Dianne RundusTriple M Consulting

rundus@bigpond.com

Measuring Up!

The MAI Growth Points for Measurement

(Time Length Mass)

Measurement…has its roots, both historically and in individual

development, in significant everyday activity. Thus it can develop in the

earliest years from children’s experiences….Further, it spans and connects mathematics and other

sciences and thus can ideally integrate subject matter area.

Clements, 2003

People numerate in measurement -

• Use the language of measurement appropriate to the task

• Choose and use measuring tools and instruments appropriate to the task

• Use estimation techniques• Use measurement techniques to solve

problems• Recognise that some measures are

obtained by combining two or more other measures

Measurement understandings

• Measures in common use• Skills needed for everyday purposes• Nature of different physical attributes that can be

measured• The way units are used to quantify amounts of such

attributes to needed levels of accuracy• Understand units ie decide what needs to be measured

and select the appropriate units to use.• Directly and indirectly measure ie select and combine

measurements, measurement relationships and formulae to determine other measures indirectly. Carry out measurements of length, capacity/volume, mass, area, time and angler to needed levels of accuracy

• Estimate units ie make sensible direct and indirect estimates and check for reasonableness of results.

Three Content StrandsNumber and Algebra

Number and place valueFractions and decimalsMoney and financial mathematicsPatterns and algebra

Measurement and GeometryUsing units of measurement -Time

Length, Mass, Capacity, Volume, Area, PerimeterShapeGeometric reasoningLocation and transformation

Statistics and ProbabilityChanceData representation and interpretation

NOUNS

Four Proficiency Strands

UnderstandingFluencyProblem SolvingReasoning

‘The proficiency strands describe the actions in which students can engage when learning and using the content. The

proficiencies are incorporated into the content descriptions of the three strands. While not all proficiency strands apply to

every content description, they indicate the breadth of mathematical actions that teachers can emphasise.’

VERBS

Measurement language• Comparative statements – shorter, taller etc• Confusion between volume (the amount of space

taken up by an object) and capacity (the amount it can hold)

• Confusion over the use of ‘mass’ and ‘weight’.Mass is the measure of the inertia of an object. Inertia is the amount of force or push required to move an object. Weight is the force that gravity exerts on an object. The mass of an object remains constant but its weight can vary eg an object weighs more at sea level than on a high mountain.

Discussion builds students’ conceptual and procedural knowledge of

measurement and gives teachers valuable information for reporting and

planning next steps. (Principles and Standards for School

Mathematics, 2000)

Geometric measures• Length – 1D concept related to direction

and line. Includes length, width, depth, thickness, nearness of objects, perimeters.

• Area – 2D concept related to the region (surface) enclosed by a plane shape. The use of formulae to calculate areas of common shapes is the appropriate final stage of the learning sequence.

• Volume and capacity – 3D concept

Learning sequence for measurement

• Identifying the attribute• Comparing and ordering• Non-standard units• Standard units• Applications

Three phases for teaching measurementPhase 1 Identifying the attributeDevelop the concept of the attribute, use play and practical activities, learn and practise the language, compare objects on the basis of the attribute identified, compare with other attributes, use informal units.

Phase 2 Learning to measureLearn to measure the quantity, usual formal units, estimate measurements. Make the transition from informal to formal units, make and use simplified instruments that highlight key features, measuring objects in various ways with increasing accuracy, acquiring a set of personal benchmarks.

Phase 3 Learning to calculate. Converting from one unit to another, calculating instead of direct measuring. Developing formulae from first principles rather than memorisation, converting between units using proportional reasoning.

MAI Growth Points for Time and ACM Descriptors

GP 0 No apparent awareness of time, its descriptive language, and some features of clock faces.

GP 1 Awareness of time, its descriptive language and some features of clock faces.

