# Math Mondays: Free ENGAGING activities from NCTM

I am teaching an integrated math class, and as such, am teaching high school geometry, a subject which I despised as a student. I had no idea how cool it could be! Teaching geometry has been a joy! All I remembered from geometry as a students is what seems to be endless amounts of proofs. When I prepared to teach geometry, I spent hours research and exploring activities and projects to make geometry "cool" or at least tolerable.

In my research, I stumbled upon the Illuminations website from NCTM (National Council of Teacher's of Mathematics). Illuminations is a rich database of activities and interactive online explorations for math concepts. Ideas for Algebra, statistics, and more are included on the free (no registration required) website. As of this writing, I have only explored geometry. I'll share just a little of what I found and used with my students:

The octagon/pinwheel: the octagon requires students to fold parallelograms and then use the parallelograms to build an octagon. Students then use problem solving skills to determine the area and perimeter of the octagon. This multi-class activity might be the crowd favorite of the activities I tried from NCTM. I loved it because this was problem solving at its best.

I did not use the worksheets from NCTM. Instead, I had students collect data at different stages of the folding of parallelograms. They used the data in different ways to determine perimeter and area of the octagon. Eery student could apply the skills they had. Some of my students used trigonometry while others worked with Pythagorean theorem. It was by far one of the most valuable activities we have done. And, the students loved it. Some even went on to play with the pinwheel extension activity.

Diagonals of quadrilaterals: this was a good activity before we did proofs with quadrilaterals. Students explore the different quadrilaterals that can be made when specifications are given about their diagonals such as if the diagonals are perpendicular bisectors or if they are congruent. After a pencil and paper activity, students use the online program to explore the diagonals of quadrilaterals and determine rules. The students made several discoveries such as "there are many ways to make parallelograms but many fewer ways to create a square." I used the activity pretty much as it was written up on the website, and it was fairly easy.

The tetrahedral kite: "EPIC!" said one student. This was a completely engaging activity from start to finish as well as fantastic for problem solving and inquiry.

This multi-class project had students building tetrahedrons, scaling them up by connecting the smaller tetrahedrons, and then making calculations about volume and more. I loved the collaborative aspect of this project. Students had to work together to build and problem solve. Similarly, to the octagon activity above, students used multiple methods for calculating information about the tetrahedral kite. This activity is well-designed for differentiation. And of course, who can resist constructing a giant kite in math class!

In my research, I stumbled upon the Illuminations website from NCTM (National Council of Teacher's of Mathematics). Illuminations is a rich database of activities and interactive online explorations for math concepts. Ideas for Algebra, statistics, and more are included on the free (no registration required) website. As of this writing, I have only explored geometry. I'll share just a little of what I found and used with my students:

The octagon/pinwheel: the octagon requires students to fold parallelograms and then use the parallelograms to build an octagon. Students then use problem solving skills to determine the area and perimeter of the octagon. This multi-class activity might be the crowd favorite of the activities I tried from NCTM. I loved it because this was problem solving at its best.

I did not use the worksheets from NCTM. Instead, I had students collect data at different stages of the folding of parallelograms. They used the data in different ways to determine perimeter and area of the octagon. Eery student could apply the skills they had. Some of my students used trigonometry while others worked with Pythagorean theorem. It was by far one of the most valuable activities we have done. And, the students loved it. Some even went on to play with the pinwheel extension activity.

Diagonals of quadrilaterals: this was a good activity before we did proofs with quadrilaterals. Students explore the different quadrilaterals that can be made when specifications are given about their diagonals such as if the diagonals are perpendicular bisectors or if they are congruent. After a pencil and paper activity, students use the online program to explore the diagonals of quadrilaterals and determine rules. The students made several discoveries such as "there are many ways to make parallelograms but many fewer ways to create a square." I used the activity pretty much as it was written up on the website, and it was fairly easy.

The tetrahedral kite: "EPIC!" said one student. This was a completely engaging activity from start to finish as well as fantastic for problem solving and inquiry.

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*Math Mondays is a bi-weekly blog post (2nd and 4th Monday of each month) sharing tips, ideas, resources, and products for teaching math. If you have questions or think there is something I should include, you can leave me a message in the comments section below or at the*

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