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Imagine you work at an
orchard and have 27 apples
Ok, but your apples are
Green
And theyre in a basket
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1
27
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Your boss at the orchard tells you to put the green ap
into bags that hold three apples each
If you had x-ray vision,this is what youd see in
this bag
I promise
= 1 2 3
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How would you figure out how many bags you would
need for the 27 apples?
6 bags is only enough for apples18
1 23
45 6
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One way to solve this problem would be to
take
3 apples out of the basket and put them inone bag.To start: 27 - 3 = 24 apples left in the basket
And one bag with 3 apples
1 2 3
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1
24
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You could repeat: take 3 more out of the
basket: 24 - 3 = 21apples left in thebasket
And you would have 2 bags
holding 6 apples in total1
2
1 2 3
4 5 6
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1
21
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Can you figure out howmany times you could
take 3 apples out of the
basket before the basketis empty?
Whats your answer?
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1234
7 6 5
9
8
If you said 9 times,
youd be correct
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How can you show all this
mathematically?
9 X 3 =27
or
273
27or 3
Because 9 groups of 3= 27
The last two both mean27 divided by 3
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You have a giant container of ice cream and youre going to makquadruple scoop cones for your friends. The container has enou
ice cream for 28 scoops. How many quadruple-scoop cones can
A quadruple scoop cone has how manyscoops of
Ice-cream4
Work on this one!!!
By the way,
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Is this Mr. R. when he was a kid
1
2
3
4
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What does the question look like mathematically?
62 = 3 equal groups with 2 in each group
62
Division is sharing or grouping a number into equal parts
3
But lets get back to the ice cream
For example
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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 mathsentence 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
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Sometimes to solve a division problem like 28 4, we
we 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 scoops
of ice cream until there are none left
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Besides subtraction, we could draw a diagram o
use manipulatives for help
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Here we use a diagram to divide the
28 ice cream scoops into groups of 4
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If 4 cones = 16 scoops
How many cones would it take to reach 28 scoops?
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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
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Finally, you can use fact families to help with division
If 7 x 4 = 28
Than 28 4 = 7
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Now its ice cream time!!!
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You have a container of ice cream and youre going to matriple 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,
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Part 2
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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
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Still not 771!!!!
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And still not at 771!!
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Anyway, your boss wants you to put 3 apples in each bag agai
wants you to keep track of how many bags you used.
Can you estimate how many bags
you would need for 771 apples?
= 1 2 3
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Do you think you would you need
more than 100 bags for the 771 apples?
Why?
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Im tired of apples, I want ice cream!!!
fourt
h
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I guess you could figure out how many bags
you would need by taking away 3 apples at a tim
771-3= 768-3= 765-3=762-3 -3=759 -3=756 -3= 753 -3= 750
But that would take a long time, wouldnt it?
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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?
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If you said bags, youd be correct
Lets put those 300 apples in 100 REDbags.
100
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How many apples
would you haveleft in your
basket?
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Well, 771-300 =
471Apples left
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Uh-oh, you have 100redbags of apples, (with 300 apples in
But you still have 471apples left in your basket
I think you NEED more bags!!
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Hey, maybe you can fill
another 100bags?
What do you think?
Why?
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Sure you can, because you have more
Applesapples left.300
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So you tell your boss you have apples le
and you need 100 more bags to holdmore apples.
471
300
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This time, you put the 300 apples in BLUEbags
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Now you have 200 bags that are holding
RED bags
and
BLUE bags
apples600
100
100
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How many apples would you have left in your bask
More than whats in
this basket!!!
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If you thought:
471 apples minus 300 apple
youd be correct
171Thats equal to ap
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No, you cant eat them- 171 apples will
upset your stomach, besides, you have to
sell them so you can buy your teachers big birgifts
Can you fill another 100 bags with apple
Why?
What will you do with those 171 apples
that are still in the basket?
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Just how many bags can you fill with your 171 a
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Can you think of any multiple of 3 th
less than 171? Lets try some
3 x 90 bags =
Thats more than 171 apples
3 x 80 bags=
Nope, still too much
270 apples
240 apples
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How can you figure out a multiple that is less
than 171
Yup, its a great time to use those
mental math multiplication skills!!!
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3 x 50 =
Thats less than 171
You can take apples
out of the basket.
150
150
How about 3 x 50
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Lets make 50more bags of 3 apples ea
Well use greenbags this time!!
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Okay, lets review
You took out 300 apples,
and put them in 100 redbags
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Then you took out 300 more apples,
And put those in 100 bluebags
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Then you took 150 apples from the bask
and put those in 50greenbags
How many bags have we used together
100 red + 100 blue + 50 green
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bags in all !!!
250
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But you still have apples in our bask
What are you ever going to do?
NO YOU CANT EAT THEM!!!
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First of all, how many apples are left
You had 171, and you took out 150.
Figure that out
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If you said,
you would be correct21 apples,
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Can you find a multiple of 3 thats
less than, or equal to 21???
Think multiplication tables
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10 x 3 = 30 apples
Too manyits more than 21 apples you
5 x 3 = 15 apples
You could use 5, because you do have 15 a
but is there a better choice?
What do you think?
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Sure, 7 x 3 = 21
Oh, so you thought of a multiple
will give you exactly 21 apples?
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So you need 7 more bags to hold the remaining
21 applesLets use purple bags
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Do you have any apples left in your basket?
I think you can tell your boss that youre done!!
No, not in this basket
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But your boss wants to know
how many bags you used altoget
Lets count our bags
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100 redbags
100 bluebags
50 greenbags
7 purplebags
bags altogether!!!257
et s cou t ou bags
Lets count our apples
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100 redbags
100 bluebags
50 greenbags
7 purplebags
= 257 bags in all
300 apples
300 apples
150 apples
21 apples
apples in all
pp
771
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So 771 divided into groups of 3 =
With a remainder of 0 apples!!!
257
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Now you can eat an apple!!!
BUT WAIT!!!!!!
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What does all of that look like as a division pro
771 3
or
7713
Lets do this on paper Please get a blank sheet out
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Let s do this on paper Please get a blank sheet out
Lets think about how you subtracted apples
7713
First we subtracted 300 apples from 771 using 100 redbag
100 bags
-300
471 left
Then we subtracted 300 more apples from the
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7713 7713
pp
remaining 471 using another 100 blue bags
100 bags
-300
471
-300
171 left
100 bags
Then we subtracted 150apples from the remaining 171
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7713 7713
pp g
using 50 greenbags
100 bags
-300
471
-300
171
100 bags
50 bags
-150
21 left
Then we subtracted 21 more 7 bags
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7713 7713
Then we subtracted 21more
apples using 7purplebags
100 bags
-300
471
-300
171
100 bags50 bags
-15021
g
-21
0 left
257
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6333
Add up the bags and thats 257bags!!!
Can you solve this one using the same met