Equivalent Expressions

Equivalent Expressions

Why do we write the same thing different ways?

​First, a quick number talk

​Rules for number talks:

• ​No writing! This is meant to be a discussion, so no writing.

• ​No scratch work! The problem is supposed to be a way for you to think through why you would do some of the scratch work.

• ​Everyone provides an answer, regardless if you think it's right or wrong.

• ​If there's an agreement on a process, we can agree. The idea is to come up with multiple ways to break down a problem.

​Here's the problem...

​What is 26 x 5?

​When you have an answer, just put a right fist over your heart. If you have more than one way you see how to do it, start putting up how many fingers with the different ways you see it.

​An Old Friend

• ​I'm going to ask a question here, when you think of PEMDAS, what is the operation that confuses you the most?

​Equivalence

• ​Take a look at the explanation on the right.

• ​In both examples, all of the intermediate steps are all considered equivalent expressions to each other.

• ​When we determine the value of an unknown, we are determining an equivalent expression to the original problem.

​Order of Operations and Equivalence

​How are the two related? We're going to take a look at the textbook and do a reading exercise today. If you've read section 1.1, I'm going to give you a five step exercise on how to read a mathematics textbook.

1. ​What is your goal in reading this section?

2. ​Skim it! What looks familiar? What do you think you'll need to pause on?

3. ​Don't skip the examples! Work through them, noting where you had to stop and look to the book for guidance.

4. ​A 10 page read can take a half an hour to an hour if done properly.

5. ​Go back and see if you can answer the questions you asked.