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Estimating Time

Age 11 to 14
Challenge Level Yellow starYellow star
Secondary curriculum
  • Problem
  • Getting Started
  • Student Solutions
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Why do this problem?


Estimating time is not a new idea for a data gathering exercise, but the tool provided in this problem allows easy collection of data that can be pasted into a spreadsheet, offering an ideal opportunity for some work on using spreadsheets to calculate statistics. See also the problem Reaction Timer.

Possible approach


You may wish to use the data in the problem Half a Minute to introduce the problem.

There are a wide range of questions that can be explored with the tool, and analysis can be performed at lots of different levels, so this is an ideal problem for all ages.

For younger students, you could draw out the idea of averaging repeated trials, and discuss which average might be most appropriate.

Older students might look at moving averages to see whether someone becomes better at estimating.

In order to compare two people's results, it might be necessary to introduce measures of spread - range and interquartile range, and for the oldest students, variance and standard deviation.

If different classes are working on this problem at the same time, there's a great opportunity for sharing data between them, and being able to work on bigger hypotheses like comparing students of different ages. If your school creates a large data set using this tool, please get in touch if you'd like to share it!

You could discuss different strategies that could be used to improve one's performance at estimating particular time intervals (such as reciting something at a steady speed or counting using a phrase exactly one second long). Then the class could design a statistical test to evaluate the different methods.

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You may like to read the article on Morse code before attempting this question. Morse's letter analysis was done over 150 years ago, so might there be a better allocation of symbols today?

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Florence Nightingale may be well known for her role as a nurse, but she was also an excellent mathematician, collecting and analysing data to help improve hospital conditions.

Reaction Timer

This problem offers you two ways to test reactions - use them to investigate your ideas about speeds of reaction.

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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