Lesson 9

This warm-up prompts students to compare four number lines. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the number lines in comparison to one another. During the synthesis, ask students to explain the meaning of any terminology they use, such as parts, partitions, mark, label, halves, fourths, or whole.

• Groups of 2
• Display the image.
• “Escojan una que sea diferente. Prepárense para compartir por qué es diferente” // “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
• 1 minute: quiet think time

• “Discutan con su pareja cómo pensaron” // “Discuss your thinking with your partner.”
• 2–3 minutes: partner discussion
• Share and record responses.

• “¿Cómo supieron que la recta numérica de la figura A terminaba en 1?” // “How did you know that the number line in A stopped at 1?” (The location of \(\frac{1}{2}\) shows that the whole number line is split in half right there and I know that 2 halves is 1. I can only fit one more half next to the first one.)
• Consider asking: “Encontremos al menos una razón por la que cada una es diferente” // “Let’s find at least one reason why each one doesn’t belong.”

The purpose of this activity is for students to locate 1 on a number line given the location of a non-unit fraction less than 1 or greater than 1. In either case, it is likely students will reason about unit fractions to locate 1.

In the first problem, students may use the size of thirds to locate 1. In the second problem, they reinforce their knowledge that the denominator of a fraction tells us the number of equal parts in a whole and the size of a unit fraction, and that the numerator gives the number of those parts (MP6). Students typically use the denominator to partition a number line, but here they need to use the numerator.

This activity uses MLR1 Stronger and Clearer Each Time.
Advances: reading, writing

• Groups of 2

• “Tómense unos minutos para ubicar el 1 en estas rectas numéricas. Después, usen cualquier recta numérica para explicar cómo ubicaron el 1” // “Take a few minutes to locate 1 on these number lines. Then use any of the number lines to explain how you located 1.”
• 5–7 minutes: independent work time

If students say they aren’t sure how to get started, consider asking:

• “¿Qué sabemos de esta fracción?” // “What do we know about this fraction?”
• “¿Cómo nos puede ayudar eso a encontrar el 1?” // “How could that help us find 1?”

MLR1 Stronger and Clearer Each Time

• “Compartan con su compañero las ideas que escribieron al razonar sobre una de las rectas numéricas. Por turnos, uno habla y el otro escucha. Si es su turno de hablar, compartan sus ideas y lo que han escrito hasta el momento. Si es su turno de escuchar, hagan preguntas y comentarios que ayuden a su compañero a mejorar su trabajo” // “Share your written reasoning for one of the 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
• Invite students to share their revised explanations of how they located 1 on the number lines.

The purpose of this activity is for students to use the location of a unit fraction to locate another fraction with a different denominator on the number line. Students can use their knowledge from the previous activity to place 1 on the number line and then use that to partition the interval from 0 to 1 to find other numbers. Because students have only located fractions with the same denominator on a single number line, they may want to use more than one number line in this activity. They may or may not label the points they find along the way to \(\frac{3}{4}\). Encourage them to use whatever strategy makes sense to them.

Monitor for students who use a single number line to show both thirds and fourths and those who use separate number lines. Select them to share during activity synthesis.

This activity is optional because it goes beyond the depth of understanding required to address grade 3 standards.

• Groups of 2
• “Ahora vamos a tratar de hacer algo un poco diferente. Usemos la ubicación de una fracción unitaria para encontrar una fracción que tiene un denominador diferente” // “Now we’re going to try something a little bit different. Let’s use the location of a unit fraction to find a fraction with a different denominator.”

• “Tómense unos minutos para ubicar \(\frac{3}{4}\) en esta recta numérica. Usen cualquier estrategia que tenga sentido para ustedes” // “Take a few minutes to locate \(\frac{3}{4}\) on this number line. Use any strategy that makes sense to you.”
• 3–5 minutes: independent work time
• As students work, consider asking:
  • “¿Cómo decidieron si usar una o dos rectas numéricas?” // “How did you decide whether to use one or two number lines?”
  • “¿Ubicaron otros números antes de ubicar \(\frac{3}{4}\)?” // “Did you locate any numbers before locating \(\frac{3}{4}\)?”
  • “¿En qué lugar de su recta numérica (o de sus rectas numéricas) está el 1?” // “Where is 1 on your number line(s)?”
• “Compartan su estrategia con su compañero” // “Share your strategy with your partner.”
• 2–3 minutes: partner discussion

• Ask the two selected students to display their work side-by-side for all to see.
• “¿Qué tienen en común estas estrategias? ¿En qué son diferentes estas representaciones?” // “What do these strategies have in common? How are these representations different?” (They both located 1 before locating \(\frac{3}{4}\). In the first strategy, the thirds are one number line and used to find 1. Then, 1 is on the second number line and used to find \(\frac{3}{4}\). In the second strategy, the thirds and fourths are marked on the same number line.)
• Consider asking: “¿Qué preguntas tienen sobre estas representaciones?” // “What questions do you have about these representations?”