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🧮 Building Thinking Classroom — Math Questions
Open-ended, collaborative problems designed to spark thinking. Set a timer for each question.
Area & Perimeter
You have 24 square tiles. How many different rectangles can you make using all 24 tiles? Which rectangle has the biggest perimeter? Which has the smallest? What if you had 36 tiles?
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Ratios & Proportions
A recipe makes purple paint using 3 parts red and 5 parts blue. How much of each do you need to make 400 mL of purple? What if you only have 45 mL of red — how much blue do you need? Can you make exactly 50 mL of purple?
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Integers
The temperature at midnight was −8°C. By noon it had risen 15°C. By evening it dropped 9°C from noon. What's the temperature at each time? At what point in the day was it 0°C?
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Patterns & Algebra
A staircase is built from cubes: step 1 uses 1 cube, step 2 adds 2 more, step 3 adds 3 more… How many cubes total for a 10-step staircase? Can you find a shortcut instead of adding them all up? What about 100 steps?
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Percent
A store has a 25% off sale. Then they take an additional 10% off the sale price. Is that the same as 35% off? You have $60 — what is the most expensive item you can buy? What if tax is 13%?
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Proportional Reasoning
Two cyclists start at the same place. One rides at 12 km/h, the other at 15 km/h. If they go the same direction, how far apart are they after 2 hours? What about opposite directions? When is one cyclist exactly 9 km ahead of the other?
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Expressions & Equations
Think of any number. Double it → add 10 → divide by 2 → subtract your original number. You always get 5! Try it with fractions or negatives. Why does this always work? Can you make a trick that always gives your original number back?
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Geometry
You have a rectangular piece of paper 20 cm × 12 cm. What is its area and perimeter? If you fold it in half, what are the new dimensions? Can you make a shape from the same piece of paper with a larger perimeter but the same area?
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Pythagorean Theorem
A 5 m ladder leans against a wall with its base 1.5 m from the wall. How high does it reach? If you push the base out to 2.5 m, how much does the top slide down? At what base distance does the ladder reach exactly 4 m high?
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Linear Relations
Toothpicks are arranged in a row of squares: 1 square = 4 toothpicks, 2 squares = 7, 3 squares = 10… How many toothpicks for 100 squares? How many squares can you build with exactly 100 toothpicks? Write a formula.
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Volume
A cylinder and a cone have the same radius and the same height. The cylinder is filled with water. How many cones can you fill from the cylinder? Does it matter what the radius or height actually is? What if you used a sphere instead?
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Linear Equations
Candle A is 20 cm tall and burns 2 cm per hour. Candle B is 14 cm tall and burns 1 cm per hour. When are they the same height? Which burns out first? Sketch both on the same graph. What if Candle B was lit 1 hour later?