OpenLab Project: Explain something to the class

Part 1 (due 10/2/23)

Claim a topic by choosing from the list below and responding to this post with a comment telling us which topic you chose.

ONLY ONE PERSON CAN CHOOSE EACH TOPIC (first come, first served)!

List of topics

1. What are the four main types of numbers, from counting numbers up through the number line, that appear in secondary school mathematics? What makes each type of number different from the previous type? What kinds of problems can/can’t we solve with each type of number?
2. Mathematicians have a complicated definition of real numbers in terms of axioms, but that is not an appropriate definition for secondary school students. Explain how to define real numbers so that secondary students can understand.
3. Starting with the definition of number, and using only the basic knowledge and skills necessary for the definition of number, explain (using an example) how to locate a particular fraction on the number line.
4. Starting with the definition of number, and using only the basic knowledge and skills necessary for the definition of number, explain how to find the sum of two numbers on the number line.
5. Explain the difference between a multiple and a divisor, with examples. Explain the meaning of GCD and LCM, with examples.
6. Explain what a linear combination of two numbers is, with examples. What is the connection between linear combinations and the GCD?
7. The Euclidean Algorithm provides a method for finding the GCD of two numbers. Explain how the Euclidean Algorithm works, using an example. Then, show how you can use the Euclidean Algorithm to write the GCD of two numbers as a linear combination of the two numbers.
8. In the real world, we can show that two objects are the same size and shape by physically putting one on top of the other. In the mathematical world of geometric shapes, however, we can’t pick things up and move them around as we can in the physical world. Explain in detail how we show that two objects are the same size and shape in the world of geometry.

Part 2 (due 10/11/23)

Instructions.

• Write a new post explaining your topic in your own words (300 words minimum).
• Give your post a title that will help others find it.
• Select the category “Student Work” for your post.
• Your post should include at least 2 images (you can always use photos of your own work without concern, otherwise please follow copyright guidelines when finding/using images on the internet).
• You can imagine that your audience is a group of students in MEDU 3000 on the first day of the semester, OR that your audience is a class of bright, motivated secondary school students.