Cogito
Grade 6 Math · Chapter 5 · Lesson 3
Equivalent Expressions
Two recipes that always give the same number.
10 problems · about 18 minutes · 6.EE.A.3, 6.EE.A.4
What this lesson teaches
The child generates equivalent expressions using the distributive property and by combining like terms.
- Like terms combine; unlike terms do not.
- Distributing multiplies everything inside the brackets.
- Test two expressions by substituting the same value.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Letters for Numbers: If a = 8, what is 4a − 5?
Answer 27
Why 27.
Review — Exponents and Order of Operations: What is 5 + 2 × 3²?
Answer 23
Why 23.
Warm Up
Straightforward practice. Get the method working first.
4 problems4(n + 3) expands to 4n + what?
Answer 12
Why 4n + 12.
How can you check two expressions are equivalent?
Answer Put the same value into both.
Why Substituting the same value must give the same answer.
6n + 2n simplifies to how many n?
Answer 8
Why 6 + 2.
3(n + 5) expands to 3n + what?
Answer 15
Why 3 × 5.
Build It Up
The same ideas with more to keep track of.
2 problems2(3n) simplifies to how many n?
Answer 6
Why 2 × 3.
Does 3n + 2 simplify further?
Answer No. They are unlike terms.
Why n and 1 are different things.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsCombining: 4n + 3n simplifies to how many n?
Answer 7
Why 7n.
Distributing: 5(n + 4) expands to 5n + what?
Answer 20
Why 5n + 20.