Work backwards through two-step function machines worksheets

What is on this worksheet

The numbers that come out of a two-step machine are shown, and students undo both steps to find the numbers that went in.

• Rules: Two steps (× N, then + or − N)
• Find the: Numbers that went in

You can change any of these settings above. Press "New problems" for a fresh set with the same settings, or pick Version A to Z to print different sheets for neighboring desks. The answer key always matches.

About function machine worksheets

Each machine shows numbers going in on the left and coming out on the right, with the rule in a window: add a number, subtract a number, multiply, or do two steps such as multiply by 2 and then add 3. Choose whether students find the numbers that come out, the numbers that went in, a mix of both, or the rule.

Working backwards is the first step towards solving equations, and finding the rule from the numbers is the first step towards writing algebra. Every machine uses numbers that always give whole-number answers, and the rule is the only one that fits.

Printing

US Letter or A4, portrait: choose your paper size above. Print at 100 percent (actual size). Use "Black and white" for the copier, or "Color" for display pages and mini books.