Math Challenge: Less than 1,000 Game

Check out this game for algebra students from the Illustrative Mathematics Project website. It's designed to address Common Core standard "Create equations that describe numbers or relationships." The website includes the task (the game), comments to instructors, and a complete solution.

Here's a game that you can play and share with your students: Bernardo and Silvia play the following game. An integer between 0 and 999, inclusive, is selected and given to Bernardo. Whenever Bernardo receives a number, he doubles it and passes the result to Silvia. Whenever Silvia receives a number, she adds 50 to it and passes the result to Bernardo. The winner is the last person who produces a number less than 1,000. What is the smallest initial number that results in a win for Bernardo?

Solving this problem is a task designed to address the following algebra standards from the Common Core State Standards:

2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.

The task can be found on the Illustrative Mathematics Project website -- a valuable resource for teachers looking for practical ways to incorporate the standards into their classrooms.

Try playing the game and solving the problem. Then check out an example of a solution at , where you will find additional tasks and solutions designed to address other standards. (From the website, select “High School Standards”, followed by “Show only illustrated standards”. Then scroll to find the A-CED standard cluster or peruse other standards with illustrations.)