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Activity 1

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

To Gather

Activity Narrative

The purpose of this activity is for students to find the area of a rectangle by tiling and multiplying the side lengths. Students use inch tiles to build rectangles with a given side length and find the area of those rectangles. They work together to compare and explain the strategies used to find the area of rectangles and make connections between strategies. Students observe how the area of rectangles with a given width varies as the length changes and make predictions about what areas are possible with the given widths (MP7).

MLR2 Collect and Display. Circulate, listen for and collect the language students use as they build rectangles. On a visible display, record words and phrases such as: “fila", "columna", "área", "longitud", "ancho", "de ancho” // “row,” “column,” “area,” “length,” “width,” “wide.” Invite students to borrow language from the display as needed, and update it throughout the lesson.
Advances: Conversing, Reading.

Launch

Display the rectangle in the student book.
“Examinen el rectángulo que ven en su página y descríbanselo a un compañero” // “Look at the rectangle on your page and describe it to a partner.” (It has 6 units. There are 2 rows and 3 columns.)
Give each group 10 tiles.
“Construyan todos los rectángulos que puedan usando 10 fichas. Descríbanselos a un compañero” // “Build all the rectangles you can using all 10 tiles. Describe them to a partner.”
2 minutes: partner discussion
“¿Quién tiene un rectángulo que mide 2 fichas de ancho?, ¿o uno que mide 5 fichas de ancho?, ¿o uno que mide 10 fichas de ancho?” // “Who has a rectangle that is 2 tiles wide, 5 tiles wide, 10 tiles wide?”
Draw each rectangle as students share their responses.

Activity

Give students more inch tiles.
“Ahora construyan cinco rectángulos diferentes, que midan 2 fichas de ancho. Anoten el área de cada rectángulo en la tabla” // “Now build five different rectangles that are each 2 tiles wide. Record the area of each rectangle in the table.”
“Repitan esto con rectángulos que midan 3 y 4 fichas de ancho” // “Repeat with rectangles that are each 3 tiles and 4 tiles wide.”
5–7 minutes: partner work time
Monitor for students who:
- Build one row or column and repeat the same number of tiles over again to build the area.
- Skip-count or multiply to determine the area of each rectangle.
- Combine skip-counting with another counting strategy.

Construye 5 rectángulos diferentes con cada uno de los anchos dados. Anota el área de cada rectángulo en la tabla.

Diagram. Rectangle partitioned into 2 rows of 3 of the same size squares.

	área del rectángulo
2 fichas de ancho
3 fichas de ancho
4 fichas de ancho

Discute con tu compañero qué observaste sobre las áreas en cada fila de la tabla.
Predice el área de otro rectángulo que tenga cada uno de esos anchos. Explica tu razonamiento.
- 2 fichas:
- 3 fichas:
- 4 fichas:

Student Response

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Advancing Student Thinking

If students count tiles by 1 to determine the area of the rectangles they build, consider asking:

“¿Cómo encontraste el área de los rectángulos que construiste?” // “How did you determine the area of the rectangles you built?”
“¿Cómo podrías contar grupos de fichas para encontrar el área?” // “How could you count groups of tiles to determine the area?”

Activity Synthesis

Collect predictions for areas of rectangles with a width of 2. (18, 14, 20, 30)
Para rectángulos que miden 2 fichas de ancho, ¿cómo podemos saber si nuestras predicciones sobre el área son verdaderas sin construir cada rectángulo?” // “For rectangles that are 2 tiles wide, how can we tell if our area predictions are true without building each rectangle?” (Each area is an even number. It is what we say when counting by 2 or multiplying by 2.)
“¿Cómo podemos comprobar nuestras predicciones para rectángulos que miden 3 o 4 fichas de ancho?” // “How can we check our predictions for rectangles that are 3 or 4 tiles wide?” (The predictions are numbers we get when we multiply a number by 3 or 4.)

