This week the Friday Five slows down, takes a deep breath, and transforms
itself into the Friday Fave. Here is one of our favorite activities from the
archives and why we love it.
System of Two Linear Equations
The Friday Fave loves this activity because, in the language of our Activity Building Code, it’s difficult to finish and easy to start. It starts by asking students to think of two numbers that sum to 12. Later, students critique a set of points, the coordinates of which are supposed to sum to 12.
Some sample student responses to this task:

Many tried by adding, others tried multiplying and some were wrong
 It’s discrete and linear
 I notice that most of the dots make a line
 DEPENDING HOW YOU SEE IT COULD BE GOING UP OR DOWN
There are some wonderful and wideranging ideas here. Students ask questions and make conjectures that are important and worth spending time talking about in class. What is the likely source of others’ errors? Is the described relationship discrete? Is it linear? Why? What is the meaning of increasing? There are objects here that will provoke conversation between teachers and students.
Then it’s the same routine for a difference of 6, and finally a conjecture about whether it’s possible for a pair of numbers to meet both criteria, together with a graph that answers this question.
This activity has many of the basic elements of our favorite lessons. It’s easy to start and difficult to finish. It offers students opportunities to be right and wrong in different, interesting ways. It incorporates a variety of verbs and nouns, from prediction to calculation and back again. For all of those reasons, it’s this week’s Friday Fave.