Solved Exercises on Units of Length in Grade 3

Master units of length: inch, foot, yard, centimeter, meter conversions and measurements through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Converting inches to feet
Exercise 1
Convert 24 inches to feet
Definition:

Conversion: Changing from one unit of measurement to another

Conversion method:
  1. Know the conversion factor: 1 foot = 12 inches
  2. Divide the number of inches by 12
  3. Express the result in feet
Given
24 inches
Conversion
÷ 12
Result
2 feet
Step 1: Identify conversion factor

1 foot = 12 inches

Step 2: Set up division

24 inches ÷ 12 inches per foot

Step 3: Calculate

24 ÷ 12 = 2

Step 4: Express result

24 inches = 2 feet

24 inches = 2 feet
Final answer:

24 inches equals 2 feet

Applied rules:

• Conversion factor: 1 foot = 12 inches

• Division rule: Divide by the conversion factor when going from smaller to larger unit

• Unit cancellation: Inches cancel out, leaving feet

2 Converting feet to yards
Exercise 2
Convert 9 feet to yards
Definition:

Yard: Unit of length equal to 3 feet or 36 inches

Given
9 feet
Conversion
÷ 3
Result
3 yards
Step 1: Identify conversion factor

1 yard = 3 feet

Step 2: Set up division

9 feet ÷ 3 feet per yard

Step 3: Calculate

9 ÷ 3 = 3

Step 4: Express result

9 feet = 3 yards

9 feet = 3 yards
Final answer:

9 feet equals 3 yards

Applied rules:

• Conversion factor: 1 yard = 3 feet

• Division rule: Divide by 3 when converting feet to yards

• Unit relationship: Yards are larger than feet, so fewer yards than feet

3 Converting centimeters to meters
Exercise 3
Convert 200 centimeters to meters
Definition:

Meter: Base unit of length in metric system, equal to 100 centimeters

Given
200 cm
Conversion
÷ 100
Result
2 m
Step 1: Identify conversion factor

1 meter = 100 centimeters

Step 2: Set up division

200 centimeters ÷ 100 centimeters per meter

Step 3: Calculate

200 ÷ 100 = 2

Step 4: Express result

200 centimeters = 2 meters

200 cm = 2 m
Final answer:

200 centimeters equals 2 meters

Applied rules:

• Conversion factor: 1 meter = 100 centimeters

• Division rule: Divide by 100 when converting centimeters to meters

• Metric system: Based on powers of 10

Rules and methods, laws,...
1 foot = 12 inches
Foot to Inch Conversion
Conversion 1
1 yard = 3 feet
Yard to Foot
Conversion 2
1 meter = 100 cm
Meter to Centimeter
Metric
1 m = 100 cm = 1000 mm
Metric System
Inch
in
Width of thumb
Foot
ft
Length of ruler
Yard
yd
Baseball bat
Centimeter
cm
Width of finger
Meter
m
Height of door
Key definitions:

Length: Distance between two points

Unit of measurement: Standard quantity used to express length

Conversion: Changing from one unit to another while maintaining the same value

Metric system: Measurement system based on powers of 10

Customary system: Measurement system used in US (inches, feet, yards)

Complete methodology:
  1. Identify units: Know what you're converting from and to
  2. Recall conversion factor: Remember the relationship between units
  3. Set up operation: Divide when going from smaller to larger unit, multiply when going from larger to smaller
  4. Calculate: Perform the mathematical operation
  5. Express result: Include the correct unit in your answer
Tip 1: When converting to a larger unit, the number gets smaller.
Tip 2: When converting to a smaller unit, the number gets larger.
Tip 3: Remember: 12 inches = 1 foot, 3 feet = 1 yard, 100 cm = 1 meter.
Tip 4: Use estimation to check if your answer makes sense.
Common errors: Forgetting conversion factors, mixing up operations (multiply vs divide), misplacing decimal points.
Memory aids: "Big to small, multiply and smile" and "Small to big, divide the dig".
Rules to know by heart:

• 1 foot = 12 inches

• 1 yard = 3 feet = 36 inches

• 1 meter = 100 centimeters = 1000 millimeters

• To convert smaller to larger: divide by conversion factor

• To convert larger to smaller: multiply by conversion factor

Solution: Exercises 4 to 5
4 Converting meters to centimeters
Exercise 4
Convert 3.5 meters to centimeters
Definition:

Multiplication conversion: When converting from larger to smaller units, multiply

Given
3.5 m
Conversion
×
Factor
100
Result
350 cm
Step 1: Identify conversion factor

1 meter = 100 centimeters

Step 2: Determine operation

Going from larger (meter) to smaller (centimeter) unit, so multiply

Step 3: Set up multiplication

3.5 meters × 100 centimeters per meter

Step 4: Calculate

3.5 × 100 = 350

3.5 meters = 350 centimeters
Final answer:

3.5 meters equals 350 centimeters

Applied rules:

• Conversion factor: 1 meter = 100 centimeters

• Multiplication rule: Multiply by 100 when converting meters to centimeters

• Decimal handling: Moving decimal point two places right when multiplying by 100

5 Multi-step conversion
Exercise 5
Convert 2 yards to inches
Definition:

Multi-step conversion: Converting through intermediate units when direct conversion isn't available

