Percent and Unit Conversion

Lesson 2 of 2: 6.RP.A.3

In this lesson:

• Find a percent of a quantity and find the whole given part and percent
• Use benchmark percents for mental calculation
• Convert measurement units using ratio reasoning

What You Will Learn Today

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

1. Find a percent of a quantity by treating the percent as a rate per 100
2. Find the whole given a part and the percent, using a tape diagram or algebra
3. Apply benchmark percents to compute tips and taxes mentally
4. Convert measurement units by multiplying by the correct conversion factor
5. Execute multi-step rate conversions by chaining two conversion factors

Opening Puzzle: The Restaurant Bill

The bill is 40 dollars. You want to leave a 15% tip.

• You know 15% is less than 40 dollars
• But how much less? What is 15% in dollars?

Think about what "15 out of every 100" means as a ratio...

Percent as a Ratio Scaled Down

"Fifteen percent" means 15 out of every 100 dollars goes to the server.

Scale the ratio 15:100 to a base of 40:

Scale factor: . Both quantities scale the same way.

The Percent Symbol Means Per Hundred

The % symbol is shorthand for "per 100."

Every percent calculation is a ratio calculation:

First step, always: rewrite % as a fraction before multiplying.

Visualize Percent on a Double Number Line

Find anchor points → subdivide → read 30% = 24

Fraction Method and Number Line Agree

Find 30% of 80:

Method 1 — Fraction:

Method 2 — Number line:

Both methods scale the ratio 30:100 to a base of 80.

Five Benchmarks for Mental Calculation

Combine benchmarks: 15% = 10% + 5% = 4 + 2 = 6 dollars on a 40-dollar meal

Apply Benchmarks: Tip and Tax

15% tip on a 40-dollar meal:

7% sales tax on a 60-dollar purchase:

No calculator needed — benchmarks and mental arithmetic.

Check-In: Find 25% of 60

What is 25% of 60?

• Which benchmark row applies?
• Compute without a calculator.

Write your reasoning: 60 ÷ 4 = ___

Find the Whole Using a Tape Diagram

"15 is 25% of what number?"

Draw a tape divided into 4 equal parts (one for each 25%):

Algebraic check:

Tape vs. Algebra for Inverse Problems

"12 is 75% of what?" — tape method:

"12 is 30% of what?" — algebra for non-benchmark:

Benchmark percents → tape. Non-benchmark percents → algebra.

Guided Practice: Finish This Calculation

"12 is 30% of what number?"

Complete the algebraic steps:

Step 1: Multiply both sides by

Finish the computation and check your answer.

Two Percent Errors and Their Fixes

Error 1: Multiply 30 × 80 = 2,400 (wrong)
→ Fix: — convert first

Error 2: Answer "15 is 25% of what?" with
→ Fix: Draw the tape — label given vs. unknown first

Check: 30% of 80 must be less than 80.

Unit Conversion Builds on Ratio Reasoning

12 inches = 1 foot

Write the equivalence as two fractions:

Multiplying by 1 preserves value. Choosing the right form of 1 changes the unit.

A Conversion Factor Always Equals One

Rule: Place the unit to eliminate in the denominator.

Wrong units in the answer = signal to flip the factor.

Unit Cancel Confirms the Right Setup

5 feet → inches:

60 inches → feet:

Units in the answer confirm the setup.

Apply the Direction Rule: Three Conversions

Apply the direction rule — write cancel marks on each:

Chain Two Factors for Rate Conversion

Convert 60 mi/hr to ft/sec — chain two factors:

Cancel mi against mi; cancel hr against hr. What remains is ft/sec.

Unscaffolded Transfer: Convert 5 m/sec

Convert 5 meters per second to kilometers per hour.

Conversion facts:

• 1 km = 1000 m
• 1 hr = 3600 sec

Write both conversion fractions. Apply in sequence. Confirm units.

No setup is provided — produce the full conversion.

Key Ideas from This Lesson

✓ Percent = ratio with denominator 100; convert % to fraction before multiplying

✓ Benchmarks (10%, 25%, 50%) enable fast mental calculation

✓ Find the whole → draw tape, label given vs. unknown, then compute

✓ Conversion factors equal 1; put the unit to eliminate in the denominator

30% of 80 ≠ 30 × 80 — convert % to fraction first

Wrong units in answer → flip the conversion factor

One Engine Behind All Four Sub-Parts

All four chunks of 6.RP.A.3 use one move: scale a ratio without changing the relationship.

In Grade 7, you'll name this "proportional relationship."