Customary Conversions Slides
Grade 6 Mathematics • Lesson 1-6
40-Minute Workshop
Convert Customary
Measurement Units
Using Unit Ratios, Ratio Tables & Visual Tape Diagrams to Scale Length, Weight, and Capacity
Lesson Objective
I can use ratio reasoning and unit ratios to convert between customary units of measurement in real-world contexts.
6.RP.4 6.RP.5
Foundation • Minutes 0–6
What is a Unit Ratio?
Compare to 1 Unit
Length
1 foot (ft) 12 inches (in.)
1 yard (yd) 3 feet (ft)
1 mile (mi) 5,280 feet
Unit Ratio: 12 in : 1 ft
Weight
1 pound (lb) 16 ounces (oz)
1 ton (T) 2,000 pounds
Unit Ratio: 16 oz : 1 lb
Capacity
1 cup (c) 8 fl oz
1 pint (pt) 2 cups
1 quart (qt) 2 pints
1 gallon (gal) 4 quarts
Unit Ratio: 8 fl oz : 1 c
Talk About It: What is the unit ratio representing pints to quarts?
2 pints : 1 quart
Method 1 • Minutes 7–14
Convert Larger to Smaller: Tape Diagrams
Problem: 6 pints = ? fluid ounces
Step 1: Start with 6 equal sections (1 pint each) Total: 6 pints
1 pint
1 pint
1 pint
1 pint
1 pint
1 pint
Step 2: Replace each pint with 2 cups (Unit ratio 2 c : 1 pt) 6 × 2 = 12 cups
2 cups
2 cups
2 cups
2 cups
2 cups
2 cups
Step 3: Replace each cup with 8 fl oz (2 cups = 16 fl oz per bar) 6 × 16 = 96 fl oz
16 fl oz
16 fl oz
16 fl oz
16 fl oz
16 fl oz
16 fl oz
Big Idea: When converting from a larger unit to a smaller unit, the numerical value increases because more smaller units fit into the space!
6 pt = 96 fl oz
Method 2 • Minutes 15–22
Multi-Step Equivalent Ratios
Marco's Fertilizer: 12 gallon = ? cups
1
Gallons → Quarts
Unit ratio: 4 quarts per 1 gallon
4 quarts1 gallon = q12 gal
12 × 4 = 2 quarts
↓ Forward to Step 2
2
Quarts → Pints
Unit ratio: 2 pints per 1 quart
2 pints1 quart = p2 quarts
2 × 2 = 4 pints
↓ Forward to Step 3
3
Pints → Cups
Unit ratio: 2 cups per 1 pint
2 cups1 pint = c4 pints
4 × 2 = 8 cups
✓ Final Answer
Direct Conversion: Marco needs 8 cups of fertilizer to mix with the soil. 12 gal × 16 cups1 gal = 8 cups
Inverse Operations • Minutes 23–29
Convert Smaller Units to Larger Units
Divide or Multiply by Unit Fraction
Example A: Length
Convert 24 inches to yards
Step 1: Inches to Feet 24 in. × 1 ft12 in. = 2 feet
Step 2: Feet to Yards 2 ft × 1 yd3 ft = 23 yard
Result: 24 in. = 23 yard
Example B: Weight
Hippopotamus: 9,920 lb to tons
Step 1: Unit Ratio Setup 2,000 lb1 ton = 9,920 lbt tons
Step 2: Multiply by Unit Fraction 9,920 × 1 ton2,000 lb = 4.96 tons
Result: 9,920 lb = 4 2425 T = 4.96 tons
Remember: Smaller unit → Larger unit = Numerical value gets smaller.
Check reasonableness before moving on!
Real-World Application • Minutes 30–35
The Hydration Challenge
Think-Pair-Share
Joaquin's Daily Goal
On Tuesday, Joaquin drank 6 glasses of water, each containing 10 fluid ounces. His goal was to drink 2 quarts. How many more fluid ounces does he need to drink to reach his goal?
Step 1: Water Drank
6 glasses × 10 fl oz
= 60 fl oz
Step 2: Goal in fl oz
2 qt × 2 pt × 2 c × 8 fl oz
= 64 fl oz
Step 3: Difference
64 fl oz − 60 fl oz
= 4 fl oz needed
Partner Discussion: Would it be faster to convert both values to cups first? Why or why not?
60 fl oz = 7 12 c vs 2 qt = 8 c
Strategy Toolkit
Which Operation Do I Use?
Golden Rules
Larger → Smaller Unit
→ MULTIPLY (×)
- • Units get smaller, so you need more of them.
- • Unit Ratio: smaller unit1 larger unit (e.g., 12 in.1 ft )
- • Example: 34 yd × 36 in.1 yd = 27 inches
N(small) = N(large) × Unit Ratio
Smaller → Larger Unit
→ DIVIDE or MULTIPLY BY FRACTION
- • Units get larger, so you need fewer of them.
- • Unit Fraction: 1 larger unitsmaller units (e.g., 1 yd3 ft )
- • Example: 24 in. × 1 yd36 in. = 2436 = 23 yard
N(large) = N(small) × 1conversion factor
Ready for independent and partner practice? Open your worksheet to Page 1!
