##
* *Reflection: Connection to Prior Knowledge
Mixed Number Multiplication - Section 2: Juliana's Problem

At my school, students learn how to use the box method to multiply whole numbers in 5^{th} grade. This method breaks down each factor by place value. You use a box to show each product and then add the products together.

Unit 4.9 Connecting to the Box Method.jpg

For instance, 43 x 27 is broken up into (40 + 3) x (20 + 7). I wrote this problem on the board and asked students how they would use the box method to find the product. I then connected this to multiplying mixed numbers. We split each mixed number into a whole number and a fraction and then create the box to model our multiplication. Students were quickly able to see the connection between the methods.

*Connection to Prior Knowledge: Connecting to the Box Method*

# Mixed Number Multiplication

Lesson 10 of 19

## Objective: SWBAT: • Create an estimate of a fraction multiplication problem. • Multiply mixed numbers using visual models.

## Big Idea: How can we use diagrams to multiply mixed numbers? How can we multiply mixed numbers without using a diagram? Students apply what they know about multiplying fractions to multiplying with mixed numbers.

*60 minutes*

#### Do Now

*10 min*

See my **Do Now** in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day. Today I want students to make reasonable estimates for multiplying mixed numbers.

Some students may round the mixed numbers to the nearest whole number and then multiply. Others will simply use the given whole number and ignore the fraction. Other students may come for a range, using a low and high estimate. The important thing is that students are creating estimates and explaining the thinking behind them. I call on students to share their estimates and their thinking.

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#### Juliana's Problem

*10 min*

Note:

- I use the data from the ticket to go from
**Representing Fraction Multiplication Day 2**and the Addition and Subtraction Quiz**Create Homogeneous Groups.**Students will work in partners.

I have students move to work with their partners. We work through this problem together. I quickly ask students to raise their hand if they like to run. I have partners do a quick **Think Pair Share **what their favorite way to exercise.

I have a volunteer read the problem. I have students work independently to create an estimate. Students may follow the same thinking they used in their do now, or they may try a different strategy that they heard from another student. I call on a couple students to share out their estimates. I ask students why they are multiplying. I emphasize that making an estimate is a great way to check the reasonableness of your answer once you’ve found it.

I ask, “How could we create a rectangle to show 4 3/5 x 2 2/3?” Some students may connect with the rectangle models they have made in the previous lessons **(Representing Fraction Multiplication **and **Representing Fraction Multiplication Day 2). **I don’t want students to test out their own idea, so I model how we can create a rectangle with the dimensions of 4 3/5 and 2 2/3. I explain that the rectangles don’t have to be drawn to scale, but they should look relatively accurate. For example, the part of the rectangle that is 7 meters long should be longer than the part of the diagram that is 2 meters. See the resource “Unit 4.9 Juliana’s Problem Example”.

I ask a student to explain our shortcut for multiplying fractions. We go through and find the product of each individual rectangle. Once that is through, I ask students what we need to do next? I want students to recognize that we need to add all of the products together. I ask, “What is an efficient way to do this?” One strategy would be to turn 8/3 and 6/5 into a mixed numbers. Then, we can add the whole numbers. Then we need to deal with the left over fractions. I want students to realize that we can create equivalent fractions that are fifteenths and then add them together. I ask students if we can simplify our answer. We revisit our estimates. How did we do? Does our answer make sense?

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#### Practice

*25 min*

I have students work on the practice problems with their partners. Students are engaging in **MP4: Model with mathematics, MP5: Use appropriate tools strategically, MP6: Attend to precision, **and** MP7: Look for and make use of structure.** I **Post A Key **so students can check their work as they go. I walk around and monitor student progress and behavior. I want to see how well students make estimates and create rectangle diagrams.

If students struggle, I may ask some of the following questions:

- What operation is does this problem require? Why?
- What is your estimate? How did you get that?
- If you were creating a diagram just to multiply the whole numbers, what would it look like?
- How can we include the fractions in your diagram?
- How do you prefer to multiply fractions? What are you going to do first?
- How can you find the exact product?
- How do you add fractions together?
- Does your answer make sense?

For problem 1, some students may see that they can easily convert the fractions to decimals and then multiply them together to find the area. This is great! I make sure that students still draw and label the rectangle. They will not be able to use this method with the practice problems that involve thirds.

If students successfully complete their work, they can choose whether to play “Smaller Answer Wins” or “Score the Difference”. Students will need rules, game sheets, and dice.

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#### Closure and Ticket to Go

*15 min*

For **Closure **I ask students to share out how they figured out the answer to Anita’s bran question. Then I ask students whether Homelie’s idea in problem 3 worked. I want students to realize that her answer would be too small. I want students to be able to look at their rectangle diagram for problem 2 in order to see what multiplication problems were missing. If students don’t mention it, I make the connection to the distributive property.

I ask students if there is a shortcut that would work. Some students may share that you can change the mixed numbers into improper fractions and then multiply them like they would regular fractions. The challenge is then turning the improper fractions back into mixed numbers. Students are engaging in **MP8: Look for and express regularity in repeated reasoning**.

I pass out the **Ticket to Go**. Then I pass out the **HW Mixed Number Multiplication.**

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##### Similar Lessons

Environment: Suburban

Environment: Suburban

###### King Fraction

*Favorites(17)*

*Resources(19)*

Environment: Suburban

- UNIT 1: Intro to 6th Grade Math & Number Characteristics
- UNIT 2: The College Project - Working with Decimals
- UNIT 3: Integers and Rational Numbers
- UNIT 4: Fraction Operations
- UNIT 5: Proportional Reasoning: Ratios and Rates
- UNIT 6: Expressions, Equations, & Inequalities
- UNIT 7: Geometry
- UNIT 8: Geometry
- UNIT 9: Statistics
- UNIT 10: Review Unit

- LESSON 1: Pretest
- LESSON 2: Many Names for Fractions
- LESSON 3: What Fraction of the Section Does Each Person Own?
- LESSON 4: Which Fraction is Greater?
- LESSON 5: Adding and Subtracting Fractions Day 1
- LESSON 6: Adding and Subtracting Fractions Day 2
- LESSON 7: Looking for Patterns + Show What You Know
- LESSON 8: Representing Fraction Multiplication
- LESSON 9: Representing Fraction Multiplication Day 2
- LESSON 10: Mixed Number Multiplication
- LESSON 11: The Multiplying Game
- LESSON 12: Connecting Multiplication and Division
- LESSON 13: Dividing Whole Numbers by Fractions
- LESSON 14: Dividing Fractions by Fractions
- LESSON 15: Strategies for Dividing Fractions
- LESSON 16: Strategies for Dividing Fractions Day 2 + Show What You Know
- LESSON 17: Unit Review
- LESSON 18: Unit Closure
- LESSON 19: Unit Test