Lesson 11

¿Qué tan largos son nuestros zapatos?

Warm-up: Observa y pregúntate: Longitud de un zapato (10 minutes)

Narrative

The purpose of this warm-up is to elicit the idea of measuring length with connecting cubes, which prepares students to measure their own shoes and solve story problems about their measurements in the next activity.

Launch

• Groups of 2
• Display the image.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
• 1 minute: quiet think time

Activity

• “Discutan con su compañero lo que pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

Student Facing

¿Qué observas?

¿Qué te preguntas?

Activity Synthesis

• “Ahora van a tener la oportunidad de medir la longitud de su propio zapato” // “Now you are going to get a chance to measure the length of your own shoe.”

Activity 1: La longitud de nuestros zapatos (20 minutes)

Narrative

The purpose of this activity is for students to measure the length of their shoe using connecting cubes and solve a Put Together, Result Unknown problem and a Compare, Difference Unknown problem about their measurements. To solve the Put Together problem, students may put the connecting cube towers together and count all, count on, use known facts, or use methods such as making a ten. To solve the Compare problems, students may draw a diagram directly comparing the lengths then count up or count back or use known facts to determine the difference. When students find sums and distances using their measurements they reason abstractly and quantitatively (MP2).

It is likely that students’ shoes will not be the length of an exact number of connecting cubes. Encourage students to write the closest number of whole units. There is no need to check students’ measuring techniques in this activity because the focus of the activity is solving story problems.

Launch

• Groups of 2
• Give each group connecting cubes in towers of 10 and singles and paper.
• “Hace algunos días, medimos la longitud del pie más grande del mundo. Hoy, cada uno de nosotros va a medir la longitud de su propio zapato y resolverá algunos problemas usando esta longitud. Primero, vamos a trazar nuestro zapato sobre una hoja de papel y después vamos a usar cubos encajables para medir la longitud de nuestro zapato” // “A few days ago we measured the length of the biggest foot in the world. Today we are each going to measure the length of our own shoe and solve some problems using the length. First we will trace our shoe on a piece of paper and then use connecting cubes to measure the length of our shoe.”
• Demonstrate tracing or have a student trace your shoe and measure the length.
• “Anoten la longitud de mi zapato en su libro” // “Record the length of my shoe in your book.”
• “Ahora su compañero trazará el zapato de ustedes sobre una hoja de papel. Después, usarán cubos encajables para medir la longitud de su propio zapato. Midan desde la punta del pie hasta la parte de atrás de su talón. Puede que el final de su zapato no coincida con el extremo de un cubo encajable. Encuentren el número de cubos que sea más cercano a la longitud de su zapato. Anoten la longitud de su zapato y la del zapato de su compañero” // “Now your partner will trace your shoe on a piece of paper and then you will use connecting cubes to measure the length of your own shoe. Measure from the tip of the toe to the back of the heel. Your shoe might not line up with the end of a connecting cube. Find the closest number of cubes to the length of your shoe. Record the length of your shoe and your partner’s shoe.”
• 5 minutes: partner work time

Activity

• “Usen sus medidas para resolver los problemas” // “Solve the problems using your measurements.”
• 3 minutes: independent work time
• 2 minutes: partner discussion
• Monitor for a student who represents the third problem with:
• two towers of cubes, one to represent the length of their shoe and one to represent the length of the teacher’s shoe
• a drawing that directly compares shoe lengths
• a subtraction equation

Student Facing

El zapato de mi profesor mide ____________ cubos encajables de largo.

Mi zapato mide ____________ cubos encajables de largo.

El zapato de mi compañero mide ____________ cubos encajables de largo.

Resuelve estos problemas sobre la longitud de los zapatos de tu grupo.
Muestra cómo pensaste. Usa dibujos, números, palabras o ecuaciones.

1. ¿Cuál es la longitud de tu zapato y el de tu compañero si los ponen uno detrás del otro, punta con talón?
2. ¿Cuál zapato es más largo: el tuyo o el de tu compañero?

¿Cuánto más largo?

3. ¿Cuál zapato es más corto: el de tu profesor o el tuyo?

¿Cuánto más corto?

Activity Synthesis

• Invite previously identified students to share.
• “¿En qué se parecen estas representaciones? ¿En qué son diferentes?” // “What is the same about these representations? What is different?” (The first two show the length of the shoes but the others just use numbers. They all find the difference between the length of the shoes.)

