Activity 01
Pair Hypothesis Challenge: Number Patterns
Pairs select a starting number and rule, like 'multiply by 3 then add 2,' to generate sequences. They hypothesize what happens after 20 terms and test with calculators. Groups share predictions and verify against actual results.
Hypothesize potential solutions to an open-ended mathematical problem.
Facilitation TipFor the Pair Hypothesis Challenge, provide a timer so students practice moving from quick ideas to deliberate testing before forming conclusions.
What to look forPresent students with a scenario, for example, 'How can we arrange 24 chairs in a rectangular formation for a school play to maximize audience visibility?' Ask students to write down two different questions they could investigate about this scenario and one potential strategy for each question.
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Activity 02
Small Group Exploration: Shape Puzzles
Provide tangram sets; groups pose questions like 'What shapes cover the most area without gaps?' They sketch hypotheses, build models, measure areas, and compare pathways in a shared chart.
Analyze the different pathways one could take to investigate a mathematical concept.
Facilitation TipDuring Small Group Exploration, circulate to ask, 'What have you tried so far?' to guide students toward documenting their process, not just the outcome.
What to look forAfter students have completed a short investigation, ask: 'What was the most challenging part of your investigation? How did you decide which pathway to follow? What would you do differently if you started again?' Facilitate a class discussion comparing approaches.
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Activity 03
Whole Class Inquiry: Data Pathways
Collect class data on hand spans; students hypothesize sorting methods by mean or range. Explore tally charts versus graphs, discuss efficiency, then vote on best report format.
Construct a clear and concise report detailing the findings of a mathematical investigation.
Facilitation TipIn the Whole Class Inquiry, display a large grid where groups can mark their routes so all students see how different strategies lead to varied solutions.
What to look forStudents swap their draft investigation reports. Provide a checklist: 'Does the report clearly state the question? Are the methods described step-by-step? Are the findings supported by data or examples? Is the conclusion logical?' Students provide one specific suggestion for improvement.
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Activity 04
Individual Report Builder: Game Strategies
Students play a dot-to-dot game, hypothesize winning paths, track trials, and write solo reports. Share one key finding in a class gallery walk for feedback.
Hypothesize potential solutions to an open-ended mathematical problem.
Facilitation TipFor the Individual Report Builder, provide a template with clear sections for question, method, findings, and conclusion to scaffold structure.
What to look forPresent students with a scenario, for example, 'How can we arrange 24 chairs in a rectangular formation for a school play to maximize audience visibility?' Ask students to write down two different questions they could investigate about this scenario and one potential strategy for each question.
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Generate Complete Lesson→A few notes on teaching this unit
Experienced teachers approach this topic by modeling curiosity themselves—posing questions without rushing to answers and normalizing uncertainty. They avoid stepping in too soon, instead asking, 'What have you noticed so far?' to keep students engaged in sense-making. Research suggests that students thrive when the teacher acts as a co-learner, celebrating partial progress and redirecting attention to process over product.
Successful learning looks like students confidently asking their own questions, testing multiple approaches, and clearly explaining their reasoning. You’ll see persistence when solutions aren’t immediate, respectful debate during group work, and pride in sharing unique findings with peers.
Watch Out for These Misconceptions
During Pair Hypothesis Challenge, watch for students assuming there is only one correct pattern or rule.
Prompt pairs to compare their starting points by asking, 'How did you decide what to look for first?' Encourage them to list all patterns they found before choosing one to explore further.
During Small Group Exploration, watch for students following steps in a fixed order without testing alternatives.
Place a 'dead end' shape or constraint in their puzzle set and ask, 'What happens if you change the order of your steps? Can you prove why this works better?' This forces them to reconsider their approach.
During Individual Report Builder, watch for students treating the report as a series of answers without explaining their reasoning.
Provide a sticky note template labeled 'What I learned from this' and require students to attach it to their report, summarizing one insight about their problem-solving process.
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