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:

- Using color tiles outline templates (like above)
- Using Color Tiles directions (for above pictured activity)
- Rectangles with Color Tiles ($1 by Kirby’s Korner @ TPT)

**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.
This encompasses composing (because they are using smaller pieces to build a larger shape), but also decomposing if the student shows multiple ways to fill in a shape — 2 trapezoids = 1 hexagon; 3 rhombus = 1 hexagon; 6 triangles = 1 hexagon. OR, 1 hexagon = 1 trapezoid and 3 triangles; 1 hexagon = 1 trapezoid, 1 rhombus, and 1 triangle, etc. This exploration is also beneficial to understanding equivalent fractions.

- Students at Level 1-2 may create shapes which have more than one property and/or fit into more than one category: symmetrical, a shape using a particular number and type of pattern blocks, those in which shapes must be manipulated (rotate, reflect, slide) to achieve the results, or shapes which substitute blocks (example: 1 triangle and 2 rhombus can make a trapezoid).

Here are some resources using pattern blocks:

- Easy pattern block task cards by Kelly Smith ($2 @ TPT)
- Composing 2D shapes with pattern blocks (1st-5th) by The Neat and Tidy Classroom ($3.50 @ TPT). Here is an answer key I made to go along with the above because some of the designs are challenging Composing 2D Shapes with Pattern Blocks Answer Key CE
- Pattern Block Designs task cards (1st-3rd) by SC Classroom Creations ($3.50 @ TPT)
- Pattern block mats (larger size designs to fill in) (FREE from Utah State University)

**Do you have any ideas to share about composing / decomposing using tiles or pattern blocks? More on composing / decomposing next time (Tangrams, etc.)**