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Activity 1

Standards Alignment

Building On

Addressing

Instructional Routines

Card Sort

Materials

To Copy (from Blackline Masters)

Card Sort Diagrams of Fractions and Decimals

Activity Narrative

In this activity, students reinforce their understanding of equivalent fractions and decimals by sorting a set of cards by their value. This sorting task gives students opportunities to analyze fractions, decimals, and diagrams closely and make connections (MP7).

Representation: Access for Perception. Synthesis: Display a 10-by-10 grid, as well as a square of the exact same size, but with only the columns shown (representing just tenths). Shade 20 hundredths on the 10-by-10 grid and write 0.20 (twenty hundredths) above it. Shade 2 tenths on the other square and write 0.2 (2 tenths) above it. Invite students to discuss how these diagrams demonstrate equivalence of the two numbers.
Supports accessibility for: Conceptual Processing, Visual-Spatial Processing

Launch

Groups of 2–4
Give each group a set of cards.

Activity

“Estas tarjetas tienen fracciones, decimales y diagramas. Clasifiquen las tarjetas según su valor. Juntos, expliquen cómo razonaron” // “This set of cards includes fractions, decimals, and diagrams. Sort the cards by their value. Work with your group to explain your reasoning.”
“Uno de los diagramas quedó sin agrupar. Escriban la fracción y el decimal que ese diagrama representa” // “One diagram has no matching cards. Write the fraction and decimal it represents.”
6–7 minutes: group work on the first two problems
Monitor for the ways students sort the cards and the features of the representations to which they attend.
“Resuelvan el último problema individualmente” // “Work on the last problem independently.”
2–3 minutes: independent work on the last problem

Tu profesor te va a dar varias tarjetas. El cuadrado grande de cada tarjeta representa 1.

Clasifica las tarjetas de manera que las representaciones de cada grupo tengan el mismo valor. Prepárate para explicar tu razonamiento.
Uno de los diagramas quedó sin agrupar. ¿Qué número representa el diagrama de esa tarjeta? Escribe el número como una fracción y en notación decimal.
¿Son 0.20 y 0.2 equivalentes? Usa fracciones y un diagrama para explicar tu razonamiento.

Student Response

to access Student Response.

Advancing Student Thinking

If students respond that 0.20 and 0.2 are not “the same,” consider asking:

“¿A qué te refieres cuando dices que estos números no son lo mismo?” // “What do you mean when you say these numbers are not the same?”
“¿Cómo representarías cada número en una cuadrícula? ¿En qué se parecen las cantidades y en qué son diferentes?” // “How would you represent each number on a square grid? What is the same about the amounts and what is not the same?”

Activity Synthesis

Invite previously selected groups to share each set of sorted cards and explain how they knew the representations belong together.
“¿Cómo supieron qué fracción y qué decimal escribir para el diagrama que no correspondía a ningún grupo?” // “How did you know what fraction and decimal to write for the diagram without any matches?”
Invite a student to share their response to the last problem. Highlight the equivalence of 0.2 and 0.20 as shown in the Student Responses.

Activity 2

Standards Alignment

Building On

Addressing

Instructional Routines

MLR1 Stronger and Clearer Each Time

Materials

None

Activity Narrative

In this activity, students apply their understanding of equivalent fractions and decimals more formally, by analyzing equations and correcting the ones that are false. The last question refers to decimals on a number line and sets the stage for the next lesson where the primary representation is the number line.

As students discuss and justify their decisions about the claim in the last question, they critically analyze student reasoning (MP3).

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

Launch

Groups of 2
“Antes, vimos ecuaciones que tenían fracciones en ambos lados del signo igual. Ahora exploremos ecuaciones que tienen fracciones y decimales, o solo decimales” // “Earlier, we saw some equations with fractions on both sides of the equal sign. Now let’s look at some equations that include fractions and decimals or just decimals.”

Activity

“Tómense unos minutos para terminar la actividad individualmente. Luego, compartan con su compañero cómo pensaron” // “Take a few minutes to complete the activity independently. Then share your thinking with your partner.”
6–7 minutes: independent work time
“En cada pregunta del primer problema, tomen turnos para explicarle a su compañero cómo supieron si la afirmación era verdadera o falsa” // “For each equation in the first problem, take turns explaining to your partner how you know whether it is true or false.”
3–4 minutes: partner discussion

En cada caso, decide si la afirmación es verdadera o falsa. Si es falsa, reemplaza uno de los números para que sea verdadera. Los números que hay a cada lado del signo igual no pueden ser idénticos.
Jada dice que si se ubican los números 0.05, 0.5 y 0.50 en la recta numérica, solo quedarían 2 puntos marcados. ¿Estás de acuerdo? Explica o muestra tu razonamiento.

Student Response

to access Student Response.

Advancing Student Thinking

Activity Synthesis

MLR1 Stronger and Clearer Each Time

“Compartan con su pareja su respuesta a la última pregunta. 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 response to the last question 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.”
3–4 minutes: structured partner discussion.
Repeat with 1–2 new 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

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Lesson 2

Decimales equivalentes

Warm-up

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Activity 1

Standards Alignment

Building On

Addressing

4.NF.C.6

Instructional Routines

Materials

To Copy (from Blackline Masters)

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Activity 2

Standards Alignment

Building On

Addressing

4.NF.C.6

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Lesson Synthesis

Standards Alignment

Building On

Addressing

4.NF.C.5

Building Toward

Building Toward

4.NF.C.7

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