When I was a classroom teacher, the one thing I hated was trying to teach basic formulas. In most textbooks, this consists of stating the formula, telling students to memorize it, then showing them how to “plug in” all the necessary information. I don’t like this approach because it doesn’t give students any ownership over their learning. Plus, it usually means learning it for a day, then forgetting it. That’s not the end result I’m going for. Instead, my goal was to provide problems for students to explore on their own, so they could create their own strategies and formulas. This leads to deeper engagement and better retention. So today I’m sharing a simple midpoint formula activity that will introduce students in a concrete way, and allow them to explore!
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Exploring Math with a Geoboard
If you’ve missed it, last week I wrote about teaching and exploring math with geoboards. The first post showed how to introduce graphing and plotting points on the coordinate plane.
Because this lesson builds on that (by graphing line segments, then finding the midpoint) you may want to read that post first.
Both lessons, however, are included in the free sample at the end of this post, so you don’t need to go to the other post to get the lesson. 🙂
Setting Up the Midpoint Formula Activity:
Because this is meant to be an introduction, and the goal is for students to see patterns and recognize the midpoint formula, the questions in this activity focus on the first quadrant.
So to set up their board, they should place a rubber band along the bottom and left sides, forming the x– and y-axes (and quadrant one).
But you could certainly follow up with more challenging midpoint problems, and create a four quadrant grid on your geoboard.
Then you’re ready to get started!
Hands On Midpoint Formula Activity
The first half of this investigation focuses on line segments in which one of the end points is the origin.
This gives students a chance to look for patterns in calculating the midpoint with fairly easy numbers.
Encourage students to estimate by pointing to the middle with their finger. Or measuring with a ruler, and dividing by 2 to find the middle. (Though you may just want to give them a ruler, not explicitly state what to do with it).
Then as they find the midpoint for the various examples, they will hopefully see the pattern emerge.
The rest of this investigation includes finding the midpoint for vertical and horizontal lines, as well as other segments (where endpoints are not the origin).
Once students are familiar with finding the midpoint on their geoboards, they will be ready to move away from the hands on manipulatives and solve problems on their own with pencil and paper.
Want to try out this (and other) hands on math investigations with a Geoboard? This lesson is part of my complete resource book: Hands On Math Exploration with Geoboards. You can purchase the complete set by clicking the image below.
Or to try out a free sample, with 5 different Algebra and Geometry lessons, simply enter your email into the box below! You’ll receive the free sample (with answer key) as well as weekly teaching tips, resources and ideas to make math fun and engaging.
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