Lesson 9

This Number Talk encourages students to use the relationship between related numbers (5 and 10, and 6, 12, and 24) and properties of operations to find products. The strategies of doubling and halving elicited here will be helpful later in the lesson when students generate equivalent fractions. In describing strategies, students need to be precise in their word choice and use of language (MP6).

• 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 los ayudaron las primeras tres expresiones a encontrar el valor de la última?” // “How did the first three expressions help you find the value of the last one?”

In this activity, students look closely at the relationships of fractions with denominator 5, 10, and 100. They use their observations and understanding to identify equivalent fractions and to explain why two fractions are or are not equivalent. When students analyze and criticize the reasoning presented in the activity statements and when the discuss their work with classmates, they are critiquing the reasoning of others and improving their arguments (MP3).

• Groups of 2
• Give students access to rulers or straightedges.
• Ask students to keep their materials closed.

• “Tómense 5 minutos en silencio para responder. Después, discutan con su compañero cómo pensaron” // “Take 5 quiet minutes to answer the problem. Afterwards, discuss your thinking with your partner.”
• 5 minutes: independent work time
• 5 minutes: partner discussion

MLR1 Stronger and Clearer Each Time

• “Compartan su razonamiento y sus rectas numéricas con su compañero. Por turnos, uno habla y el otro escucha. Si es su turno de hablar, compartan sus ideas y lo que han escrito hasta ese momento. Si es su turno de escuchar, hagan preguntas y comentarios que ayuden a su compañero a mejorar su trabajo” // “Share your reasoning and number lines with your partner. Take turns being the speaker and the listener. If you are the speaker, share your ideas and writing so far. If you are the listener, ask questions and give feedback to help your partner improve their work.”
• 3–5 minutes: structured partner discussion
• Repeat with 2–3 different partners.
• “Ajusten su borrador inicial basándose en los comentarios que les hicieron sus compañeros” // “Revise your initial draft based on the feedback you got from your partners.”
• 2–3 minutes: independent work time

This activity gives students opportunities to practice explaining or showing whether two fractions are equivalent. Students may do so using a visual representation, by reasoning about the number and size of the fractional parts in each fraction, or by thinking about multiplicative relationships between the numbers in the given fractions. 

Students participate in a gallery walk in which they generate equivalent fractions for the numbers on the posters. Students visit at least two of six posters (or as many as time permits)—at least one poster with two fractions (posters A–C) and one poster with three fractions (posters D–F). Here are the sets shown on the blackline master:

Because at the posters with two fractions (A–C) students would need to generate an equivalent fraction that hasn’t already been written by others, generating equivalent fractions becomes more difficult as the activity goes on. Consider using this to differentiate for students who may need an additional challenge: start them at the posters with three fractions (D–F).

• Each group needs 4 sticky notes. 

• Groups of 3–4
• Give each group 4 sticky notes
• Read the task statement as a class. Solicit clarifying questions from students.
• Invite a couple of students to recap the directions in their own words or to demonstrate the process, if helpful.
• Consider assigning each group a starting poster and giving directions for rotation.

• 10 minutes: gallery walk
• Tell students who are visiting posters A–C that they could leave feedback about the fraction on a sticky note if they disagree that it is equivalent to the fractions on the poster. They should include their name and be prepared to explain how they know.

• See lesson synthesis.