The purpose of this activity 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.
This activity assumes the students have experience in the following areas:
The problem is sufficiently open ended to allow the students freedom of choice in their approach. It may be scaffolded with guidance that leads to a solution, and/or the students might be given the opportunity to solve the problem independently.
The example responses at the end of the resource give an indication of the kind of response to expect from students who approach the problem in particular ways.
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 following prompts illustrate how this activity can be structured around the phases of the Mathematics Investigation Cycle.
Introduce the problem. Allow students time to read it and discuss in pairs or small groups.
Discuss ideas about how to solve the problem. Emphasise that, in the planning phase, you want students to say how they would solve the problem, not to actually solve it.
Allow students time to work through their strategy and find a solution to the problem.
Allow students time to check their answers and then either have them pair share with other groups or ask for volunteers to share their solution with the class.
The student calculates, with guidance, values in standard form, giving an answer to an appropriate degree of accuracy.
Prompts from the teacher could be:
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The student calculates values in standard form, giving an answer to an appropriate degree of accuracy. The student incorporates wider aspects of the context to make a valued judgement.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/bridging-gaps at 8:53pm on the 26th February 2024