Dramatic dimensional drawings

Teaching Pre K-8, Mar 2001 by Naylor, Michael

Fun ways to help students think about spatial relationships.

Students love to make 3-D structures and drawings, especially when they can be successful. Besides being popular with students, activities with three-dimensional objects are a great way to develop spatial reasoning. By manipulating objects physically and mentally, children develop mental tools that will serve them as they make sense of their world through geometry.

Activity 1: Hidden Buildings (K and above)

Give each child a supply of snap cubes. Secretly snap together four or five cubes. Keeping the structure hidden from view, describe it to your students and have them try to build the shape from your description. Do this a few times, until your students are comfortable with the activity, then pair them up. Have them take turns, with one student creating a building and describing it to the other student, who tries to duplicate it. This is also a great exercise in giving and following directions. Depending on the number of cubes, this activity can be used at any grade level.

Making 3-D sketches (grades three and above)

Triangular dot paper is great for making 3-D sketches. You can download it from www.wvu.edu/~mnaylor/dotpaper If you use an overhead projector, copy at least one sheet onto a transparency.

Give each of your students snap cubes and a sheet of dot paper. Show them how to draw a single cube, and then have them try it. Ask your students to sketch a few multi-cube structures.

Some students will be able to draw the shapes very quickly, while others may need help from you. It helps to point out that each dot has six neighbors you can connect it to, and while you can make vertical lines, it's impossible to make a horizontal line. Figures may be shaded for dramatic results.

Students will use 3-D dot paper drawings to record their findings in the following activities.

Activity 2: Tetracubes (grades three and above)

Working in teams of three or four, have your students find and build all the shapes possible with four snap cubes. Suggest that the shapes lie flat on the table (you'll lift this restriction momentarily). Tell your students that if two shapes can be turned or flipped to look like each other, then they count as the same shape.

Your students should record each shape by drawing a 3-D picture of it on dot paper. When they have found all five flat shapes, challenge them to find additional shapes which do not lie flat on the table.

Discussion: The five flat shapes can be described as the letters S (or Z), I, L, T and a square. You might find it easier to think of it as the word TOILS. The S/Z shape can be flipped, but this doesn't count as a different shape. Three more shapes (shown below) are possible, which do not lie flat.

Notice that two of the shapes are reflections - they can't be turned or flipped to look alike. Expect your students to engage in some interesting arguments and discussions regarding these shapes. Students are often surprised that the shapes are actually different. Mathematicians would say that one of the shapes is "right-handed" and the other is "left-- handed."

Extension: Finding all the shapes that are possible with five snap cubes is a real challenge - consider using it as a longterm project. As an in-class activity, expest it to take at least one class period, if not more.

Activity 3: Three Views (grades five and above)

Have your students build structures using four to six snap cubes, then ask them to draw what their structures look like as seen from the top, from the front and from the right side. Their drawings will be composed entirely of squares and can be done on graph paper, or even on regular paper if the work is done neatly. An example of a structure and its three views is shown below.

You can turn this activity into a game! Have each student build a larger structure (using about 10 snap cubes) and draw the three views. Each student places his or her structure into a bag and attaches the paper with the three views to the outside of it. Students then exchange bags and try to replicate the three-dimensional structure by studying the top, front and side view drawings.

Discussion: It's possible for some drawings to describe more than one structure. If a student discovers this, discuss why that happens with some shapes but not others.

Visit

www.TeachingK-8.com for more activities.

Michael Naylor is a professor of math education at Western Washington University, Bellingham, WA and a Teaching Editor of Teaching K-8. E-mail: mnay lor@cc.wwu.edu