Activity 2: Historias de zapatos (15 minutes)

Narrative

The purpose of this activity is for students to solve familiar story problem types in a measurement context. Students represent their thinking using drawings, numbers, words, or equations (MP2). Students may use the cubes or drawings to make sense of the problems if they choose. The activity synthesis focuses on a problem that can be represented as either addition or subtraction.

MLR6 Three Reads. Keep books or devices closed. To launch this activity, display only the first problem stem, without revealing the question. “Vamos a leer este problema-historia tres veces” // “We are going to read this story problem three times.” After the 1st Read: “Cuéntenle a su compañero lo que ocurrió en la historia” // “Tell your partner what happened in the story.” After the 2nd Read: “¿Cuáles son todas las cosas de esta historia que podemos contar?” // “What are all the things we can count in this story?” Reveal the question. After the 3rd Read: “¿De qué formas diferentes podemos resolver este problema?” // “What are different ways we can solve this problem?”
Representation: Access for Perception. Provide appropriate reading accommodations and supports to ensure student access to all the word problems.
Supports accessibility for: Language, Social-Emotional Functioning

Launch

• Groups of 2
• Give students access to connecting cubes in towers of 10 and singles.
• “Resolvamos más problemas sobre la longitud de diferentes zapatos” // "Let's solve more problems about the length of different shoes."

Activity

• 6 minutes: independent work time
• “Hablen sobre lo que hicieron con su compañero” // “Discuss your work with your partner.”
• 3 minutes: partner discussion
• Monitor for a student who uses addition, and another who uses subtraction, for the story about Diego and his father.

Student Facing

Muestra cómo pensaste. Usa dibujos, números, palabras o ecuaciones.

1. El zapato de Clare mide 9 cubos de largo.
El zapato de Han mide 7 cubos de largo.
¿Cuántos cubos de largo miden el zapato de Clare y el de Han cuando se pone uno detrás del otro, punta con talón?

2. El zapato de Kiran mide 7 cubos de largo.
El zapato de su hermano mayor mide 9 cubos de largo.
El zapato de su hermano menor mide 4 cubos de largo.
¿Cuál es la longitud total de sus zapatos cuando se ponen uno detrás del otro, punta con talón?

3. El zapato de Diego mide 8 cubos de largo.
El zapato de su papá mide 13 cubos de largo.
¿Cuántos cubos más largo es el zapato del papá de Diego que el zapato de Diego?

4. El zapato de Jada mide 8 cubos de largo.
Ella pone su zapato detrás del de Elena, punta con talón.
Juntos, los zapatos miden 17 cubos de largo.
¿Cuánto mide el zapato de Elena?

Student Response

If students find the sum of the lengths in the problems about Diego and Jada, consider asking:

• “¿Qué te pide encontrar el problema-historia?” // “What does the story problem ask you to find?”
• “¿De qué manera tu representación corresponde a la historia?” // “How does your representations match the story?”
• “¿Cómo podrías usar tus herramientas o un diagrama para resolver el problema?” // “How could you use your tools or a diagram to solve the problem?”

Activity Synthesis

• Invite previously identified students to share.
• “¿Cómo muestran ambos métodos la longitud del zapato de Diego, la del zapato de su papá y la diferencia entre los dos zapatos?” // “How do both methods show the length of Diego's shoe, his father’s shoe, and the difference between the two shoes?”
• “¿En qué se parecen los métodos? ¿En qué son diferentes?” // “How are the methods the same? How are they different?”

Lesson Synthesis

Lesson Synthesis

Display the story problem and equations:

Jada’s shoe is 8 cubes long.
She put her shoe together with Elena’s shoe.
Together the shoes are 17 cubes long.
How long is Elena’s shoe?

$$8 + \boxed{9} = 17$$ and $$17 - 8 = \boxed{9}$$

“Hoy resolvimos problemas-historia relacionados con medidas. Algunos problemas se resolvieron usando suma o resta. ¿Qué representan los números en estas ecuaciones?” // “Today we solved story problems about measurement. Some problems were solved using addition or subtraction. What do the numbers in these equations represent?” (8 is the length of Jada's shoe. 17 is the length of their shoes together. 9 is the length of Elena’s shoe.)