Experience First

Today students reason about linear relationships in the context of the cost of ice cream. The idea of the additional price in the larger size accounting for the additional toppings gives meaning to the slope formula of ∆y/∆x. When students graph in question 2, look for groups that use point-by-point graphing in contrast to groups that simply plot two points and “connect the dots”. For students who choose the latter, ask why this is allowed. For the former, ask how many points they need to find in order to be confident of their graph. Also push students to articulate what the $3.90 means and what it looks like on a graph. Students’ comfort with question 4 may vary depending on their experience with point slope form in previous classes. During the activity, try not to use this language unless students bring it up themselves.

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Formalize Later

Although these topics are familiar to students, students may still struggle to interpret slopes and y-intercepts in context. Encourage language around “for each additional topping…” When debriefing question 3, make a VERY big deal about how students were able to find the 5-toping price without actually knowing the base price. For students using the expression “8.06+3(0.89)” in the second half of the question, push students to articulate where the 3 came from. (I thought it was 7 toppings!) In our experience, students love slope-intercept form and are not immediately hospitable to point-slope form. We hope that this activity invites students to see the usefulness of point-slope form as a way to predict values without actually knowing the y-intercept. We say that any point, not just the y-intercept, can be used as an anchor point, or point of reference.