Assess the Reasonableness of Solutions
10 min
Narrative
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.
Launch
- Display the image.
- Explain that the names are Native American languages.
Teacher Instructions
- “What do you notice? What do you wonder?”
- 1 minute: quiet think time
- Share and record responses.
Student Task
What do you notice? What do you wonder?
Horizontal bar graph. Translation: Do you speak Navajo? Vertical axis labeled Pima, Zuni, Choctaw, Ojibwa, Cherokee, Keres, Apache, Dakota, Yupik, Navajo. Length of bar: 6 thousand 9 hundred ninety, 9 thousand 6 hundred 15, 9 thousand 6 hundred 35, 9 thousand 7 hundred 35, 11 thousand 4 hundred sixty 5, 13 thousand 1 hundred ninety, 13 thousand 4 hundred 45, 17 thousand 8 hundred fifty 5, 19 thousand 7 hundred fifty, 1 hundred sixty 6 thousand 8 hundred 26.
Sample Response
Students may notice:
- One language, Navajo, has the highest number and the longest bar in the graph.
- There are 10 Native American languages shown.
- Five of the languages have numbers between 10,000 and 20,000.
- Four languages have numbers in the thousands.
Students may wonder:
- What do the numbers represent? Do they represent the number of words in the language? The number of people speaking the language?
- Why does one language outnumber the other ones by so much?
- Where are all these languages spoken?
- Are there other Native American languages?
Activity Synthesis (Teacher Notes)
- Reveal that the infographic 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.
- “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:
Standards
Addressing
- 4.OA.2·Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
- 4.OA.3·Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
- 4.OA.A.2·Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.<span>See Glossary, Table 2.</span>
- 4.OA.A.3·Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
20 min
15 min
Knowledge Components
All skills for this lesson
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Assess the Reasonableness of Solutions
10 min
Narrative
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.
Launch
- Display the image.
- Explain that the names are Native American languages.
Teacher Instructions
- “What do you notice? What do you wonder?”
- 1 minute: quiet think time
- Share and record responses.
Student Task
What do you notice? What do you wonder?
Horizontal bar graph. Translation: Do you speak Navajo? Vertical axis labeled Pima, Zuni, Choctaw, Ojibwa, Cherokee, Keres, Apache, Dakota, Yupik, Navajo. Length of bar: 6 thousand 9 hundred ninety, 9 thousand 6 hundred 15, 9 thousand 6 hundred 35, 9 thousand 7 hundred 35, 11 thousand 4 hundred sixty 5, 13 thousand 1 hundred ninety, 13 thousand 4 hundred 45, 17 thousand 8 hundred fifty 5, 19 thousand 7 hundred fifty, 1 hundred sixty 6 thousand 8 hundred 26.
Sample Response
Students may notice:
- One language, Navajo, has the highest number and the longest bar in the graph.
- There are 10 Native American languages shown.
- Five of the languages have numbers between 10,000 and 20,000.
- Four languages have numbers in the thousands.
Students may wonder:
- What do the numbers represent? Do they represent the number of words in the language? The number of people speaking the language?
- Why does one language outnumber the other ones by so much?
- Where are all these languages spoken?
- Are there other Native American languages?
Activity Synthesis (Teacher Notes)
- Reveal that the infographic 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.
- “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:
Standards
Addressing
- 4.OA.2·Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
- 4.OA.3·Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
- 4.OA.A.2·Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.<span>See Glossary, Table 2.</span>
- 4.OA.A.3·Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.