Students will construct tangrams out of paper and will then use those to create designs with their polygons.

**Class:** First Grade

**Duration:** Two class periods, 30-40 minutes each

**Materials:**

- construction paper squares, 9 x 9 inches or 10 x 10 inches
- envelopes for each student
- scissors (optional)
- one large piece of white construction paper
- gluestick (optional)

**Key Vocabulary:** tangram, triangle, square, parallelogram

**Objectives:** Students will decompose a square into a trapezoid, a parallelogram, triangles and squares.

**Standards Met:** 1.G.2. Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shapes, and compose new shapes from the composite shape.

**Lesson Introduction:**
Find tangram pictures here. Post on the board. Ask student to try to identify the shapes found in each of these pictures.

**Step-by Step Procedure:**

- Starting with whole square, show students how to fold along the diagonal to decompose it into two large triangles. Put one triangle aside. (*Note - scissors may be the best way to cut apart these triangles, but if you are using construction paper, you can also have students lightly lick the fold line, and then the pieces come apart easily.)
- Take one large triangle, place it so that the longest side is at the bottom. Show students how to fold it from the right to the left side, into two small triangles.
- This is when it gets tricky. Take some time with students, and definitely model each step before asking them to do it. Take other large triangle, and have students again place it on their desks so that the longest side is at the bottom. Fold the top point straight down so that exactly hits the middle of the bottom side. You'll end up looking at a trapezoid, but you don't need to tell them this yet. Have them cut along the fold line, which leaves you a small triangle and a trapezoid.
- Lay the trapezoid out on the desk so that again, the largest side is on the bottom. Show students how to fold the trapezoid from side to side so there is a vertical fold in the middle. Cut along that line. They will be left with two smaller, irregular trapezoids, but again, you do not need to focus on that vocabulary at this point unless you feel the students are ready.
- Pick up one of the small trapezoids. With young children, it is effective to call this a shoe, and use language like this for the rest of the activity. At this point, ask them to fold the
**toe**of the show to the**heel**of the shoe. If they cut on this fold line, they'll have a very small triangle and a square. - With the last trapezoid, you'll have students making a parallelogram and a triangle, but this is the hardest part. Remind them of the parts of a shoe - the heel, the toe, and the laces. Have them hold the
**heel**of the shoe, and fold it to the**laces**. Cut along that fold. This is a good time to let them play with their shapes, as they have worked very hard to create their tangrams, and have learned quite a bit of geometry in the process! - When the next class period begins, have students lay out every shape on their table. Write the names of each shape on the board. Ask students to copy these onto their shapes so they always know what they are.
- See if the students can put the shapes back into their original square. This is tricky!
- Put up the tangram pictures again, and see if students can do a better job of identifying the shapes that make up these objects. Tell them that they can now do the same thing with their tangrams.
- Give students time to play with the shapes and create pictures with their tangrams. As soon as they find a picture they like, have them create a picture of it. If you don't want to save the tangrams for later, have students glue their tangrams to the larger sheet of paper, and display the pictures. If you do want to save them for later, have students trace one of their favorite tangram arrangements, and color it in.

**Homework/Assessment:** No homework for this lesson.

**Evaluation:** As students are working, walk around the classroom and discuss their work with them. Take notes, work with small groups, and pull aside students who need help.