A Closer Look at Measurement Lead Teacher Symposium 2009 Marie Hirst (Many thanks to Michael Drake from VUW, Bruce Moody, Monica North and Bev Dunbar whose research and ideas have contributed to this workshop)

Objectives Have a deeper understanding of a framework for measurement (focusing on NC Levels 1 to 3). Be aware of common misconceptions that children may have and how they might be addressed. Be aware of useful resources available to teach measurement Follow up by taking a similar workshop with your own staff in school. (use wikispace for resources)

Measurable Qualities/Attributes What attribute is this arrangement of balls ordered by? Objects have many attributes that can be measured. Measurement is the quantification of spatial attributes. Time is a special attribute as it is not tangibly attached to physical objects. Guess the secret attribute!

Prior knowledge In 2 minutes brainstorm everything you know about your focus measurement attribute. Organise these into National Curriculum Levels 1- 4 Now add any questions you may have. Share 1 question

Look at the achievement objectives for each national curriculum level and highlight any key words. Add the strategy stages for each level. Add the appropriate number range children should be working with at each stage.

Ttributes co Five phases L1 L1/2 L2/3 L4/5 Identifying the attribute Volume / Capacity Time Ttributes co Five phases Identifying the attribute Comparing and Ordering Non-Standard Units Standard Units Applying & Interpreting L1/2 L1 L4/5 L2/3

Identify the attribute Look at the giant handprint. What attributes could be measured? Which language could be used? - Play Will They Fit? (Bev Dunbar resource) - Too Heavy (Bev Dunbar resource)

Order and Compare Direct Comparison: Compare the giant handprint with your own. Indirect Comparison: In groups of 4, compare your hand length with the person on your left only. Now order all 4 hand lengths. Play ‘Order the Children’. Order 3 or more objects by using a third party e.g. string to measure against.

Non-Standard Units The Kings Foot 1 2 3 What is happening? Counting the steps rather than the ‘interval of space’. How do you count the interval of time in seconds?..”1001” If a foot didn’t fit - it was turned on it’s side and counted as another unit! Some kids thought the faster you walk, the less number of steps it takes!! Children may think that 6 finger lengths are longer than 4 feet.

Key ideas when teaching non-standard units focus on the process of repeatedly using a unit as a measuring device. Generalise principals of counting to measuring. Develop key ideas how units work: - Units are a part of the attribute being measured. - Units must be the same size. - Units must fit together with no overlaps or gaps, ‘tiling’ N.B.children tend to choose units matching the shape - Units can be partitioned (e.g. halves) and joined. - Choose appropriate units of measure. - Understand the limitations of non-standard units. Estimation should be encouraged early.

Standard Units Misconceptions when using standard rulers Measure the length of the stick with the broken ruler. What do you think counters (stages 1-4), and adders (stages 5-6) would do? Compare your thoughts with research undertaken by Michael Drake. Need time to study the instruments used before using the instruments to measure!

Why might EA and AC thinkers struggle with mm on a ruler?

Level 2 Old Curriculum Level 2 New Curriculum M2:1 carry out practical measuring tasks, using appropriate metric units for length, mass, and capacity; Level 2 New Curriculum GM1: Create and use appropriate units and devices to measure length, area, volume and capacity, weight (mass), turn (angle), temperature and time. My answers: Lots of reasons really – firstly the curriculum we have been following Flick up the ruler Started using the ruler too early The ruler has no zero – how can you learn to start from zero if there isn’t one? The cm scale is actually 2 scales nested together. How do you teach using that? (2 options – measure in whole centimetres then change units - cos you use little units for measuring little things, or measure in whole centimetres and swap to points) Second: Differences between measuring length and counting processes [model with unifix cubes or counters on OHP]

Creating a ‘feel’ for size of units by using the teaching model Using Number Properties Using Imaging Using Materials New Knowledge & Strategies Existing Knowledge & Strategies

Standard Units using information from the Measurement ”Units of Work” section on nzmaths Read the section on “standard units” Everyone on your table will have a different attribute to focus on. Share with your partner: - the sequence of introduction of units - an example of how the unit(s) might be given meaning, i.e. create a feel for. - your own benchmark for the unit - another point of interest (if any)

Understanding a ‘ruler’ Understand that linear scales are created by additively joining the units together The standardised King’s Foot ruler! Explore the straw 1cm pieces to develop an understanding of the size of the standard unit. Establish your own reference/benchmark for 1 cm. Create a 10 centimetre ruler by threading 10 straw cm pieces together on string or mark these intervals alongside a cardboard strip. Introduce a standard ruler. This involves reading linear scales where the cm marks show the endpoints of units and has a baseline (zero).