ACM Compare and order the duration of events using the everyday language of time (ACMMG007) F

GP 2 Knowing some clock times, some days of the week and months of the year, and relating key events

(personal, community) to theseACM Connect days of the week to familiar events and actions (ACMMG008 F

Foundation Achievement Standard. Students connect events and the days of the week. They explain the order and duration of

events

GP 3 Knowing clock times to half hour, all days of the week and months of the year (in order)

ACM Tell time to the half hour ACMMG020) Year 1 Describe duration using months, weeks, days and hours (ACMMG021) Year 1Name and order months and seasons (ACMMG040 Yr 2

Achievement Standard Yr1. They tell time to the half hour

GP 4 Facility with clocks and calendars (can read analogue times to the nearest five minutes and has a good working

facility with calendars)ACM Tell time to the quarter-hour, using the language of 'past' and 'to' (ACMMG039) Yr 2 Use a calendar to identify the date and determine the number of days in each month (ACMMG041) Yr 2

Achievement Standard Yr 2. They tell time to the quarter hour and use a calendar to identify the date and the months included in seasons.

GP 5 Extending and applying knowledge, skills and concepts with time (can solve a range of problems

involving duration, and digital and analogue time to the nearest minute)

ACM Tell time to the minute and investigate the relationship between units of time (ACMMG062) Yr 3

Achievement Standard Yr 3. Tell time to the nearest minute. ACM Convert between units of time (ACMMG085) Yr 4

Use am and pm notation and solve simple time problems (ACMMG086) Yr 4

Achievement Standard Yr 4 They solve problems involving time duration. They convert between units of time.

ACM Compare 12- and 24-hour time systems and convert between them (ACMMG110) Yr 5Achievement Standard Yr 5They convert between 12 and 24 hour

time. ACM Interpret and use timetables (ACMMG139) Yr 6

Achievement Standard Yr 6 They interpret timetables.

The Human ClockIn your Growth Points Activities

books this activity is on pages 21 and 22

The importance of context

Research shows that young children can solve problems in a familiar context but

may be unable to solve the same problem if it is in an unfamiliar context.

The context provides a framework for exploring mathematical ideas and

practising skills.Context provides a strong cognitive structure within which children can

recognise and explore inter-relationships.

MAI Growth Points for Length and ACM Descriptions

GP 0 No apparent awareness of the attribute of length and use of descriptive language

GP 1 Awareness of the attribute of length and use of descriptive language

Achievement Standard F They compare objects using mass, length and capacity.

GP 2 Comparing, ordering and matching with the attribute of lengthACM Use direct and indirect comparisons to decide which is longer, heavier or holds more, and explain reasoning in everyday language (ACMMG006 F

Achievement Standard Yr 1 Students order objects based on lengths and capacities using informal units.

GP 3 Quantifying length accurately, using units and attending to measurement principles. Uses uniform units appropriately, assigning number and unit to the measure.ACM Measure and compare the lengths and capacities of pairs of objects using uniform informal units (ACMMG019) Yr 1ACM Compare and order several shapes and objects based on length, area, volume and capacity using appropriate uniform informal units (ACMMG037) Yr 2

Achievement Standard Yr 2. Students order shapes and objects using informal units.

GP 4 Choosing standard units for estimating and measuring length with accuracy . Uses standard units for estimating and measuring length with accuracy.ACM Measure, order and compare objects using familiar metric units of length, mass and capacity (ACMMG061) Yr 3Achievement Standard Yr 3 Students use metric units for length, mass and

capacity.

GP 5 Applying knowledge, skills and concepts of length. Can solve a range of problems involving key concepts of lengthACM Choose appropriate units of measurement for length, area, volume, capacity and mass (ACMMG108) Yr 5ACM Calculate the perimeter and area of rectangles using familiar metric units (ACMMG109) Yr 5ACM Connect decimal representations to the metric system (ACMMG135) Yr 6

Achievement Standard Yr 4 Students use scaled instruments to measure temperatures, lengths, shapes and objects.

Achievement Standard Yr 5 They use appropriate units of measurement for length, area, volume, capacity and mass, and calculate perimeter and area

of rectangles.Achievement Standard Yr 6 Students connect decimal representations to

the metric system and choose appropriate units of measurement to perform a calculation. They make connections between capacity and

volume. They solve problems involving length and area.

Estimating lengthActivity 1Everyone lines up.They are asked to move forward eg 25 m.Teacher or leader then moves forward that distance using the trundle wheel.Discuss how accurate their estimates were.Return to starting point and estimate a different distance.

