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Activity 1

Standards Alignment

Building On

Addressing

Instructional Routines

None

Materials

None

Activity Narrative

The purpose of this activity is for students to think of different ways of using multiplication expressions to represent a non-unit fraction. Students informally use the associative property as they work toward generalizing that .

Action and Expression: Develop Expression and Communication. Provide access to fraction strips or pre-formatted tape diagrams, including sevenths, fifths, and tenths.
Supports accessibility for: Visual-Spatial Processing, Fine Motor Skills

Launch

Groups of 2

Activity

“Completen el primer problema con su compañero. Hablen sobre cómo saben qué números hacen que las ecuaciones sean verdaderas” // “Work with your partner to complete the first problem. Talk about how you know what numbers make the equations true.”
3 minutes: partner work time
Monitor for students who use the factors of 12 to complete the equations.
“Ahora, durante unos minutos, completen el resto de problemas individualmente. Luego, compartan sus respuestas con su compañero” // “Now take a few minutes to complete the rest of the problems independently. Afterward, share your responses with your partner.”
7 minutes: independent work time
3 minutes: partner discussion
“¿Escogieron los mismos números que su compañero? Si no, ¿ambas ecuaciones son correctas?” // “Did you choose the same numbers as your partner? If not, are both equations correct?”

Completa cada ecuación con el número que hace que sea verdadera. Si te ayuda, dibuja un diagrama.
Estos son dos conjuntos de números:

Conjunto A:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11

Conjunto B:
1. Escoge un número del conjunto A y un número del conjunto B para completar esta ecuación y hacer que sea verdadera:
2. Escoge un número diferente del conjunto A y un número diferente del conjunto B para completar esta ecuación y hacer que sea verdadera.
Explica o muestra cómo sabes que las dos ecuaciones que escribiste son verdaderas.

Activity Synthesis

“¿Cómo supieron qué fracciones usar para completar cada ecuación del primer problema?” // “How did you know what fractions to use to complete each equation in the first problem?” (We looked for the numbers to multiply to get . The denominator stays the same, so we find the whole number and the numerator by knowing the factor pairs of 12.)
Select 2–3 partners to share the following equations from the second problem:
“¿Por qué son verdaderas todas estas ecuaciones?” // “Why are all these equations true?” (To get , we can multiply the whole number by the numerator and then keep the denominator the same. In all of these, multiplying the whole number and the numerator gives 6. There are different ways to multiply to get 6 as a numerator: , , , and .)

Activity 2

Standards Alignment

Building On

Addressing

Instructional Routines

None

Materials

None

Activity Narrative

In this activity, students analyze multiplication expressions, match each to one of a given set of fractions, and explain how they know that certain expressions represent the same fraction (MP7).

MLR8 Discussion Supports. Students should take turns finding a match and explaining their reasoning to their partner. Display the following sentence frame for all to see: “Observé ____, entonces asocié . . .” // “I noticed ____ , so I matched . . . .” Encourage students to challenge each other when they disagree.
Advances: Speaking, Conversing

Launch

Groups of 2

Activity

“Asocien cada expresión con una fracción que muestre su valor. Prepárense para explicar cómo saben cuáles expresiones se asocian con cuál fracción” // “Match the expressions to a fraction that shows its value. Be prepared to explain how you know which expressions match which fraction.”
“Es posible que no todas las fracciones tengan el mismo número de expresiones asociadas” // “Each fraction may not have the same number of matching expressions.”
5–7 minutes: partner work time
Pause for a discussion before students continue to the second half of the activity.
Select students to share their matches and their explanations.
“¿Hubo expresiones que no pudieron asociar? ¿Cómo lo saben?” // “Are there any expressions without a match? How do you know?” (Yes, Expressions G and I. Their values are and .)
“Se han dado cuenta de que varias expresiones pueden representar la misma fracción. Algunas de las expresiones tienen dos factores y algunas tienen tres. En todas hay fracciones unitarias” // “You've seen that multiple expressions can represent the same fraction. Some of the expressions have two factors, some have three. All of them show unit fractions.”
“Ahora completen cada ecuación del segundo problema con dos factores que hagan que la ecuación sea verdadera. Traten de usar factores que no sean fracciones unitarias” // “Now complete each equation in the second problem with two factors that would make the equation true. See if you can use factors that are not unit fractions.”
5 minutes: independent work time

Este es un conjunto de expresiones:

Asocia cada expresión, si es posible, con una de las siguientes fracciones. Anota a cuál fracción asociaste cada una de las que se podían asociar.
Completa cada ecuación para que sea verdadera. Intenta hacerlo sin usar fracciones unitarias.

Student Response

to access Student Response.

Advancing Student Thinking

Activity Synthesis

Ask selected students to share expressions for each fraction.
Display the possible expressions for the final equation:
“¿Cómo podemos explicar por qué el valor de estas expresiones es ?” // “How can we explain why these expressions have the value ?”

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Lesson 5

Expresiones de multiplicación 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.B.4.b

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Activity Synthesis

Activity 2

Standards Alignment

Building On

Addressing

4.NF.B.4.b

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Lesson Synthesis

Standards Alignment

Building On

Addressing

4.NF.B.4.b

Building Toward

Student Response

Advancing Student Thinking

4.NF.B.4.c

Building Toward

4.NF.B.4.c

Building Toward