Lesson 4

This Number Talk encourages students to look for structure in multiplication expressions and rely on properties of operations to mentally solve problems. Reasoning about products of whole numbers helps to develop students' fluency with multiplication within 100.

• 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.

• “¿Cómo les ayudaron las primeras expresiones a encontrar el valor de la última expresión?” // “How did the earlier expressions help you find the value of the last expression?”
• Consider asking:
  • “¿Alguien usó la misma estrategia, pero la explicaría de otra forma?” // “Did anyone have the same strategy but would explain it differently?”
  • “¿Alguien pensó en el problema de otra forma?” // “Did anyone approach the problem in a different way?”

The purpose of this activity is for students to learn the Secret Fractions center and build non-unit fractions from unit fractions. Students use unit fractions to build “secret fractions,” which are non-unit fractions. For example, to complete a secret fraction card with \(\frac{3}{4}\), students need three cards with \(\frac{1}{4}\). After completing each secret fraction, they reveal the fraction they’ve made and shade the gameboard to represent it. The synthesis highlights strategies students used to build their non-unit fractions.

Here are the images of the cards for reference and planning:

Unit Fractions

Secret Fractions

• Create a set of cards from the blackline master for each group of 2.
• Print extra gameboards for the launch and groups that have time for an extra game.
• Students might want a folder or divider so their partner doesn’t see their cards.

• Groups of 2
• Give each group a set of cards and a gameboard.
• “Vamos a jugar un juego llamado ‘Fracciones secretas’. Leamos las instrucciones y juguemos 1 ronda juntos” // “We’re going to play a game called Secret Fractions. Let’s read through the directions and play 1 round together.”
• Read through the directions with the class and play a round against the class, displaying the fractions from the cards and thinking through decisions aloud.
• Show students how to place an object, such as a folder, between them to obstruct the view of the other player.
• Give each group that wants a divider a folder or other divider.

• “Ahora jueguen ‘Fracciones secretas’ con su compañero” // “Now, play Secret Fractions with your partner.”
• 10–15 minutes: partner work time
• Monitor for students who:
  • trade their secret fractions for new ones because most of their unit fractions have a different denominator
  • keep track of the unit fractions they have as they try to make their non-unit fractions

• “¿Qué estrategias les ayudaron a construir sus fracciones secretas?” // “What strategies did you find helpful for building your secret fractions?” (When \(\frac{5}{8}\) was my secret fraction, I was keeping track of how many \(\frac{1}{8}\) cards I had to make \(\frac{5}{8}\). When I had \(\frac{3}{4}\) as a secret fraction, I knew I needed \(\frac{1}{4}\) cards, but I had a bunch of \(\frac{1}{6}\) cards, so I traded for different secret fractions.)

The purpose of this activity is for students to use diagrams to represent situations that involve non-unit fractions. The synthesis focuses on how students partition and shade the diagrams and how the end of the shaded portion could represent the location of an object. When students interpret the different situations in terms of the diagrams they reason abstractly and quantitatively (MP2).

• Groups of 2
• “¿Qué juegos les gusta jugar con sus amigos?” // “What are some games that you like to play with friends?”
• Share responses.
• “Pilolo es un juego popular en Ghana. Un jugador esconde palos, piedras o monedas de un centavo. Los otros jugadores tienen que encontrar uno de los objetos y ser los primeros en llegar a la línea de meta para obtener un punto. Miren la foto de unos niños que están jugando Pilolo y piensen en algunas estrategias que podrían usar si jugaran este juego” // “Pilolo is a game played in Ghana. One player hides sticks, rocks, or pennies. The other players have to find one of the objects and be the first to reach the finish line to get a point. Look at the picture of some children playing Pilolo and think about some strategies you might use if you played this game.” (I would try to hide the objects in a good hiding spot. I would run fast to be the first one to the finish line.)
• 30 seconds: quiet think time
• Share responses.
• “Vamos a representar algunas situaciones sobre estudiantes que juegan Pilolo” // “We’re going to represent some situations about students playing Pilolo.”

• “En la actividad, cada tira representa la longitud de una calle donde juegan Pilolo” // “In the activity, each strip represents the length of a street where Pilolo is played.”
• “Individualmente, representen cada situación en un diagrama” // “Work independently to represent each situation on a diagram.”
• 3–5 minutes: independent work time
• “Con un compañero, escojan una de las situaciones y hagan un póster que muestre cómo representaron la situación con una tira de fracciones. Incluyan detalles, como notas, dibujos, marcas, etc., para ayudarle a los demás a entender cómo pensaron” // “With a partner, choose one of the situations and make a poster to show how you represented the situation with a fraction strip. You may want to include details such as notes, drawings, labels, and so on, to help others understand your thinking.”
• Give students materials for creating a visual display.
• 5–7 minutes: partner work time

If students partition into sixths or eighths by creating 6 or 8 parts, but the parts aren’t equal, consider asking:

• “¿Cómo partiste la tira en sextos?, ¿en octavos?” // “How did you partition the strip into sixths? Eighths?”
• “¿Cómo podrías usar tercios para partir en sextos? ¿Cómo podrías usar cuartos para partir en octavos?” // “How could you use thirds to partition into sixths? Use fourths to partition into eighths?”

• Display posters around the room.
• “Mientras observan cada póster, discutan cómo se muestra cada situación en el diagrama” // “As you look at each poster, discuss how each situation was shown on the diagram.” (The diagram was partitioned into 6 equal parts. 5 of the equal parts were shaded.)
• 2–3 minutes: partner discussion
• Share responses.
• “¿Qué parte de cada diagrama representa el lugar donde estaba escondido el objeto?” // “What part of each diagram would represent where the object was hidden?” (The end of the shaded part.)