standard_description: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.
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.


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