R. Pwy Dunnit
| Introduction |
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| An activity on data handling, involving an investigation of ratios of personal measurements. Children first collect data on their own personal measurements and find ratios (decimals from calculations), using appropriate rounding. They then take detailed data for the whole class and reduce it to a range and a single representative value. These are used to find a new value appropriate to the solution of the problem posed in the introduction. |
| This activity has two episodes. Each episode consists of an introduction, paired or group work and whole class sharing. The session must finish with a whole class reflection phase, regardless of how far the class has got. |
| Episode 1: Personal measurement ratios |
| Children find how to use a hat and a glove left at the scene of a burglary to estimate the height of the intruder(s). Two people, one short and one tall, were seen nearby. They set out to look for realistic estimates of ratios. Working in groups, children record each other’s heights, head circumferences and hand lengths. They use calculators to get height:head and height:hand-length ratios. In the sharing phase the ratios are collected as they appear on the calculators, and then appropriately rounded or truncated – which is easier – to two decimal places. The objective is to obtain the median ratio, or the mode ratio, and the full range of values for the ratios. |
| Episode 2: the ratios to help solve the original problem |
| The children are now set the inverse task of using the representative ratio to decide the most likely height of the person to whom the hat and glove belong. This can either be done using a simple whole-class value, or using a wider range, and comparing what emerges from the two ratios. |
| Reflection |
| Children go over the steps of moving from understanding a problem to systematically collecting data and rationalising it. They may talk about the power that working with ratios gives and the implications of converting from ratios to real-life measurements. They may also discuss how mathematics can be related to real-life problems. |
| BEFORE YOU TEACH |
| Avoid spending too long on measurements. Demonstrate and help children with these and focus on the meaning of the ratios they find on the calculators. When collecting the data, truncating or rounding to two decimal places will keep the focus on the meaning of the ratios. |