Math 1 · Lesson 2

Commute, Associate, Distribute

The properties are named after ordinary words. If you know what the word means, you know what the numbers are allowed to do.

About 25 minutes Say the everyday word, then the math

The big idea

Only addition and multiplication pass every test: they commute, they associate, and multiplication distributes. Subtraction and division do not. That is why algebra treats addition and multiplication as its two operations, and puts the other two in disguise: subtracting is adding the opposite, and dividing is multiplying by the reciprocal (Lesson 1). Once they are in disguise, every property works again.

The parts of this lesson

Each part is its own short page. Go in order, or pick the one you need.

1The Words We UseThe vocabulary for this lesson, in one place.Start here 2How to use this pageTry each problem yourself first. 3Warm-up: three ordinary wordsBefore any math, write one sentence for each. 4The scoreboard: which operations pass?Test each property with numbers. 5Practice ProblemsTry them, get help one step at a time, then print how it went.

Printables

The worksheet has Parts A to E with an answer key. The lesson plan has the 25-minute timeline, the vocabulary table, the scoreboard, and the misconceptions to listen for.

Study guide (PDF) Download the Worksheet (PDF) Lesson Plan for Grown-Ups (PDF)

Where this goes next

Previous lesson: The Do-Nothing Numbers and Their Undo PartnersIdentity and inverse: 0 and 1, opposites and reciprocals, and the disguise that makes every property work. Next lesson: Step One, Translate Subtraction and DivisionBefore you can solve, turn every subtraction into adding the opposite and every division into multiplying by the inverse. Then multiply fractions, handle negatives, and reveal the invisible 1s. Back to the Math 1 mapEvery Math 1 lesson, in course order. Tell us what you thoughtA few quick questions about this lesson. It takes a minute, and it is how the lesson gets better.