Properties of Operations with Variables
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Grades 7–8 Math · Teaching handout
Properties of Operations with Variables
Teaches the commutative, associative, and distributive laws, identity, and inverse, written with letters, and that they hold for every number, negative numbers too.
Print handout
Your first print is free, with no sign-in. Then 10 sheets a month with a free account. Prints on Letter paper, or print on A4.
Print the answer key for Try it together
- Grades
- Grades 7 and 8
- Pages
- 1
- Time
- About 15 minutes
- Answer key
- Included, for Try it together
- Printing
- Tinted accents, also fine in black and white
What is on a handout
- The big idea: the rule, in a few short sentences.
- Watch me: worked examples, each with why it changes as it does.
- Watch out: the mistakes children often make, struck through beside the right answer.
- Try it together: a few items or problems to do as a class, with an answer key.
- On your own: the practice sheet that comes next.
How to teach with it
- Test a law by putting a negative number and a fraction in for the letters. If it fails once, as 7 − 2 and 2 − 7 do, it is not a law. At Grade 8, name the property behind each step of simplifying or solving: doing the same to both sides keeps an equation true, and dividing an inequality by a negative number turns its sign around.
- Read the big idea aloud, then work through Watch me together, saying why each one changes.
- Ask the class to find the mistake in each Watch out before you show the answer.
- Do Try it together as a class, check it with the answer key, then hand out the practice sheet.
Practice worksheets
After the handout, in this order: the main practice sheet first, then more practice, then quick checks.
