Basic Math

Units of measurement | Sixth Grade

Units of Measurement - Sixth Grade

Complete Notes & Formulas

1. Customary Units of Length

Conversion Chart

UnitConversionFormula
1 foot (ft)12 inches (in)1 ft = 12 in
1 yard (yd)3 feet (ft)1 yd = 3 ft
1 yard (yd)36 inches (in)1 yd = 36 in
1 mile (mi)5,280 feet (ft)1 mi = 5,280 ft
1 mile (mi)1,760 yards (yd)1 mi = 1,760 yd

Conversion Rules

Larger to Smaller → MULTIPLY

Smaller to Larger → DIVIDE

Example: Convert 5 yards to inches

1 yard = 36 inches

5 yards × 36 = 180 inches

Answer: 180 inches

2. Customary Units of Weight

Conversion Chart

UnitConversionFormula
1 pound (lb)16 ounces (oz)1 lb = 16 oz
1 ton (T)2,000 pounds (lb)1 T = 2,000 lb

3. Customary Units of Capacity

Conversion Chart

UnitConversionFormula
1 cup (c)8 fluid ounces (fl oz)1 c = 8 fl oz
1 pint (pt)2 cups (c)1 pt = 2 c
1 quart (qt)2 pints (pt)1 qt = 2 pt
1 gallon (gal)4 quarts (qt)1 gal = 4 qt

4. Metric Units of Length

Metric Prefixes

kilo- (k) = 1,000 (thousand)

hecto- (h) = 100 (hundred)

deka- (da) = 10 (ten)

base unit = 1 (meter, gram, liter)

deci- (d) = 0.1 (tenth)

centi- (c) = 0.01 (hundredth)

milli- (m) = 0.001 (thousandth)

Metric Length Conversions

ConversionFormula
1 kilometer (km)1,000 meters (m)
1 meter (m)100 centimeters (cm)
1 meter (m)1,000 millimeters (mm)
1 centimeter (cm)10 millimeters (mm)

Metric Memory Tool: King Henry

King Henry Died By Drinking Chocolate Milk

Kilo - Hecto - Deka - Base - Deci - Centi - Milli

Move decimal right when going down, left when going up!

5. Metric Units of Mass and Capacity

Metric Mass (Weight)

UnitConversion
1 kilogram (kg)1,000 grams (g)
1 gram (g)1,000 milligrams (mg)
1 metric ton (t)1,000 kilograms (kg)

Metric Capacity (Volume)

UnitConversion
1 kiloliter (kL)1,000 liters (L)
1 liter (L)1,000 milliliters (mL)

6. Converting Between Customary and Metric

Common Conversions

CustomaryMetric
Length
1 inch (in)≈ 2.54 centimeters (cm)
1 foot (ft)≈ 0.3048 meters (m)
1 mile (mi)≈ 1.61 kilometers (km)
Weight/Mass
1 ounce (oz)≈ 28.35 grams (g)
1 pound (lb)≈ 0.454 kilograms (kg)
Capacity
1 quart (qt)≈ 0.946 liters (L)
1 gallon (gal)≈ 3.785 liters (L)

Note: ≈ means "approximately equal to" because these are rounded values!

7. Temperature Conversion: Celsius & Fahrenheit

Conversion Formulas

Celsius to Fahrenheit:

°F = (°C × 9/5) + 32

Fahrenheit to Celsius:

°C = (°F − 32) × 5/9

Key Temperatures

EventCelsius (°C)Fahrenheit (°F)
Water freezes0°C32°F
Room temperature≈ 20-25°C≈ 68-77°F
Body temperature37°C98.6°F
Water boils100°C212°F

Example: Convert 25°C to Fahrenheit

°F = (°C × 9/5) + 32

°F = (25 × 9/5) + 32

°F = (25 × 1.8) + 32

°F = 45 + 32

°F = 77

Answer: 77°F

8. Working with Mixed Units

Example: Add Mixed Units

Problem: 3 ft 8 in + 2 ft 9 in

Step 1: Add feet: 3 ft + 2 ft = 5 ft

Step 2: Add inches: 8 in + 9 in = 17 in

Step 3: Convert extra inches: 17 in = 1 ft 5 in

Step 4: Add: 5 ft + 1 ft 5 in = 6 ft 5 in

Answer: 6 ft 5 in

Example: Multiply Mixed Units

Problem: 4 lb 6 oz × 3

Step 1: Multiply pounds: 4 lb × 3 = 12 lb

Step 2: Multiply ounces: 6 oz × 3 = 18 oz

Step 3: Convert: 18 oz = 1 lb 2 oz (16 oz = 1 lb)

Step 4: Add: 12 lb + 1 lb 2 oz = 13 lb 2 oz

Answer: 13 lb 2 oz

9. Estimating Measurements

Customary Estimation Benchmarks

Length:

• 1 inch ≈ width of your thumb

• 1 foot ≈ length of a ruler

• 1 yard ≈ one big step

Weight:

• 1 ounce ≈ slice of bread

• 1 pound ≈ loaf of bread

Metric Estimation Benchmarks

Length:

• 1 millimeter ≈ thickness of a dime

• 1 centimeter ≈ width of your pinky finger

• 1 meter ≈ width of a doorway

• 1 kilometer ≈ 10 minute walk

Mass:

• 1 gram ≈ paperclip

• 1 kilogram ≈ textbook

Quick Reference: Conversion Rules

To ConvertOperation
Larger to SmallerMULTIPLY
Smaller to LargerDIVIDE
Metric (same type)Move decimal (powers of 10)
Between systemsUse conversion factor

💡 Important Tips to Remember

Larger to smaller → MULTIPLY

Smaller to larger → DIVIDE

Memorize: 12 inches = 1 foot

Memorize: 3 feet = 1 yard

Metric is based on 10s (easy to convert!)

King Henry mnemonic for metric prefixes

Water freezes: 0°C = 32°F

Water boils: 100°C = 212°F

1 inch ≈ 2.54 cm (key conversion)

Always write units in your answer!

🧠 Memory Tricks & Strategies

Customary Capacity:

"Good Queen Victoria Purchased Tea" (Gallon, Quart, Pint, Cup)

Metric Prefixes:

"King Henry Died By Drinking Chocolate Milk"

Temperature:

"30 is hot, 20 is nice, 10 is cold, 0 is ice!" (Celsius)

Feet to Inches:

"A foot has 12 inches, just like a year has 12 months!"

Conversion Direction:

"Big to little, multiply a lot! Little to big, divide - that's the trick!"

Master Units of Measurement! 📏 ⚖️ 🌡️

Remember: Larger to Smaller = Multiply!

Shares: