Key Concepts Explained
- Customary Units of Length: Inch (in), foot (ft), yard (yd), mile (mi).
- Customary Units of Liquid Volume: Teaspoon (tsp), tablespoon (tbsp), fluid ounce (fl oz), cup (c), pint (pt), quart (qt), gallon (gal).
- Customary Units of Weight: Ounce (oz), pound (lb), ton.
- Perimeter: The distance around a 2D shape. For a rectangle: P = 2(l + w).
- Area: The space inside a 2D shape. For a rectangle: A = l × w.
- Volume of a Solid: The space inside a 3D object. For a rectangular prism: V = l × w × h.
- Time: Units include second (s), minute (min), hour (h), day, week, month, year.
- Temperature: Measured in degrees Fahrenheit (°F) in customary, Celsius (°C) in metric.
- Metric Units of Length: Millimeter (mm), centimeter (cm), meter (m), kilometer (km).
- Metric Units of Liquid Volume: Milliliter (mL), liter (L).
- Metric Units of Mass: Milligram (mg), gram (g), kilogram (kg).
- Perimeter, Area, and Volume in Metric: Use metric units for all formulas.
- Customary to Metric: Use conversion factors, e.g., 1 inch ≈ 2.54 cm.
- Metric to Customary: Use conversion factors in the other direction, e.g., 1 cm ≈ 0.39 in.
My Preference for Concepts to Focus On:
- Understanding conversion between units
- Calculating perimeter, area, and volume
- Knowing when to use which measurement unit
- Estimating measurements
Worked Examples
Customary Length:
Example: 3 feet = 36 inches (since 1 foot = 12 inches; 3 × 12 = 36)
Example: 3 feet = 36 inches (since 1 foot = 12 inches; 3 × 12 = 36)
Customary Liquid Volume:
Example: 2 quarts = 8 cups (since 1 quart = 4 cups; 2 × 4 = 8)
Example: 2 quarts = 8 cups (since 1 quart = 4 cups; 2 × 4 = 8)
Customary Weight:
Example: 16 ounces = 1 pound
Example: 16 ounces = 1 pound
Perimeter:
Example: Rectangle with l = 5 in, w = 3 in
P = 2(5 + 3) = 2(8) = 16 in
Example: Rectangle with l = 5 in, w = 3 in
P = 2(5 + 3) = 2(8) = 16 in
Area:
Example: Rectangle with l = 7 cm, w = 2 cm
A = 7 × 2 = 14 cm2
Example: Rectangle with l = 7 cm, w = 2 cm
A = 7 × 2 = 14 cm2
Volume:
Example: Rectangular prism: l = 4 m, w = 3 m, h = 2 m
V = 4 × 3 × 2 = 24 m3
Example: Rectangular prism: l = 4 m, w = 3 m, h = 2 m
V = 4 × 3 × 2 = 24 m3
Time:
Example: 2 hours 30 minutes = 150 minutes (2 × 60 + 30)
Example: 2 hours 30 minutes = 150 minutes (2 × 60 + 30)
Temperature:
Example: 68°F to Celsius: (68 - 32) × 5/9 ≈ 20°C
Example: 68°F to Celsius: (68 - 32) × 5/9 ≈ 20°C
Metric Length:
Example: 1000 meters = 1 kilometer
Example: 1000 meters = 1 kilometer
Metric Liquid Volume:
Example: 250 mL = 0.25 L
Example: 250 mL = 0.25 L
Metric Mass:
Example: 1000 g = 1 kg
Example: 1000 g = 1 kg
Customary to Metric Conversion:
Example: 10 inches × 2.54 = 25.4 cm
Example: 10 inches × 2.54 = 25.4 cm
Metric to Customary Conversion:
Example: 100 cm × 0.39 ≈ 39 inches
Example: 100 cm × 0.39 ≈ 39 inches
Pre-Test: Check Your Understanding!
Questions & Answers
What is the difference between weight and mass?
Weight is the force of gravity on an object (measured in pounds or newtons), while mass is the amount of matter in an object (measured in grams or kilograms).
How do you convert inches to centimeters?
Multiply inches by 2.54 to get centimeters.
How do you find the perimeter of a rectangle?
Add all sides or use the formula: P = 2(l + w).
What is a liter?
A metric unit of liquid volume. 1 L = 1000 mL.
What are the main metric units for measuring length?
Millimeter (mm), centimeter (cm), meter (m), kilometer (km).
How do you convert Fahrenheit to Celsius?
Subtract 32, then multiply by 5/9.