Imagine you work at an orchard and have 27

apples…

Ok, but your apples areGreen…

And they’re in a basket

1

27

Your boss at the orchard tells you to put the green apples into bags that hold three apples each…

If you had x-ray vision, this is what you’d see in this bag…I promise…

= 1 2 3

How would you figure out how many bags you would need for the 27 apples?

6 bags is only enough for apples…18

1 2 3

4 5 6

One way to solve this problem would be to take 3 apples out of the basket and put them in one bag.

To start: 27 - 3 = 24 apples left in the basket…

And one bag with 3 apples…

1 2 3

1

24

You could repeat: take 3 more out of the basket: 24 - 3 = 21 apples left in the basket…

And you would have 2 bags holding 6 apples in total…

1

2

1 2 3

4 5 6

1

21

Can you figure out how many times you could take 3 apples out of the basket before the basket is empty?

What’s your answer?

11223344

77 66 55

99

88

If you said 9 times,you’d be correct…

How can you show all this mathematically?9 X 3 =

27or

27÷3

27or 3

Because 9 groups of 3= 27

The last two both mean27 divided by 3

You have a giant container of ice cream and you’re going to makequadruple scoop cones for your friends. The container has enough ice cream for 28 scoops. How many quadruple-scoop cones can you make?

A quadruple scoop cone has how many scoops ofIce-cream

4

Work on this one!!!

By the way,

Is this Mr. R. when he was a kid?

1

2

3

4

What does the question look like mathematically?

6÷2 = 3 equal groups with 2 in each group

62

Division is sharing or grouping a number into equal parts

3

But let’s get back to the ice cream…

For example

We have 28 scoops of ice cream and we need to find out how many equal groups of 4 we can make. How can we write a math sentence to represent this?

Is it 28 ÷ 4Is it 4 x 28?

Is it 28 + 4

Is it 28 - 4

Is it 28 - 8?

Which one of these is used to share 28 into equal groups of 4?

Sometimes to solve a division problem like 28 ÷ 4, wewe may use a lot of subtraction…

28 - 4 = 24

24 - 4 = 20

20 - 4 = 16

1 cone

2 cones

3 cones

You can continue subtracting 4 scoopsof ice cream until there are none left…

Besides subtraction, we could draw a diagram oruse manipulatives for help…

Here we use a diagram to divide the 28 ice cream scoops into groups of 4…

How many ice cream scoops would you use for4 cones?

Our multiplication facts (and fact families) can really help in division…

If 4 cones = 16 scoops

How many cones would it take to reach 28 scoops?

What number (of cones), multiplied by 4 (scoops of ice cream) = 28 scoops in all?

6 x 4 =

7 x 4 =

5 cones x 4 scoops = 20 scoops

24 scoops

28 scoops

Finally, you can use fact families to help with division…

If 7 x 4 = 28

Than 28 ÷ 4 = 7

Now it’s ice cream time!!!

You have a container of ice cream and you’re going to maketriple scoop cones for your friends. The container holds 18 scoops. How many triple-scoop cones can you make?

A triple scoop cone has h scoops of ice-cream3

Work on this one!!!

By the way,

Part 2

What in the world would you do if you had 771 applesin your basket???

We would need a bigger basket…

First of all, you would need a bigger basket…

Still not 771!!!!

And still not at 771!!!!

Anyway, your boss wants you to put 3 apples in each bag again…and she wants you to keep track of how many bags you used.

Can you estimate how many bagsyou would need for 771 apples?

= 1 2 3

Do you think you would you need more than 100 bags for the 771 apples?

Why?

I’m tired of apples, I want ice cream!!!

fourth

I guess you could figure out how many bagsyou would need by taking away 3 apples at a time again…

771-3 = 768-3 = 765-3=762-3 -3=759 -3=756 -3= 753 -3= 750

But that would take a long time, wouldn’t it?

What if you took 300 apples out of the basket all at once?

Can you figure out how many bags you would need to hold 300 apples?

