Measurement and Geometry 21 September 2011 Dianne Ogle Acknowledgement to Marie Hirst Team Solutions from 2009 Hui presentation

Objectives Have a deeper understanding of a framework for geometry and measurement (focusing on NC Levels 1 and 2). Be aware of common misconceptions that children may have and how they might be addressed. Be aware of useful resources available to teach measurement

Number Early measurement activities are a very meaningful context for counting. Measurement of important objects in the familiar environment connects ideas of number to the real world, enhancing number sense. John van de Walle

Place Value Multiples of ten are profitably used by young children in counting nonstandard measures such as the height of the door in terms of connecting cubes. The metric system of measurement is built on the base-ten system of numeration. An understanding of each topic enhances the use of and understanding of the other. John van de Walle

To measure something means that the attribute being measured is “filled” or “covered” or “matched” with a unit of measure with the same attribute. John van de Walle

To measure something we perform three steps: Decide on the attribute to be measured. Select a unit that has that attribute. Compare the units, by filling, covering, matching or using some other method with the attribute of the object being measured. The number of units required to match the object is the measure. John van de Walle

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

Book 9 Look at the beginning pages of book 9. What is the emphasis at each level? Are there any surprises? What are the implications for your teaching, planning?

Elaborations for Measurement Look at the elaborations for your level. What are the big ideas? What are suitable activities for each level. Feedback to whole group so that we all have a an overview of what measurement looks like at level one and level two.

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.

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).

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 Further support in Key Ideas Elaborations and supporting teaching resources

Time to Process Key Ideas What do you think were the key messages from this afternoon. Choose 2 things that you found out today that you found surprising or didn’t know before.

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