First, students are given a set of Cuisenaire Rods. They will need 2 lime rods, 2 orange rods, 2 red rods, 2 fuchsia rods, and 1 of every other color. This exploration will likely work best in groups, so you could easily give one group of students a set of rods, rather than each student a set. Note: If you don't have Cuisenaire Rods, You could probably cut down some popsicle stick or something. It'll just be a lot of cutting.
First, explain to students that this is a complete set of Cuisenaire Rods:
Next, students will need access to the problems. I have the problems in a PowerPoint file, but I'm thinking each group probably needs a handout at their seat so they can work at their own pace. Regardless, here are the questions as a converted PDF file. If you want the PowerPoint, click HERE.
Ask the kids to work through the problems and solve. You will need to circulate around the room and prompt students when they are stuck. This activity will likely come easily to some and less easily to others.
After students have successfully solved for the lengths of these bars, the should check their solutions against the whole set to see if their solutions make sense. They could also double check themselves with a ruler( Note: measurements are all in cm).
Then, the last four slides of the PowerPoint is hopefully where the geometric representations and algebraic thinking gels. What similarities did students notice? Differences?
The last three slides takes you through the three different types of problems encountered in the activity and asks students to discuss how they viewed and solve that particular type of problem.
I am excited about trying this lesson in a classroom soon. Special thanks to @pamjwilson and @mrdardy for their help in developing this activity.