OLD Resources. The resources on this page have NOT yet been updated to align with the revised elementary mathematics TEKS. These revised TEKS were adopted by the Texas State Board of Education in 2005, with full implementation scheduled for 2006–07. These resources align with the original TEKS that were adopted in 1998 and should be used as a starting point only.

Clarifying Lessons

Grade 4: Tantalizing Tangrams

Lesson Overview

Students explore polygons by manipulating tangram pieces.

Mathematics Overview

Students identify attributes of polygons and practice geometric vocabulary.

Set-up (to set the stage and motivate the students to participate)

  1. Tell the legend of the tangram as a flannel-board story, using Grandfather Tang's Story by Ann Tombert.
  2. Demonstrate how to make the tangrams and have students follow along with you. Use appropriate terminology as the tangram pieces are created (e.g., isosceles right triangle, congruent, similar, etc.). (4.8A)
  3. Have students compare the attributes of various pieces.(4.8A, B, C; 4.9B, C)
  4. Have students learn a specific name or description (such as medium right triangle) for each tangram piece to aid in communication within and between groups. (4.8A, 4.15A)
  5. Discuss the definitions and characteristics of the shapes listed on the Tangram Grid. For example, How many pairs of parallel sides does a trapezoid have? Why is it important for us to decide on one particular definition of trapezoid? (4.8A, B, C; 4.9C)
  6. Have students work in small groups to find the given shapes with the given number of pieces to complete the Tangram Grid. (4.9A, B, C)

Teacher Notes (to personalize the lesson for your classroom)

Guiding Questions (to engage students in mathematical thinking during the lesson)

  • Could you reflect, rotate, or replace pieces to make a new shape? (4.9A, B)
  • Could you make that shape another way? (4.9B)
  • What strategies are you using? (4.16A)
  • Could you replace one piece in a shape with two pieces? Two pieces with one piece? (4.9B)
  • Which piece seems to be the easiest to use? The hardest? Why?(4.9A, B, C; 4.15A)
  • Which pieces do you seem to use most often? Least often? Why?(4.9A, B, C; 4.15A)
  • How do you know that what you have made is a square (trapezoid, etc.)?(4.8A, B, C; 4.15A)

Teacher Notes (to personalize the lesson for your classroom)

Summary Questions (to direct students' attention to the key mathematics in the lesson)

To determine students' abilities to identify shapes' characteristics and use appropriate geometric vocabulary, ask questions such as:

  • What kinds of triangles did you make? (4.8A)
  • How did you decide if your shape was a square, a trapezoid, etc.? (4.8A, B, C; 4.15A)
  • How did the definitions of the shapes help you? (4.8A, B, C; 4.15A)

To encourage students to reflect on their problem-solving processes, ask questions such as:

  • Which pieces did you tend to use more than others? Why? (4.9A, B, C; 4.15A)
  • What are some other ways to construct each of the shapes? (4.9A, B; 4.15A, 4.16A)
  • What strategies did your group use for finding shapes? (4.16A)

Teacher Notes (to personalize the lesson for your classroom)

Assessment Task(s) (to identify the mathematics students have learned in the lesson)

  • Have students compile a class glossary.
  • Have students make a class poster display.
  • Have students write summary statements or a paragraph about what they learned about polygons.

Teacher Notes (to personalize the lesson for your classroom)

Extension(s) (to lead students to connect the mathematics learned to other situations, both within and outside the classroom)

  • Students can find all the ways to make each shape with a given number of pieces.
  • Students can develop an argument for why there is no six-piece square.
  • Students can design a display where all the solutions could be posted (perhaps one poster for each shape).

Teacher Notes (to personalize the lesson for your classroom)