Geogebra is a great tool for exploring geometric concepts. While I have used it for years, I really became a fan during distance learning. In the classroom, it is easy to help correct misconceptions about graphing or using the geometry tools (compass, protractor). But online it becomes next to impossible. And students did not have access to those tools at home. So Geogebra to the rescue.

My district is using Illustrative Mathematics curriculum which has numerous activities for Geogebra to accompany their curriculum. All of these activities are freely available on the internet. IM Geometry Activities by Unit Here are some of my favorite.

Note: Some of the online activities use a “classic” version of Geogebra. The tools are in a different format. It still works the same, all the tools are still there, the settings are the same but because it looks differently students need some modeling to show that it is the same program and how to use the tools in a drop down box opposed to being in a left hand side bar.

## Construct a Square

One of the best uses in Geometry is to perform Geometric constructions with Geogebra. The first few of copying a segment, constructing a perpendicular line, parallel line need to be practiced enough to be able to perform easily. Once that is done, I like to have students to construct a square, which requires all of those basic skills.

## Building a House

Building on the skills we learned about constructing a square, students were asked to complete a house. This requires students to build a house of a specific dimension in a specific place. We need to have our roof on top of the house and it needs to cover the house–otherwise we get wet when it rains.

Despite having a discussion about houses and roofs before the activity began, I still got a few houses with the roof on the side of the house, or the house was way too small or too big. But the practice was invaluable and told me where to address misconceptions.

## Transformations

I remember doing transformations in the coordinate plane and even the simple activities would take the entire period. Plotting points on graph paper takes forever and students tend to slow down and take their time instead of focusing on the activity. Using Geogebra means that students will get to the activity right away instead of slowly plotting points, finding an error and then starting over.

In this activity, Students need to use their transformation skills to find a sequence. These types of activities allow creativity and options because there are several possible solutions. Once the activity is completed, students should discuss their approach and compare with other students.

## Graphing Circles

As mentioned before, graphing takes time. And the time saved by using Geogebra is time in a more rigorous portion of the lesson. In this case, graphing a circle given in a standard form requires students to understand where the center of the circle is placed as well as the radius. And then students are expected to know whether additional points are located on the circle, outside the circle or inside the circle.

Yes, they can just plot points to determine the location of additional points, but they will need to prove their answer and that will require the distance formula.

## 180

This is an activity I used at the beginning of the year. It is a discovery activity about the sum of the angles in a triangle. It is also a review of construction techniques because it requires students to use the midpoints and extend the sides, and create a parallel line. Activities that are rich in content that use the prior skills to build new content are the goal.

I hope you will try some of these activities. In the early years of teaching, those of us in the math department would beg, borrow, and steal to get enough graph paper to last the entire school year. Quite often, we would start to run out and then have to make trades to get more.

With Geogebra, that bartering is no longer necessary. If you have any favorite Geogebra activities to share, drop a comment or email me at bluemountainmath@gmail.com.

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