Math Intervention and The Remainders Game

I’m in a new building with a different role this year, math interventionist. A big part of my job is working with the 6th-8th graders during their homeroom periods, pushing in to the sixth grade classrooms for reteaching, plus creating math curriculum for the after school Title 1 program.

Officially the intervention period is not a replacement class, but I do see specific students twice a week supporting the day’s learning objectives while shoring up foundational skills and problem solving strategies.  A twice weekly intervention period is not an ideal situation, but it’s the best we can offer students right now. The period also gives me a chance to pilot some of the lessons/activities I’m considering for the after school program.

One great example which fits perfectly with factors is NRICH’s The Remainders Game. The object is to deduce what number between 1-100 the computer is thinking in the fewest moves possible. The player chooses the divisor between 2-10 and the computer gives a clue–its remainder. We’ve played the game several times as a class and I’m at a point where I can now share a Remainders Game worked solution which the after school tutors can follow, plus a Remainders Game worksheet so students can play independently.

Discuss the first move. What number should we divide by to narrow the list of possibilities?
remainders game
What possible numbers between 1 and 100 can the computer be thinking?

In this scenario we’re working with the numbers 18, 28, 38, 48, 58, 68, 78, 88, and 98. We don’t know what we’re going to do with those numbers yet but we need to keep track of our work. I led students to roughing out a table by hand. I later created the worksheet.

Introducing factors as a strategy comes into play when you’ve determined the possibilities. For example when the computer is thinking of an even number, is dividing by 2 a wasted move? Can finding the factors of each of the numbers help us rule out some of the possibilities?

For time’s sake each student was assigned a number to factor and we shared out. In the future students will be able to do this independently now that they know the process. Next was a great discussion on which number to divide by next.


We chose 4, and the computer told us there was a remainder of 0. What numbers did we eliminate? What number should we divide by next?

This task builds stamina while studying the composition of numbers. I think a scaffolded approach is giving my students access to a challenging problem.