Intent

The activities in Reaching the Unknown support students’ understanding of linear functions and their representations by emphasizing symbolic representations and connecting this work to that done in earlier activities.

Mathematics

The emphasis of these activities is on symbol sense. Students focus on symbolic representations of linear functions and on developing a meaningful understanding of some of the symbol-manipulation procedures used to solve equations. The context of the unit, the distributive property, and a mathematical model for symbol manipulation all help support these procedures. The context supports understanding of what the symbols and their relationships represent. The distributive property allows students to derive equivalent equations. The “mystery bags” model, a pan-balance model of equations, gives students a metaphor for symbol manipulation.

Flexible algebraic thinking includes the processes of “doing” and “undoing,” such as the ability to find equations with given solutions as well as to find solutions to given equations. In these activities, students will work explicitly on developing this algebraic flexibility.

Progression

Students will answer a variety of questions by writing and solving symbolic equations and systems of equations. They will revisit previous questions solved graphically and solve them symbolically. In addition, they will present their results on the final POW of the unit, compile unit portfolios, and complete in-class and take-home unit assessments.

Fair Share on Chores

Fair Share for Hired Hands

More Fair Share on Chores

More Fair Share for Hired Hands

Water Conservation

The Big Buy

The California Experience

Getting the Gold

The Mystery Bags Game

More Mystery Bags

Scrambling Equations

More Scrambled Equations and Mystery Bags

Family Comparisons by Algebra

Starting Over in California

Beginning Portfolios

The Overland Trail Portfolio