Apply Properties of Operations to Get Equivalent Expressions

Grade 6 — Expressions and Equations

In this lesson:

• Expand expressions using the distributive property
• Factor expressions by pulling out the common factor
• Combine like terms to simplify expressions

Learning Objectives for This Lesson

By the end, you will be able to:

1. Expand —
2. Factor — pull out the common factor:
3. Combine like terms — simplify to

You Already Know This: Mental Math Trick

How would you compute 4 × 37 mentally?

• Split it: 4 × 37 = 4 × 30 + 4 × 7
• = 120 + 28
• = 148

This is the distributive property — and it works with variables too.

The Distributive Property: Area Model

Each section gets multiplied by the factor outside.

The Distributive Property with Variables

• The factor outside multiplies every term inside
• Variables represent numbers, so all arithmetic properties apply
• If : and — same result for any

Expanding: Two Examples Step by Step

Example 1:

Example 2:

Write every multiplication step explicitly — don't skip steps.

Expanding with Two and Three Terms

Example 3:

Example 4:

Every term inside gets multiplied — including the constant.

Quick Check: Expand This Expression

Expand .

Try it before the next slide.

Expand 6(n + 4): Check Your Answer

Watch Out: Missing a Term When Distributing

Error: ✗ — forgot to multiply

Fix: draw arrows from 3 to every term inside:

Factoring Reverses the Distributive Property

• Expand:
• Factor:

Factoring: Find the GCF First

Procedure:

1. Find the GCF of all the coefficients
2. Divide each term by the GCF
3. Write:
4. Verify by expanding back — you should get the original

The GCF of the terms inside must equal 1 (fully factored).

Factor 24x + 18y Using the GCF

GCF of 24 and 18 is 6

Verify: ✓

GCF of 4 and 3 is 1 — fully factored.

Factoring Practice: Two More Examples

Factor : GCF = 4

Factor : GCF = 5

Always verify by expanding back to the original.

Quick Check: Factor This Expression

Factor .

Find the GCF, then write the factored form.

Factor 12x + 8: Check Your Answer

GCF of 12 and 8 is 4

Verify: ✓

What Makes Terms "Like Terms"?

Like terms share the same variable raised to the same power.

• — distributive property in reverse
• Like: and — same variable, same exponent
• Unlike: and — different variables; cannot combine

Combining Like Terms: Worked Examples

• — add coefficients
• — stays alone
• cannot combine — different types

Multi-Step Challenge: Expand Then Combine

Simplify

Step 1 — Expand:

Step 2 — Combine like terms:

Your Turn: Try These Three Problems

1. Expand
2. Factor
3. Simplify

Pause and work through each before the next slide.

Check Your Work: Practice Problem Answers

1.

2. GCF = 6:

3.

Key Takeaways for This Lesson

• Expand:
• Factor: find GCF → divide → verify by expanding
• Combine: same variable, same exponent → add coefficients

Draw arrows — don't miss a term
Use the GCF, not just any factor
Only like terms combine

Coming Up Next: Identifying Equivalent Expressions

Next lesson — 6.EE.A.4:

• Given two expressions, decide if they are equivalent
• Test equivalence by substituting values for the variable
• Today's skills — expanding and combining — are the key tools

Is equivalent to ? You'll find out next.