You may have heard me say this before, but this is one of my favorite units. I love teaching proofs with a numerical application. It makes a lot more sense to students than the usual proofs that are all letters and symbols. Continue reading to see how I use a geometry interactive notebook to teach the coordinate geometry unit. I will also share how I adapted this unit for distance learning.
Equations of Lines Review
Every year, we start our coordinate geometry unit with a review of equations of lines. It is important to examine slope, forms of lines, and graphing. In our class we focus on the slope-intercept form of a line, but students will often need to convert from the standard form of a line. For distance learning, we added a digital practice using Google Form.
Slope of Parallel & Perpendicular Lines – Geometry Interactive Notebook
Our next lesson is on the slope of parallel and perpendicular lines. We start by graphing 3 lines. Two are parallel, and the third is perpendicular. Students analyze the slope of the lines to determine criteria for slope of parallel and perpendicular lines. After a few simple practice problems, we do a sorting activity. Students take pairs of linear equations, and determine if the lines are parallel, perpendicular, or neither. Normally, we do this activity in our notebooks, but this year we did a digital slope sort. Additionally, we added a bonus digital review practice.
Equations of Parallel & Perpendicular Lines
The next day, we combine our lesson on equations of lines with our lesson on slope of parallel and perpendicular lines. Thanks to our previous lessons, students are ready and able to write equations of parallel and perpendicular lines. This year, we added a digital practice activity where students identified the mistake made in writing parallel and perpendicular equations.
Perpendicular Bisectors
To start our lesson on perpendicular bisectors, we learn about and practice applying the midpoint formula. Students enjoy this because it is simple. I always relate it to finding the average of two numbers so students don’t have yet another formula to memorize. Then we discuss the steps for finding the perpendicular bisector of a line segment, and practice with a few examples.
Line Dilations
For line dilations, we distinguish between lines that have the center of dilation on and off of them. We talk about what to look for in the equation of a line after a dilation was performed, and we do some practice examples for each.
Partitioning Segments
When we get to partitioning segments, we start with the steps to partition segments. However, students really need to experience the process. So we take the time to do a few practice examples. For this lesson during distance learning, I included these slides for additional support. I love how they include how to partition segments graphically.
Geometry Interactive Notebook: Distance Formula
To prepare for applying distance formula, we start by reviewing simplifying radicals. I explain the distance formula to students, and we apply it in the first example. Before moving on to the next example, we look at how to find the distance between points using the Pythagorean Theorem. Then, we compare the two methods side by side to help students determine which method they prefer. After that, students practice with a few more examples, including finding the perimeter of a polygon and the area of a triangle. This year, I included a Google Form to practice.
Coordinate Geometry Proofs
For teaching coordinate geometry proofs, I like to split the topic into two parts. On the first day, we complete proofs using the distance formula, and on the second day we use the slope formula. Prior to both lessons, we review properties of triangles and quadrilaterals in terms of side length and parallelism and perpendicularity. In the classroom, we would spend a few days practicing proofs in groups. For online learning, I prepared some proofs for students to complete in Google slides. Instead of focusing on the work that students would have to show, we focused on making a plan and writing a concluding statement.
Geometry Interactive Notebook: Coordinate Geometry Resources
Are you looking for materials to teach this unit? Look no further! All of the pages you see in my Geometry Interactive Notebook: Coordinate Geometry are available!
Looking for more resources? Check out my interactive notebook resources page!
