## Wednesday, April 20, 2016

### Linear Functions (part 1) - Interactive Notebook Pages

The second unit I covered in Math 1 focused on linear functions, which was suppose to last for four weeks. In actuality it lasted for over a month and a half due to many days off and early releases/delays because of snow! In the future I need to make this two units because it got super long; a unit of linear functions and a unit of linear regression. Today's post will have pictures and descriptions from the first half of the Linear Functions unit. I will try to post on the second half tomorrow.

Students have covered linear functions in 8th grade however it is a key part of the Math 1 curriculum. In Math 1 students are responsible for interpreting linear functions and comparing linear functions to quadratic & exponential functions. Even though it was thoroughly covered last year, students still need quite an extensive review.

I started this unit with a review of writing and solving equations with word problems, since my goal was to incorporate them through the semester, instead of having one unit of review. We just practice solving equations as they come up naturally in the curriculum but I did want my students to have a point of reference in their notebooks. These files were adapted from Sarah Carter at MathEqualsLove. You will notice I get a lot of my ideas for my interactive notebooks from Sarah. She does an excellent job of blogging about her class. In fact, without her resources, I don't think I would have been able to incorporate interactive notebooks into my classroom.

We then jumped into sequences, as students in Math 1 must be familiar with arithmetic and geometric sequences and writing equations in Now-Next form and function notation. I decided to cover both types at one time simply because we had already discussed (briefly in unit 1) exponential functions and it flowed well together.

We started with the green cards and students had to fill in the next three terms and come up with a pattern; we then matched the sequences to a graphs. Afterwards, we formally went over the recursive and explicit formulas and they wrote the corresponding equations for each sequence. The equation notes were also adapted from Sarah Carter at MathEqualsLove

After sequences, we jumped into formalizing linear functions by discussing slope.

The types of slope foldable is from Jessie Hester at Mrs .Hester's Classroom.  On the inside we included a visual of Slope Dude's path.

I adapted the finding slope from different representations from Julie Reulbach at ispeakmath.

Then we discussed y-intercept and putting the slope and y-intercept together to write the linear equation in function notation. We used color with a purpose on these notes so that students could refer back to the slope and the y-intercept individually.

Then we discussed various forms of linear functions including: horizontal & vertical lines, slope-intercept form, and standard form. This foldable was inspired by Sarah Carter at MathEqualsLove.

We then went over multiple representations of linear functions. Students were given four problems each with a given representation then they had to create the other representations. This semester my page only has the blank problems as I spent my time working with groups on these problems and I didn't go back and fill in the page. However, I have pictures of this page from last semester.

To end the first half of the linear unit, we covered parallel & perpendicular lines and their equations. We started by discussing where parallel and perpendicular lines appear in real life (and the most creative response was rewarded with a Starburst) then we moved onto the algebra.

If you would like the files to any of the documents I've created I'll be glad to share. :)