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

Finding out how many equal groups of something can be made So what is division? Finding out how many equal groups of something can be made Repeated Subtraction Finding out how many of something you will have in a given number of equal groups Torturous problems given by math teachers to watch kids scream…Yes, all math teachers are secretly honorary members on the counsel of evil witches….<see slide 1>

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: The question for this diagram is, “If I split 36 into 4 equal groups, how much would be in each group?” The question for this diagram is, “How many groups of 4 are in 36?” 36 36 X 4 1 2 3 4 1 2 x

We can show them with area Models… 𝟏 𝟑 Let’s start off with one whole! Let’s now divide that 1 whole by 3 So we’ve determined that 1 whole divided into 3 equal parts is 𝟏 𝟑 So, 1÷3= 𝟏 𝟑

Brain Break part 2: Which panda do you like the best?

But what if we start with 𝟏 𝟑 and divide by 4 Let’s start off with 𝟏 𝟑 Let’s now divide that 𝟏 𝟑 by 4 Our new size piece is smaller than 𝟏 𝟑 . You might want to say that it’s 𝟏 𝟒 but that’s wrong! Let’s see what it is in relation to the whole… It would take 12 of the new size pieces to make 1 whole, so our new piece is 𝟏 𝟏𝟐 𝒐𝒇 𝒕𝒉𝒆 𝒘𝒉𝒐𝒍𝒆 So, 𝟏 𝟑 ÷ 4= 𝟏 𝟏𝟐

We could show the exact same problem in this way too… 1 whole We’ve been asking the question, “If I split 𝟏 𝟑 into 4 equal groups, how much would be in each group?” Let’s start off with 𝟏 𝟑 1 3 Let’s now divide that 𝟏 𝟑 by 4 𝟏 𝟑 Our new size piece is smaller than 𝟏 𝟑 . You might want to say that it’s 𝟏 𝟒 but that’s wrong! Let’s see what it is in relation to the whole… It would take 12 of the new size pieces to make 1 whole, so our new piece is 𝟏 𝟏𝟐 𝒐𝒇 𝒕𝒉𝒆 𝒘𝒉𝒐𝒍𝒆 So, 𝟏 𝟑 ÷ 4= 𝟏 𝟏𝟐

Brain break 3: What’s your favorite drink?

But what if we start with 𝟏 𝟒 and divide by 4 Let’s start off with 𝟏 𝟒 Let’s now divide that 𝟏 𝟒 by 4 Our new size piece is smaller than 𝟏 𝟒 . You might want to say that it’s 𝟏 𝟒 but that’s wrong! Let’s see what it is in relation to the whole… It would take 16 of the new size pieces to make 1 whole, so our new piece is 𝟏 𝟏𝟔 𝒐𝒇 𝒕𝒉𝒆 𝒘𝒉𝒐𝒍𝒆 So, 𝟏 𝟒 ÷ 4= 𝟏 𝟏𝟔

We could show the exact same problem in this way too… 1 whole We’ve been asking the question, “If I split 𝟏 𝟒 into 4 equal groups, how much would be in each group?” Let’s start off with 𝟏 𝟒 1 4 Let’s now divide that 𝟏 𝟒 by 4 𝟏 𝟒 Our new size piece is smaller than 𝟏 𝟒 . You might want to say that it’s 𝟏 𝟒 but that’s wrong! Let’s see what it is in relation to the whole… It would take 16 of the new size pieces to make 1 whole, so our new piece is 𝟏 𝟏𝟔 𝒐𝒇 𝒕𝒉𝒆 𝒘𝒉𝒐𝒍𝒆 So, 𝟏 𝟒 ÷ 4= 𝟏 𝟏𝟔

Brain break 4: What’s your favorite toy in this picture?

You can also ask the question, “how many groups of 1 5 are in 4?” That problem would be written: 4 ÷ 1 5 Let’s start off with 4 wholes 1 2 3 4 5 Let’s now divide those 4 wholes by 1 5 With division we can ask, “How many groups of 1 5 are there in 4 wholes?” Splitting the 4 wholes into fifths will help us see better. 6 7 8 9 10 We can count the pieces now to see how many 1 5 size pieces are in 4 wholes. 11 12 13 14 15 16 17 18 19 20 20 of the 1 5 size pieces are in 4 wholes.

how many groups of 1 8 are in 3?” That problem would be written: 3 ÷ 1 8 Let’s start off with 3 wholes 1 2 3 4 5 6 7 8 Let’s now divide those 3 wholes by 1 8 With division we can ask, “How many groups of 1 8 are there in 3 wholes?” Splitting the 3 wholes into eighths will help us see better. 9 10 11 12 13 14 15 16 We can count the pieces now to see how many 1 8 size pieces are in 3 wholes. 17 18 19 20 21 22 23 24 24 of the 1 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