Lesson 24

This warm-up familiarizes students with a context of the first activity and elicits observations that will be useful when students analyze population data more closely in later activities. Students are likely to notice and wonder many things about the infographics, especially the great discrepancy between the first data point and the rest. They will have the chance to reason about this gap in multiplicative terms and in terms of difference.

• Display the image.
• Explain that the names are Native American languages.

• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
• 1 minute: quiet think time
• Share and record responses.

• Reveal that the infographics shows the top ten most widely spoken Native American languages in the United States, collected in 2009–2013. The numbers represent people over 5 who speak the language.
• Consider sharing that about 170 Native American languages are spoken in the U.S., but many are on the verge of disappearing.
• “Basándose en lo que ven aquí, ¿podrían predecir cuántas personas hablan la lengua que está en la posición número 20 de las más habladas?, ¿la lengua que está en la posición número 100?” // “Based on what you see here, could you predict how many people speak the 20th most widely spoken language? The language in the 100th place?”
• Consider showing a census map showing the distribution of Native American languages. Here is one from a survey done by the U.S. Census in 2006–2010:

  

  

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).

• Groups of 2
• Give students access to grid paper.
• “¿Qué idiomas hablan en su familia o en su barrio?” // “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.“

• 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 question 1b
  • use estimation or rounding to assess whether their response is reasonable
  • group some numbers selectively to make estimation or computation more efficient

• 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.)

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. Students who look for structure may notice that the number of digits in each row in the table changes by one digit as we move down the table. They make use of this observation to simplify their estimation or calculation (MP7).

Note that the data shown here do 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. 

• 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.

• 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)

• 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: 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.)