MAE3270 Module 5 - Lecture 3: Measurement

Chapter 1: Estimation, Accuracy and Error

Since all measurements are approximate, students need to understand the following terms:

  • Estimation

    • Approximate value for a measurement using the available info

  • Accuracy

    • How close a measurement is to the true value. Required accuracy depends on intented purpose of the measurement.

  • Error

    • The amount by which a measurement differs from accepted value.

Using reference items or benchmarks

Compare standard units to everyday objects:

  • childs finger - 1cm wide

  • rulers - 30cm long

  • A4 paper - 21 × 30 cm

  • Soft drink can holds 375mls

  • Classroom door is about 2m high

  • Carton of milk - 2L

  • A litre of water has a mass of 1kg

  • Room temp is approx 25 degrees

Indirect measurements involve the use of formulas

  • Formulas are introduced later in primary and secondary education

  • Example: area is calculated by multiplying length by width

Chapter 2: Relationships Between Units

1ml of water has a volume of 1cm3

1ml of water has a mass of 1g

1L of water has a mass of 1kg

  • Difficulties with measuring instruments

    • Interpreting and reading scales appropriately

    • Do not understand that measurement occurs from zero

    • Allocate incorrect units of measure

    • Choose inappropriate instruments to measure

Chapter 3: Pythagoras’ Theorem

  • Pythagoras's theorem

    • Ancient Egyptians used rope stretchers with a rope tied in a circle with 12 evenly spaced knots

    • Pythagoras observed that the rule applies to all right-angled triangles

  • Triangles with sides of lengths 3, 4, 5 units had a 90 degree angle

  • The long side of the triangle is the hypotenuse

  • The square of the hypotenuse is equal to the sum of the squares of the other sides:

Chapter 4: Getting A Sense Of Scale

  • Using microscopes for small quantities and telescopes for large quantities

  • Recommended texts and literature to develop a sense of scale

    • Example: Isaboo whale and 100,000,000,000,000,000 stars

Chapter 5: Time

  • Time is an abstract concept because it is not an attribute of objects that can be seen or felt

  • Two attributes of events that can be measured:

    • time of occurrence: eating afternoon tea at 4.03pm

    • duration of time: journey lengths

  • Skills needed for telling time

    • Identifying hour and minute hands on an analog clock

    • Telling time and moving the hands of a clock

    • Identifying the hour that a time is ‘after’. Use language ‘quarter past’ and ‘half past’ for times 15 and 30 mins past the hour.

    • Counting by 5s and 1s to tell how many minutes before the hour using language ‘quarter to’ for 15 mins before

    • Counting by 5s to tell time to the nearest 5 minutes

    • Counting on by 1s from multiples of 5s

    • Writing time in digital notation

    • Matching digital and analog clock representations

  • Advantages of the analogue clock:

    • Shows times in multiples of 5

    • Easier to visualise passage of time

    • Assists with developing understanding of rotation

    • Useful when teaching angles

Chapter 7: Conclusion

  • Learning to measure involved understanding the attribute being measured, the instrument being used to measure it, and the units in which the measurement is expressed

  • All measurement ivolves some defree of error, so students need to understand estimation and rounding

  • Measurement is the topic from primary mathematics that provides many applications to everyday life

  • Students find learning about measurement engaging and interesting