1. how would you explain meaningfully to 5 th graders so that they can understand why the answer for...
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1. How would you explain meaningfully to 5th graders so that they can understand why the answer for 1 ÷ 2/5 is 2½.
1
2/5
1 ÷ 2/5
“1 ÷ 2/5 = ?” means “how many two-fifths are in one?”
There are 2½ two-fifths in 1.
↔ 1 ÷ 2/5 = 2½2½ 2/5 = 1
2. Without computing, predict in a meaningful manner the answer in each case
(a)
(b)
(c)
(d)
(e)
3. Suppose that you have 2/3 of a large pizza. If each child eats 1/6 of a pizza, how many children can the 2/3 pizza feed?(a) Write an equation using division to represent the
problem (let n be the answer).
(b) Write another equation using division to represent the problem (let n be the answer).
(c) Write an equation using multiplication to represent the problem (let n be the answer).
(d) How are the three equations conceptually different?
2/3 ÷ 1/6 = n
2/3 ÷ n = 1/6
n 1/6 = 2/3
Repeated-subtraction view of division
Sharing-equally view of division
Repeated-addition view of multiplication
4. 1/3 of a cake makes 1 serving. How many servings can we get from 4/5 of a cake?(a) Write an equation to represent the problem.
Let x be the answer.
4/5 ÷ 1/3 = x
4. 1/3 of a cake makes 1 serving. How many servings can we get from 4/5 of a cake?(b) Solve this problem in a way such that it is
meaningful for a 5th grader.
1/3
4/5
4/5 ÷ 1/3 ?
4. 1/3 of a cake makes 1 serving. How many servings can we get from 4/5 of a cake?(b) Solve this problem in a way such that it is
meaningful for a 5th grader.
1/3
4/5
4/5 ÷ 1/3What does 4/5 ÷ 1/3 actually mean?
How many 1/3 are in 4/5?
4. 1/3 of a cake makes 1 serving. How many servings can we get from 4/5 of a cake?(b) Solve this problem in a way such that it is
meaningful for a 5th grader.
1/3
4/5
4/5 ÷ 1/3 How many 1/3 are in 4/5?More than 2 but less than 3.
4. 1/3 of a cake makes 1 serving. How many servings can we get from 4/5 of a cake?(b) Solve this problem in a way such that it is
meaningful for a 5th grader.
1/3
4/5
4/5 ÷ 1/3 How many 1/3 are in 4/5?
How do you find the exact answer?
Answer: 225
1/3
4/5
4/5 ÷ 1/3 How many 1/3 are in 4/5?
We have seen why the answer is 2 2/5.
Answer: 225 or 12
5
Can you see 12/5 in these pictures?
How many 1/3 are in 4/5?
We have seen why the answer is 2 2/5.
Answer: 225 or 12
5
Can you see 12/5 in these pictures?
1/3
4/5
4/5 ÷ 1/3
4. 1/3 of a cake makes 1 serving. How many servings can we get from 4/5 of a cake?(c) What is the referent whole for the dividend 4/5?
1/3
4/5
4/5 ÷ 1/3 How many 1/3 are in 4/5?Answer: 22
5
One cake
of a cake
or 12 5
4. 1/3 of a cake makes 1 serving. How many servings can we get from 4/5 of a cake?(d) What is the referent whole for the divisor 1/3?
1/3
4/5
4/5 ÷ 1/3 How many 1/3 are in 4/5?Answer: 22
5
One cake
of a cake
of a cake
or 12 5
How many 1/3 of a cake
are in 4/5 of a cake?
Can you see 12 5?
4. 1/3 of a cake makes 1 serving. How many servings can we get from 4/5 of a cake?(d) What is the referent whole for the divisor 1/3?
1/3
4/5
4/5 ÷ 1/3
Answer:
One cake
of a cake
of a cake
12 5
How many 5/15 of a cake
are in 12/15 of a cake?
How many 5 pieces
are in 12 pieces?
12 5 =
4. 1/3 of a cake makes 1 serving. How many servings can we get from 4/5 of a cake?
1/3
4/5
4/5 ÷ 1/3 How many 1/3 are in 4/5?Answer: 22
5
1/3 of a cake
of a cake
of a cake
(e) What is the referent whole for the quotient 2 ?25
of 1/3 cake is equal to 4/5 cake.
2 25
2 =2 1 45 3 5
or 12 5
÷ = 24 1 25 3 5
2 =2 1 45 3 5
÷ = 24 1 25 3 5
2 2/5 is a fraction of another fraction. Its referent whole is the
multiplicand.
The referent whole for the quotient is
the divisor.
In repeated-subtraction view of division, the referent whole for the dividend and
divisor are by default 1 unit.
In fractional part of a quantity view of multiplication,
the referent whole for the multiplicand and the product
is by default 1 unit.
In summary, what is the referent whole for each of these numbers?
Use this Virtual Manipulative at this link to reason about Division involving Fractions
http://nlvm.usu.edu/en/nav/frames_asid_265_g_3_t_1.html?open=activities&from=category_g_3_t_1.html