Week 4: Grouping symbols, the distributive idea, and surface area

Field Book

13 to 16

Due

Test 2 due

Method

Paper first, every step

Brackets stack up this week and the distributive idea earns its name: what multiplies a group multiplies every member of it. Surface area joins in, which is nothing but area applied to every face of a solid, one face at a time.

What you have to be able to do

Simplify expressions with nested grouping symbols
Distribute a multiplier across a group
Evaluate an expression by substitution
Find the surface area of a rectangular solid

The procedures

Nested grouping

Work from the innermost symbols outward.
Finish everything inside a bracket before touching what is outside it.
Rewrite the whole line after each layer so nothing gets dropped.

The distributive idea

a(b + c) is ab + ac: the outside multiplies every inside term.
Signs ride along with their terms when you distribute.
Distributing a minus flips every sign in the group.

Surface area

A solid is wrapped in faces; surface area is the sum of their areas.
Count the faces first. A box has six, in three matching pairs.
Find each face’s area, then add. Square units, always.

Worked

WORKED

Simplify 5 + [2(3 − 8) − (4 − 9)].
Inside first: 3 − 8 is −5, and 4 − 9 is −5.
So it is 5 + [−10 + 5], which is 5 + (−5).
ANSWER: 0

WORKED

Find the surface area of a box 4 by 3 by 2.
Three pairs of faces: 4 × 3, 4 × 2, and 3 × 2.
2(12) + 2(8) + 2(6) is 24 + 16 + 12.
ANSWER: 52 square units

Terms

Term	Meaning
variable	the letter standing in for the missing value
substitution	trading a letter for what it equals
surface area	the total area of every face of a solid

Check yourself

1. Distribute: 6(x + 4)

2. Evaluate 3a − b for a = 5 and b = 7

3. Find the surface area of a cube with edge 3

reveal answers

6x + 24 · 8 · 54 square units

This page is the summary, not the lesson. The full working, every step of every example, is on the board in class. Come here to remember what the week was about. Go there to learn how it is done.