If you said bags, you’d be correct…

Let’s put those 300 apples in 100 RED bags….

100

How many apples would you have left in your basket?

Well, 771-300 =

471 Apples left

Uh-oh, you have 100 red bags of apples, (with 300 apples in them)

But you still have 471 apples left in your basket…

I think you NEED more bags!!!

Hey, maybe you can fill another 100 bags?

What do you think?

Why?

Sure you can, because you have more thanApples apples left….300

So you tell your boss you have apples left,and you need 100 more bags to holdmore apples.

471300

This time, you put the 300 apples in BLUE bags…

Now you have 200 bags that are holding

RED bags

and

BLUE bags

apples…600

100

100

How many apples would you have left in your basket?

More than what’s inthis basket!!!

If you thought:

471 apples minus 300 apples, you’d be correct

171That’s equal to apples…

No, you can’t eat them- 171 apples willupset your stomach, besides, you have tosell them so you can buy your teachers big birthdaygifts…

Can you fill another 100 bags with apples?Why?

What will you do with those 171 applesthat are still in the basket?

Just how many bags can you fill with your 171 apples?

Can you think of any multiple of 3 that’s less than 171? Let’s try some…

3 x 90 bags =

That’s more than 171 apples

3 x 80 bags=

Nope, still too much

270 apples

240 apples

How can you figure out a multiple that is lessthan 171…

Yup, it’s a great time to use thosemental math multiplication skills!!!

3 x 50 =

That’s less than 171…

You can take apples out of the basket….

150

150

How about 3 x 50

Let’s make 50 more bags of 3 apples each!

We’ll use green bags this time!!

Okay, let’s review… You took out 300 apples, and put them in 100 red bags…

Then you took out 300 more apples,And put those in 100 blue bags…

Then you took 150 apples from the basketand put those in 50 green bags…

How many bags have we used together?

100 red + 100 blue + 50 green

bags in all !!!

250

But you still have apples in our basket…What are you ever going to do?

NO YOU CAN’T EAT THEM!!!

First of all, how many apples are left?

You had 171, and you took out 150….

Figure that out…

If you said,

you would be correct…

21 apples,

Can you find a multiple of 3 that’s less than, or equal to 21???

Think multiplication tables…

10 x 3 = 30 apples

Too many…it’s more than 21 apples you have

5 x 3 = 15 apples

You could use 5, because you do have 15 apples,but is there a better choice?

What do you think?

Sure, 7 x 3 = 21

Oh, so you thought of a multiple thatwill give you exactly 21 apples?

So you need 7 more bags to hold the remaining21 apples…Let’s use purple bags…

Do you have any apples left in your basket?

I think you can tell your boss that you’re done!!!

No, not in this basket

But your boss wants to know how many bags you used altogether…

100 red bags

100 blue bags

50 green bags

7 purple bags

bags altogether!!!257

Let’s count our bags…

100 red bags

100 blue bags

50 green bags

7 purple bags

= 257 bags in all

300 apples

300 apples

150 apples

21 apples

apples in all

Let’s count our apples…

771

So 771 divided into groups of 3 =

With a remainder of 0 apples!!!

257

Now you can eat an apple!!!

BUT WAIT!!!!!!

What does all of that look like as a division problem?

771 ÷ 3

or

7713

Let’s do this on ‘paper’…Please get a blank sheet out…

Let’s think about how you subtracted apples…

7713

First we subtracted 300 apples from 771 using 100 red bags

100 bags

-300471 left…

7713 7713

Then we subtracted 300 more apples from the remaining 471 using another 100 blue bags…

100 bags

-300471

-300171 left…

100 bags

7713 7713

Then we subtracted 150 apples from the remaining 171using 50 green bags

100 bags

-300471

-300171

100 bags50 bags

-150 21 left…

7713 7713

Then we subtracted 21 more apples using 7 purple bags

100 bags

-300471

-300171

100 bags50 bags

-150 21

7 bags

-210 left

6333

Add up the bags and that’s 257 bags!!!

Can you solve this one using the same method?