Lesson 13

Multiply Fractions Game Day

Warm-up: Number Talk: Multiply One Third (10 minutes)

Narrative

The purpose of this Number Talk is for students to demonstrate strategies and understandings students have for multiplying fractions. These understandings help students develop fluency and will be helpful later in this lesson when students will need to multiply fractions.

Launch

• Display one expression.
• “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

Activity

• Keep expressions and work displayed.
• Repeat with each expression.

Student Facing

Find the value of each expression mentally.

• $$\frac{1}{3}\times3$$
• $$\frac{1}{3}\times4$$
• $$\frac{1}{3}\times\frac{6}{3}$$
• $$\frac{1}{3}\times\frac{1}{4}$$

Student Response

For access, consult one of our IM Certified Partners.

Activity Synthesis

• Display: $$\frac{1}{3} \times \frac{6}{3}$$
• “How did you find this product?” (I took the products of the numerators and denominators. I knew $$\frac{6}{3}$$ is 2, so it’s $$\frac{2}{3}$$.)

Activity 1: Fraction Multiplication Compare (15 minutes)

Narrative

The purpose of this activity is for students to practice multiplying fractions. Students spin a spinner and use the numbers to generate fractions with a goal of making the largest product. Monitor for students who use their understanding of fractions (MP7) to:
• put larger numbers in the numerator and smaller numbers in the denominator
• use the Wild possibility to their advantage
MLR8 Discussion Supports. Prior to solving the problems, invite students to make sense of the situations and take turns sharing their understanding with their partner. Listen for and clarify any questions about the context.

Required Materials

Materials to Gather

Required Preparation

• Each group of 2 needs a paper clip.

Launch

• Groups of 2
• “Take a minute to read over the directions for Fraction Multiplication Compare.”
• 1 minute: quiet think time
• Give each group a paper clip.
• “Play Fraction Multiplication Compare with your partner.”

Activity

• 10–12 minutes: partner work time

Student Facing

1. Use the directions to play Fraction Multiplication Compare with your partner.
• Spin the spinner.
• Write the number you spun in one of the empty blank boxes. Once you write a number, you cannot change it.
• Player two spins and writes the number on their game board.
• Continue taking turns until all four blank boxes are filled.
• The player with the greatest product wins.
• Play again.

Round 1 $$\frac{\boxed{\phantom{111\frac{1}{1}}}}{\boxed{\phantom{111\frac{1}{1}}}}\, \times \,\frac{\boxed{\phantom{111\frac{1}{1}}}}{\boxed{\phantom{111\frac{1}{1}}}}\, = \,\underline{\hspace{1cm}}$$

Round 2 $$\frac{\boxed{\phantom{111\frac{1}{1}}}}{\boxed{\phantom{111\frac{1}{1}}}}\, \times \,\frac{\boxed{\phantom{111\frac{1}{1}}}}{\boxed{\phantom{111\frac{1}{1}}}}\, = \,\underline{\hspace{1cm}}$$

2. What strategy do you use to decide where to write the numbers?

Student Response

For access, consult one of our IM Certified Partners.

Activity Synthesis

• “Which numbers were easiest to choose where to put on the game board? Why?” (When I got an 8 or 9 I knew to put it in the numerator to make a bigger fraction. When I got a 1 or 2 I knew to put it in the denominator to get the biggest possible fraction.)
• “Which numbers were hardest to choose where to put on the game board? Why?” (The middle numbers like 4, 5, and 6. I did not want them in the denominator because they make the fraction pretty small. But I did not want them in the numerator because they won’t give a very big fraction unless the denominator is 1 or 2.)
• “How did you use the ‘wild’ when you spun it?” (I put a 1 in the denominator where I had an 8 in the numerator.)

Activity 2: Fraction Multiplication Compare Round 2 (20 minutes)

Narrative

The purpose of this activity is for students to practice multiplying fractions. The structure of the activity is identical to the previous one except that the goal is to have the smallest product. Monitor for students who identify the common structure with the previous game and place the larger numbers in the denominator and the smaller ones in the numerator (MP8).