Activity 2

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

To Copy (from Blackline Masters)

Centimeter Grid Paper - Standard

To Gather

Activity Narrative

The purpose of this activity is for students to explore the idea of multiples through an area context. Students learn that a multiple of a number is the result of multiplying any whole number by another whole number. As students build and find the area of rectangles given one side length, they see that every area is a multiple of each of the side lengths of a rectangle.

Representation: Develop Language and Symbols. Synthesis: Maintain a visible display to record new vocabulary. Invite students to suggest details (words, pictures, or equations) that will help them remember the meaning of the terms. In this lesson, include the terms “múltiplo” // “multiple,” “par” // “even,” and “impar” // “odd.” Throughout the unit, add the terms “factor” // “factor,” “pareja de factores” // “factor pair,” “compuesto” // “composite,” and “primo” // “prime.”
Supports accessibility for: Language, Memory

Launch

Groups of 2
Give each group inch tiles and access to grid paper.
“Estoy pensando en un rectángulo que mide 2 fichas de ancho. ¿Cuál podría ser el área de mi rectángulo?” // “I am thinking of a rectangle that is 2 tiles wide. What could be the area of my rectangle?”
1 minute: partner discussion
Share and record responses.
“¿Cómo sabemos que todas estas áreas son posibles?” // “How do we know all of these are possible areas?” (We can multiply another number by 2 to get those numbers.)

Activity

“En esta actividad, vamos a pensar en cuál podría ser el área del rectángulo si solo sabemos una de las longitudes de sus lados. Respondan estas preguntas con su pareja” // “In this activity, we are going to think about what the area of a rectangle could be if we only know one side length. Work with your partner to answer these questions.”
5–7 minutes: partner work time
Monitor for students who notice that areas you can build are a result of multiplying 3 by another possible side length.

Elena construye rectángulos con un ancho de 3 unidades y un área de 30 unidades cuadradas o menos.
1. Construye los rectángulos que Elena podría haber hecho y dibújalos en papel cuadriculado. Marca el área y las longitudes de los lados de cada rectángulo.
2. ¿Cuál es el área de cada rectángulo que construiste?
3. ¿Qué observas sobre las áreas?
¿Por qué 28 unidades cuadradas no es un área posible para un rectángulo con un ancho de 3 unidades?
Elena decide que el área del rectángulo puede ser mayor que 30 unidades cuadradas. Encuentra otras 2 áreas posibles. Explica o muestra tu razonamiento.
¿Cuál es un área que no es posible para un rectángulo con un ancho de 3 unidades? Explica o muestra tu razonamiento.

Activity Synthesis

Display a set of student-generated areas that are less than 30 square units.
“¿Qué notaron sobre las áreas que encontraron?” // “What did you notice about the areas you found?”
Ask students to explain why the rectangle couldn’t have an area of 28 square units.
“En las últimas dos preguntas, ¿cómo supieron si un rectángulo que mide 3 unidades de ancho podía tener esa área?” // “For the last two questions, how did you know whether a rectangle with a width of 3 units could have that area?”
“Podríamos tener un área de 12 unidades cuadradas cuando el ancho del rectángulo es 3 unidades. Esto es porque 12 es un múltiplo de 3” // “We could have an area of 12 square units when the width of the rectangle is 3 units. That is because 12 is a multiple of 3.”
“Un múltiplo de un número es el resultado de multiplicar ese número por un número entero” // “A multiple of a number is the result of multiplying a number by a whole number.”
“Revisen su trabajo y discutan con su compañero: ¿Qué números son múltiplos de 3?” // “Look back at your work and discuss with your partner: Which numbers are multiples of 3?” (3, 6, 9, 12, 15, 18, 21, 24, 27, and 30)
“¿Qué números no son múltiplos de 3?” // “Which numbers are not multiples of 3?” (29, 28, 26, 25, 23, 22, 20, 19, 17, 16, 14, 13, 11, 10, 8, 7, 5, 4, 2, 1)
2 minutes: partner discussion