Lesson 7.2
If We Can Measure the Angle, We Can Measure Anything
Focus: solving right triangles — class table as estimation anchor — clinometer design and build — field measurement
This lesson puts the discovery from 7.1 to work. Day 1 builds fluency with right triangle trig — always estimating from the class table before reaching for a calculator — and culminates in the clinometer design challenge. Day 2 takes the devices into the field.
The habit of estimating from the class table before using a calculator matters. It reinforces that trig values are predictable quantities tied to angles, not mysterious outputs. Require a written estimate before every calculator use.
The clinometer day produced dramatically different results in the two classes where it was taught. Period 4 — where most groups had built functional devices, thought carefully about how to use them, and could set up the diagram to measure the gym ceiling — was exactly what the lesson was designed to produce. Period 6 was a different story: devices lacked precision, bases were not held parallel to the floor, angles were marked only every 10°, thick rulers replaced string, and many students had not thought through how their device would actually work before arriving in the gym. They seemed lost. They rushed the project sheet. The outcome was disappointing.
The difference between the two periods was not ability. It was ownership. Period 4 treated the clinometer as a scientific instrument they had built and were proud of. Period 6 treated it as a task to complete. That distinction — between pride in work and compliance with a requirement — is not reliably produced by the task itself. It is produced by the culture around it. Address this explicitly at the start of Day 2: precision matters, your device is an instrument, the accuracy of your answer depends entirely on the care you brought to building and using it.
The percent-error question on the back of the project sheet is worth defending. Better to give students time to struggle with it on their own before providing any scaffolding. This question asks: if your angle measurement was 1° off, what height would you have calculated? What percent error does that create? Would a 1° error always create the same percent error? The last part is the richest question and the most commonly skipped. Give it time.