Equation Ducks
Solving linear equations through balance and cancellation
This workshop introduces first-degree equations through a hands-on game using puppet ducks and beans (some hidden in the ducks, some in view). Students reason about equality by comparing quantities on the two sides of a river model.
Workshop Structure
- Students first build a river model from simple classroom materials, creating two banks.
- Puppet ducks and bean tokens are placed on both sides of the river.
- All ducks contain the same number of beans; only the bean color differs by duck color.
How Equation Solving Emerges
Beans of opposite colors can cancel each other out when paired on the same side, mirroring additive inverses in algebra. After all possible cancellations, the remaining bean totals on the two sides of the river are equal.
By reasoning through these steps, students determine the unknown number of beans hidden inside each duck, without looking inside them.
Learning Outcomes
- Understand linear equations as statements of balanced quantities
- Solve first-degree equations through logical cancellation
- Identify situations with no solution or infinitely many solutions
- Connect concrete models to symbolic algebraic expressions
Safety note: This is a classroom game. Uncooked beans can be harmful to ducks.