# Lesson video

In progress...

Hello everyone, welcome to math with Ms. Dobrowolski.

Today we'll be subtracting two-digit numbers involving regrouping.

Now let's have a look at today's lesson agenda.

First we'll review subtraction with dienes, then we'll be completing some mental calculations using a number line.

So for this lesson you will need a pencil and a notebook.

If you don't have these items, pause the video now and go get them.

Great, let's get started.

So, let's look at doing mental calculations using dienes.

I'm sure you've seen them at school before.

So here we have the builders, and the builders have been hard at work today.

In fact, they started with 31 bricks, and they used 16 bricks.

So how many bricks do they have left? Do you see, I know the whole.

The whole is 31, so I have to subtract the part that I know, the 16, I'm going to subtract the part that I know from the whole to find the other part.

Let's look at this using my dienes.

So we can also represent this calculation on our whole part model.

So you can really easily draw a whole part model at home.

First you draw a big box to represent where you're going to put your whole, and then two smaller boxes that will represent your parts.

Just like this.

Great.

First let's identify the whole, hm.

Well I know 31 is the whole, because that's the number we'll be subtracting from.

So let's use our dienes and fill in our whole.

31 has three 10s, 10, 20, 30, and one one.

Just like that.

One of our parts is 16, and the other part, well we don't know yet, that's what we need to figure out.

So how can we subtract 16 from 31? One strategy I really like is partitioning the second number.

I know 16 has one 10 and six ones.

So let's subtract our tens first.

I know three tens minus one ten is equal to two tens, so that must mean 31 minus 10 is equal to 21.

10, 21, and then move the 10 I subtracted into my part.

Great, now we need to subtract our ones.

Hm, I know that 21 minus one is equal to 20, so I'm going to partition six into one and five.

One plus five is equal to six.

Okay.

So remember, 21 minus one is equal to 20, and I still need to subtract five.

But oh no, I only have these two tens left.

Hm, I think I need to regroup.

So I'm going to regroup one 10 for 10 ones.

Count with me, one, two, three, four, five, six, seven, eight, nine ten, so I still have 20.

I have 10, 20, great.

So now we can subtract five.

One, two, three, four, five.

So 20 minus five.

Well I know 10 minus five is equal to five, so 20 minus five is equal to 15.

10, 11, 12, 13, 14, 15.

Great.

So the missing part was 15.

You see, all we did was subtract 31 minus 10 minus one minus five, and that was equal to 15.

I can solve the same equation by using a number line.

Let's have a look.

31 minus 16, well I'm going to solve this equation by partitioning the second number.

I know that 16 has one 10 and six ones.

So first, I'm going to subtract the 10.

31 is where we start, and now we'll subtract 10.

One, two, three, four, five, six, seven, eight, nine, 10.

So we jump from 31 to 21, minus 10.

Now we need to subtract the ones.

Well I know 21 minus one is equal to 20, so I can partition the six into one and five.

Great, so 21 minus one brings us to 20, and then we have to subtract another five.

One, two, three, four, five.

So 20 minus five is equal to 15.

So 31 minus 16 is equal to 15.

See, all we did was take 31, subtract 10, then we subtracted one, and then we subtracted five.

10 plus one plus five is still equal to 16.

So all we did was partition the 16.

Let's try one more example.

Now I know it's really tempting to see oh, 31 minus 14, why don't we just count back 14? Well you see, that's not always the most efficient way of going about things.

Sometimes it's faster to partition the number.

So as we did before, we start at 31, and we have to partition our 14.

I can partition 14 into one 10 and four ones.

So let's subtract our tens first.

31 minus 10, one, two, three, four, five, six, seven, eight, nine, ten.

31 minus 10 is equal to 21.

So then we just write that up here, 31 minus 10.

Now I know that 21 minus one is equal to 20, so I can partition the four into one and three.

One plus three is equal to four.

So 21 minus one, oops that's not a good one.

21 minus one is equal to 20, just write that up there for myself.

And then I still need to subtract three.

So 20 minus three.

Well I know 10 minus three is equal to seven, so 20 minus three must be equal to 17.

One, two, three, excellent.

