Three Phases for Teaching Measurement

There are 3 broad phases for teaching about each of the measurement attributes for objects (such as length, area, volume, capacity, mass, angle, temperature) and for events (such as time and chance).

• Phase 1: Identifying the attribute
• Phase 2: Learning to measure
• Phase 3: Learning to calculate

The sections below show the purposes for each phase and the generic teaching strategies that will be useful for each phase. These strategies are the same for all the attributes but interpreted differently. Three examples are given here. The phases are essentially sequential, although will sometimes be revisited (e.g. to learn more advanced language).

Illustrating the phases

• Atrribute of length
• Attribute of volume
• Attribute of chance

 

Illustrating the phases: Attribute of length

Phase 1 - Identifying the attribute

Purpose

• Develop the concept of the attribute.
• Distinguish it from other attributes.
• Gain intuitive understanding of properties.

 

Teaching strategies

• Play and practical activities
  (trace straight and curvy paths, step out distances, sort pencils by length…)
• Learning language
  (how far, how long, tall, short, wide, distance around tree, length…)
• Comparing objects on basis of attribute
  (which snake is longer, who is taller, which house is further away, sort pens by length …)
• Comparing with other attributes
  (this box is longer, but that box is bigger; he is taller, but I am older)
• Using informal units
  (it is 5 giant steps to the window, this table is 12 books long …)

Phase 2 - Learning to measure

Purpose

• Learn to measure the quantity.
• Use formal units.
• Estimate measurements.

Teaching strategies

• Make the transition from informal units to formal units
  (make ‘ruler’ for informal unit (e.g. popstick length, discuss value of agreed unit, make own ruler measuring in centimetres …)
• Make and use simplified ‘instruments’ that highlight key features
  (rulers with only centimetres marked, one-handed clock, mark a jug with ‘cups’…)
• Measuring objects in various ways, to increasing accuracy, with different equipment
  (correct use of ruler, tape measure, trundle wheel …)
• Acquiring a set of personal benchmarks that can be used for estimating
  (my hand span is about 15 cm; I am about 130cm tall…)

Phase 3 - Learning to calculate

Purpose

• Convert from one unit to another.
• Calculate, instead of direct measure.

 

Teaching strategies

• Formulas derived from first principles, rather than only memorised
  (perimeter of rectangle = 2 × length + 2 × width, circumference of circle = 2 πr)
• Conversions between units draws on principles of proportional reasoning
  (sketch dual number line to see 3.2 km = 3200 m etc)

 

Illustrating the phases: Attribute of volume

Phase 1 - Identifying the attribute

Purpose

• Develop the concept of the attribute.
• Distinguish it from other attributes.
• Gain intuitive understanding of properties.

Teaching strategies

• Play and practical activities
  (fill containers with sand, tip from one to the other, pack boxes with cubes …)
• Learning language
  (how much does it hold, (later) volume, capacity …)
• Comparing objects on basis of attribute
  (this dress up box can hold more clothes than that one …)
• Comparing with other attributes
  (the cornflakes packet is bigger than the butter, but weighs the same …)
• Using informal units
  (this drink bottle holds 5 cups full, 15 cubes fit in the box …)

Phase 2 - Learning to measure

Purpose

• Learn to measure the quantity.
• Use formal units.
• Estimate measurements.

Teaching strategies

• Make the transition from informal units to formal units
  (put gradations on jug in terms of own cup size, discuss usefulness of agreed unit e.g. litre )
• Measuring objects in various ways, with different equipment
  (measuring jugs, unit cubes in boxes …)
• Acquiring a set of personal benchmarks that can be used for estimating
  (my drink bottle holds half a litre, an Olympic swimming pool holds a million litres, my medicine spoon holds 10 ml …)

Phase 3 - Learning to calculate

Purpose

• Convert from one unit to another.
• Calculate, instead of direct measure.

 

Teaching strategies

• Formulas derived from first principles, not only memorised
  (volume of cube, volume of cylinder = πr²h …)
• Conversions between units
  (1000000cubic centimetres = 1 cubic metre …)

 

Illustrating the phases: Attribute of chance

Phase 1 - Identifying the attribute

Purpose

• Develop the concept of the attribute.
• Distinguish it from other attributes.
• Gain intuitive understanding of properties.

Teaching strategies

• Play and practical activities
  (throwing dice in board games and observing randomness …)
• Learning language
  (likely, unlikely, possible, common, uncommon, equally likely …)
• Comparing events on basis of attribute
  (“it seems easier to throw 11 on two dice than to throw 12”, “there is more red on your spinner, so you will get red more often than I do”…)

Phase 2 - Learning to measure

Purpose

• Learn to measure the quantity.
• Use formal units.
• Estimate measurements.

Teaching strategies

• Make the transition from informal units to formal units
  (probability is equal to the number of successes divided by number of trials )
• Measuring objects in various ways, with different equipment
  (find the probability of getting a double 6 by tossing 2 dice many times …)
• Acquiring a set of personal benchmarks that can be used for estimating.
  (the chance of getting hit by lightning is about one in 3 million …)

Phase 3 - Learning to calculate

Purpose

• Convert from one unit to another.
• Calculate, instead of direct measure.

 

Teaching strategies

• Formulas derived from first principles, not only memorised
  (probability of compound events …)
• Conversions between units
  (probabilities to odds)