11-Plus Mathematics: Measurement and Units

Measurement and Units

Understanding units of measurement is essential for solving various mathematical problems in the 11-plus examination. This topic focuses on both metric and imperial units, as well as the ability to convert between them.

Metric Units

In the metric system, the following units are commonly used:

• Length: millimeters (mm), centimeters (cm), meters (m), kilometers (km)
• Mass: grams (g), kilograms (kg)
• Capacity: milliliters (ml), liters (l)

Converting Between Metric Units

To convert between metric units, it is important to understand the relationships between them. For example:

• 1 meter = 100 centimeters
• 1 kilometer = 1,000 meters
• 1 kilogram = 1,000 grams
• 1 liter = 1,000 milliliters

When converting, you can multiply or divide by the appropriate factor. For instance, to convert 2.5 meters to centimeters:

Worked Example

Problem: Convert 2.5 meters to centimeters.

Solution:

• Since 1 meter = 100 centimeters, multiply 2.5 by 100.
• 2.5 m × 100 = 250 cm

Understanding Imperial Units

Imperial units are also important, especially in certain contexts. Common imperial units include:

• Length: miles
• Mass: pounds (lbs)
• Capacity: pints

Converting Between Metric and Imperial Units

To convert between metric and imperial units, you will need to use specific conversion factors. Here are some common conversions:

• 1 mile ≈ 1.609 kilometers
• 1 pound ≈ 0.4536 kilograms
• 1 pint ≈ 0.568 liters

For example, to convert 5 miles to kilometers:

Worked Example

Problem: Convert 5 miles to kilometers.

Solution:

• Using the conversion factor, multiply 5 by 1.609.
• 5 miles × 1.609 = 8.045 kilometers

Conclusion

Mastering measurement and units is crucial for success in the 11-plus mathematics exam. Practice converting between different units and familiarize yourself with both metric and imperial systems to enhance your problem-solving skills.