So that means 31 minus 14 is equal to 17.

So 31 minus 14 is equal to 31 minus 10 minus one minus three because all we did was partition the 14, and we still subtracted 14.

Let's look at mental calculations using a number line again.

If you're feeling super confident after my explanation, you can pause the video now and complete these on your own.

However, if you're not feeling super sure, just stay on with me, and we'll do these examples together.

So here's my first equation, 54 minus 16.

I start at 54, and I know that when I subtract 16 I need to use some kind of strategy.

Well I like partitioning the second number, so I'll partition the 16 into one 10 and six ones.

First let's subtract the 10.

Well 54 minus 10, one, two, three, four, five, six, seven, eight, nine, ten.

So 54 minus 10 is equal to 44.

Now I still need to subtract six ones.

Well I know 44 minus four is equal to zero, so I'm partitioning six into four and two.

44 minus four, well 44 minus four is equal to 40, as we said and 40 minus two, well I know 10 minus two is equal to eight, so 40 minus two must be equal to 38.

Now I want to check to make sure I got the answer correct.

What I'm going to do is the inverse, or the opposite.

I'm going to do 38 plus 16, and hopefully that will be equal to 54.

So 38 plus 16, we can just count up.

One, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, excellent.

38 plus 16 is 54, I know I got that right.

Let's try the next one, and remember, at any point, if you're feeling super confident, just pause the video, try these on your own, and resume when you want to go over the answers.

65 minus 16, I know 65 is my whole, and I'm going to subtract 16 by partitioning into one ten and six ones.

So I start at 65, and I subtract 10.

65 minus 10.

So one, two, three, four, five, six, seven, eight, nine, ten.

65 minus 10 is equal to 55.

55 minus five is equal to 50, so I can partition 16 into five and one.

55 minus five is equal to 50, as we've already said.

Now I still need to subtract one.

50 minus one, well I know 10 minus one is equal to nine, so 50 minus one must be equal to 49.

As always, let's make sure that we check our answer by doing the inverse, or the opposite.

So hopefully 49 plus 16 will be equal to 65.

Let's check.

I'm going to partition the 16 to add it as well.

So one ten and six ones, 49 plus 10 is equal to 59.

59 plus one is equal to 60, and 60 plus five is equal to 65.

Yay, I got that correct.

Last but not least, 73 minus 16.

So I start at 73, that's my whole, and I'm going to partition 16 into one ten and six ones.

73 minus 10 is equal to 63, and 63 minus three is equal to 60, so I'll partition the six into three and three.

So 63 minus three is equal to 60, and now I need 60 minus three.

Well 10 minus three is equal to seven, so 60 minus three must be equal to 57.

As always, let's double-check our answers.

What is the inverse of this operation? Tell your screen, what is the inverse we must do? That's right, 57 plus 16 should be equal to 73.

Let's check.

57, so I'll partition 16 into one ten and six ones.

57 plus 10 is equal to 67.

67 plus three is equal to 70, 70 plus three is equal to 73.

Excellent, we got all of those correct.

For this independent task, you have two steps you need to take.

Step one is to solve the equation with the help of the number line.

So 54 minus 25, I'll do that as an example before you go off on your own.

I start at 54, because that's my whole.

I'm going to partition 25 into two tens and five ones.

So 54 minus 20, well I know five minus two is equal to three so 54 minus 20 must be equal to, can you guess? 34, well done.

54 minus 20 is equal to 34.

I still have to subtract five ones.

Well 34 minus four is equal to 30, so I'm going to partition the five into four and one.

34 minus four is equal to 30, and 30 minus one, well I know 10 minus one is equal to nine, so 30 minus one is equal to 29.

Hopefully 29 plus 25 will be equal to 54.

So 29 plus 25, so let's do 29 plus two tens, 29 plus two tens is equal to 49.

49 plus one is equal to 50, and 50 plus four is equal to 54.

Excellent, I got that correct.

Great job everyone.

So pause the video now and take a look at my answers, and double-check your own.

Now you should have been able to double-check because you used the inverse of the operation to make sure you were correct.

But again, pause the screen and make sure you're having a look at the answers, great job.