The Algebra of 7

The Algebra of 7 is a Grade 4 divisibility investigation that works backward from a divisibility-by-7 rule to construct numbers divisible by 7. Students use an equation of the form 3X + L, choose a last digit, solve for the remaining digits, and test whether the resulting three- or four-digit number is divisible by 7. The challenge turns divisibility into an algebraic construction task.

Use it in small groups when students are ready for a deeper look at divisibility beyond memorized tests. Comparing successful and unsuccessful choices for the last digit can reveal useful number patterns. Create a free Find a Math Game account to generate teacher-ready lesson support for The Algebra of 7. No credit card is required, with 3 lifetime lesson generations.