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 file from 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.

*Click here for a practice page (three additional problems)

SketchUp Activity

Overview: Create and place Integer Rods in space - anchor the first one 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.

Construction steps

Step 1: Create a 1x1x1 cube and group into an object. Step 2: Copy and paste more cubes into the file. Color cubes with the paint tool. Step 3: Move (snap) to position. Hint - drag a corner point to another corner point. You should see them line up correctly. Example #1 Download the SketchUp file for the model shown below

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 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 file from 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.

*Click here for a practice page (three additional problems)

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

Step 1: Create a 1x1x1 cube and group into an object.Construction stepsStep 2: Copy and paste more cubes into the file. Color cubes with the paint tool.

Step 3: Move (snap) to position. Hint - drag a corner point to another corner point. You should see them line up correctly.

Example #1Download the SketchUp file for the model shown below

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

1. Find the surface area of the shape.Discussion Questions2. 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 #2Download this file and sketch the front, right side and top views on your centimeter graph paper.

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.

Page Updated - June 2014