The purpose of this activity is to engage students in using deductive steps, including the applications of Pythagoras' theorem to solve a problem.
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: A land based windsurfer is being constructed by affixing a mast and sail to a skateboard. The sail has a bar fixed to the side of the mast and going across the sail as shown in black in the diagram.
The sail is a right angled triangle with a base of 1m and the length of the hypotenuse is 2m. The bar starts at the vertex of the sail as shown and meets the hypotenuse at right angles.
Find the length of the bar.
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 constructs a scale diagram to solve the problem to a reasonable degree of accuracy and uses Pythagoras' theorem to verify their result.
Click on the image to enlarge it. Click again to close.
The student solves a right angled triangle problem using trigonometric ratios and Pythagoras' theorem.
Click on the image to enlarge it. Click again to close.
The student solves a right angled triangle problem using Pythagoras' Theorem algebraicly and expresses the length with specified accuracy.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/how-long-bar at 8:53pm on the 26th February 2024