Lesson 13

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.

• Display one expression.
• “Hagan una señal cuando tengan una respuesta y puedan explicar cómo la obtuvieron” // “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

• Record answers and strategy.
• Keep expressions and work displayed.
• Repeat with each expression.

• Display: \(\frac{1}{3} \times \frac{6}{3}\)
• “¿Cómo encontraron este producto?” // “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 \(\frac{2}{3}\).)

• put larger numbers in the numerator and smaller numbers in the denominator
• use the Wild possibility to their advantage

• Each group of 2 needs a paper clip.

• Groups of 2
• “Tómense un minuto para leer las instrucciones de ‘Comparemos multiplicaciones de fracciones’” // “Take a minute to read over the directions for Fraction Multiplication Compare.”
• 1 minute: quiet think time
• Give each group a paper clip.
• “Jueguen ‘Comparemos multiplicaciones de fracciones’ con su compañero” // “Play Fraction Multiplication Compare with your partner.”

• 10–12 minutes: partner work time

• “¿Para qué números fue más fácil decidir dónde ponerlos en el tablero de juego? ¿Por qué?” // “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.)
• “¿Para qué números fue más difícil decidir dónde ponerlos en el tablero de juego? ¿Por qué?” // “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.)
• “¿Cómo usaron el ‘comodín’ cuando les salió?” // “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.)

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).

• Each group of 2 needs a paper clip.

• Groups of 2
• “Vamos a jugar otra ronda de ‘Comparemos multiplicaciones de fracciones’, pero esta vez gana la persona que tenga el menor producto” // “We are going to play another round of Fraction Multiplication Compare, but this time the person with the smallest product is the winner.”
• “¿Van a usar la misma estrategia que usaron cuando estaban intentando formar el mayor producto?” // “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.
• “Jueguen ‘Comparemos multiplicaciones de fracciones’ con su compañero” // “Play Fraction Multiplication Compare with your partner.”

• 10–15 minutes: partner work time

• “¿En qué se parece este juego a la versión anterior de ‘Comparemos multiplicaciones de fracciones’?” // “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.)
• “¿Cómo cambió su estrategia al intentar formar el menor producto?” // “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).