## Mat Plans

• Lesson
6-8
1

Students explore drawing a mat plan when given a three dimensional figure built from cubes. Students also explore building a three dimensional figure when given the mat plan.

In this activity, students will compare isometric drawing with another type of representation, a mat plan. A mat plan is a top view of a solid, with the number of cubes appearing in each vertical column displayed in the corresponding box.

For example, project the following images for the students:

 Isometric Representation Mat Plan

As in previous lessons, these images are available in a PDF for you to download and print onto a color transparency.

 Mat Plans Images

Discuss with the students any observations they have made after looking at each of these images. If necessary, draw other examples for the students to make observations.

Using the Isometric Drawing Tool, students should create the two figures, as shown below.

Students should sketch a mat plan for each figure on paper. Then, using the figures they have just created using the Isometric Drawing tool, they should click on the View tool and select the mat drawing.

Ask students if their mat plans were correct. If not, they should look at the correct mat plan to help them figure out their mistakes. Students can practice creating new three dimensional figures and drawing corresponding mat plans as needed.

For the next part of this lesson, students will build isometric drawings given a mat plan. Encourage students to make several different drawings for each mat plan, if possible. If needed, students can transfer their drawings for each mat plan onto isometric dot paper. Students may wish to keep the View tool open while they draw.

Draw these mat plans on the board for students (or project the images from the previously mentioned PDF). Using the Isometric Drawing Tool, students should now make their drawings.

Questions for Students

• In the previous problems, you saw that sometimes two different solids have the same mat plan. Can you think of some restrictions you could place on solids so that mat plans are unique?
• When might mat plans be more useful than isometric drawings or FRT views? When are they less useful? Why?

### Common Core State Standards – Mathematics

• CCSS.Math.Content.6.G.A.1
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

• CCSS.Math.Content.6.G.A.4
Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

• CCSS.Math.Content.7.G.A.2
Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

• CCSS.Math.Content.7.G.B.6
Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

### Common Core State Standards – Practice

• CCSS.Math.Practice.MP1
Make sense of problems and persevere in solving them.
• CCSS.Math.Practice.MP4
Model with mathematics.
• CCSS.Math.Practice.MP5
Use appropriate tools strategically.
• CCSS.Math.Practice.MP7
Look for and make use of structure.