

The middle one used 76,000 subtract 16,000 is equal to 50,000 as a known fact and the bottom one used one subtract 0.

46 is equal to 0.

54 as a known fact.

The unticked expression needs regrouping, and there's a comparison there of the tenths and hundredths in the minuend and the subtrahend.

You can see that the subtrahends tenths hundreds exceed the minuends tenths and hundreds, meaning that regrouping would be needed.

Here's number three, then.

We add 7.

22 for a and we had 330,000 for b.

Which did you find to be more efficient? Well, Sofia said, "I found adjustment more efficient because it was quicker and I could make use of known facts that were useful." Okay, let's move on to the second part of the lesson, then, solving problems in context.

Jacob and Sofia play an arcade game against one another.

They each get a different score, which is shown in the table below.

Also, each of them get penalty points for mashing the buttons.

These are subtracted to calculate the final score.

Who won the game? So we can see that Sofia scored 578,000 but had 28,000 penalty points, which will be reduced from her score, and Jacob scored 589,000 but needed that to be reduced by 38,000.

Sofia says, "I think we will need to use a written method here.

There's too much to think about." "No, we won't.

I think we can calculate mentally." Well done, Jacob.

What do you think? Well, let's have a look.

Jacob uses adjustment to calculate the scores.

I'll work out Sofia's score first using a known fact.

He writes out the equation 578,000 subtract 28,000.

This is the known fact he uses, 78,000 subtract 28,000 is equal to 50,000.

He can see that there's an adjustment of 500,000.

It's been subtracted, so he adds 500,000 using that inverse to give him the final difference, which is 550,000.

That's Sofia's score.

"Now I'll work at my score," he says.

He starts with 589,000 subtract 38,000.

The known fact he uses is 89,000 subtract 38,000 is equal to 51,000.

And he can see that there's been an adjustment of, again, subtracting 500,000.

So, he adds that to the resulting difference to give him the initial difference, which is 551,000.

Oof, that was close.

"Woohoo, I won." Okay, your turn to have a go and think about what we've just learned about.

Sofia has a second go.

She calculates her score mentally.

Can you spot a mistake in the workings? Hmm, have a good look there and see if you can spot the mistake.

Pause the video here.

Welcome back.

Did you manage to spot that the difference with the known fact was actually incorrect.

It should have been 29,000.

And of course, that had a knock on effect to a lot of the other parts of the working as well.

In fact, the resulting should have been 629,000, so her jotting should have been 629,000 as well.

It's always important to make sure your known facts are definitely accurate.

Sofia sets Jacob a challenge.

He has to sort out three expressions into the inequality statement.

We've got three blank spaces there with less than symbols in between.

And these are the three expressions that need calculation.

Jacob works out the value of each expression mentally using adjustment.

63 subtract 0.

78.

He starts with the known fact one subtract 0.

78 equals 0.

22.

He can see there's been an adjustment of subtract 62, so he adds 62 back to give him a difference of 62.

22.

That's the first one done.

Time for the second, 62.

89 subtract 0.

43.

Well, he starts with a known fact 89 subtract 43 is equal to 46.

Hmm, that seems a bit strange.

It's not the same place value.

What's he thinking? Ah, he's now going to use that as his known fact by changing the place value.

0.

89 subtract 0.

43 is equal to 0.

46.

That makes sense.

There's an adjustment of subtracting 62, so he adds 62 back using that inverse process.

That gives him 62.

46.

Now for the third one, 62.

64 subtract 0.

36.

His known fact is 0.

64 subtract 0.

36 is equal to 0.

28.

He got that by using his understanding of 64 subtract 36 is equal to 28.

He can see there's been an adjustment of subtract 62, so he adds 62 back on to give him 62.

28.

Is he finished though? Well, let's look back at the original question.

No, he's not.

He now needs to put them into the correct places by comparing their values.

He puts 63 subtract 0.

78 is equal to 62.

22 first.

That is less than 62.

64 subtract 0.

36, which is equal to 62.

28, which is less than 62.

89 subtract 0.

43, which is equal to 62.

46, and he's finished.

Well done.

Okay, your turn.

Have a look at each of these inequality statements.

What's the same? What's different? Can you explain it? Pause the video and have a go.

Welcome back.

Here's Sofia's explanation.

The expressions are the same in both statements.

They have moved position in the second statement because a less than symbol has been switched to a greater than symbol.

If you peer in really closely, you can see that.

Compare the second symbol in each of those inequality statements.

Okay, it's time for your practise task, your second one.

In number one, the table shows the scores of some of the other children who played the arcade game.

Calculate each mentally and then rank them from greatest to smallest, and you've got the ranking there going from first to fifth.

For number two, similar to what Jacob just did, place the expressions into the correct place on the inequality statements.

Really take note of which symbols have been used here.

Okay, pause the video and have a go at those questions, and I'll be back in a little while with some feedback.

Enjoy.

Welcome back.

Let's look at number one to begin with.

Quite a lot of calculation needed here.

To start with, we might have done 672,000 subtract 18,000 is equal to, well, let's use a known fact.

72,000 subtract 18,000 is equal to 54,000.

That was an adjustment of subtract 600,000, so we need to add 600,000 back on, giving us 654,000.

That's the first one calculated.

Here were the others.

Andeep got 487,000.

Sam got 644,000.

Alex got 594,000.

Laura got 602,000.

Now we need to rank them.

So here they go.

Izzy was first, Sam was second, Laura was third, Alex was fourth, and Andeep was fifth.

You might have written the numbers into the rank instead of the characters.

That's okay, as long as you check that the numbers you used were the ones that that character scored.

Here's number two, then.

These are the values for the expressions, and they fit in like this.

112.

78 subtract 0.

69 is equal to 112.

09, which is less than 112.

64 subtract 0.

54, which is equal to 112.

1, and is more than, did you spot that? More than 112 subtract 0.

95, which is equal to 111.

05.

Sofia helps us here and says that, "The first and last equations expressions to start with could be swapped." So you could have swapped those ones 'round.

Pause the video here if you need some more time to mark that carefully.

That brings us to the end of the lesson, then.

Here's a summary.

When looking at subtraction calculations, it is easy to go straight to using a written method.

However, there are more efficient methods available with closer inspection of the Minuend and subtrahend.

Sometimes adjustment can easily be used if the correct known fact can be identified and used.

Firstly, a known fact is identified that helps adjustment and then the inverse is used to find the difference.

My name is Mr. Tazzyman.

I've really enjoyed that lesson and I hope you have too.

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

Bye for now.