# Geometry Part 3: Composing and Decomposing

by C. Elkins, OK Math and Reading Lady Composing and decomposing geometric shapes (2D and 3D) should be centered around concrete and pictorial methods. In this and upcoming posts, I will illustrate some methods using various manipulatives and line drawings which help students take a shape apart or put shapes together. If you refer back to  Geometry Part 1: The Basics, all grade levels KG-5th have standards dealing with this issue. Some of the experiences I plan to share will also help students relate to multiplication, division, fractions, area, and other geometry concepts (such as rotations, reflections, slides).

Refer to Geometry Part 2: van Hiele levels to determine if the activities you are choosing are appropriate for Level 0, 1, or 2 students.

One Inch Color Tiles: 1.  Can you make a larger square out of several individual squares?

• Level 0 students will be using the visual aspect of making it look like a square.
• Level 1 students will be checking properties to see if their squares are indeed squares (with the same number of tiles on each side).
• Level 2 students will be noticing they are creating an array (ex: 3 x 3 = 9) and perhaps learning about squared numbers. 3 squared = 9. They might be able to predict the total number of tiles needed when given just the length of one side.

2.  How many rectangles can you make using 2 or more squares? (Level 0-1) • Level 1:  Are the green and blue rectangles the same size (using properties to determine)?

3. How many different ways can you make a rectangle using 12 tiles?  24 tiles?  Record on graph paper. (Level 1 or 2)

• Connect to perimeter and area lessons by noticing the area might be the same, but the perimeter changes. • Connect to factoring lessons.  Example:  12 can be factored as 1 x 12, 3 x 4, and 2 x 6; 24 can be factored as 1 x 24, 2 x 12, 3 x 8, 4 x 6
• Connect to multiplication commutative property (3 x 4 = 4 x 3).

4. Make a rectangle using 24 tiles. If you decompose it, how many different smaller rectangles or squares can you make?  Explore with tiles first, then record results on graph paper.

5.  How can you use color tiles to decompose a polygon into smaller rectangular shapes?  For students to master this skill, they must have a good understanding that opposite sides of rectangles are equal length. This is also crucial for determining area. Here are some resources using one inch tiles:

Pattern Blocks: Put pattern blocks together to create another shape:

• Students at a level 0 would be choosing shapes to combine in any manner. They may or may not match equal edges together. It may or may not make a recognizable design / shape.
• Students moving into a level 1 are paying attention to the properties of the shapes they are combining. What is a side? What are corners? Equal size edges must match together.
• Students combine shapes that fit exactly into an outline.  