This is an open-ended task involving calculation, measures and estimation. Students are given some data about the density of various materials. They are then asked to decide whether or not they could lift various objects.

Overview of task

This is an open-ended task involving calculation, measures and estimation. Students are given some data about the density of various materials. They are then asked to decide whether or not they could lift various objects.

Strand

Nunber and Measures

Prior knowledge

There is little or no prerequisite knowledge beyond what students will be familiar with from GCSE mathematics. They will need to be able to make reasonable estimates of the volume of material contained in the suggested objects and what a sensible lifting weight might be. Students may use formulae for volumes of common 3D shapes, and knowledge of Standard Form may also be useful.

Relevance to Core Maths qualifications

•AQA

•C&G

•Eduqas

•Pearson / Edexcel

•OCR

Suggested approaches

This task could take about an hour, is suitable for group work and could be used at any time within the course. Simply distribute the data and question sheets to each pair, and describe the format in which you would like results to be presented; brief presentations from each pair to the whole class might work well, and would provide an opportunity to discuss assumptions and calculations.

Resources/documentation

The data sheet includes density information for a large number of common (and not so common!) materials. The question sheet suggests objects that students should consider.

Relevant digital technologies

Students could use spreadsheets to calculate the volume and mass of the standard 3D shapes that constitute the suggested objects.

Possible extensions

Students could challenge each other to estimate and then calculate the mass of other objects; this could become a game, with a points system based on percentage error. They could also use scales to weigh objects and check the accuracy of estimates.

Acknowledgement

Developed by the mathematics department at Queen Elizabeth School, Dorset.