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Activity 1

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

None

Activity Narrative

In this activity, students use their knowledge of feet and inches and the perimeter of a rectangle to solve problems in context. Given the perimeter and one length of a room, they determine its width, in feet, and the distance along two walls, in inches. Students could reason about each problem in a number of ways. As they interpret the quantities in the situation and represent them with expressions or equations, students practice reasoning quantitatively and abstractly (MP2).

MLR7 Compare and Connect. Synthesis: Invite students to prepare a display that shows the strategy they used to determine how many inches the ant traveled. Encourage students to include details that will help others interpret their thinking. Give students time to investigate each others’ work. During the whole-class discussion, ask students: “¿Alguien resolvió el problema de la misma manera, pero lo explicaría de otra forma?” // “Did anyone solve the problem the same way, but would explain it differently?” and “¿Qué tuvieron en común las estrategias?” // “What did the strategies have in common?” “¿En qué fueron diferentes?” and // “How were they different?”
Advances: Representing, Conversing

Launch

Groups of 2
“Resolvamos algunos problemas sobre las longitudes de los lados y el perímetro de una habitación” // “Let’s solve some problems about the side lengths and perimeter of a room.”

Activity

6–8 minutes: independent work time
4–5 minutes: partner discussion
Monitor for the different ways students reason about the number of inches traveled by the ant in the last problem. They may:
- Convert the perimeter from feet to inches and divide by 2.
- Convert the length and the width into inches separately, and then add them.
- Find the sum of the length and the width in feet, and then convert that sum to inches.

Una habitación rectangular tiene un perímetro de 39 pies y un largo de pies.

¿Cuál es el ancho de la habitación, en pies? Explica o muestra cómo razonaste.
Una hormiga se paró en una esquina. Caminó a lo largo de una pared, en línea recta. Luego caminó a lo largo de la siguiente pared, también en línea recta, hasta terminar en la esquina opuesta a la esquina donde comenzó. ¿Cuántas pulgadas recorrió? Explica o muestra cómo razonaste.

Student Response

to access Student Response.

Advancing Student Thinking

If students subtract feet from 39 feet, and show they may think the difference is the width, consider asking:

“¿Cómo encontraste el ancho de la habitación, en pies?” // “How did you determine the width of the room, in feet?”
“Dibuja un diagrama que muestre la habitación rectangular. ¿Qué observas?” // “Draw a diagram to show the rectangular room. What do you notice?”

Activity Synthesis

Invite students to briefly share their responses to the first problem, and then focus the discussion on the last problem.
Select students, with different strategies to find the distance the ant walked, to share their reasoning.

Activity 2

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

To Copy (from Blackline Masters)

Unknown Measurements Large Cards (groups of 12), Spanish

Unknown Measurements Small Cards (groups of 4), Spanish

Activity Narrative

This activity allows students to consolidate their learning from the past few units to solve problems about length measurements in a mathematical context.

First, students find the perimeter or unknown side length of various quadrilaterals. To do so, they apply what they know about adding and subtracting fractions and about rewriting certain fractions as whole numbers. Next, they determine which pairs of figures have a certain multiplicative relationship—for instance, which figure has a perimeter that is 9 times that of another figure. Because the measurements are in different units, students need to attend to the relationship between the units and perform conversions accordingly.

The activity can be done in the format of a Gallery Walk or by giving each group a full set of the diagrams from the blackline master.

Representation: Develop Language and Symbols. Invite students to represent each problem as an equation to help them identify strategies for solving, and to give them practice interpreting mathematical language.
Supports accessibility for: Conceptual Processing, Language

Launch

Groups of 3–4
As a class, read the opening paragraph and the first two problems. As a class, read the opening paragraph and the first two problems. Display the six diagrams (the large image cards on the blackline master). Give students a minute to ask clarifying questions.
“Recuerden que los cuadriláteros son figuras de cuatro lados. Los cuadrados y los rectángulos son ejemplos de cuadriláteros, pero no son los únicos cuadriláteros que hay” // “Recall that quadrilaterals are four-sided shapes. Squares and rectangles are examples of quadrilaterals, but they are not the only quadrilaterals.”
If done as a Gallery Walk, ask each student in a group to visit at least 2 posters, ensuring that, collectively, the members of each group visit all the posters.
Alternatively, give each group the small image cards from the blackline master, and ask each member to work on 2 of the diagrams.
“Pónganse de acuerdo con su grupo para asegurarse de que contesten los seis problemas” // “Coordinate with your group to make sure that all six problems are answered.”

Activity

7–8 minutes: independent work time on the first problem
10 minutes: group work time on the remainder of the task
Monitor for students who can distinguish customary units and standard units and consider them as categories of related units (for instance, yards, feet, and inches in one category, and kilometers, meters, and centimeters in another.)

Tu profesor colgó 6 cuadriláteros alrededor del salón. Cada uno tiene una longitud de lado desconocida o un perímetro desconocido.

Escoge dos diagramas (uno que tenga una longitud desconocida y otro que tenga un perímetro desconocido). Asegúrate de que cada figura sea escogida por al menos una persona de tu grupo.

Encuentra los valores desconocidos. Muestra cómo razonaste y recuerda incluir las unidades.
Discute las respuestas con tu grupo hasta que todos estén de acuerdo en cuáles son las medidas desconocidas de las 6 figuras.
Responde una de las siguientes preguntas. Explica o muestra cómo razonaste.
1. ¿El perímetro de la figura B es cuántas veces el perímetro de la figura D?
2. El perímetro de una figura es 1,000 veces el perímetro de otra figura. ¿Cuáles son las dos figuras?
3. ¿El perímetro de la figura F es cuántas veces el perímetro de la figura B?

Activity Synthesis

See the Lesson Synthesis.

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Audience

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Lesson 17

Más problemas sobre perímetros

Warm-up

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Activity 1

Standards Alignment

Building On

Addressing

4.MD.A.2

4.MD.A.3

Building Toward

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Activity 2

Standards Alignment

Building On

Addressing

4.MD.A.2

4.MD.A.3

4.OA.A.2

Building Toward

Instructional Routines

Materials

To Copy (from Blackline Masters)

Activity Narrative

Launch

Activity

Activity Synthesis

Lesson Synthesis

Student Section Summary

Standards Alignment

Building On

4.NF.B.3.b

Addressing

Building Toward

Student Response

Advancing Student Thinking