Prologue
I have used this lesson successfully with first, second, and third grade gifted students and a third grade regular education class.
Lesson Instructions
Introduction (5 minutes): Ask students to describe their experiences of measuring things. They will likely describe one-dimensional measurements using inches, centimeters, feet, etc. Identify these as units. Show how one might measure the edge of a book with a ruler using inches as a unit, then place the book on a table and ask how we could determine how much flat space on the table it covers. Introduce the concept of area. Using a side-to-side hand motion with the palm flat and pointing down every time you say the word area can help English Language Learners remember the meaning of the word. Demonstrate covering a book with color tiles (call them square units) and counting to express the book cover’s area in square units.
Free exploration with tangrams (5-10 minutes): The kids are going to going to play with the tangrams whether you want them to or not, so allow them some time to do so. Tell them to think about comparing the sizes of the pieces and challenge them to make one of the convex shapes (illustration attached) using all 7 pieces.
Tangram areas (30 minutes): Have students stop playing with tangrams. Pick up a tangram square and tell students that we will consider it one square unit. Pass out tangram areas sheet and refer students to the first box, which contains a picture of the square piece. Instruct students to label it “1 square unit.” Explain that even though the other pieces are not squares, they still have area, and that area can be expressed as a number of square units. Encourage students to use the square unit (which has a known area) to determine the areas of the other pieces. Give hints as needed:
Encourage kids to lay the small triangles on top of the square. How many small triangles do you need to cover the square? What does this mean about the area of the small triangles?
Encourage students to use the small triangles to cover other pieces (they can exactly cover the medium triangle and the parallelogram).
Encourage students to continue using the areas of known pieces to determine the areas of the large triangles.
Extensions (Optional)
Tangram Area Art: Have students create their own shapes or figures using several (or all) of the tangram pieces, trace them onto construction paper, glue them onto a background, and express the area of their new shapes.
All Tangram Pieces as Fractions: Present the same lesson, but have students assemble all tangram pieces into a large square, then designate this large square as one square unit. Students must then determine what fraction of the whole is represented by each tangram piece.
Materials
- Tangrams (Tangram template is attached and can be printed on card stock)
- Tangram Area Sheet (attached)
- Color Tiles or other small, square pieces
Downloads
Lesson Duration
45 minutes – 1 hour
Placement
This lesson can serve as an introduction to the concept of area. Students should be familiar with one-dimensional measurement and units. If you choose to use the more challenging version of this lesson, students should be familiar with the concept of fractions.
Categories
Standards
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Other/Alternative Standard(s)
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