1. TTT Workshop
Fraction Division
Sep 2014
Type 1: “How many groups?”

2. Fraction Division Type 2: “How many in one group?” TTT Workshop
Sep 2014
Type 2: “How many in one group?”

3. 1. Pick one of the two types of division for 3 ÷ 2/5.
TTT Workshop
Sep 2014
1. Pick one of the two types of division for 3 ÷ 2/5.
Write a simple word problem for 3 ÷ 2/5.
Solve 3 ÷ 2/5 with the aid of a strip diagram.
Solve 3 ÷ 2/5 with the aid of a table.
Solve 3 ÷ 2/5 with the aid of a double number line.
2. Which type of division is easier to model for 3 ÷ 2/5. Why?

4. 3. List the difference between the two types of division:
TTT Workshop
Sep 2014
3. List the difference between the two types of division:
Quotitive division
Partitive division
Measurement model
Modeled by sharing equally.
Modeled by subtracting repeatedly.
The divisor is the number of groups.
The divisor is the number of objects in each group.
The number of partitions is fixed.
The number of objects in each partition is fixed.
The dividend and the divisor usually have the same unit of measurement.
The dividend and the quotient usually have the same unit of measurement.

5. TTT Workshop
Sep 2014
4. Write a simple “how many groups?” word problem for 1/3 ÷ 2/5. Solve your problem with the aid of (i) a strip diagram, (ii) a table, and (iii) a double number line.
5. Write a simple “how many in one unit?” word problem for 1/3 ÷ 2/5. Solve your problem with the aid of (i) a strip diagram, (ii) a table, and (iii) a double number line.

6. 6. Which type of division is easier to model for 1/3 ÷ 2/5. Why?
TTT Workshop
Sep 2014
6. Which type of division is easier to model for 1/3 ÷ 2/5. Why?
7. Conceptually, why is more difficult for students to model 1/3 ÷ 2/5 than 3 ÷ 2/5?

7. 3. List the difference between the two types of division:
TTT Workshop
Sep 2014
3. List the difference between the two types of division:
Quotitive division
Partitive division
Measurement model
Modeled by sharing equally.
Modeled by subtracting repeatedly.
The divisor is the number of groups.
The divisor is the number of objects in each group.
The number of partitions is fixed.
The number of objects in each partition is fixed.
The dividend and the divisor usually have the same unit of measurement.
The dividend and the quotient usually have the same unit of measurement.
Easy to model if the divisor is smaller than the dividend.
Easy to model if the divisor is a whole number.

8. 8. How are the two types of division related to multiplication?
TTT Workshop
Sep 2014
8. How are the two types of division related to multiplication?

9. 3. List the difference between the two types of division:
TTT Workshop
Sep 2014
3. List the difference between the two types of division:
Quotitive division
Partitive division
Measurement model
Modeled by sharing equally.
Modeled by subtracting repeatedly.
The divisor is the number of groups.
The divisor is the number of objects in each group.
The number of partitions is fixed.
The number of objects in each partition is fixed.
The dividend and the divisor usually have the same unit of measurement.
The dividend and the quotient usually have the same unit of measurement.
Easy to model if the divisor is smaller than the dividend.
Easy to model if the divisor is a whole number.
In terms of multiplication problem, the multiplier is missing.
In terms of multiplication problem, the multiplicand is missing.

10. TTT Workshop
Sep 2014
9. What have we learned?