Lesson video
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Hi there.
I'm Mr. Tazzyman and I'm really excited to be doing some learning with you today.
If you're all ready, we can get started.
Okay, here's our lesson outcome.
By the end of the lesson, I'd like you to be able to say, I can subtract two digit numbers by finding the difference.
Here are the keywords that you're gonna come across during this lesson.
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 say it back.
My turn, minuend.
Your turn.
My turn, subtrahend.
Your turn.
My turn, difference.
Your turn.
Okay, let's have a look at what those words mean so that you can try to use them while you're thinking through some of the prompts you'll see in these slides.
The minuend is the number being subtracted from.
A subtrahend is a number subtracted from another.
The difference is the result after subtracting one number from another.
You can see the equation at the bottom there and it's been labelled with each of these three terms. I think that's probably one of the best ways of thinking about these different keywords.
The minuend has the subtrahend subtracted from it, and that gives you the difference.
Here's today's lesson outline then.
Subtract a pair of two-digit numbers by finding the difference and we're gonna spend the first part of the lesson thinking about when to find the difference and the second part of the lesson, we're gonna be finding the difference efficiently.
Ready to get started? Okay.
Here are two friends who are gonna help us with the maths whilst we learn.
They'll be chipping in with some discussion points, some answers and some responses to some of the prompts you'll see on the slides.
We've got Jun and Sofia.
Jun and Sofia are looking at problems that use the word difference.
They're thinking carefully about what it means.
Jun says, "Difference means subtraction, right?" And Sofia answers, "I think so.
The difference is the answer to a subtraction equation." Jun says, "I think I know some ways to work out difference." What is the difference in height between a giraffe and an elephant? Sofia says, "What does the question mean? The giraffe is taller than the elephant.
How can I think about the difference?" Jun replies with, "If I represent the heights with bars, the difference is the gap between them." You can see it there represented below.
The arrow shows the difference.
Let's try a new example.
What is the difference in mass between a banana and a pineapple? A pineapple is heavier than a banana.
Jun says, "If I represent the masses with bars, the difference is the gap between them." So we've got a similar representation again.
The pink is the mass of the pineapple and the green is the mass of the banana.
The arrow shows us the difference between them.
Okay, let's check your understanding.
Tell your partner a different difference problem.
Can you sketch a bar model to represent it? Pause the video here, have a go at that and I'll be back in a moment to see how you got on.
Welcome back.
How did you get on? Here are some examples that Jun and Sofia came up with.
Jun says, "What's the difference between the length of the table and my pencil?" And Sofia says, "How many more sweets did I eat compared to Jun?" Okay, let's get going again.
Jun scored 86 points on a computer game.
Sofia scored 92 points.
What's the difference between their points? How many more points did Sofia get? Jun says, "If I represent the point with bars, the difference is the gap between them." So he's drawn out a similar representation again.
You can see 92 and 86 and there's an arrow to show that difference.
He says, we can work out how many more by calculating the value of the gap.
Our scores are really close together.
What's the difference between our points? How many more points did Sofia get? Well, Sofia says, "The gap is the difference.
The top bar is the minuend and the bottom bar is the subtrahend." We can write it out as an equation.
Sofia says, "We can show the difference on a number line, what step can be made between the two?" You can see the number line there and we've got 92, 86 and that arrow again showing the gap between them, the difference.
Sofia wonders, what do we do to subtract from 92 to get to 86? Or what can we add on to 86 to get to 92? Sofia draws a clearer number line to think about the difference between 86 and 92.
She's separated out those two points on the number line.
She says, "I could count back in steps of one to see what the difference is, but I think I can be more efficient.
I can count back.
92 subtract 2 is 90." She's drawn that on her number line.
"90 subtract 4 is 86.
I have subtracted 6.
The difference between 86 and 92 is 6.
I think I can also count forwards to find the difference and the result will be the same." So this time she's gonna start in 86 and she's gonna add 4, which is 90.
It's a tens number so it's easier to work with.
90 add 2 is 92.
I have added 6.
The difference between 86 and 92 is 6." Jun shows Sofia's working out using base 10 blocks.
You can see there he's created 92 using base 10.
He says, "First Sofia counted back from 92 to 86," so she took off the 2 and she took off the 4.
"I took 6 ones away to equal 86.
Then Sofia counted on from 86 to 92." So we start with 86 as shown there on the base 10, we add 4 to get to 90 and then we add 2 to get to 92.
"I added 6 ones to equal 92." Jun scored 86 points on a computer game.
Sofia scored 92 points.
The difference is six.
Sofia scored six more points than Jun.
Unlucky Jun.
"We found the difference by counting on or back to find the missing part." "Yes," says Jun, "when the minuend and subtrahend are close together, this is a great strategy." So if they're both close together, you can find the difference really easily and it's an efficient way to go about it.
"You can count back from the minuend to the subtrahend, but I prefer to count forward from subtrahend to minuend." I wonder which you prefer, would you prefer to count on or would you prefer to count back? Now it's time for you to put all that learning into practise.
We've got some questions here for you to have a go at.
I'll read them to you and then I'll give you the chance to try and work them out.
Jun and Sofia continued to play the game.
Who won each time? By how much? Count on or back to find the difference.
1A, in this game Jun scored 45 points and Sofia scored 39 points.
B, in this game Jun scored 51 points and Sofia scored 59 points.
And C, in this game Jun scored 63 points and Sofia scored 72 points.
Here's number two.
I'd like you to write your own worded problem to match this bar model and then work out the difference.
