Cogito
Grade 6 Math · Chapter 5 · Lesson 6
Expanding Brackets
The distributive property, forwards.
10 problems · about 18 minutes · 6.EE.A.3, 6.NS.B.4
What this lesson teaches
The child expands a product over a sum and recognises the result as an equivalent expression.
- A number outside a bracket multiplies every term inside it.
- The area model shows why: the rectangle splits into two pieces.
- Expanding and pulling out a common factor are the same move in opposite directions.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Combining Like Terms: Simplify 6n + 3n. How many n?
Answer 9
Why 9n.
Review — Writing Expressions from Words: Evaluate 4n − 3 when n is 5.
Answer 17
Why 17.
Review — Equivalent Expressions: 4(n + 3) expands to 4n + what?
Answer 12
Why 4n + 12.
Warm Up
Straightforward practice. Get the method working first.
3 problemsExpand 5(n + 3). What is the number term?
Answer 15
Why 5n + 15.
Expand 3(n + 5). What is the number term?
Answer 15
Why 3 × 5.
Expand 7(n + 2). What is the number term?
Answer 14
Why 7 × 2.
Build It Up
The same ideas with more to keep track of.
2 problemsIs 3(n + 4) the same as 3n + 4?
Answer No. The 4 must be multiplied too.
Why Try n = 1 in both.
Evaluate 2(n + 6) when n is 4.
Answer 20
Why Brackets first.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Check: Expand 5(n + 2), then evaluate when n is 3.
Answer 25
Why 25.
The Constant: In 6(n + 5), what number does the 6 multiply the 5 by to give?
Answer 30
Why 30, so the expansion is 6n + 30.