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Activity 1

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

To Gather

Grid paper

Activity Narrative

The purpose of this activity is for students to practice using estimation and using the standard algorithm for addition and subtraction to solve problems involving large numbers. The same data from the Warm-up is used as a context. The last two questions prompt students to first examine the data set and make some estimations before deciding which pairs of numbers to use to find the answers.

Students reason abstractly and quantitatively with several operations in order to estimate and solve the problems (MP2).

MLR8 Discussion Supports. During group work, invite students to take turns sharing their responses. Ask students to restate what they heard using precise mathematical language and their own words. Display the sentence frame: “Te escuché decir . . .” // “I heard you say . . .” Original speakers can agree or clarify for their partner.
Advances: Listening, Speaking

Representation: Access for Perception. Read the problems aloud. Students who both listen to and read the information will benefit from extra processing time.
Supports accessibility for: Language, Memory

Launch

Groups of 2
Give students access to grid paper.
“¿Qué idiomas hablan en su familia o en su vecindario?” // “What languages are spoken in your family or your neighborhood?“
“¿Ustedes o sus amigos usan idiomas diferentes en distintos lugares o en distintas ocasiones?” // “Do you or your friends use different languages in different places or occasions?“
“Para esta actividad, van a necesitar consultar los datos que vieron en el calentamiento” // “For this activity, you'll need to refer to the data you saw in the Warm-up.“

Activity

7–8 minutes: quiet work time
3–5 minutes: partner discussion
Monitor for students who:
- Use the bar graphs from the Warm-up to help them estimate the first question.
- Use estimation or rounding to assess whether their response is reasonable.
- Group some numbers selectively to make estimation or computation more efficient.

En la lista de las diez lenguas nativas más habladas en los Estados Unidos, las que más se hablan son el navajo y el yupik.

¿Cuántas personas más hablan navajo que yupik? Explica o muestra cómo razonaste.

lengua	número de personas que lo hablan
Navajo	166,826
Yupik	19,750
Dakota	17,855
Apache	13,445
Keres	13,190
Cherokee	11,465
Ojibwa	9,735
Choctaw	9,635
Zuni	9,615
Pima	6,990

¿El número de personas que hablan navajo es aproximadamente cuántas veces el número de personas que hablan yupik? Explica o muestra cómo razonaste.

El navajo, el apache y el cherokee se han usado en épocas de guerra para ayudar a los militares de los Estados Unidos a mantener seguras sus comunicaciones.
1. Basándote en estos datos, ¿cuántas personas podrían haber sido capaces de entender las comunicaciones? Explica o muestra cómo razonaste.
2. ¿Cómo sabes que tu respuesta es razonable?
¿Hay más personas que hablan navajo que el total de personas que hablan las otras nueve lenguas? Muestra cómo lo sabes.

Activity Synthesis

Invite students to share their responses and reasoning.
“¿Cómo supieron qué operaciones usar para responder el primer problema?, ¿el segundo problema?, ¿el último problema?” // “How did you know what operations to use to answer the first set of problems? The second problem? The last problem?”
“¿Cómo saben que su respuesta es razonable?” // “How do you know that your answer is reasonable?” (Mentally use a standard algorithm to find the differences, round the numbers, or look only at certain digits to estimate.)

Activity 2

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

None

Activity Narrative

In this activity, students continue to analyze population data and to use addition and subtraction skills to solve problems. The first question, which prompts students to compare two population groups, could be answered by rounding and estimating rather than precise calculations.

Note that the data shown does not represent all language types spoken in the two major cities. If desired, consider finding local data or data that reflect the languages spoken in your students' community. Then ask students to make comparisons as shown in the activity.

Launch

Display the two sets of data.
“¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
1 minute: quiet think time
Share and record responses.

Activity

5 minutes: independent work time
Monitor for:
- The different strategies students use to answer the first question.
- The different ways in which students decide to add numbers (for example, the largest numbers first, or three numbers at a time).

Filadelfia es una ciudad diversa y es el hogar de personas que tienen distintos orígenes.

La tabla muestra datos del 2020 sobre algunos idiomas que se hablan en Filadelfia y el número de personas que habla cada uno.

idioma	número de personas que lo hablan en Filadelfia
Solo inglés	1,131,303
Español	159,343
Otros idiomas indoeuropeos	81,924
Asiático	77,706

Usa los datos de la tabla para decidir si en Filadelfia hay más personas que solo hablan inglés o más personas que hablan un idioma diferente al inglés. Muestra cómo lo sabes.
¿Cuál es la diferencia entre el número de personas que solo hablan inglés y el número de personas que hablan otro idioma? Muestra cómo lo sabes.

La ciudad de Chicago tiene una población con características similares a las de Filadelfia.

Esta tabla muestra datos sobre algunos tipos de idiomas que hablan las personas en Chicago.

idioma	número de personas que lo hablan en Chicago
Solo inglés	1,634,103
Español	600,655
Otros idiomas indoeuropeos	150,354
Asiático	105,790

¿Cuántas personas más hablan español y otros idiomas indoeuropeos en Chicago que en Filadelfia? Explica o muestra cómo razonaste.
¿Cómo sabes que tu respuesta es razonable?

Student Response

to access Student Response.

Advancing Student Thinking

Activity Synthesis

Select students to share their responses and reasoning.
If no students answered the first question by estimation, ask if it could be done and how.
Discuss potential pros and cons of rounding. (Pro: It would be quicker. Con: Some of the data for each group of languages have a different number of digits, so it’s hard to choose the place to which the numbers should be rounded. If we round to different places for each group, we’d end up over- or under-estimating some groups much more than others.)

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Lesson 25

Analicemos qué tan razonables son las soluciones

Warm-up

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Activity 1

Standards Alignment

Building On

Addressing

4.NBT.B.4

4.OA.A.3

Building Toward

Instructional Routines

Materials

To Gather

Activity Narrative

Launch

Activity

Activity Synthesis

Activity 2

Standards Alignment

Building On

Addressing

4.NBT.B.4

4.OA.A.3

Building Toward

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Lesson Synthesis

Student Section Summary

Standards Alignment

Building On

Addressing

4.OA.A.2

4.OA.A.3

Building Toward

Student Response

Advancing Student Thinking