Imagine you work at an orchard and have 27 apples… And they’re in a basket Ok, but your apples are Green…

1 27

Your boss at the orchard tells you to put the green apples into bags that hold three apples each… = 1 2 3 If you had x-ray vision, this is what you’d see in this bag… I promise…

18 How would you figure out how many bags you would need for the 27 apples? 1 2 3 4 5 6 18 6 bags is only enough for apples…

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… 4 5 6 2

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?

If you said 9 times, you’d be correct… 9 7 8 6 5 3 2 4 1

How can you show all this mathematically? 9 X 3 = 27 Because 9 groups of 3= 27 or 27÷3 The last two both mean 27 divided by 3 or 3 27

Work on this one!!! You have a giant container of ice cream and you’re going to make quadruple scoop cones for your friends. The container has enough ice cream for 28 scoops. How many quadruple-scoop cones can you make? By the way, 4 A quadruple scoop cone has how many scoops of Ice-cream

Is this Mr. R. when he was a kid? 4 3 2 1

What does the question look like mathematically? Division is sharing or grouping a number into equal parts For example 6÷2 = 3 equal groups with 2 in each group 3 2 6 But let’s get back to the ice cream…

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 4 x 28? Is it 28 ÷ 4 Is it 28 - 8? Is it 28 + 4 Is it 28 - 4 Which one of these is used to share 28 into equal groups of 4?

Sometimes to solve a division problem like 28 ÷ 4, we we may use a lot of subtraction… 28 - 4 = 24 1 cone 2 cones 24 - 4 = 20 20 - 4 = 16 3 cones You can continue subtracting 4 scoops of ice cream until there are none left…

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

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

Our multiplication facts (and fact families) can really help in division… How many ice cream scoops would you use for 4 cones?

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? 5 cones x 4 scoops = 20 scoops 6 x 4 = 24 scoops 7 x 4 = 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!!!

Work on this one!!! You have a container of ice cream and you’re going to make triple scoop cones for your friends. The container holds 18 scoops. How many triple-scoop cones can you make? By the way, 3 A triple scoop cone has h scoops of ice-cream

Part 2

First of all, you would need a bigger basket… What in the world would you do if you had 771 apples in 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. = 1 2 3 Can you estimate how many bags you would need for 771 apples?

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 bags you 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?

100 If you said bags, you’d be correct… Let’s put those 300 apples in 100 RED bags….

How many apples would you have left in your basket?

Well, 771-300 = 471 Apples left

I think you NEED more bags!!! 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 than Apples apples left…. 300

So you tell your boss you have apples left, and you need 100 more bags to hold more apples. 471 300

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

600 Now you have 200 bags that are holding apples… RED bags and BLUE bags 600 apples… 100 100

How many apples would you have left in your basket? More than what’s in this basket!!!

171 If you thought: 471 apples minus 300 apples, you’d be correct That’s equal to apples…

What will you do with those 171 apples that are still in the basket? No, you can’t eat them- 171 apples will upset your stomach, besides, you have to sell them so you can buy your teachers big birthday gifts… Can you fill another 100 bags with apples? Why?

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 = 270 apples That’s more than 171 apples 3 x 80 bags= 240 apples Nope, still too much

How can you figure out a multiple that is less than 171… Yup, it’s a great time to use those mental math multiplication skills!!!

How about 3 x 50 3 x 50 = 150 That’s less than 171… You can take apples out of the basket…. 150

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…

100 red + 100 blue + 50 green Then you took 150 apples from the basket and put those in 50 green bags… How many bags have we used together? 100 red + 100 blue + 50 green

250 bags in all !!!

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?

Oh, so you thought of a multiple that will give you exactly 21 apples? Sure, 7 x 3 = 21

So you need 7 more bags to hold the remaining 21 apples…Let’s use purple bags…

I think you can tell your boss that you’re done!!! Do you have any apples left in your basket? No, not in this basket I think you can tell your boss that you’re done!!!

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

Let’s count our bags… 257 100 red bags 100 blue bags 50 green bags 7 purple bags 257 bags altogether!!!

Let’s count our apples… 100 red bags 300 apples 300 apples 100 blue bags 50 green bags 150 apples 7 purple bags 21 apples 771 = 257 bags in all apples in all

So 771 divided into groups of 3 = 257 With a remainder of 0 apples!!!

Now you can eat an apple!!! BUT WAIT!!!!!!

What does all of that look like as a division problem? 771 ÷ 3 or 3 771

Let’s do this on ‘paper’…Please get a blank sheet out… Let’s think about how you subtracted apples… First we subtracted 300 apples from 771 using 100 red bags 100 bags 3 771 -300 471 left…

Then we subtracted 300 more apples from the remaining 471 using another 100 blue bags… 100 bags 100 bags 3 3 771 771 -300 471 -300 171 left…

50 bags 100 bags 100 bags 3 3 771 771 -300 471 -300 171 -150 21 left… Then we subtracted 150 apples from the remaining 171 using 50 green bags 50 bags 100 bags 100 bags 3 3 771 771 -300 471 -300 171 -150 21 left…

7 bags Then we subtracted 21 more apples using 7 purple bags 50 bags 100 bags 100 bags 3 3 771 771 -300 471 -300 171 -150 21 -21 0 left

Can you solve this one using the same method? Add up the bags and that’s 257 bags!!! Can you solve this one using the same method? 3 633