Wrap-Up • Minutes 36–40
Exit Ticket & Pause to Reflect
Check for Understanding
Quick Solve
How many yards are in 54 inches?
Step 1 (Inches to Feet): 54 ÷ 12 = 4 12 ft (4.5 ft)
Step 2 (Feet to Yards): 4 12 ÷ 3 = 1 12 yd (1.5 yd)
Direct Unit Fraction: 54 × 1 yd36 in. = 1 12 yd
Record your work on the exit ticket slip.
Pause and Reflect
"Why does the number of fluid ounces (96) become greater than the number of pints (6), even though the actual amount of liquid has not changed at all?"
Write 1–2 complete sentences explaining the relationship between unit size and unit count.
Be prepared to share with your shoulder partner!
Great mathematical reasoning today! Please submit your completed practice sheet before dismissal.
Customary Conversions Worksheet
Grade 6 Mathematics • Ratios & Rates
Convert Customary Measurement Units
Apply unit ratios, ratio tables, and visual tape diagrams to solve conversions.
Name:
Date:
Period:
Length
1 ft = 12 in. • 1 yd = 3 ft • 1 mi = 5,280 ft
Weight
1 lb = 16 oz • 1 ton = 2,000 lb
Capacity
1 c = 8 fl oz • 1 pt = 2 c • 1 qt = 2 pt • 1 gal = 4 qt
A Visual Models: Bar / Tape Diagrams
Show how larger units partition into smaller units
1. Use the tape diagram below to convert 4 pints to fluid ounces. Complete each step.
Step 1: 4 Pints (4 equal sections) Total: 4 pints
1 pint
1 pint
1 pint
1 pint
Step 2: Replace each pint with cups (Unit ratio 2 cups : 1 pint) Total cups: ______
___ c
___ c
___ c
___ c
Step 3: Since 1 cup = 8 fl oz, calculate total fluid ounces: 4 pints = ________ fluid ounces
2. Marco is mixing fertilizer and needs 34 gallon of water.
Partition the tape diagram to find how many quarts are in 34 gallon, then convert that to cups.
Tape Diagram for Gallon to Quarts
34 gallon = ________ quarts
Equivalent Ratio for Cups
Quarts to Cups = ________ cups
B Equivalent Ratio Conversion Tables
Fill in the missing values in each table
Length: Inches, Feet & Yards 12 in = 1 ft | 3 ft = 1 yd
| Inches (in.) | Feet (ft) | Yards (yd) |
|---|
| 12 | 1 | 13 |
| 24 | ______ | 23 |
| 36 | 3 | ______ |
| ______ | 6 | 2 |
| 108 | ______ | ______ |
Weight: Pounds & Ounces 1 lb = 16 oz
| Pounds (lb) | Ounces (oz) | Unit Ratio |
|---|
| 1 | 16 | 16 : 1 |
| 2 12 (2.5) | ______ | 16 : 1 |
| ______ |
Customary Conversions Answer Key
Teacher Resource Answer Key & Guide
Convert Customary Measurement Units
Step-by-step solutions, equivalent ratio setups, and common misconception flags.
Total Points: 25 pts
Estimated Practice Time: 15–20 min
Watch Out: Remind students to distinguish fluid ounces (volume: 8 fl oz/cup) from ounces (weight: 16 oz/lb).
A Section A: Visual Models Solutions (5 Points)
✓ Fully Worked Solutions
1. Convert 4 pints to fluid ounces (3 pts) Answer: 64 fl oz
Step 2: Replace each pint with 2 cups (Unit ratio 2 c : 1 pt)
2 cups
2 cups
2 cups
2 cups
Total Cups: 4 × 2 = 8 cups
Step 3: 8 cups × 8 fl oz/cup = 64 fl oz 4 pt = 64 fl oz
2. Marco's 34 gallon fertilizer (2 pts) Answer: 3 quarts = 12 cups
Gallons → Quarts
Tape partitioned into 4 equal quarters (1 quart each).
34 × 4 qt = 3 quarts
Quarts → Cups
1 quart = 4 cups (or 2 pt × 2 c).
3 qt × 4 c/qt = 12 cups
B Section B: Ratio Table Solutions (8 Points)
1 pt per filled blank
Table 1: Length Key
| Inches | Feet | Yards |
|---|
| 12 | 1 | 13 |
| 24 | 2 | 23 |
| 36 | 3 | 1 |
| 72 | 6 | 2 |
| 108 | 9 | 3 |
Table 2: Weight Key
| Pounds (lb) | Ounces (oz) | Unit Ratio |
|---|
| 1 | 16 | 16 : 1 |
| 2 12 (2.5) | 40 | 16 : 1 |
| 4 | 64 | 16 : 1 |
| 5 | 80 | 16 : 1 |
| 14 (0.25) | 4 | 16 : 1 |
Module 1 Lesson 1-6 • Teacher Solution Guide Page 1 of 2
Customary Unit Conversions | Answer Key: Applications & Reflection
Sections C, D, E • 12 Points
