# Integer Rods

## INTEGER RODS - Introduction

Integer Rods are used to represent the lengths of 1 to 10 centimeters.
White cubes are 1 cm x 1 cm x 1 cm. The longest rod is orange with a measure of 1 cm x 1 cm x 10 cm.
A set of classroom activities can be found in this NCTM Illuminations Lesson

Integer Rods provide a useful manipulative when finding surface area and volume.
Different views can be created to assist students with visualization of 3D objects as well as finding surface area and volume.

A complete set of Integer Rods can be found in the Integer Rod filefrom the 3D Warehouse. This model was created by Ball State student Michael Winn. Explode the group so you can move the rods around. Duplicate them as necessary.

### SketchUp Activity

Overview: Create and place Integer Rods in space - anchor the first rod at the origin.
Goal: Create front, right, left, top, bottom or isometric views of the configuration to support the discussion of surface area and volume.

Note: The front side of the shape is to your left and the right side view is to your right as you look straight at the graphic.

### Construction steps

Step 1: Create a 1x1x1 cube and group into an object.
Step 2: Copy and paste more cubes into the file. Color the rods with the paint tool. HEX color codes and RGB color codes are listed at the bottom of this page.
Step 3: Move (snap) to position. Drag a corner point of one cube to the corner point of the second cube. You should see them line up correctly and snap together.

Example #1

Students should be able to identify a configuration given the views below. In most cases, you will not need all of the views.

### Discussion Questions

1. Find the surface area of the shape.

2. Find the volume of the shape.

3. Is it possible to create two figures with the same volume and surface area where some (but not all) of the views match?

Example #2
Download this file and sketch the front, right side and top views on your centimeter graph paper.

 Integer Rod Example #2

If you create your own rods in SketchUp, consider using the color-coding as follows.
I will leave it for you to complete the surface area column.
 Color size Hex Code RBG Volume Surface area white 1x1x1 #FFFFFF (255,255,255) 1 cubic centimeters 6 square centimeters red 1x1x2 #FF0000 (255,0,0) 2 cubic centimeters 10 square centimeters Green 1x1x3 #00FF00 (0,255,0) 3 cubic centimeters 14 square centimeters Lavender 1x1x4 #FF00FF 255,0,255) 4 cubic centimeters Yellow 1x1x5 #FFFF00 (255,255,0) 5 cubic centimeters Dark Green 1x1x6 #006400 (0,100,0) 6 cubic centimeters Black 1x1x7 #000000 (0,0,0) 7 cubic centimeters Brown 1x1x8 #663300 (102,52,0) 8 cubic centimeters Blue 1x1x9 #0000FF9 (0,0,255) 9 cubic centimeters Orange 1x1x10 #FFA500 255,165.0 10 cubic centimeters
http://www.rapidtables.com/web/color/RGB_Color.htm

Page Updated - June 2014