# Quadrilateral Tangram Investigations

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## Objective

SWBAT investigate properties of quadrilaterals using tangrams

#### Big Idea

This lesson is a pre-assessment to identify what the students know about the properties of quadrilaterals. They use tangrams to form shapes and write about what they discover.

## Do Now

7 minutes

As the students walk into the classroom, I hand them each a set of tangrams, which consists of two large right isosceles triangles, two small right isosceles triangles, one medium sized isosceles triangle, a square and a parallelogram. I ask them to draw or trace each unique piece into their notebook and identify the specific type of shape they have drawn. After they have drawn the shapes, I allow time for the students to play with the shapes and create their own shapes or designs.

Teacher's Note: I have enough tangrams in my classroom for each of my students to work with, but if tangrams are not available, they can be printed out tangram template 1 or even created by folding paper. An alternative Do Now would be to have your students create their own set of tangrams; however, that takes more time and may take away from the time students have for the activity.

## Mini-Lesson

5 minutes

In today's Mini-Lesson, we talk about tangrams. Some students have used them before and know what they are for, while others are seeing them for the first time. Tangrams are Chinese puzzles, or models of shapes (see Tangram Puzzles). Each piece is called a "tan." They are used to create different shapes, the base shape being a square (see Tangram Color Puzzles). The specific origins of the puzzle are not known, but they were introduced to the West in the early 19th century and became popular in the late 19th century. In this lesson, we will use only some of the tans to investigate properties of quadrilaterals.

After the introduction to tangrams, we look at the individual shapes and discuss their properties, i.e. all three sizes of the triangles are similar. Identifying the properties and seeing the relationships between the shapes will help students create their shapes in the activity part of the lesson.

## Activity

28 minutes

In this activity, my students will use their tangrams to investigate the properties of quadrilaterals. I use the activity as an informal assessment to identify what they know already about quadrilaterals. The hands-on work with tangrams will build on our prior work with triangles and provide an introduction to the work that we will do in this unit on  Proving Theorems about  Parallelograms (G.CO.11).

The worksheet asks students to construct shapes using a specific number of tans. Then, they have to sketch the shapes and answer questions about the shape. Some questions involve creating the same shape using different tans. Most require students to analyze the structure of the shape (MP7).

Because some students struggle with tangrams at first, I usually have my students work in pairs. I find things go better when students can help each other see which tans are needed to form a shape. Since some questions have more than one right answer, students benefit by discussing their answers and justifying to each other how they know their shapes are correct (MP3). As they work, I circulate and ask guiding questions. This video shows my students working and  some of the questions that I ask.

## Summary

5 minutes

At the end of the lesson, we go over the questions on the activity worksheet. Students answer the questions and describe the properties of the quadrilaterals they found out.  I call on students to show some of their solutions to the questions on the document projector. Several of the answers have multiple solutions. As the students present their answers, they justify their solutions. This discussion prepares students for the proofs they will write in the lessons that follow, which address standard G.CO.11.