Engagement: Internalize Self-Regulation. Synthesis: Provide students an opportunity to self-assess and reflect on their own progress. For example, ask students to compare their calculated products to their partner’s. Encourage students to include how each factor impacted the product in their comparisons.
Supports accessibility for: Conceptual Understanding, Language

Required Materials

Materials to Gather

Required Preparation

• Each group of 2 needs a paper clip.

Launch

• Groups of 2
• “We are going to play another round of Fraction Multiplication Compare, but this time the person with the smallest product is the winner.”
• “Will you use the same strategy that you used when trying to make the greatest product?" (No because there the goal was to get the biggest product.)
• 1 minute: quiet think time
• 1 minute: partner discussion
• Give each group a paper clip.
• “Play Fraction Multiplication Compare with your partner.”

Activity

• 10–15 minutes: partner work time

Student Facing

1. Use the directions to play Fraction Multiplication Compare with your partner.
• Spin the spinner.
• Write the number you spun in one of the four blank boxes.
• Player two spins and writes the number on their game board.
• Continue taking turns until all four blank boxes are filled.
• The player with the smallest product wins.
• Play again.

Round 1 $$\frac{\boxed{\phantom{111\frac{1}{1}}}}{\boxed{\phantom{111\frac{1}{1}}}}\, \times\, \frac{\boxed{\phantom{111\frac{1}{1}}}}{\boxed{\phantom{111\frac{1}{1}}}}\, =\, \underline{\hspace{1cm}}$$

Round 2 $$\frac{\boxed{\phantom{111\frac{1}{1}}}}{\boxed{\phantom{111\frac{1}{1}}}}\, \times \, \frac{\boxed{\phantom{111\frac{1}{1}}}}{\boxed{\phantom{111\frac{1}{1}}}}\, = \,\underline{\hspace{1cm}}$$

2. What strategy did you use to choose where to write the numbers?

Student Response

For access, consult one of our IM Certified Partners.

Activity Synthesis

• “How was this game the same as the earlier version of Fraction Multiplication Compare?” (I knew where to put big numbers like 8 and 9 and small numbers like 1 and 2. It was hard to know where to put the middle numbers like 4 or 5.)
• “How did your strategy change when trying to make the smallest product?” (It was the opposite of the first game. I tried to put the biggest numbers in the denominator and the smallest numbers in the numerator).

Lesson Synthesis

Lesson Synthesis

“Today, we practiced multiplying fractions. How is multiplying fractions the same as multiplying whole numbers? How is multiplying fractions different from multiplying whole numbers?” (When I multiply fractions, I have both numerators and denominators to multiply. So I have to use what I know about multiplying whole numbers but I need to do it twice.)

Cool-down: Reflect on Multiplication (5 minutes)

Cool-Down

For access, consult one of our IM Certified Partners.

Student Section Summary

Student Facing

We played games with fractions and decimals, trying to make the largest or smallest number with given digits. Let's use the numbers 1, 3, 5, and 6. What is the smallest sum of two fractions we can make with these numbers? We want to use the smaller numbers, 1 and 3, for the numerators and the larger numbers, 5 and 6, for the denominators. This gives two possibilities, $$\frac{1}{6} + \frac{3}{5}$$ and $$\frac{1}{5} + \frac{3}{6}$$. The expression $$\frac{1}{5} + \frac{3}{6}$$ has the smaller value which makes sense since we want the larger numerator, which means more equal pieces, to go with the larger denominator which makes those pieces smaller.

The smallest difference we can make with these numbers is $$\frac{3}{6} - \frac{1}{5}$$ which is a little smaller than $$\frac{3}{5} - \frac{1}{6}$$. Finally, the largest product we can make is $$\frac{6}{3} \times \frac{5}{1}$$ or $$\frac{5}{1} \times \frac{6}{3}$$ which both have the value $$\frac{30}{3}$$ or 10.