Unit 1: Measurement

In this lesson I provide a quick summary of the narrative that we'll follow in the course, and give some context for how this course is situated in the broader narrative of mathematics.

Lesson 1 - What is Measurement?

In this lesson I explain my definition of measurement, and talk about some of the sorts of things that we can measure. Then I give you some measurement challenges to go and do yourself.

Lesson 2 - Proportionality and Similar Triangles

In this lesson, I introduce the concepts of proportionality and similar triangles, two valuable tools for measuring.

Lesson 3 - The Tangent Ratio

In this lesson, we'll take another approach to measuring a tree which doesn't depend on it's shadow (an approach that work work on a cloudy day).

Lesson 4 - Sine and Cosine

In this lesson we'll use shadows and slopes to understand the sine and cosine ratios.

Lesson 5 - SOH CAH TOA (Right Triangle Trigonometry)

Lesson 6 - Applications of Right Triangle Trigonometry

In this lesson we'll look at how we can use the three trigonometry ratios--sine, cosine and tangent--that we learned about in the previous lesson to solve application problems related to real-world situations. Be sure to watch the first video, the others are optional (but highly recommended!) for now.

Lesson 7 - The Pythagorean Theorem

In this lesson we will look at a proof of the Pythagorean Theorem and then work through some examples and application problems.

Lesson 8 - An Introduction to Area

In this lesson we begin to look at how we can find the areas of some basic shapes including rectangles, triangles and parallelograms. We also begin to look a bit more closely at some of the assumptions that we're making.

Lesson 9 - Circles

A quick introduction to circles.

Unit 1 Readings

The readings for this unit will not focus on the concept of measurement specifically. Rather, they will focus on the issues of sexism and racism in mathematics in general. To me it's important to draw students' attention to this issue at the beginning of the course, so that they have context for why we don't see more female/BIPOC mathematicians show up in a typical math class. We will also highlight and celebrate some of the work done by female/BIPOC mathematicians later in the course.

https://blogs.scientificamerican.com/roots-of-unity/that-time-it-took-a-student-44-years-to-get-her-degree-because-she-was-a-woman/

https://www.agnesscott.edu/lriddle/women/granvill.htm

https://www.nytimes.com/2019/02/18/us/edray-goins-black-mathematicians.html

https://www.theguardian.com/commentisfree/cifamerica/2012/apr/12/black-mathematicians-john-derbyshire-fields-medal

Unit 1 Reflection

Write a one-paragraph response to each of the following prompts:

How is taking this class online going for you so far? What is going well? What do you find challenging? What would you like to see changed (give any suggestions you have)?
How did this unit advance your understanding of trigonometry and measurement? What did you know already? What did you learn that you didn't know before? What would you keep/change about the unit?
What did you learn about issues of DEI (diversity, equity and inclusion) in the field of mathematics from the readings? What did you find particularly interesting/disturbing? What do you think the mathematical community (including teachers like myself) needs to do to resolve these issues? Give examples.
What did you learn about assumptions in this unit? Is making assumptions good? Bad? Both? Neither? What kind of assumptions did we make? What kinds of assumptions are good to make? Bad to make? Why are assumptions necessary?

Unit 1 Practice Quiz

Practice Quiz 1a

Practice Quiz 1a - Solutions

Practice Quiz 1b

Practice Quiz 1b - Solutions

Solutions to Practice Problems

Below are videos showing solutions and hints to some of the practice problems.

Collaborative solutions document - F23

Selected answers to some of the practice work

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