teaching measurement early stage 1 and stage 1. understanding measurement length when measuring...

Teaching measurementEarly Stage 1 and Stage 1

Understanding measurement Length

• When measuring length, area and volume, the units of measure are aligned spatially.

• Most adults can confidently estimate and measure length, distance or height and are familiar with the units used to measure length - centimetres, metres and kilometers.

Understanding measurementArea

• However, fewer adults can confidently estimate area.

• Many learnt to calculate area by using the

L x B formula, without understanding what the formula does.

• Students often apply the area and perimeter formulae wrongly or invent their own formulae.

• The use of units cm2, m2 and hectares is frequently confused.

Calculating area by identifying rows or columns as composite units and adding, skip counting, or multiplying.

Understanding measurementVolume

• And even fewer adults are confident of how to estimate or calculate volume.

• Students or adults who don’t understand how the area formula works, will have difficulty in understanding how to calculate volume.

Understanding measurementVolume

• Volume can be modelled as repeated layers. An understanding of how one layer is constructed (as in area) is necessary for the confident use of the formula L X B X H.

• Sometimes the formula is applied with no understanding of what the units of measure will be.

12

24

36

Calculating volume by identifying horizontal layers and adding, skip counting, or multiplying.

9 18 27 36

Calculating volume by identifying vertical layers and adding, skip counting, or multiplying the number of layers

Understanding measurement Capacity, Mass

• In measurement of capacity or mass, the spatial arrangement of the units is not important.

• Finding the capacity of a container by filling with liquid or sand or rice is different from packing with blocks, which must be arranged spatially.

• When finding the mass of a quantity by balancing with blocks or weights, the arrangement of the mass does not matter.

Understanding measurement Capacity, Mass

•The measurement framework generally refers to capacity as liquid measure and volume as cubic measure.

•Within the framework, mass is slightly different from the other sub-strands:

– Level 1.3 is an additional sub-level, to introduce the concept of an equal-arm balance

– There is no sub-level 3.1, as Structure of repeated units does not apply to mass.


The resource Teaching measurement: Early Stage 1 and Stage 1 contains -

the measurement framework

lesson ideas

lesson plans

for the measurement sub-strands of length, area, volume and capacity and mass.


• The measurement framework provides the fine detail of how students’ concepts develop.

• The framework focuses on an understanding of quantities, terminology used to describe measurements, the use of units to measure and the pattern created by repeated, tessellating units.

The measurement framework Levels 1and 2

Level 1Identification of the attribute

1.1 Make direct comparisons of quantities1.2 Order two or more quantities by direct comparison

Level 2Informal measurement

2.1 Choose and using appropriate units for measuring a quantity

2.2 Compare and order quantities by using identical units

The measurement framework Level 3

Level 3

Structure of repeated units3.1 Use one unit to work out how many will be needed

altogether when making indirect comparisons.

3.2 Explain the relationship between unit size and the number of units used to measure a quantity.

The measurement frameworkLevel 1


Level Length Area Volume andCapacity

Mass

Informal Measurement

2.1 Choose and useappropriate unitsfor measuringlength

Choose and useappropriate unitsfor measuring area.

Choose and useappropriate unitsfor measuringvolume andcapacity

Choose appropriateunits and use them tomeasure a mass

2.2 Compare and orderlengths by usingidentical units foreach length

Compare and orderareas by coveringeach area withidentical units

Compare and ordervolumes andcapacities by fillingor packing withidentical units

Compare and ordermasses usingidentical units foreach mass


Level Length Area Volume andCapacity

Mass

Structure of repeated unitsRelationshipbetween units

3.1 Use one unit towork out how manywill be neededaltogether whenmaking indirectcomparisons

Use one unit towork out how manywill be neededaltogether whenmaking indirectcomparisons

Use one unit orcomposite unit towork out how manywill be neededaltogether whenmaking indirectcomparisons

3.2 Explain therelationshipbetween unit sizeand the number ofunits used tomeasure length

Explain therelationshipbetween unit sizeand the number ofunits used tomeasure area

Explain therelationshipbetween unit sizeand the number ofunits required to fillor pack a container

Explain therelationship betweenunit size and thenumber of unitsrequired to balance amass

The measurement framework Levels 4-6

Level 4Measuring using conventional units

Level 5Relationships between formal units

Level 6Knowing and representing large units


• The knowledge and strategies are listed for each level, in each substrand.

• These are the skills, understandings, and mathematical terminology which students use in demonstrating achievement of that level.


Level Knowledge and strategies

L1.1 Identificationof the attribute

Make directcomparisons oflength

1. use length vocabulary, e.g. long, high, tall; short or low; thesame as

2. put two lengths side by side to compare their lengths3. straighten a curved or bent length to check if two lengths are

the same

L1.2 Identificationof the attribute

Order two or morelengths by directcomparison

1. use comparative language e.g. longer, higher, taller than;shorter or lower than; the same as; shortest, longest

2. ensure that ends are aligned for comparison by establishing abaseline

3. compare lengths systematically and explain why a length fitsinto a particular ordering

Group activity Read, summarise, share and discuss

• Work in your table group.• Each teacher chooses and reads an

introductory page from length, area, volume and capacity or mass. Highlight the important points.

• Share your readings.

Discuss: – What issues have been raised?– What are the implications for teaching measurement,

K-6?

Lesson ideas

• Five lesson ideas have been listed for each sub-level.

• Each lesson idea includes:

syllabus references

materials

knowledge and strategies.

• The lesson ideas in each sub-level are in approximate order.

Lesson ideas (Area 3.1)

Lesson plans

• One lesson idea in each sub-level has been expanded to a full lesson plan.

• All of the lessons have the same basic structure of: introduction, followed by practical activity and then whole-class discussion.

• The suggested questions provide samples of open-ended questioning.

• Teachers are strongly encouraged to modify or adapt the lessons to suit their students.

Lesson plans


The introductory section of the book contains important information about:• Fundamental measurement ideas

– Identification of the attribute being measured– Knowledge of units is fundamental to the process of

measuring– The principle of conservation is fundamental to

understanding measurement– Knowledge of unit iteration is fundamental to the

process of measuring spatially organised quantities.


The introductory section of the book contains important information about: • Components of teaching measurement

– Estimation– Recording– Questioning

• The measurement framework• Before you begin• Glossary

Where should I start?

• Refer to the lists of knowledge and strategies

• Check the references to syllabus Stages on lessons

• Try a lesson, observe students’ knowledge, and then plan further lessons. You may need to go forwards or backwards in the framework.

Where should I start?

• It is not necessary to teach all of the lessons in each sub-level.

• Teach a block of 4 or 5 lessons before moving on to another substrand.

• Remember the sequence of concept development: length, then area, then volume and capacity.

Teaching measurementEarly Stage 1 and Stage 1 - a summary

An emphasis on:• developing an understanding of the attributes of

length, area, volume and capacity, mass• using mathematical terminology to discuss and

record measurements• using knowledge of the structure of repeated

units to measure• developing and practising measurement skills.

* Systematically hefting 3 bags to compare mass – each bag had 4 objects eg 4 beads, 4 blocks, 4 cotton reels, 4 feathers

Collection of everyday objects to compare mass

Systematic hefting

Using identical units to balance a given mass

Work Samples

teaching measurement early stage 1 and stage 1. understanding measurement length when measuring...

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