Participate
Invite every student to observe, question, test, record, or explain. Before sharing out, ask each student to describe one contribution and one idea from the group.
Thinking Math is a classroom strategy for teachers: launch a meaningful problem, facilitate collaborative reasoning, and help students explain how and why their mathematics works. Use this guide to plan the routine, support discussion, and respond to student thinking.
Plan and facilitate a problem-solving routine that makes student strategies visible, so you can identify understanding and choose the next instructional step.
Invite every student to observe, question, test, record, or explain. Before sharing out, ask each student to describe one contribution and one idea from the group.
Ask “How did you decide?” and “Why does that work?” Have students connect their explanation to a table, diagram, equation, or concrete example.
Model how to restate a classmate’s idea before responding. Ask students to compare strategies and test a claim with evidence.
Use brief individual think time before group discussion. Invite quieter voices into the conversation and ask frequent speakers to listen and paraphrase.
Choose whiteboards, manipulatives, rulers, or calculators that fit the learning target. Ask students to explain what their tool or representation reveals.
When a group is stuck, ask what they know, what they have tried, or what simpler case they could test. Offer a question or representation before supplying a procedure.
Choose one problem with an accessible entry point and more than one possible strategy. State the mathematical target and success criteria before students begin.
Give students quiet time to notice, estimate, sketch, or try a first idea.
Prompt students to explain a strategy, question a claim, and listen to a teammate’s reasoning.
Rotate the marker or recording role so one student does not do all the visible work.
Ask groups to record a representation and a justification that another group could follow.
Before the debrief: Ask a student other than the recorder to explain the group’s approach. Select two strategies to compare, then use a brief individual check to see what each student understands.
Student-friendly target: “I can compare unit prices using a ratio table so I can justify which cereal is the better deal.”
Share the success criteria: “I know I am successful when I compare the same unit, show equivalent costs accurately, and justify my choice with evidence.”
Launch: Show the two packages above and ask, “Which is the better deal, and how can you prove it?” Let students try before revealing the model.
Compare the same amount. Cereal A costs $3.00 ÷ 12 = $0.25 per ounce. Cereal B costs $4.14 ÷ 18 = $0.23 per ounce.
| Weight (oz) | Cereal A | Cereal B |
|---|---|---|
| 6 | $1.50 | $1.38 |
| 12 | $3.00 | $2.76 |
| 18 | $4.50 | $4.14 |
A complete explanation: Cereal B is the better deal per ounce because $0.23 is less than $0.25. At 18 ounces, B costs $4.14 while the equivalent amount of A costs $4.50, a difference of $0.36.
The table compares equivalent costs; the store may sell only the stated package sizes. “Per ounce” names the unit we are comparing.
Sentence frame: “I compared ___ by ___. My table shows ___. This makes sense because ___.”
Check for understanding: Ask students individually, “Why is comparing only $3.00 and $4.14 incomplete?” Listen for the need to compare equal amounts. If a student compares package prices alone, return to the 12-ounce row before asking for a revised explanation.
Use the five categories below as an optional 25-point observation guide, with up to five points per category. Discuss expectations before the task and explain partial-credit decisions with specific evidence. Record mathematical understanding separately from participation so a quiet student’s reasoning remains visible.
Mathematical Reasoning — 5 points
Logical strategy, strong mathematical thinking, and clear progress toward a solution.
Showing & Recording Work — 5 points
Organized work using equations, tables, diagrams, numbers, or written explanations.
Explanation & Justification — 5 points
Explains the strategy, why it works, and why the final answer makes sense.
Participation & Collaboration — 5 points
Participates, listens, shares ideas, asks questions, and helps the group work together.
Think • Talk • Rotate • Record — 5 points
Follows the routine and uses class time and resources responsibly.
Collect a table, annotated diagram, or individual explanation. Identify the success criterion the student has met and the part that needs revision.
Try: “Your table compares equal amounts. Now label dollars per ounce and explain how that rate supports your choice.” Give time to revise.
Offer a partially completed table or sentence frame when needed. Extend the thinking by changing a package size or asking students to find a price that would make the deals equal.
Exit check: Ask students to explain one strategy in their own words. Use the responses to decide who needs another model, a small-group conference, or a more challenging comparison.