This unit consolidates students' understandings of sine, cosine and tangent through practical experiences that apply trigonometry to a variety of outside-the-classroom situations.
This unit is a ‘hands on’ unit, meaning the focus is not on students learning new mathematical concepts, but on applying familiar concepts in practical situations. The aim of these experiences is to both convince the students that trigonometry can be used for practical purposes, and to consolidate the understandings they already have.
The learning opportunities in this unit can be differentiated by providing or removing support to students, and by varying the task requirements. Ways to support students include:
To increase the relevance of the learning in this unit, support students to use their clinometers and measure the height of relevant tall objects (e.g. school buildings, the marae, their house).
Te reo Māori kupu such as pākoki (trigonometry), ine-rōnaki (clinometer), koki (angle), ine-koki (protractor), teitei (altitude, height, high, tall), pātapa (tangent), aho (sine), whenu (cosine), ahopae (latitude), and weheruatanga o te ao (equator) could be introduced in this unit and used throughout other mathematical learning.
In this session the students are grouped in threes. Each group constructs a clinometer, uses it to measure angles, and prepares for a practical application of trigonometry to be undertaken in Session 2. You might show students a video of a clinometer being used first, to engage them in the unit.
The clinometer allows the students to measure the angle ABC, and therefore calculate the angle BAC. Subsequently, students can visit different locations around your school and use their clinometer to measure different angles. Usually it is best for one person to hold the clinometer in such a way that his or her eye looks along the ruler to the top of the object concerned, and a team member to read off the angle. Students can take turns doing this. The aim is for students to become proficient at measuring angles so that this is not an issue during Session 2. For each measurement, the students should sketch a diagram like the one above and calculate the angle BAC.
In this session students learn how to measure the height of one or more suitable objects, apply this knowledge to a practical task, and create a poster explaining how this procedure is carried out.
In this session we measure slightly more inaccessible objects, such as hills or trees surrounded by a lake.
The method here involves taking a reading from the point A, then moving a fixed distance towards the hill to a new point B - in this case exactly 100m - and then taking another reading. Perhaps surprisingly, by using a combination of algebra and trigonometry, we can find the height of the hill.
In this session the students measure the height of a nearby hill in the way outlined in Session 3. Once this is done each student prepares a poster that details the method and the calculations done in the practicum.
In this session students are given an insight into how trigonometry might be used, under the appropriate circumstances, to measure the height of the moon. But first the students need to be reminded what ‘latitude’ means, and what the moon rising or setting over the horizon means.
A friend of yours is at the equator, at E. You are at P, at latitude 89 degrees. Your friend and you are in phone contact. Accordingly you are able to establish that, just as the moon is directly overhead for your friend, it is just setting for you. You know that the radius of the earth is approximately 6000km. What is the distance, d, from the earth to the moon?
Dear families and whānau,
Recently we have been investigating how trigonometry can be used to find the height of a tall building or tree. Ask your child to share this learning with you. Together, find the height of a tall building or tree in your local area.
Printed from https://nzmaths.co.nz/resource/trigonometric-applications-outside-classroom at 5:18pm on the 26th April 2024