Ask students “Is there anybody whose partner followed a different strategy? Can you explain their strategy? After students have shared strategies, make a note of their various drawings and thinking.

Strategies and tools for solving fraction division word problems.

Typically, I teach fraction division and word problems after the ratio and rates units. Students are likely to use strategies from fraction division and using ratio tables to solve problems like these. Here are some sample drawings and thinking you are likely to see.

Drawing circles

This comes naturally to students since this is how they would they have learned about fractions since elementary school.

Number line

Students would have have been exposed to this kind of thinking when going over dividing a whole number by a fraction.

Repeated addition

Students might keep adding `1/4` till they reach `2` wholes. Or they might add `1/4` till they reach `1` whole and then conclude that you can make `4` baggies from `1` pound, so you can make `8` baggies from `2` pounds.

Ratio tables

Students who are comfortable with ratio tables might express their thinking this way. Encourage to explain why they set it up this way, what the `4` and `1` mean, and what does multiplying by `2` mean. This helps them to make connections between their ratio table operations and the actual problem.

Number of groups and size of groups

You can also encourage students to think about what do they know in the problem:

Total
Number of groups
Size of each group

This kind of thinking helps students to solve multiplication and division problems. You can give problems like to help them identify what they are given and what is missing.

Once you work through these problems, students might conclude that when the number of groups and size of groups is given, you would multiply. When the total is given and either number or size are given, you would divide. You do not want to enforce this as a rule… you really want to provide them with various tools to think through word problems.

Fraction division word problems with mixed numbers

In this problem you are given the total and the size of a group and the number of groups is missing. We have given a tape diagram as a model to represent this problem; you could also use a number line.

Start with an open-ended question and see what relationships students can identify. Then ask more targeted questions around number, size, and total. Ask them what they are given and what is missing.

You would then identify the total and the size of the group. The total is `3\frac{1}{3}` and the size of each group is `2/3`.

Ask students if they can figure out the number of groups. Students are likely to show this kind of work.

Write the division equation

The next step is to formalize this thinking. Tell students to set up an equation to represent this problem. Some might set up a multiplication equation and some might argue that this problem is represented by a division equation.

Once students have `3\frac{1}{3} \div 2/3 = 5`, ask them if they can use the division algorithm to check whether the answer is correct. Hopefully students will show this work:

`3\frac{1}{3} \div 2/3 = \frac{10}{3} \div 2/3 = 10/3 \times 3/2 = 30/6 = 5`

Always encourage students to write an answer sentence so that they make a connection between their calculations and the problem.

Fraction division word problems with dividing by a whole number

In this problem, the total and the number of groups is given but the size of groups is missing. Typically you would represent such a problem using an area model.

Students might struggle to see that `7/8` is the total since it is less than `1`. Once they have convinced each other that the total and the number of groups is given, ask them these questions:

What does the size of each group represent?
Do you expect the size of each group to be less than `1` or more than `1`? Less than `7/8` or more than `7/8`?

This helps students to check for reasonableness of their final answer.

Ask students to now divide the total into `4` groups. This is a representation of what students might draw. Ideally, you should use their drawings to work through the problem. If students are stuck, you can use this slide as a backup.

The next question is how much pizza did each friend get? Ask students to work with their partner to highlight the row that shows how much one friend got.

Once they have highlighted one row, ask them what fraction of the whole pizza did each friend get? Students might have some trouble identifying the denominator. They might want to use `28` as the denominator since `28` cells have some color. This will inspire a good debate. Hopefully some students will point out that we are looking for a fraction of the whole pizza and that the whole pizza has `32` parts out of which each friend get `7` parts.

You should again ask students to set up the division equation and check if it is true.

Building flexibility in using strategies

As students work through word problems, you should let them use the tools and strategies that they are comfortable with and make sense to them. You should ask students to share their strategies with the class so that students are exposed to different ways of thinking.

Typically, i give division problems mixed up with multiplication problems so that students don’t automatically know that it is a division problem. The key in word problems is to understand the situation and use any tools and strategies they know to solve the problem.

Partner Activity

This partner activity allows students to work together to draw a model for a dividing fraction word problem. Give each student a copy of the partner activity.

Have students read the scenario, and work together to decode the problem. They can draw a model to help them. Tape diagrams or fraction models are great visual pictures to create for dividing fractions.

When it seems like students are finished, have a group come to the front of the room to share how they were able to solve the problem. If any groups drew their picture other ways, allow them to come up and explain too. It is interesting to see the similarities and differences between the way each student draws their picture, but how they are able to answer the same question.

The last question of the activity has to do with leftovers. This will be a great transition into dividing fraction word problems with leftovers. Being able to interpret what leftovers mean is a very important part of division of fractions.

Number System Math Problems- 6th Grade

Number System

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