ESTIMATION PRACTICE · SET L02
A sense of scale
Practise moving from familiar dimensions to larger spaces and stacks. This set uses a swimming pool, a collection of books and a pile of paper. The dimensions are given, but metres, centimetres, millimetres and litres need careful handling. Sketching the shape can help you decide which dimensions belong in the calculation.
Three questions · Untimed solo practice · Calculator and scratch notes available
Answers and worked explanations appear after you submit each estimate. Replaying keeps your first completed score.
Questions and ways to approach them
QUESTION 1 · Space
How many litres of water fill a rectangular pool 50 m long, 25 m wide and 2 m deep?
Answer in: litres
Multiply the three dimensions to find volume in cubic metres. Only then convert the volume to litres. Do not use the surface area of the pool as a substitute for its capacity.
QUESTION 2 · Everyday
How many metres of shelving would you need for 10,000 books, each 2.5 cm thick?
Answer in: metres
Treat the books as a single row, with every spine contributing its thickness. Work out the total length before converting centimetres to metres. The question asks for shelf length, not the number of bookcases.
QUESTION 3 · Everyday
How tall, in metres, would a stack of 100,000 sheets of paper be? Each sheet is 0.1 mm thick.
Answer in: metres
Multiply sheet thickness by the sheet count and keep the intermediate result in millimetres. Convert to metres once. A stack has one thickness dimension; there is no need to multiply by page width or height.
Review the reasoning, then try again
A close answer is useful, but so is knowing where an estimate went wrong. After each reveal, compare your assumptions with the worked explanation. Look for a unit conversion, a repeated factor or an uncertain starting value before deciding what to change on a replay.
Each round scores the ratio of the larger number to the smaller. A perfect estimate is 1×. Your three-round score is the arithmetic average of those ratios, so a large miss can outweigh two close answers. Read the scoring rules and examples.