Using Understanding to Teach Linear Equations |Free Math Lessons
Did you know that I have a lot of FREE math lessons and investigations on my website? Most of these are lessons that I used during my time in the classroom. Today I’m highlighting lessons on linear functions.
These lessons address standards 8.F.4, 8.F.5, F.IF.7, and G.GPE.5. You can find all these lessons on my K-8 and High School Math Lessons pages.
Teaching Through Investigations
I love to teach using investigations! Students are engaged, and they are required to think and reason. When doing these types of activities, I try to put my students in pairs. That way each person must contribute. Using investigations in math class helps students grow in the Math Practice Standards such as constructing viable arguments and critiquing the reasoning of others (SMP.3), looking for and making use of structure (SMP.7), and looking for and expressing regularity in repeated reasoning (SMP.8).
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Graphing Exploration 1
This is a great way to start the functions unit. Students are required to graph their movement. It is always a hit with kids as they can walk around and do experiments. I typically took students to the hallways by the gym, so they wouldn’t disturb other classes. Students time themselves walking forward, backwards, and stopping and then they graph the results. For many kids, it’s a surprise that stopping makes a horizontal line.
Following this lesson, I would typically talk about graphing stories and have students create their own stories with corresponding graphs (clearly labeled) and present them to the class via PowerPoint or Google slides.
You can find all this lesson on my K-8 and High School Math Lessons pages.
Graphing Exploration 2 (unavailable at this time)
For the life of me, I can’t find this lesson; although I taught it almost every year. It’s one of the most essential graphing activities that I used. The idea is that you use patterning and prediction to teach graphing linear equations. I’ve had students graph it by hand using T-charts, but I’ve also had them do it on TI-NSPIRE that graphs in color. It goes something like this:
Have students graph the following equations on the same plane using a T-chart:
- y = x in red; y = 2x in orange, y = 3x in yellow, etc. Then ask them what they noticed and have them predict what they think y = 100x would look like.
- Repeat the process above with negative coefficients.
- Repeat the process above with fractional coefficients where just the denominator changes such as y = x in red, y = (1/2)x in orange, y = (1/3)x in yellow etc.
- Repeat the process above with fractional coefficients where just the numerator changes such as y = (8/8) x in red, y = (7/8)x in orange, y = (6/8)x in yellow etc.
- Then do similar patterning with the intercept changing.
Don’t forget to explicity ask student what patterns they notice and to make predictions.
Horizontal Line Exploration
As you know, many students struggle with graphing horizontal lines. They try to memorize the rules and get themselves confused. Avoid the confusion by giving students this Horizontal Line Exploration. This will allow them to create their own understanding of what constitutes a horizontal line.
If I recall correctly, at one time I had a vertical line exploration. However, I can no longer find it. If you need one for your class, you can just switch the word horizontal and vertical in the student worksheet.
You can find all this lesson on my K-8 and High School Math Lessons pages.
Intercept Exploration
You would think graphing an equation using intercepts would be easy. But alas, many students struggle with it. Once again the trick is to use patterning to help students create understanding.
You can find all this lesson on my K-8 and High School Math Lessons pages.
Parallel and Perpendicular Line Explorations
This is another exploration where students create their own rules about parallel and perpendicular lines using patterns. This would either be an Algebra 1 or Geometry lesson depending on your curriculum/standards.
You can find all this lesson on my K-8 and High School Math Lessons pages.
Ohio’s Model Curriculum with Instructional Supports
For more tips, examples, and resources on graphing linear functions, check out Ohio’s Math Model Curriculum with Instructional Supports. Here is the Grade 8 and Algebra 1 documents. The documents includes ways to address common student misconceptions in the classroom. The Table of Contents is clickable, so you can easily find the information for the standard(s) associated with this week’s lesson.
Share & Subscribe
I’m continually adding to the list of available resources, so be sure to subscribe for updates. Share these lessons with your math teacher friends on social media.
Additionally for subscribers, I have several free printable rubrics on problem solving, perseverance, and gumption.
