Lesson 5

This Number Talk encourages students to rely on what they know about tenths and hundredths and about equivalent fractions to mentally solve problems. The reasoning elicited here will be helpful later in the lesson when students compare and order fractions and decimals.

• 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.

• Consider asking:
  • “¿Alguien puede expresar el razonamiento de _____ de otra forma?” // “Who can restate _____’s reasoning in a different way?”
  • “¿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 la expresión de otra forma?” // “Did anyone approach the expression in a different way?”
  • “¿Alguien quiere agregar algo a la estrategia de _____?” // “Does anyone want to add on to _____’s strategy?”

In this activity, students encounter both fraction and decimal notation for tenths and hundredths and are asked to arrange them in order by size. To do so, they need to rely on their knowledge of equivalent fractions and of the relationship between these two ways of expressing values. Students look for and make use of structure (MP7), for instance, by identifying the digits that tell us about the ones, tenths, and hundredths in each number.

• Create a set of cards from the blackline master for each group of 2–4.

• Groups of 2–4
• Give each group one set of cards from the blackline master.

• “En grupo, ordenen las fracciones y los decimales de menor a mayor. Anoten los números en orden” // “Work with your group to put the fractions and decimals in order, from least to greatest. Record your ordered set.”
• 4–5 minutes: group work time
• “Ahora, encuentren un grupo que tenga tarjetas diferentes a las suyas. Ordenen todos los números de menor a mayor. Anoten los números en orden” // “Next, find a group with a set of cards different than yours. Put all the numbers in order, from least to greatest. Record your ordered set.”
• 8–10 minutes: group work time
• Monitor for the ways students compare fractions and decimals.
• “Completen el último problema individualmente” // “Complete the last problem independently.”
• 3–4 minutes: independent work time

Students may choose to order just the fractions and order all the decimals separately. Consider asking: “¿Cómo ordenarías las fracciones y los decimales?” // “How might you order both the fractions and decimals?” and “¿Qué decimales nos ayudaría convertirlos a fracciones (o al contrario)?” // “Which decimals would be helpful to think about as fractions (or the other way around)?”

• Select students to share their ordered collection of 10 cards. Invite the class to agree or disagree with the arrangement.
• “¿Qué fue lo primero que hicieron o miraron para empezar a ordenar? ¿Qué fue lo siguiente? ¿Y después?” // “What was the first thing you did or looked at to start ordering? What was the next thing? What came after that?” (We first looked at the digit in the ones place. Next, we decided to write the decimals with the same whole number as fractions and ordered the fractions.)

In this activity, compare and order decimals and fractions to solve problems about distances. As they do so, they practice reasoning about tenths and hundredths expressed in different notations. Some of the distances are written to the tenths of a meter and others are written to the hundredths, prompting students to attend to the size of the decimals.

When students interpret and order the distances, they reason abstractly and quantitatively (MP2).

• Groups of 2
• “¿Cuánto creen que podrían saltar si corrieran muy rápido para tomar impulso? ¿Podrían saltar desde un lado del salón hasta el otro?” // “How far do you think you could jump if you run really fast to gain speed for the jump? Could you jump from one side of the classroom to the other?”
• “Piensen en esto por un momento. Luego, compartan su estimación con su compañero” // “Think about it for a moment, and then share your estimate with your partner.”
• 1 minute: partner discussion
• Familiarize students with the long jump in track and field. Explain that the best long jumpers in the world, including Carl Lewis, can jump more than 8 meters or more than 26 feet.
• Consider showing a video clip of long jumps.

• “Tómense unos minutos para trabajar en la actividad. Luego, compartan sus respuestas con su compañero” // “Take a few minutes to work on the task. Then, share your responses with your partner.”
• 6–7 minutes: independent work time
• 3–4 minutes: partner discussion
• Monitor for the ways students compare and order decimals and mixed numbers in the last problem.

• See lesson synthesis.