The Hidden Question: Cracking Two-Step Word Problems
Shared by A STEM Educator
Students will solve two-step word problems using all four operations, represent solutions with equation chains using a letter for the unknown, model with tape diagrams, and assess reasonableness using mental estimation.
Lesson Overview
Students discover that most real-world problems hide a secret first step — the 'hidden question' — before they can answer the real question. Through progressive thin-slices at vertical whiteboards, they build from guided two-step structures to writing their own equation chains, tape diagrams, and estimation checks.
Materials
- Vertical whiteboards or large chart paper (one per group)
- Dry-erase markers (1 per group, passed between members)
- Erasers or socks
- Random grouping cards (playing cards or popsicle sticks)
- Printed consolidation note sheets (one per student)
- Desmos interactive display (teacher device + projector)
Scaffolded Task Progression
Mia the baker puts trays of cupcakes in the oven. Each tray holds cupcakes. After baking, a customer brings back extra cupcakes from yesterday.
Step A — Find the Hidden Question: How many cupcakes came OUT of the oven? Write:
Step B — Answer the Real Question: How many cupcakes does Mia have in total? Write:
Solve both steps. Draw a tape diagram showing both parts.
The bakery made boxes of cookies with cookies in each box. Then cookies were set aside for the tasting table.
How many cookies are left for customers?
*This time, NO steps are labeled for you. Find the hidden question yourself, write TWO equations using letters for unknowns, and draw a tape diagram.*
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