Key ideas when Teaching Level 2 Extend understanding of non-standard units; - Units can be partitioned or joined, - Choose appropriate units of measure - Understand the limitations of non-standard units). Create ‘measurement devices’ before more structured instruments are introduced. Progress to simple standard units. (A diversity of metric units are required at Level 3). Consider numeracy links when using units (standard or non-standard).

Key Ideas when Teaching Level 3 Strong focus on diverse range of standard units, specifically the metric system. Choose appropriately. Know the names, prefixes and ‘feel’ for the size of units. Use scaled instruments such as rulers and protractors effectively and read graduated containers. Connect place value understanding to relationships between units of the same attribute e.g. 1cm is one tenth of 1 metre. Begin to see relationships between length and area or length and volume for rectangles and cuboids. (second AO in the new curriculum)

Level 3 “A Giant Mystery” http://www.nzmaths.co.nz/node/412 Can we use the hand print of the giant to to determine her size? Discuss the possible relationship between hand size (length and span) and body height. Can you identify a relationship… A person is ? times her hand length? Measure your groups hand length and height. Enter each persons details onto the excel spreadsheet. Create a scatterplot graph to show the relationship Using the data is it possible to predict the giants height? What other factors may you need to consider when making your statement?

How does this compare to the Guiness Book of Records world’s tallest man? Robert Wadlow (1918 - 1940) (Illinois, USA) 2.72m (8ft 11inches) Wadlow's greatest recorded weight was 222.71 kg (35st 1lb) on his 21st birthday and he weighed 199 kg (31st 5lb) at the time of his death. His shoe size was 37AA (47 cm, 18½ inches long) and his hands measured 32.4 cm (12¾ inches) from the wrist to the tip of the middle finger. He wore a size 25 ring. His arm span was 2.88m (9 ft 5¾ in) and his peak daily food consumption was 8000 calories.

Reading and Using linear Scales Level 3: Use linear scales and whole numbers of metric units for length, area,…... What do you think the term ‘linear’ scales refers to? Explore some scales assessments sourced from the ARBs. Discuss Michael Drake’s research on scales with Y7/8 children. What implications for numeracy need to be considered when teaching reading scales?

Scales using a number stick Book 9 p6 - 10

Measurement Game Created by Cathy from Corran School for Girls Roll 2 die to randomly get selections. Then invent a question that would use this combination of attribute and quantity in the answer. E.g. How long is my finger? Time Mass Length Area Temperature Free Choice Millimetre Centimetre Metre Kilometre Light year Free choice

Measurement Resources Figure It Out NZMaths website Units of work 2nd tier support material BSM and Book 9 Bev Dunbar (levels 1/ 2)

Curriculum Support

Measurement Units of Work on nzmaths

Numeracy Project Books BSM and Book 9

Student Profiles

Measurement as a context for number Read, write and order numbers and decimals (Number Knowledge) e.g. put lengths in order Ordering and Comparing - find the difference e.g. my hand is 4cm longer than your hand. Estimating and finding the difference e.g.I thought the door was 187cm high, but it was really 215cm high. That’s a difference of 28cm. Solve number story problems using measurement as the context. e.g. the plant was originally 12cm high, after two weeks it was 19cm, how much had it grown? Specific attribute problem types e.g. finding perimeters using additive strategies Interpreting Scales e.g. reading unmarked intervals between 0g and 250g Finding equivalence between units (AA / AM) e.g. 3 km = 3000m, 1.25m = 125cm

Time to Process Key Ideas What do you think were the key messages from this workshop. Choose 2 things that you found out today that you found surprising or didn’t know before. If you were running a follow up workshop with your staff - what key points would you choose to share - how?

Objectives Have a deeper understanding of a framework for measurement (focusing on NC Levels 1 to 3). Be aware of common misconceptions that children may have and how they might be addressed. Be aware of useful resources available to teach measurement Follow up by taking a similar workshop with your own staff in school. (use wikispace for resources)

Measurement units you may not have heard of! 365.25 days of drinking low-calorie beer : 1 lite year Half of a large intestine: 1 semicolon 1000 aches: 1 megahurtz 1 million bicycles: 2 megacycles 2000 mockingbirds: two kilomockingbirds 1 millionth of a fish: 1 microfiche 1 trillion pins: 1 terrapin 10 rations: 1 decoration Marie Hirst m.hirst@auckland.ac.nz

Resources required for workshop Number stick and labels I have who has game, 6 balls for ordering A3 back to back : NC Objectives and Attribute brainstorm Measurement game and dice Straws, string, cardboard rulers Example scale reading assessments from ARBs Bev Dunbar Level 1 Activities Order the children game Broken paper rulers and sticks A3 Giant Hand, rulers, tape measures etc Handout to include: Front Cover with website links/wikispace Scale reading research by Michael Drake Summary of measurement Measurement game, Copies of Bev Dunbar Game and reference Measurement links to sub-strands and strands