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
- Record answers and strategy.
- 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
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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
- put larger numbers in the numerator and smaller numbers in the denominator
- use the Wild possibility to their advantage
Advances: Reading, Representing
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
- 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.
- Multiply your fractions.
- 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 \(\frac{\boxed{\phantom{111\frac{1}{1}}}}{\boxed{\phantom{111\frac{1}{1}}}}\, \times \,\frac{\boxed{\phantom{111\frac{1}{1}}}}{\boxed{\phantom{111\frac{1}{1}}}}\, = \,\underline{\hspace{1cm}}\)
- What strategy do you use to decide where to write the numbers?
Student Response
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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).
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
- 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.
- Multiply your fractions.
- 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 \(\frac{\boxed{\phantom{111\frac{1}{1}}}}{\boxed{\phantom{111\frac{1}{1}}}}\, \times \, \frac{\boxed{\phantom{111\frac{1}{1}}}}{\boxed{\phantom{111\frac{1}{1}}}}\, = \,\underline{\hspace{1cm}}\)
- What strategy did you use to choose where to write the numbers?
Student Response
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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
Cool-down: Reflect on Multiplication (5 minutes)
Cool-Down
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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.