In a graduate-level class about constructionism, we designed a collaborative game for geometry topics related to line segments and angles. Here are the steps for making a collaborative, hands-on game.

## Step 1: What Will I Need?

You will need:

- A specific learning objective
- At least eight weighted blocks with posts for attaching yarn
- Yarn or string
- A large room

## Step 2: Learning Objective(s)

Think about what specific learning objective you are aiming for students to understand when participating in this game. Your learning objective should:

- Focus on geometry topics related to line segments and angles
- Be somewhat open-ended so students can be creative with solutions Include some constraints for learning goals so students have guidance (for example, directing students to make congruent triangles)
- Broad enough to encourage exploration and multiple solutions but specific enough that it encourages specific types of thinking

In our game, our learning objective is for students to understand distance and angles, explore configurations of different polygons, and how these geometry concepts are related. Students can also develop their own challenges for others to solve, such as relocating where the “vertex blocks” are placed. Learning objectives could easily incorporate topology, combinatorics, set theory, and much more. This game is easily adapted to a range of users’ abilities and math standards.

## Step 3: Prepare a Tutorial

Think of how you can support students’ learning using physical and/or virtual means. Consider the following questions:

- How can students make something that helps them reach your learning objective?
- What basic content or skills do students need to know?
- How can students discover content or skills through making?

In our game, students first complete two tutorial puzzles (see details in Step 5 below) to understand how they can create shapes within a larger shape using line segments and angles. Students also learn geometry terminology for describing puzzles to others by interpreting examples in the tutorial.

## Step 4: Game Set Up

- The teacher gathers eight anchors, such as boards with nails in them, and several spools of differently colored yarn.
- The teacher places eight anchors around their room so that the anchors serve as vertices of a regular octagon.
- Finally, the teacher should develop a series of challenges and constraints for the game. Examples include:
- CHALLENGES - Make two non-congruent triangles, Make a free floating kite
- CONSTRAINTS - Include at least 5 separate vertices, Cannot include two shapes with overlapping lines

## Step 5: Choose a Game Mode

__Competitive mode walkthrough__

- First, students form groups of two to four.
- The teacher then gives the class one puzzle to solve that involves the use of geometry terminology.
- The teams discuss how to interpret the puzzle (looking up terminology as needed), then race each other to see who can accurately solve the puzzle first.
- Teams use their skein of yarn to place lines between anchor vertices.
- Teams may need to justify how their shape or design meets the challenge or solves the puzzle. Multiple interpretations of the puzzle are allowed, per the teacher’s judgement.

__Collaborative mode (class or groups) walkthrough __

- Students work in teams of two to four. All teams solve an initial challenge, looking up terminology as needed.
- Once students have solved the challenge, a constraint card is given that students need to incorporate in a redesign of their original solution. They do this by adding on to their original design. All teams are given the same constraints.
- If students can successfully do this, the teacher continues to draw constraints. Teams may accommodate these constraints in different ways, which allows for open-ended solutions.
- The game ends when students can no longer solve the puzzle while incorporating new challenges.
- Teams then share their solutions, and verbally explain how their design accommodates constraints and why certain constraints may or may not be compatible. Alternative: The class works together to find a solution to a given challenge.
*Extension*: Teachers may create additional challenges for students to solve. Both teachers and students may create constraints to include in puzzles, such as making a spoon shape with the yarn.

## Step 6: Discussion

This game provides great opportunities for discussion around geometry understanding as well as negotiating novel solutions to puzzles. For example, you may discuss why you can add some constraints and not others within an existing design. Students may also enjoy developing constraints.

**This project was designed as part of the Constructionism & Making Class at UW-Madison, taught by Professor Matthew Berland.*