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
The purpose of this activity is to remind students of a few details to keep in mind when doing arithmetic with signed numbers, particularly that subtracting a number has the same result as adding its opposite, and the sign of the product when multiplying two negative numbers, or a positive by a negative number.
Student Facing
Sort these into two groups, so that the expressions in each group all have the same value.
\(3-5\)
\(5+3\)
\(4 \boldcdot 2\)
\(\text- \frac13 \boldcdot 6\)
\(5 - \text-3\)
\(\text-4 \boldcdot \text-2\)
\(3 + \text-5\)
\(\frac13 \boldcdot \text-6\)
Student Response
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Activity Synthesis
Use students’ explanations for why expressions are equal to draw attention to things to keep in mind when doing arithmetic on signed numbers. For example:
Subtracting a number has the same result as adding its opposite.
\(3-5=3+\text-5\)
Multiplying a negative number by a negative number results in a positive product.
\(\text-4  \boldcdot \text-2\)
and
\(4 \boldcdot 2\)
are both equal to 8.
Multiplying a negative number by a positive number results in a negative product
\(\text- \frac13 \boldcdot 6\)
and
\(\frac13  \boldcdot \text-6\)
are both equal to -2.


aligns: no