MAE3270 Module 5 - Lecture 1: Measurement

Chapter 1: Measurement and Geometry

  • Measurement and geometry are closely linked

  • Measurement is used to quantify aspects of the world e.g. distance, area, volume, mass, time, angles, temperature

  • Many numeration models are based on measurement. For example:

    • number line - lengths

    • area of rectangle -multiplication

    • fractions and angles - analogue clock

  • Conversion between units of measure requires multiplying and dividing

  • Measurement and geometry are used to describe positions, shapes, and transformations

  • Measurement can be represented as whole numbers, fractions, decimals, or negative numbers

  • Measurement has connections to other learning areas

Chapter 2: Principles of Measurement

  1. The unit of measurement must remain constant

  2. A measurement must include both a number and the unit

  3. Estimation is important in the measurement process

  4. Two measurements may be easily compared if the same unit is used

  5. One unit may be more appropriate than another to measure an object

  6. There is an inverse relationship between the number of units and the size of the unit

  7. Standard units are needed to communicate effectively

  8. A smaller unit gives a more exact measurement

  9. Units may be combined or subdivided to make other units

  10. Units must match the attribute that is being measured

Chapter 3: Learning Sequence for Measurement

  • Identifying the attribute being measured

  • Comparing and ordering attributes

  • Non-standard units of measurement

  • Standard units of measurement

  • Indirect measurement and the use of formulas

  • Students develop measurement language and the concept of conservation

Chapter 4: Confusing Attributes

  • The importance of understanding measurement

    • Students can have difficulties with measurement if they don't completely understand it

    • Hands-on experience is crucial in the early years

    • Comparing, ordering, lifting, hefting, and feeling objects help develop a sense of attributes

  • Example of misunderstanding measurement

    • A student couldn't lift a box of wooden blocks because she thought it would be too heavy

    • Attributes and their standard units of measure

      • Length: metres

      • Area: square metres

      • Volume: cubic metres

      • Capacity: litres

      • Mass: kilograms

      • Time: seconds

Chapter 5: Conclusion

  • Additional units of measure

    • Temperature: Kelvin

    • Angles: radians

  • Transition from degrees Celsius to Kelvin in higher education