## Reflection: Diverse Entry Points The Spending & Saving Project, Day 3 - Section 2: It's a Work Day, and Here's Part 2

One way to differentiate this lesson is to vary the amount of help I provide for students in labeling their axes on the graphs they'll make for Part 2.  I can decide to tell students how to label their axes and to fill in the table or to let them figure it out on their own, scaffolding as necessary while asking students to think about what x and f(x) represent in each scenario.

I've already written about scaling the axes above.  Upon teaching this lesson again, I've found it natural to offer different levels of help to each student as they get started.  If I know that a student has demonstrated mastery of scaling number lines or coordinate axes before, I won't help much at all.  For other students, I'll simply tell them to look at the values in their table and decide how to fit these points on a graph.

If I know that students still struggle with setting up a graph, I'll still give them a few minutes to think about it on their own, but then I'll offer as much help as they need.  That help can range from a question, like, "What should you count by if your y-axis has to go from 0 to 1000?" or fully modeling how to set up the axes on the first example, before leaving students to complete the second graph on their own.

I can also front-load the help by telling students what to "count by" in the x-column of their tables.  For example, to see the x-intercept of the function f(x) = 1000 - 40x in the table provided, counting by 1's won't quite get us there, because the intercept is at x = 25, and there are only 17 rows in the table provided.  Counting by 2's, on the other hand, not only shows where f(x) intercepts the x-axis, but it also builds in the opportunity to discuss why the f(x) column is decreasing by 80 at each step.  Deciding whether or not to tell a students what to count by, or letting them decide on their own (and possibly requiring them to reconsider a decision after trying it) is a way to differentiate this task.

Scaffolds for Labeling Axes
Diverse Entry Points: Scaffolds for Labeling Axes

# The Spending & Saving Project, Day 3

Unit 8: Linear and Exponential Functions
Lesson 12 of 19

## Big Idea: Now that students have some practice with function notation, it's time to create some tables and graphs, and see what we can see!

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### James Dunseith

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