DIVIDING WITH FRACTIONS
PRESENTED BY THE HIGH COUNSEL OF WITCHES IN AN EFFORT TO DRIVE
MORE KIDS AWAY FROM SCHOOL AND INTO THE FOREST LIKE POOR
OLD HANSEL AND GRETEL
SO WHAT IS DIVISION?
Finding out how
many of something
you will have in a
given number of
equal groups
BRAIN BREAK: DO YOU RECOGNIZE ANY OF THESE
SNACKS?
SO WHAT DOES DIVISION LOOK LIKE?
The problem
36 ÷ 4
Can look like both of these:
36
The question for this diagram is,
“How many groups of 4 are in 36?”
The question for this diagram is, “If I
split 36 into 4 equal groups, how
much would be in each group?”
36
X
X
X
X
4
4
4
1
2
3
4
1
2
x
WE CAN SHOW THEM WITH AREA MODELS…
Let’s start off with one whole!
𝟏
𝟑
Let’s now divide that 1 whole by 3
So, 1÷3=
𝟏
𝟑
So we’ve determined that 1 whole divided
𝟏
into 3 equal parts is 𝟑
BRAIN BREAK PART 2: WHICH PANDA DO YOU LIKE
THE BEST?
BUT WHAT IF WE START WITH
𝟏
AND
𝟑
Let’s start off with
𝟏
𝟑
DIVIDE BY 4
𝟏
𝟑
𝟏
Let’s now divide that 𝟑 by 4
𝟏
Our new size piece is smaller than 𝟑.
𝟏
You might want to say that it’s 𝟒 but
that’s wrong!
Let’s see what it is in relation to the
whole…
𝟏
𝟑
So, ÷ 4=
𝟏
𝟏𝟐
It would take 12 of the new size pieces
to make 1 whole, so our new piece is
𝟏
𝒐𝒇 𝒕𝒉𝒆 𝒘𝒉𝒐𝒍𝒆
𝟏𝟐
WE COULD SHOW THE EXACT SAME PROBLEM IN
THIS WAY TOO…
1 whole
Let’s start off with
1
3
𝟏
𝟑
𝟏
Let’s now divide that 𝟑 by 4
𝟏
Our new size piece is smaller than 𝟑.
𝟏
You might want to say that it’s 𝟒 but
that’s wrong!
𝟏
𝟑
Let’s see what it is in relation to the
whole…
𝟏
𝟑
So, ÷ 4=
𝟏
𝟏𝟐
It would take 12 of the new size pieces
to make 1 whole, so our new piece is
𝟏
𝒐𝒇 𝒕𝒉𝒆 𝒘𝒉𝒐𝒍𝒆
𝟏𝟐
BRAIN BREAK 3: WHAT’S YOUR FAVORITE DRINK?
BUT WHAT IF WE START WITH
𝟏
AND
𝟒
Let’s start off with
𝟏
𝟒
DIVIDE BY 4
𝟏
𝟒
𝟏
Let’s now divide that 𝟒 by 4
𝟏
Our new size piece is smaller than 𝟒.
𝟏
You might want to say that it’s 𝟒 but
that’s wrong!
Let’s see what it is in relation to the
whole…
𝟏
𝟒
So, ÷ 4=
𝟏
𝟏𝟔
It would take 16 of the new size pieces
to make 1 whole, so our new piece is
𝟏
𝒐𝒇 𝒕𝒉𝒆 𝒘𝒉𝒐𝒍𝒆
𝟏𝟔
WE COULD SHOW THE EXACT SAME PROBLEM IN
THIS WAY TOO…
1 whole
Let’s start off with
1
4
𝟏
𝟒
𝟏
Let’s now divide that 𝟒 by 4
𝟏
Our new size piece is smaller than 𝟒.
𝟏
You might want to say that it’s 𝟒 but
that’s wrong!
𝟏
𝟒
Let’s see what it is in relation to the
whole…
𝟏
𝟒
So, ÷ 4=
𝟏
𝟏𝟔
It would take 16 of the new size pieces
to make 1 whole, so our new piece is
𝟏
𝒐𝒇 𝒕𝒉𝒆 𝒘𝒉𝒐𝒍𝒆
𝟏𝟔
BRAIN BREAK 4: WHAT’S YOUR FAVORITE TOY IN THIS
PICTURE?
YOU CAN ALSO ASK THE QUESTION, “HOW MANY
1
GROUPS OF ARE IN 4?”
5
That problem would be written:
1
4÷5
Let’s start off with 4 wholes
1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Let’s now divide those 4 wholes by 5
With division we can ask, “How many
1
groups of 5 are there in 4 wholes?”
Splitting the 4 wholes into fifths will
help us see better.
We can count the pieces now to see
1
how many 5 size pieces are in 4
wholes.
1
16
17
18
19
20
20 of the 5 size pieces are in 4 wholes.
1
8
HOW MANY GROUPS OF ARE IN 3?”
That problem would be written:
1
3÷8
Let’s start off with 3 wholes
1
1
9
17
2
10
18
3
11
19
4
12
20
5
13
21
6
14
22
7
15
23
8
16
24
Let’s now divide those 3 wholes by 8
With division we can ask, “How many
1
groups of 8 are there in 3 wholes?”
Splitting the 3 wholes into eighths will
help us see better.
We can count the pieces now to see
1
how many 8 size pieces are in 3
wholes.
1
24 of the 8 size pieces are in 3 wholes.
BRAIN BREAK 5: DO YOU RECOGNIZE ANY OF THESE
MAGAZINES?
EXTERNAL LINKS:
https://learnzillion.com/lessons/3787-divide-a-unit-fraction-by-a-whole-number
https://learnzillion.com/lessons/199-use-visual-models-for-division-of-whole-numbers-by-unit-fractions