standard_description: Summarize numerical data sets in relation to their context, such as by:
- Reporting the number of observations.
- Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
- Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.
- Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
problem_activity: Warm-up
By now students have written many division equations based on verbal descriptions of situations. This warm-up prompts them to go in the other direction: to interpret a division expression and write a fitting question the expression could help answer. Then, they trade descriptions with a partner and reason about the value of the same expression in someone else’s story.
As students write their descriptions, look out for scenarios that are unclear and ask their authors clarifying questions. Select 2–3 students whose descriptions clearly match the expression to share later.
Students may struggle to answer their partner’s question because the descriptions are confusing or do not match the given expression. Encourage them to ask the questions they have about the description, but still try to find the answer to the given expression.
Launch
Arrange students in groups of 2. Explain to students the two halves of this activity: to write a situation and a question that can be represented by the equation
\(12 \div \frac23 = ?\)
, and to trade papers with their partner and find the answer to their partner’s question.
Give 2 minutes of quiet think time for the first question, another minute for the second question, and follow with a whole-class discussion.
Student Facing
Think of a situation with a question that can be represented by the equation
\(12 \div \frac23 = \,?\)
Describe the situation and the question.
Trade descriptions with your partner, and answer your partner’s question.
Student Response
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Anticipated Misconceptions
Some students may struggle writing a context. Ask them to reflect on the work they have done and what the division expression means for them, or suggest that they write related multiplication expressions to help them understand the division expression.
Activity Synthesis
Ask selected students to share their stories with the whole group. After each student shares, have another student explain how the story matches the division equation. Afterward, ask these and other students for the value of the given expression, and write and display the completed division equation for all to see.
If not already mentioned by students, highlight that the answer is the same for all scenarios because they are all based on the same division expression.


aligns: no