Week Eight: Measurement

Synthesise the big ideas

• There are four main steps that are involved in the teaching sequence for measurement:
  - Identifying the attribute/concept
  - Choose an appropriate unit of measurement for the attribute being measured
  - Measure the object using the chosen unit
  - Report the number of units (Jamieson-Proctor, 2016a) 
• Standardised and non-standard units can be used measurement (Jamieson-Proctor, 2016a) 
• Measurement can help children to learn about other topics in mathematics (Reys et al., 2012)
• Estimation is the mental process of arriving at a measurement without the aid of measuring instruments  (Reys, Lindquist, Lambdin, Smith,, Rogers, Falle, Frid, & Bennett, 2012)
• Formulas for measurements:
  - Area of rectangles and parallelograms: A = b x a
  - Area of a triangle: A = 1/2 (a x b)
  - Area of a trapezium: A = 1/2 [a x (b + B)]
  - Volume: V = l x w x h  (Reys et al., 2012, pp. 417-418) 
• "Measurement is a process by which number is assigned to an attribute of an object or event" (Reys et al., 2012, p. 405)
• There are four steps to the measurement process:
  - Identify the attribute being measured and compare objects and events
  - Measure with informal units
  - Measure with standard units
  - Apply the measurement to real-life concepts (Reys et al., 2012, p. 405)
• Different types of measurement include:
  - Length: the distance between 2 points
  - Perimeter: the distance around a region
  - Circumference: the distance around a circle
  - Capacity: how much a 3D container can hold
  - Mass: the amount of a substance
  - Weight: the pull of gravity on that substance
  - Area: the amount of surface within a plane shape or region within a boundary
  - Volume: how much space a 3D object takes up
  - Time, temperature, speed and density (Reys et al., 2012, pp. 406-411)

How have the big ideas changed your understanding of the topic?

• Although I had a basic understanding of the ideas presented this week I was unsure about how effectively to teach them. I also lacked an understanding, until this week, that non-standardised units were encouraged in teaching measurement before using standardised units 

Demonstrate your understanding of the mathematical concept and related skill and strategies children need to assimilate and be able to use, that are related to the topic of measurement

• Many different concepts this week were covered including; measurement, money, time, volume, area, length, angle, perimeter, weight, mass, capacity, temperature, 
• Length is the distance between 2 points. This concept is one that children learn early on (Reys et al., 2012)
• The skills of length:
  - Identify the attribute being measured and compare objects and events
  - Measure with informal units
  - Measure with standard units
  - Apply the measurement to real-life concepts (Reys et al., 2012, p. 405)
• Teaching strategies for length:
  - Maths picture books
  - Tapes, cubes, rulers, trundle wheel, string, paperclips, pencils, straws (Jamieson-Proctor, 2016a; Reys et al., 2012)

Language model for concept

Figure 1.34: Language model for length
Retrieved from http://leo.acu.edu.au/mod/book/view.php?id=1238196&chapterid=36568

Describe/demonstrate a specific teaching strategy and appropriate resource/s that could be used to assist children to understand a key mathematical concept related to measurement 

Different teaching strategies that are appropriate to assist children to understand the concept of length include:

• Units of length
• Measurement song
• Standardised - centimetres 
• Non-standardised - paper clips 

Describe/demonstrate a specific misconception children might have in relation to measurement

• A specific misconception that students might have in relation to the concept of length is the that if an object, such as a belt, changes shape, than the length changes. This misconception shows that children do not understand that units remain the same (Reys et al., 2012) 
• A way to remediate this specific misconception is to have children measure the same object in different shapes but explain that it is still the same length 

Provide appropriate URL links to the ACARA year, strand, substrand, content description, elaborations and Scootle resources for the earliest mention of measurement 

• Measurement can be seen in the Foundation year, ACMMG006, Measurement and Geometry strand, Using units of measurement sub-strand (ACARA, 2016)
• The content descriptors for ACMMG006 is "use direct and indirect comparisons to decide which is longer, heavier or holds more, and explain reasoning in everyday language" (ACARA, 2016, p. 1) 
• The elaborations for ACMMG006 are:
  - "comparing objects directly, by placing one object against another to determine which is longer or pouring from one container into the other to see which one holds more;
  - using suitable language associated with measurement attributes, such as 'tall' and 'taller', 'heavy' and 'heavier', 'holds more' and 'holds less'" (ACARA, 2016, pp. 2-3)
• The following are some Scootle resources that could be used to aid in the teaching of ACMMG006: 

Figure 1.35: Scootle Resource One
Retrieved from http://www.scootle.edu.au/ec/search?accContentId=ACMMG006&userlevel=(0)

Figure 1.36: Scootle Resource Two
Retrieved from http://www.scootle.edu.au/ec/search?accContentId=ACMMG006&userlevel=(0)

Figure 1.37: Scootle Resource Three
Retrieved from http://www.scootle.edu.au/ec/search?accContentId=ACMMG006&userlevel=(0)

