An estimation question asks for a sensible rough number instead of an exact answer. Pick one of these 30 questions, make a guess, then open the worked estimate to compare your thinking. Use the ten-minute activity below in class or try a question together at home.
The two younger groups let you estimate, then check with everyday objects. The older group uses linked public figures and stated assumptions. Agree on your own assumptions before opening an answer. Each range follows the assumptions shown, so a different well-explained estimate can also make sense. The ages are a starting point; choose a group that suits your students.
Allow ten minutes for one question. You need paper, pencils and a way to show or read out the question. Keep the worked estimate closed.
Guess first, then count or measure together. The worked ranges are examples, not targets. Your classroom may give a different answer.
Use identical clips, end to end along the long edge, with no gaps.
Answer range: 30 to 50 clips in this example.
Then check it: Lay out the clips along the edge and count them. Count the last clip even if it sticks out.
Walk normally in a straight line. Count every step, including the last one.
Answer range: 20 to 40 steps in this example.
Then check it: Have a partner tally your steps as you walk the route.
Use the width of the closed door and your spread thumb-to-little-finger span. A part-span counts.
Answer range: 6 to 8 hand spans in this example.
Then check it: Move your hand across the door, marking each span with removable tape. Estimate the final part-span.
Choose a pot containing only pencils. Look from above before guessing.
Answer range: 15 to 25 pencils in this example.
Then check it: Empty the pot and count the pencils in groups of five.
Choose one shelf with a single row of books. Count every book, thick or thin.
Answer range: 20 to 35 books in this example.
Then check it: Count along the shelf, using a finger to keep your place.
Use identical loose cubes on a level desk, one above another, without joining them. A tower must stand for three seconds to count.
Answer range: 10 to 15 cubes in this example. Cube shape and careful hands can change it a lot.
Then check it: Build until it falls. Record the last stack that stood for three seconds, then try again.
Start with ten separate cups upright on a desk. Make rows of four, three, two and one.
Answer range: 25 to 40 seconds in this example.
Then check it: Ask a partner to time you from the first touch until the pyramid stands on its own.
Use loose buttons from a classroom collection. Fill one cupped hand without piling them above its rim.
Answer range: 16 to 24 buttons in this example. Small buttons may give many more.
Then check it: Tip them onto a tray and count them.
Use one sheet, cut strips about two fingers wide across its short direction, and make one loop per strip.
Answer range: 6 to 10 links in this example.
Then check it: Draw the strips, cut them with classroom scissors and tape each into a loop. Count the links; leave out a strip too narrow to use.
Use identical full crayons and a capped glue stick on a classroom balance.
Answer range: 6 to 9 crayons in this example.
Then check it: Add crayons to the other pan. If you jump past balance, report the two neighbouring counts.
Try a small experiment. Use a sample, a comparison or a short trial to make your estimate, then test it. Results outside these example ranges are welcome too.
Use a clean, dry coin lying flat. Drop plain water onto its centre from just above it.
Answer range: 16 to 32 drops in this example. Coin size, soap traces and drop size matter.
Then check it: Count drops until the first spill. Record the count just before that drop, dry the coin and repeat three times.
Use your usual handwriting, legible enough for a partner to read. Count only complete names.
Answer range: 10 to 20 complete names in this example. Name length changes the result.
Then check it: Write for exactly one minute, then ask a partner to count the complete, readable names.
Choose one page with mostly text. Count the story text, leaving out the heading and page number.
Answer range: About 160 to 250 words in this example, possibly fewer with lots of short lines.
Then check it: Count every word line by line and add the counts. Treat a hyphenated word as one word.
Bridge a 10 cm gap between two equal-height books with one flat sheet. Put identical coins at its centre.
Answer range: 3 to 9 coins in this example. Thin paper may collapse with the first coin.
Then check it: Add coins one at a time until the paper touches the desk. Record the last successful count, which could be zero.
Submerge one dry sponge, then lift it and let it drip for five seconds without squeezing.
Answer range: 30 to 60 ml in this example.
Then check it: Use a measuring jug to record the water before and after soaking and lifting the sponge. Catch the five seconds of drips back in the jug; subtract the readings.
Use an empty round bottle on its side. Mark a starting line and roll it without slipping.
Answer range: 100 to 150 cm in this example.
Then check it: Put a mark on the bottle, count five complete turns and measure the distance from start to finish.
Hang a strip vertically with its bottom 1 cm in water. Measure height above the water surface.
Answer range: 3 to 8 cm in this example. Different towels can give very different results.
Then check it: Start a timer when the strip touches the water. At one minute, measure from the water surface to the highest wet point.
