Explain to students that they are going to be experimenting with linear functions. They are going to be determining how changing the slope of a linear function and changing the y-intercept of a linear function can effect the way the graph appears. Have students write for 5-7 minutes making predictions about how changing the slope and y-intercept will effect the graph of the function. Tell students that they are writing for mathematics so diagrams are encouraged. They should consider positive and negative values for both the slope and y-intercept. They should also consider very small values (between 0 and 1 or between -1 and 0) and very large values. When they complete their writing, explain to them that they will be reflecting on what they wrote at the end of class. They should keep what they wrote in mind when doing the day's investigation.
Using the DESMOS graphing calculator or other graphing software that allows for sliders (such as Geogebra) (MP5) have students set up their screen as shown on the investigation worksheet. Explain to students that they are not trying to complete the questions as fast as possible. They should spend about 4 minutes on each question.
Encourage students to try lots of different values that meet the criteria given in each question. They do not need to write about every value they try, but they should generalize their results to talk about groups of values. When writing their explanations, students can refer to specific values but then also refer to the general values as well (MP2).
Students can go back through their writing from the beginning of class with two ideas in mind:
(1) What was I right about?
(2) What did I change my mind about?
If possible, students can use two different highlighters or colored pencils to underline parts of their writing piece. After students have had time to do this, call on students to share the things they changed their mind about first.
Celebrating that students changed their mind will help to build a culture in the classroom where learning is the goal; not being right. Ask for students to share values that they used in their investigation that helped them to change their mind about a concept dealing with slope and y-intercept.