Is it possible for two numbers to have a difference of 8, and a sum of 1? What about a sum of 12 and a difference of 5? Are all such combinations of sums and differences possible? Systems of Two Linear Equations—this week’s Friday Fave—helps students explore tools for answering these questions.

With these tools, students become more powerful. We begin gently, by asking students whether they think it’s possible. Then we ask them for a pair of numbers with a difference of 8.

We put those numbers on the coordinate plane. They see everyone’s points, notice that these constraints produce lines, and only then do we ask students to write equations for these lines.

Over the course of 12 quick and targeted screens, we build from students’ informal ideas about numbers to the solution of a system of two linear equations.

Students’ arithmetic knowledge builds into algebra knowledge. We don’t ask them to forget what they know; we ask them to make what they know more robust. That’s why it’s this week’s Friday Fave.