Release it without a push over a hard floor. Compare the bottom of the ball at release and at the first bounce peak.
Answer range: 50 to 80 cm in this example. A softer ball or floor may give much less.
Then check it: Place a metre ruler upright nearby. A partner watches the first bounce against it; repeat three times and record the range.
Choose a lace in a shoe. Include both tips, the bow and every section through the holes.
Answer range: 70 to 110 cm in this example.
Then check it: Unlace it and measure from tip to tip without stretching it.
Include the bag and everything inside it, just as it is now.
Answer range: 2 to 4 kg in this example. This is a guess, not advice about what to carry.
Then check it: Weigh the bag on suitable scales, or weigh its contents in batches and add them to the empty bag’s mass.
Start with a real published figure, then make your assumptions. These ranges describe the model shown, not a promise about every school.
Assume an established red-wiggler bin, suitable chopped plant scraps and steady conditions for seven days.
NC State Extension says red wigglers can consume about one-quarter to one-third of their body weight daily. NC State Extension: vermicomposting.
Answer range: About 1.8 to 2.3 kg in this model. Conditions can reduce consumption; this is not a feeding schedule.
Model 300 pupils over a term of 50 to 60 school days, using the historical study’s rate. Include preparation waste and leftovers.
WRAP’s 2011 study estimated 72 g of food waste per primary-school pupil per day in England. WRAP: Food waste in schools, 2011.
Answer range: About 1.1 to 1.3 tonnes in this model. This is a historical benchmark, not a measurement of your school.
Assume 3 to 5 full loads a week for a 12-week season. Compare the two published machine averages, with the same number of loads.
ENERGY STAR gives 14 US gallons per load for a full-sized certified washer, compared with 20 for a standard machine. ENERGY STAR: clothes washers.
Answer range: 216 to 360 US gallons saved in this model. Actual machines and programmes vary.
Assume 20 identical LED fittings, each producing 4,200 lumens at 140 lumens per watt, lit for 1,000 to 1,400 hours a year.
The US Department of Energy specifies a minimum efficiency of 140 lumens per watt for its qualifying 2-by-4-foot commercial LED fittings. US Department of Energy: commercial LED lighting.
Answer range: 600 to 840 kWh in this model. Use actual power ratings and switching hours for your corridor.
Model a standard-sized certified domestic dishwasher using 2.5 to 3.2 US gallons per cycle. The 2.5 figure is our assumption, not a published minimum. Exclude pre-rinsing.
ENERGY STAR’s standard dishwasher criterion caps water use at 3.2 US gallons per cycle. ENERGY STAR: dishwasher criteria.
Answer range: 31 to 40 complete loads under these assumptions. A machine using less than 2.5 gallons could run more.
Use the US annual mileage benchmark. Assume 10% to 20% of its miles are empty journeys to and from the route.
The US Department of Energy’s vehicle-distance chart lists 14,084 annual miles for a school bus. US Department of Energy: annual vehicle miles.
Answer range: About 1,400 to 2,800 empty miles in this model. The empty fraction is a guess to check with route records.
Imagine a rectangular patch 8 to 10 metres long and 5 metres wide. Use the published sowing rate, with no extra for spills.
BBC Gardeners’ World recommends 1½ ounces of grass seed per square metre for its new-lawn method. BBC Gardeners’ World: sowing a lawn.
Answer range: 60 to 75 ounces of seed in this model. Follow the actual seed packet when sowing.
Use 10 to 15 pounds of fruit per standard plant over a growing season. Assume all plants thrive and all harvested fruit is usable.
Virginia Cooperative Extension says a properly cared-for standard tomato plant yields 10 to 15 pounds or more of fruit. Virginia Tech: tomatoes.
Answer range: 8 to 12 plants in this model. Weather, variety and losses can mean needing more; exceptional yields can mean fewer.
Suppose mowing produces 60 to 90 litres of clippings. Use Cornell’s volume recipe and bags holding 30 litres of loose leaves each.
Cornell’s composting guide suggests mixing one part grass clippings with three parts leaves. Cornell University: composting ingredients.
Answer range: 6 to 9 bags of loose leaves in this model. Bag size and packing change the count.
Use Charles Warren Academy’s published annual projection. Assume the summer break accounts for 15% to 25% of the year’s generation.
A 2025 UK government announcement projects 15,000 kWh of yearly solar generation at Charles Warren Academy. UK government: school solar installations.
Answer range: 2,250 to 3,750 kWh in this model. The holiday share is an assumption; this is generation, not electricity necessarily used by the school.
For more practice, try our Fermi questions with answers. Read how to estimate for a method you can reuse, or choose from these estimation games for groups.
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