Start
2 yd
Step 1
× 3 = 6 ft
Step 2
× 12 = 72 in
Step 1: Convert yards to feet

2 yards × 3 feet per yard = 6 feet

Step 2: Convert feet to inches

6 feet × 12 inches per foot = 72 inches

Step 3: Alternative direct method

1 yard = 36 inches, so 2 yards × 36 inches per yard = 72 inches

Step 4: Verify result

2 yards = 6 feet = 72 inches ✓

2 yards = 72 inches
Final answer:

2 yards equals 72 inches

Applied rules:

• Chain conversion: Convert through intermediate units

• Alternative method: Direct conversion (1 yard = 36 inches)

• Verification: Check with multiple methods when possible

Units of Length: Complete Guide
1 yard = 3 feet = 36 inches
Length Unit Relationships
Key definitions:

Length: The measurement of distance between two points

Unit: A standard quantity used to measure length

Conversion: The process of changing from one unit to another while preserving the measured value

Customary system: Measurement system primarily used in the United States (inches, feet, yards)

Metric system: International decimal-based measurement system (centimeters, meters)

Complete methodology:
  1. Identify the starting and ending units
  2. Recall the conversion relationship between the units
  3. Determine the operation: Divide when converting to larger units, multiply when converting to smaller units
  4. Perform the calculation using the conversion factor
  5. Express the result with the correct unit
  6. Verify the answer makes logical sense
Tip 1: When converting to a larger unit, the numerical value decreases (e.g., 24 in → 2 ft).
Tip 2: When converting to a smaller unit, the numerical value increases (e.g., 2 m → 200 cm).
Tip 3: For metric conversions, think in terms of powers of 10 (move decimal point).
Tip 4: For customary conversions, remember: 12-3-36 (12 inches in foot, 3 feet in yard, 36 inches in yard).
Common errors: Mixing up conversion factors, performing the wrong operation (multiply vs divide), forgetting to include units in the final answer.
Key concepts: Larger units require fewer of them to measure the same length; smaller units require more of them.
Essential formulas and rules:

• Customary: 1 foot = 12 inches, 1 yard = 3 feet, 1 yard = 36 inches

• Metric: 1 meter = 100 centimeters, 1 centimeter = 10 millimeters, 1 meter = 1000 millimeters

• Conversion direction: Smaller to larger → divide, Larger to smaller → multiply

• Unit cancellation: Keep track of units during calculations

• Estimation: Use benchmarks to verify reasonableness of answers

Unit Abbreviation Relationship to Others Approximate Size
Inch in 12 in = 1 ft Width of thumb
Foot ft 1 ft = 12 in, 3 ft = 1 yd Length of ruler
Yard yd 1 yd = 3 ft = 36 in Baseball bat length
Centimeter cm 100 cm = 1 m Width of finger
Meter m 1 m = 100 cm Height of door

Questions & Answers

Question: Why do we have different units for measuring length? Why not just use one unit for everything?

Answer: Great question! We have different units because they're practical for different situations:

  • Inches: Perfect for measuring small things like pencils, books, or the width of a paper
  • Feet: Good for measuring people's height, room dimensions, or furniture
  • Yards: Useful for measuring longer distances like a football field or a garden
  • Centimeters: Great for measuring medium-sized objects like notebooks or small toys
  • Meters: Ideal for measuring rooms, buildings, or large objects

Imagine trying to measure your height in inches versus feet - you'd say "5 feet 6 inches" instead of "66 inches," which is much easier! Or measuring a pencil in miles would give you a very tiny decimal number that's hard to understand.

Different units make measurements more meaningful and easier to understand in daily life.

Question: I always forget whether to multiply or divide when converting. How do I remember?

Answer: Here's a helpful memory trick:

  • "Big to Small, Multiply and Smile" - When going from a larger unit to a smaller unit, multiply
  • "Small to Big, Divide the Dig" - When going from a smaller unit to a larger unit, divide

Think about it logically:

  • Going from feet to inches (big to small): 1 foot = 12 inches, so multiply by 12
  • Going from inches to feet (small to big): 12 inches = 1 foot, so divide by 12

Also remember: the number should make sense. If you're converting to a smaller unit, you'll need more of them, so the number gets bigger. If you're converting to a larger unit, you'll need fewer of them, so the number gets smaller.

Question: My child is struggling with metric conversions. How can I help them understand the relationship between centimeters and meters?

Answer: The metric system is based on tens, which makes it logical once you understand the pattern:

  • Explain that "centi" means 100, so 1 meter = 100 centimeters (like 100 cents in a dollar)
  • Use physical objects: a meter stick has 100 small marks (centimeters)
  • Point out that 100 centimeters lined up end-to-end would equal 1 meter
  • Practice with real measurements: measure a desk in meters and then in centimeters

Here are some practical activities:

  • Have them measure items with both a ruler (cm) and a meter stick (m)
  • Count the centimeters on a meter stick together (1, 2, 3... up to 100)
  • Use the "moving decimal" rule: to convert meters to centimeters, move the decimal point 2 places right

The key is connecting the abstract numbers to concrete experiences with actual measuring tools.