Bridging the Gaps

Purpose

The purpose of this multi-level task is to engage students in using their knowledge of place value, standard form and rounding, to solve a problem involving a range of orders of magnitude.

Description of Mathematics

The background knowledge and skills that need to be established before and/or during this task are outlined in the diagram below:

This task may be solved following with guidance as to the steps to take and rounding decisions to make, or with greater independence, encourage the students to make decisions around appropriate accuracy. The approach should be chosen in sympathy with their skills and depth of understanding.

Activity

Task: An engineer is designing a bridge that is to stretch 2.434 km. She wants the bridge to be constructed from aluminium or from steel. Metals expand or contract with a change in temperature.

The rule to find the total length a metal will expand by is the product:

original length x change in temperature x expansion constant

The expansion constant for aluminium is 2.22 x 10-5 per °C 

The expansion constant for steel  is 1.30 x 10-5 per °C.

While she would prefer to use Aluminium because it is much lighter, her design can only allow for up to 2.8 m of expansion for the full length of the bridge. If the local climate experiences temperatures that range from an average of -10 °C (winter nights) to mid 30's of °C (midday summer), which material should the engineer choose for the bridge? Comment on any rounding decisions you made.

The procedural approach (show more)

  • The student is able to calculate, with guidance, values in standard form, giving an answer to an appropriate degree of accuracy.

The conceptual approach (show more)

  • The student is able to calculate values in standard form, giving an answer to an appropriate degree of accuracy. The student is able to incorporate wider aspects of the context to make a valued judgement.

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