Activity 2Give a few children pedometers and ask them to wear them for the whole day. At the end of the day record the number of steps they have taken.Calculate the length of an average pace for each child.Calculate the total distance they have covered.Use a map to work out where they could have travelled eg from Geraldton to _______.They can work in teams over a period of time, to see if they could walk from Perth to Broome..;……….. (This involves lots of place value work as well as measurement, scale, direction etc

MAI Growth Points for Mass and ACM Descriptions

GP 0 No apparent awareness of the attribute of mass and use of descriptive language

GP 1 Awareness of the attribute of mass and use of descriptive language

GP 2 Comparing, order and matching with the attribute of lengthACM Use direct and indirect comparisons to decide which is longer, heavier or holds more, and explain reasoning in everyday language (ACMMG006 FAchievement Standard F. They compare objects using mass, length

and capacity

GP 3 Quantifying mass accurately, using units and attending to measurement principles. Uses uniform units appropriately, assigning number and unit to the measure.ACM Compare masses of objects using balance scales (ACMMG038 Yr 2

Achievement Standard Yr 2. Not mentioned.

Compare and order several shapes and objects based on length, area, volume and capacity using appropriate uniform informal units (ACMMG037) Yr 2

GP 4 Choosing standard units for estimating and measuring mass with accuracy. ACM Compare masses of objects using balance scales (ACMMG038 Yr 2Measure, order and compare objects using familiar metric units of length, mass and capacity (ACMMG061) Yr 3Achievement Standard Yr 3. Students use metric units for length, mass and capacity.

GP 5 Applying knowledge, skills and concepts of mass. Can solve a range of problems involving key concepts of mass.

ACM Use scaled instruments to measure and compare lengths, masses, capacities and temperatures (ACMMG084) Yr 4Achievement Standard Yr 4. Students use scaled instruments to measure

temperatures, lengths, shapes and objects.Choose appropriate units of measurement for length, area, volume,

capacity and mass (ACMMG108) Yr 5

Achievement Standard Yr 5. They use appropriate units of measurement for length, area, volume, capacity and mass, and calculate perimeter and

area of rectangles.ACM Connect decimal representations to metric system (ACMMG135) (Yr 6)Convert between common metric units of length, mass and capacity (ACMMG136) Yr 6Achievement Standard Yr 6Students connect decimal representations to the metric system and choose appropriate units of measurement to perform a calculation.

Estimating mass

On your table are five bags containing various amounts of sand.By hefting them, place them in order from lightest to heaviest. Discuss what you are doing.Do you all agree on the order?What language did you use?What criteria were you using?

Tony Ryan’s Thinkers’ KeysQuestion Key Reverse Key

Improvements KeyWhat if? Key

Construction Key

BAR Key

Bigger Add Replace

Alphabet Key

Alternatives KeyBrainstorming Key

An idea to make it more challenging!Question KeyThe answer is 1000m. What

might the question be?

Reverse KeyList 10 things you would

NOT measure using centimetres.

Improvements KeyDesign a new ruler to

measure height.Explain your

changes.

What if? KeyWhat if there were no

km signposts on highways?

Construction KeyConstruct a measuring

tape that can be used to measure things around

your size.

Alphabet KeyList words from A to Z

which relate to measurement.

BAR Key (Bigger Add Replace)Discuss the use of a tape measure and suggest ways you could improve it.

Alternatives KeyList ways you could

measure the length of the classroom without using a ruler or tape

measure. Order them from least to most

effective.

Brainstorming KeyBrainstorm all the different ways you

could measure something.

A possible planning sequence

Identify the topic• Examine curriculum content and proficiency

statements• Use data to inform decisions on emphasis and

specific content needs• Select, then sequence, appropriate activities• Identify the mathematical actions in which you want

students to engage• Identify and explicitly teach and model the required

language• Model the effective use of any instruments required• Teach LENGTH, AREA, VOLUME in that order.

Possible approach:

Prepare a 4 or 5 lesson sequence and teach that before moving onto the next sub-strand.Allow children to practise their skills, language and understandings.Begin every lesson by discussing the attribute to be measured, the appropriate units of measurement, the measurement device to use and the recording method.Ask questions which help them to see connections.

Does the measurement instrument match the attribute to be measured?