Grouping Symbols: Evaluate the Group First

Lesson 1 of 2: Parentheses and Placement

In this lesson:

• What parentheses tell you to do
• Evaluate expressions with one set of grouping symbols
• See how placement changes the result

Learning Objectives

By the end of this lesson, you should be able to:

1. Explain that grouping symbols indicate which part of an expression to evaluate first
2. Evaluate a numerical expression containing one set of grouping symbols by computing the grouped part first
3. Recognize that the same numbers arranged with different grouping can yield different values

A Math Disagreement

Parentheses Mean "Compute This First"

• Step 1: Evaluate the group: (2 + 3) = 5
• Step 2: Continue with that result: 5 × 4 = 20

Example Pair 1: Parentheses Determine What Goes First

Expression A: (2 + 3) × 4

• Group: (2 + 3) = 5 → becomes: 5 × 4 = 20

Expression B: 2 + (3 × 4)

• Group: (3 × 4) = 12 → becomes: 2 + 12 = 14

Same numbers. Same operations. Different answers.

Example Pair 2: Another Pair to Examine

Expression A: (9 − 3) × 2

• Group: (9 − 3) = 6 → becomes: 6 × 2 = 12

Expression B: 9 − (3 × 2)

• Group: (3 × 2) = 6 → becomes: 9 − 6 = 3

Both groups equal 6 — but the answers are 12 and 3.

Your Turn

Evaluate these expressions — write the intermediate step first:

1. (6 + 4) × 3 = _____ × 3 = _____
2. 6 + (4 × 3) = 6 + _____ = _____

Don't skip the middle line — show the contracted expression before the final answer

Quick Check

Evaluate: (7 + 5) ÷ 4

Write the intermediate expression, then the final answer.

Think before the next slide...

Placement Changes the Value

Moving the parentheses changes which operation goes first — and changes the answer.

Step by Step: (5 + 3) × 6

Step 1: Identify the group
Parentheses mark (5 + 3)

Step 2: Evaluate the group
5 + 3 = 8 → expression becomes: 8 × 6

Step 3: Evaluate the remaining expression
8 × 6 = 48

This matches: "Add 5 and 3, then multiply the sum by 6"

Step by Step: 5 + (3 × 6)

Step 1: Identify the group
Parentheses mark (3 × 6)

Step 2: Evaluate the group
3 × 6 = 18 → expression becomes: 5 + 18

Step 3: Evaluate the remaining expression
5 + 18 = 23

This matches: "Multiply 3 by 6, then add 5 to the product"

Quick Check

Which expression matches: "Multiply 4 and 5, then add 3"?

• A: (4 × 5) + 3
• B: 4 × (5 + 3)

Evaluate both to confirm — what are the two answers?

From Words to Expression

Description: "Subtract 4 from 10, then multiply by 3"

What must be grouped? → The subtraction: (10 − 4)

Write the expression: (10 − 4) × 3

Evaluate:

• Group: (10 − 4) = 6 → becomes: 6 × 3
• Result: 6 × 3 = 18

Insert the Parentheses Challenge

Start with: 12 − 4 + 2 (no parentheses — evaluate as written: 10)

Can you insert one set of parentheses to produce:

• Target 6 → try: _______________
• Target 10 → already achieved — what other placement also gives 10?

There are only a few places to put one set of parentheses — try them all

Key Takeaway: Grouping Changes the Value

• Parentheses tell you: evaluate this part first
• Moving parentheses changes which operation goes first
• Same numbers + same operations + different grouping = different answers
• The first action in a verbal description is what to group

Key Takeaways

✓ Parentheses say: evaluate the group first, then continue with its value
✓ Always show the intermediate step — replace the group with its value before the next operation
✓ Same numbers with different grouping → different answers

Watch out: Ignoring parentheses and working left to right gives the wrong answer
Watch out: Parentheses are grouping symbols — they do NOT mean multiply

Coming Up: Lesson 2 of 2

In the next lesson, you will:

• Meet two more grouping symbols: brackets [ ] and braces { }
• Learn to evaluate nested expressions — groups inside groups — from the inside out
• Write expressions with multiple grouping levels

All three symbols follow the same rule: evaluate what's inside first