Figure 1.38: Scootle Resource Four
Retrieved from http://www.scootle.edu.au/ec/search?accContentId=ACMMG006&userlevel=(0)

Figure 1.39 Scootle Resource Five
Retrieved from http://www.scootle.edu.au/ec/search?accContentId=ACMMG006&userlevel=(0)

Provide appropriate links to resources and ideas you have sourced personally to assist students to develop concepts, skills and/or strategies related to measurement 

Resources for students to understand the concept of length:

• Units of length
• Measurement song

Resources for students to understand the skills associated with length: 

• Measuring using standardised units and non-standardised units if I were to use this video I would pause it before the man started explaining the non-metric system of measuring and explain how we measure, using centimetres, millimetres, metres...

Resources for students to understand the teaching strategies in length:

• These videos are examples of measuring in standardised and non-standardised unit:
  - Standardised - centimetres 
  - Non-standardised - paper clips 

Provide a concise synthesis of the textbook chapter/s related to measurement

Chapter 17 - Measurement 

• Measurement provides many application to everyday life and can be used to help learn about other topics of mathematics (Reys et al., 2012)
• Children must develop estimation skills with measurement (Reys et al., 2012) 
• "Measurement is a process by which number is assigned to an attribute of an object or event" (Reys et al., 2012, p. 405)
• There are four steps to the measurement process:
  - Identify the attribute being measured and compare objects and events
  - Measure with informal units
  - Measure with standard units
  - Apply the measurement to real-life concepts (Reys et al., 2012, p. 405)
• Different types of measurement include:
  - Length: the distance between 2 points
  - Perimeter: the distance around a region
  - Circumference: the distance around a circle
  - Capacity: how much a 3D container can hold
  - Mass: the amount of a substance
  - Weight: the pull of gravity on that substance
  - Area: the amount of surface within a plane shape or region within a boundary
  - Volume: how much space a 3D object takes up
  - Time, temperature, speed and density (Reys et al., 2012, pp. 406-411)
• A unit must always remain constant (Reys et al., 2012)
• Informal units include:
  - digits, inches, hands, hand spans, feet, straws, handprints, envelopes, tiles, spoonfuls, cups, bottles, marbles, table tennis balls, rocks, buttons, fruit, coins (Reys et al., 2012, pp. 413-414) 

Figure 1.??: Standardised units (Reys et al., 2012, p. 415)

• Formulas for measurements:
  - Area of rectangles and parallelograms: A = b x a
  - Area of a triangle: A = 1/2 (a x b)
  - Area of a trapezium: A = 1/2 [a x (b + B)]
  - Volume: V = l x w x h  (Reys et al., 2012, pp. 417-418) 
• To be able to change from one unit to another, children must know the equivalence or relation between 2 units  (Reys et al., 2012)
• Estimation is the mental process of arriving at a measurement without the aid of measuring instruments  (Reys et al., 2012)

References 

Australian Curriculum Assessment and Reporting Authority. (2016). Mathematics. Retrieved from http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=1

Education Services Australia. (2016). Scootle: Mathematics. Retrieved from http://www.scootle.edu.au/ec/search?accContentId=ACMNA005&userlevel=(0)

Iken Edu. (2011). Maths for kids: Units of length. Retrieved from https://www.youtube.com/watch?v=Ll21j2r8gDc

Jamieson-Proctor, R. (2016a). EDMA202/262 mathematics learning and teaching 1: Week 8 Part 1. Retrieved from http://leo.acu.edu.au/mod/book/view.php?id=1238194&chapterid=36561

Jamieson-Proctor, R. (2016b). EDMA202/262 mathematics learning and teaching 1: Week 8 Part 2. Retrieved from http://leo.acu.edu.au/mod/book/view.php?id=1238194&chapterid=36562

Jamieson-Proctor, R. (2016c). EDMA202/262 mathematics learning and teaching 1: Week 8 Part 3. Retrieved from http://leo.acu.edu.au/mod/book/view.php?id=1238194&chapterid=36563

Matholia Channel. (2013). Measuring length in centimetres. Retrieved from https://www.youtube.com/watch?v=tuBLuIW1U70

Murdock, L. (2014). Math monsters standard and nonstandard measurement. Retrieved from https://www.youtube.com/watch?v=OetmuNyzblQ

Numberock. (2015). Metric system song for kids: Measurement music video. Retrieved from https://www.youtube.com/watch?v=djTNUp4XIRo  

Reys, R., Lindquist, M., Lambdin, D., Smith, N., Rogers, A., Falle, J., Frid, S., & Bennett, S. (2012). Helping children learn mathematics. Queensland, Australia: John Wiley & Sons Australia, Ltd.

Teaching Without Frills. (2015). Introduction to non-standard measurements for kids: Using paper clips to measure. Retrieved from https://www.youtube.com/watch?v=q8o7n-A0SC0