# 13. Students Will Design a Single Die That Meets The Symmetry and Dimension Requirements

## Roll The Dice

Standards
Symmetry
CCSS.MATH.CONTENT.4.G.A.3

Standards for Mathematical Practice
CCSS.MATH.PRACTICE.MP1: Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2: Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP3: Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP4: Model with mathematics.
CCSS.MATH.PRACTICE.MP5: Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6: Attend to precision.
CCSS.MATH.PRACTICE.MP7: Look for and make use of structure.

Learning Objectives

• Students will design and produce a single die that meets the symmetry and dimension requirements.
• Students will apply their knowledge of symmetry to design faces of a die that are geometrically sound.
• Students will apply their knowledge of dimensions and spatial reasoning to include the values on each face of the die.
• Students will apply their knowledge of constructions to place the dots on each face of the die.

Recommendations
Group Size: 3 to 4 students, depending on how many dice you would like students to compare within the class setting. For a smaller class, groups of 2 would be ideal.

Class Size: up to 40 students

Materials Required

Introduction

• Students have a good understanding of 3D modeling. Prior to incorporating this lesson into a unit, it is recommended that students have had training on Google SketchUp.
• Students have a good understanding of SAE (Imperial) and/or Metric units.
• Students have a good understanding of using a ruler.
• Students have a good understanding of a compass.
• Students have a good understanding of midpoint and using constructions in geometry.

To begin the lesson, show students the varieties of unique dice sets that exist. Also, some sizes of dice would be handy. Ahead of time, asking students to bring in some dice that are around their house might be a fun introduction as well. This will be more of a direct lesson without variance, so showing some varieties may help for subsequent lessons.

Next, present students with their challenge:

Create an 8mm die (or pair of dice) that has (have) perfectly symmetrical dots and opposite sides add to 7. Without handing out any tools, have students draw out 6 squares of equal size. Once students have attempted this, require students to fill each square with the dots ranging from 1 to 6, again without handing out any tools.

Now, wouldn’t it be nice to have some sort of tool to help with this? At this point, hand students a compass and/or ruler and have them attempt the same task. Host a discussion about how much easier it was to create symmetry with certain tools. Depending on the level of students in the room, reach a point of certain frustration or success and move on to the computer modeling.

The Meat
Within Google SketchUp, groups will need to design their layouts for the die with perfect symmetry. Each side should be 8 mm. Each dot should have a diameter of 2 mm. Opposite sides of the die add up to 7. All integers from 1 to 6 are included on the die.

When printing, it is advisable to print at least 2 perimeter layers thick, so take this into consideration during the design. Each perimeter layer is 0.3 mm thick.

To ensure that everything lines up accurately, groups will check their classmates’ designs prior to showing the instructor. The instructor will need to confirm the students’ designs as best as possible before sending it to print.

Once the design has been printed, students will clean it up and verify all measurements for accuracy with a ruler.

Discussion
What were some of the challenges in designing the product?

What did you learn during the discussion?

What would happen if you used a different value for cube instead of 8 mm?

After seeing the other groups, what would you do differently?

Each one of these questions can provoke thoughtful responses rich in mathematical reasoning.

Just like in a Research and Design lab for major companies, the feedback and reflection on these projects will be the best part. Give students an opportunity to talk within their group and among their classmates to seek advice on improvements.

Desired Outcomes
A desired outcome is a die that has the requirements listed:

Each side should be 8 mm. Each dot should have a diameter of 2 mm. Opposite sides of the die add up to 7. All integers from 1 to 6 are included on the die.

Some Possible Extensions/Modifications
Use the dice created during the lesson for a later unit on probability and statistics. Either way, you will have quite a few dice in the classroom. This would be a great time to build in some statistics, game creation, and enjoy the product. The project itself won’t take long to print, so each group could even print out a set of dice for the group to work with.

Check out these games to play with kids using dice.

Once You’re Finished
Keeping these around for a rainy day or project incorporating number sense would be a good idea. Sure, you can give them away, but who has enough dice in a math classroom?!

Content & Instruction Developed by:
John Stevens – Airwolf 3D STEM Consultant
Instructional Coach – Technology
Chaffey Joint Union High School District
CUE Rockstar Faculty & Organizer