Pause the video here, have a go at questions one and two, and I'll be back in a little while to give you some feedback.
Good luck.
Welcome back.
Ready for some feedback? Let's get marking.
Here's 1A and B.
In 1A, Jun won.
He scored six more points than Sofia.
You can see it represented on the number line here.
And the subtrahend has been partitioned into five and one to help.
In B, Sofia won.
She scored eight more points than Jun.
And again, we've got a number line represented here, but there's no partitioning necessary because you didn't need to bridge to find the difference.
I'll give you a moment to mark those.
Pause the video and I'll be back in a sec.
Okay, C, in this game, Jun scored 63 points and Sofia scored 72 points.
So Sofia won.
She scored nine points more than Jun.
And you can see on the number line again that the subtrahend has been partitioned into seven and two to help with bridging.
Okay, let's look at number two.
Here you had to write your own worded problem to match the bar model, then work out the difference.
Here's some examples.
A chocolate bar cost 69 pence and a pack of fizzy sweets cost 77 pence.
How much more do the sweets cost? A pack of fizzy sweets cost 77 pence, I have 69 p.
How much more money do I need? You might have chosen a completely different context for this bar model.
Hopefully you enjoyed it and hopefully you're ready to move on because it's time for the second part of the lesson.
We're gonna be finding the difference efficiently now.
Jun and Sofia are looking for equations they can solve by finding the difference.
Jun says, "We know other strategies for subtraction, but want to practise finding the difference.
We want equations where the minuend and subtrahend are close together.
11 and 86 are far apart and I can partition to subtract, I think." So that one's been crossed through.
"93 and 32 are also far apart.
We won't calculate these." Then Sofia comes in with, "37 and 29 are close together, but I think I would adjust 29 to subtract.
We'll leave that one, too." So they've managed to find three subtractions that can use finding the difference for a solution.
Let's see how they get on with them.
Sofia chooses one of the remaining equations to find the difference, 86 subtract 74.
She says, "I'm gonna find the difference between subtrahend and minuend by counting on." She counts on 6 to 80 and then 6 to 86.
"I counted on six and six more so the difference is 12." 86 subtract 74 equals 12.
Let's check your understanding of what we've just been through.
Sofia chooses one of the remaining equations to find the difference.
She counts back from the minuend.
41 subtract 37.
So she's drawn out her number line and she started on 41, she subtracted 1 to get to 40, then she subtracted 3 to get to 37.
That's all fine, but what you need to do is draw a number line to show how Sofia can get the same difference by counting on from the subtrahend.
Pause the video here, have a go at drawing out that number line and I'll be back in a moment to show you the answer.
Good luck.
Welcome back.
Let's see how you did.
Here's the number line.
You can see that Sofia has started on 37 and then added 3 to get to 40.
Then she's added 1 to get to 41.
So she knows that the difference is 4.
Jun's had a go as well and we'll use this to check your understanding too.
He's chosen one of the remaining equations to find the difference.
93 subtract 86.
He says, "I'm gonna find the difference between the subtrahend and minuend by counting on." But he's made a mistake.
Can you spot on his number line, what mistake he's made? Have a look and I'll be back in a moment to reveal the mistake.
Okay, have you spotted it? Let's have a look.
It's incorrect.
Jun counted on 5 from 86 to 90 when he should have added 4.
Nevermind Jun, you can't always get them right.
Okay, let's have a look at some practise questions now.
There's two parts to this.
First I want you to look through all of these equations and circle them if you think they would be solved most efficiently by finding the difference.
Then count on or count back to find the difference.
Use a number line to show the steps if you need to.
Pause the video here and give it a really good go and I'll be back in a little while to give some feedback.
Good luck.
Welcome back.
Let's see how you got on.
Here are the circled equations that would be best for finding the difference.
94 subtract 86.
71 subtract 63.
71 subtract 67.
35 subtract 27.
51 subtract 44.
49 subtract 44.
And with all of these you'll notice that the subtrahend and the minuend are close together, so finding the difference is the most efficient strategy to use.
So let's have a look at each of those selected equations and how you might have found the difference.
94 subtract 86 equals 8.
And this time we chose to count on, but you might not have done.
You might have counted back.
71 subtract 63 equals 8, and again, we've counted on.
71 subtract 67 equals 4.
Again, we counted on.
For all of these the number line has been drawn out and if you want to know how to solve 'em counting back, then all you'll need to do is reverse the arrows and use the inverse operation, subtract each time.
Let's have a go at these ones now.
51 takeaway 44 equals 7.
Again, we've counted on.
You can see that there.
35 takeaway 27 equals 8 and 49 takeaway 44 equals 5.
You'll notice that on the last number line, there aren't two jumps and that is because no partitioning was necessary.
We didn't need to bridge.
For the rest of the equations there were two jumps and that's because we needed to bridge, we need to partition the subtrahend into the right parts so that we could go to the nearest boundary and then count on from there.
Thanks for learning so well today.
Here's a summary of all the things that we've thought about.
When the minuend and subtrahend are close together, the difference can be found efficiently.
The difference can be found by counting or adding on from the subtrahend to the minuend.
The difference can be found by counting back or subtracting from the minuend to the subtrahend.
It's really important for you as a mathematician to decide which method you would rather use.
That can be done for each question or you might just be someone who wants to count on straight away or wants to count back straight away.
Okay, thanks very much for your participation today.
My name's Mr. Taziman, and I've really enjoyed learning with you, and I hope to see you again soon for another maths lesson.
Take care.
