More Division Stories

New York State Common Core Math Grade 6, Module 2, Lesson 6

Worksheets for Grade 6

Lesson 6 Student Outcomes

• Students demonstrate further understanding of division of fractions when they create their own word problems.
• Students choose a partitive division problem, draw a model, find the answer, choose a unit, and then set up a situation. Further, they practice trying several situations and units before finding which are realistic with given numbers.

Lesson 6 Summary

The method of creating division stories has five steps, to be followed in order:
Step 1: Decide on an interpretation (measurement or partitive). Today we used only measurement division.
Step 2: Draw a model.
Step 3: Find the answer.
Step 4: Choose a unit.
Step 5: Set up a situation. This means writing a story problem that is interesting, realistic, short, and clear and that has all the information necessary to solve it. It may take you several attempts before you find a story that works well with the given dividend and divisor.

Classwork
Opening
Discussion
Partitive division is another interpretation of division problems. What do you recall about partitive division?

• We know that when we divide a whole number by a fraction, the quotient will be greater than the whole number we began with (the dividend). This is true regardless of whether we use a partitive approach or a measurement approach.
• In other cases, we know what the whole is and how many groups we are making and must figure out what size the groups are.

Example 1
Partitive Division.
Divide 50 ÷ 2/3

Exercise 1
Using the same dividend and divisor, work with a partner to create your own story problem. You may use the same unit, dollars, but your situation must be unique. You could try another unit, such as miles, if you prefer.
Possible story problems:

1. Ronaldo has ridden 50 miles during his bicycle race and is 2/3 of the way to the finish line. How long is the race?
2. Samantha used 50 tickets (2/3 of her total) to trade for a kewpie doll at the fair. How many tickets did she start with?

Example 2
Divide 45 ÷ 3/8

Exercise 2
Using the same dividend and divisor, work with a partner to create your own story problem. Try a different unit. Remember spending money gives a “before and after” word problem. If you use dollars, you are looking for a situation where 3/8 of some greater dollar amount is $45.

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Opening
Example 1
Partitive Division.
Divide 50 ÷ 2/3

Example 2
Divide 45 ÷ 3/8

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Lesson 6 Problem Set
Solve.

1. 15/16 is 1 sixteenth groups of what size?
2. 7/8 teaspoons is 1/4 groups of what size?
3. A 4-cup container of food is 2/3 groups of what size?
4. Write a partitive division story problem for 6 ÷ 3/4.
5. Write a partitive division story problem for 5/12 ÷ 1/6.
6. Fill in the blank to complete the equation. Then, find the quotient, and draw a model to support your solution.
   1/4 ÷ 7 = 1/□ of 1/4
   5/6 ÷ 4 = 1/□ of 5/6
7. There is 3/5 of a pie left. If 4 friends wanted to share the pie equally, how much would each friend receive?
8. In two hours, Holden completed 3/4 of his race. How long will it take Holden to complete the entire race?
9. Sam cleaned 1/3 of his house in 50 minutes. How many hours will it take him to clean his entire house?
10. It took Mario 10 months to beat 5/8 of the levels on his new video game. How many years will it take for Mario to beat all the levels?
11. A recipe calls for 1 1/2 cups of sugar. Marley only has measuring cups that measure 1/4 cup. How many times will Marley have to fill the measuring cup?

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Lesson 6 Problem Set Sample Solution

1. Write a partitive division story problem for 45 ÷ 3/5
2. Write a partitive division story problem for 100 ÷ 2/5

Lesson 7 Student Outcomes

Students formally connect models of fractions to multiplication through the use of multiplicative inverses as they are represented in models.
The reciprocal, or inverse, of a fraction is the fraction made by interchanging the numerator and denominator.
Two numbers whose product is 1 are multiplicative inverses.
Example 1:
3/4 ÷ 2/5

Lesson 8 Student Outcomes
Students divide fractions by mixed numbers by first converting the mixed numbers into a fraction with a value larger than one.
Students use equations to find quotients.

Example 1: Introduction to Calculating the Quotient of a Mixed Number and a Fraction

Carli has 4 1/2 walls left to paint in order for all the bedrooms in her house to have the same color paint. However, she has used almost all of her paint and only has 5/6 of a gallon left. How much paint can she use on each wall in order to have enough to paint the remaining walls?

Calculate the quotient. 2/5 ÷ 3/4

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Lesson 1 to Lesson 8 Review

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