Will it Tessellate?

Near the end of our Shapes and Designs unit, students completed a project that focused on creating tessellations with various polygons or combinations of polygons.  Their project had 2 parts: First, a proposal, in which they had to identify regular polygons that will or will not tessellate, and combinations of polygons that will or will not tessellate.  For each shape or combination of shapes, students needed to clearly explain why the combination of angles/sides resulted in a design that could or couldn't tessellate. For the second part of the project, students took on the role of designers for a flooring company, and needed to create a catalog of tessellated designs for their boss.  To see a copy of the project assignment, click here.

This student's catalog had a very specific theme. This is her cover.....

....and her various floor designs

All of the designs from the designers of Floored on display 

Here are explanations from two students' proposals explaining why certain shapes or combinations of shapes tessellated and others didn't

WILL IT MAKE A TRIANGLE?

Another focus of the unit was to understand characteristics of triangles.  In this activity, students are attempting to create triangles with specific side lengths.  Through this activity, students arrived at the conclusion that in order for 3 side lengths to form a triangle, the sum of the lengths of the 2 shorter sides must be greater than the length of the 3rd side.

Check back in a few weeks for an update on our current unit!

Shapes and Designs

The 7th graders have been learning about polygons and angles.  Some highlights of the unit include:

INVESTIGATION 1

• Estimating rotations and angle measures
• Measuring angles with angle rulers and protractors
• Drawing shapes with given conditions

INVESTIGATION 2

• Discovering formulas for finding angle sums of polygons
• Understanding why certain shapes tessellate
• Creating tessellations

INVESTIGATION 3

• Discovering properties of triangles
• Designing triangles and quadrilaterals with given conditions
• Angle relationships

Enjoy the pics!

These students are attempting to find angle sums of triangles and quadrilaterals by tracing the shapes onto a piece of paper and the cutting off the angles to see if, when put together, they form either a straight line (180 degrees) or a full circle rotation (360 degrees).

Collaborative learning is evident in math class on a daily basis.  In this pic, a team of students are working to find patterns in the angle sums  that they discovered in polygons.

Students used a variety of strategies to find the various angle sums.  In both models shown here, students used the angle sum of a triangle to find  the angle sums of other polygons.

The eventual discovery, a formula for finding the angle sum of any polygon, and visual model to show why it works!

Thanks for visiting the 7th grade math blog!  The goal of this blog is to provide you with a sense of what happens in 7th grade math classes.  Once up and running, students will be updating the blog with descriptions of class activities, which will often be accompanied by pictures and/or videos. Please check back at least monthly for updates.

If you have any feedback that will help enhance the site or make this blog more useful, please let me know. Thanks!