# 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)?

# Using Color Tiles to Measure Area of Irregular Shapes

by C. Elkins

I have heard from a few 4th grade teachers that a new standard is difficult for their students to grasp. It is 4.GM.2.2: Find the area of polygons that can be decomposed into rectangles.

I have a couple of suggestions which help students with a concrete-pictorial-abstract progression approach to this problem (which is more developmentally appropriate).

1. I have attached an activity which involves the use of 1” color tiles to partition off irregular shapes and then determine the area of each smaller rectangle. It’s free and in 2 parts:
2. I located an excellent reference which shows pictorially how to do this step-by-step. It also includes good information about perimeter. It is:  Area and Perimeter