Theory
Common Student Misconceptions
Length
Volume
Mass
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Area
Time
Angles
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Mathematics Language - Measurement
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Early years
Comparing socks Early years: Key learning concept of measurement through comparing processes that include observing and describing similarities and differences between objects, and sorting, matching, ordering and classifying objects according to attributes such as size and shape. Objective: Student will develop knowledge of language relating to length comparisons. (Adapted from NRICH, n.d.)
Foundation Comparison and Ordering Use direct and indirect comparisons to decide which is longer, heavier or holds more, and explain reasoning in everyday language (ACMMG006) Objective: Children will demonstrate their ability to compare the size of their feet with other feet (including area and length) and then demonstrate their ability to place the feet in order of length. (Adapted from TES Australia, 2013)
Year 6 Greenhouses Calculate the perimeter and area of rectangles using familiar metric units (ACMMG109) Objective: Students demonstrate a comparison of length and areas between two areas to solve a problem |
We need to rearrange the classroom for storytelling. How many desks can I fit in a row along the back of the classroom?
The Cirque de Soleil show runs for 2 hours and 10 mins. If the show finishes at 7:40pm what time does the show start? A soccer field needs to be fenced. The area of the field is 7000 square metres. How many metres of fencing will be required? I am buying 6 chickens and need to build a chicken pen. Each chicken requires 1 square metre of pen. How much space will I require? The space I have is 5.5 metres by 4.5 metres, do I have enough space? A cube has a surface area of ninety-six square centimetres. What is the volume of the cube? (Adapted from Purple Maths, n.d.) |
(Adapted from Suh, n.d.)
Resources
Curriculum Map
In the Early Years Learning Framework (Document 16, outcome 5, p. 6) children will learn the key learning concept of measurement through comparing processes that include observing and describing similarities and differences between objects, and sorting, matching, ordering and classifying objects according to attributes such as size and shape. They will also develop predicting and estimating skills that includes thinking about objects and data and making informed deductions and inferences, for example estimating numbers and measurements. They will develop concepts such as height, length and mass. (Charles Sturt University Early Years Learning Framework Consortium, 2009)
Measurement is found in the Australian Curriculum from Foundation to Year 6.
FOUNDATION
YEAR 1
YEAR 2
YEAR 3
YEAR 4
YEAR 5
YEAR 6
Measurement is found in the Australian Curriculum from Foundation to Year 6.
FOUNDATION
- Use direct and indirect comparisons to decide which is longer, heavier or holds more, and explain reasoning in everyday language (ACMMG006)
- Compare and order the duration of events using the everyday language of time (ACMMG007)
- Connect days of the week to familiar events and actions (ACMMG008)
YEAR 1
- Measure and compare the lengths and capacities of pairs of objects using uniform informal units (ACMMG019)
- Tell time to the half-hour (ACMMG020)
- Describe duration using months, weeks, days and hours (ACMMG021)
YEAR 2
- Compare and order several shapes and objects based on length, area, volume and capacity using appropriate uniform informal units (ACMMG037)
- Compare masses of objects using balance scales (ACMMG038)
- Tell time to the quarter-hour, using the language of 'past' and 'to' (ACMMG039)
- Name and order months and seasons (ACMMG040)
- Use a calendar to identify the date and determine the number of days in each month (ACMMG041)
YEAR 3
- Measure, order and compare objects using familiar metric units of length, mass and capacity (ACMMG061)
- Tell time to the minute and investigate the relationship between units of time (ACMMG062)
- Identify angles as measures of turn and compare angle sizes in everyday situations (ACMMG064)
YEAR 4
- Use scaled instruments to measure and compare lengths, masses, capacities and temperatures (ACMMG084)
- Compare objects using familiar metric units of area and volume (ACMMG290)
- Convert between units of time (ACMMG085)
- Use am and pm notation and solve simple time problems (ACMMG086)
- Compare the areas of regular and irregular shapes by informal means (ACMMG087)
- Compare angles and classify them as equal to, greater than or less than a right angle (ACMMG089)
YEAR 5
- Choose appropriate units of measurement for length, area, volume, capacity and mass (ACMMG108)
- Calculate the perimeter and area of rectangles using familiar metric units (ACMMG109)
- Compare 12- and 24-hour time systems and convert between them (ACMMG110)
- Estimate, measure and compare angles using degrees. Construct angles using a protractor (ACMMG112)
YEAR 6
- Connect decimal representations to the metric system (ACMMG135)
- Convert between common metric units of length, mass and capacity (ACMMG136)
- Solve problems involving the comparison of lengths and areas using appropriate units (ACMMG137)
- Connect volume and capacity and their units of measurement (ACMMG138)
- Interpret and use timetables (ACMMG139)
- Investigate, with and without digital technologies, angles on a straight line, angles at a point and vertically opposite angles. Use results to find unknown angles (ACMMG141)
References
Charles Sturt University Early Years Learning Framework Consortium. (2009). Document 16 outcome 5: Children are effective communicators. Retrieved
from http://www.earlyyears.sa.edu.au/files/links/16_Outcome_5.pdf
Dudgeon, J. & Hansen, A. (2011). Measures. In S. Hansen (Ed.), Children’s errors in mathematics: Understanding common misconceptions in primary schools
(2nd ed.) (pp. 99-121). Exeter, England: Learning Matters.
Education Services Australia. (n.d.) Curriculum. Retrieved from http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=1
Haylock, D. (2014). Mathematics explained for primary teachers. London, England: SAGE Publications.
Lehrer, R., Jaslow, L., & Curtis, C. (2013). Developing an understanding of measurement in the elementary grades. In D. Clements & G. Bright (Eds.), Learning and teaching measurement: 2003 yearbook (pp. 100-121). Reston, VA: The National Council of Teachers of Mathematics.
McDonough, A., Cheeseman, J., & Ferguson, S. (2013). Young children's emerging understandings of the measurement of mass. Australasian Journal of
Early Childhood 38(4), 13-20. Retrieved from http://search.informit.com.au.ezproxy1.acu.edu.au/fullText;dn=200348;res=AEIPT
NRICH. (n.d.). Socks. Retrieved from http://nrich.maths.org/content/id/11218/Socks.pdf
Suh, J. (n.d.). Finding perimeter and area. Retrieved from http://illuminations.nctm.org/lesson.aspx?id=2176
TES Australia. (2013). Early childhood maths activities. Retrieved from http://www.tesaustralia.com/ResourceDetail.aspx?storyCode=6024949&
Van de Walle, J., Karp, K., & Bay-Williams, J. (2014). Elementary and middle school mathematics teaching developmentally (8th ed.). Essex, England: Pearson Education.
from http://www.earlyyears.sa.edu.au/files/links/16_Outcome_5.pdf
Dudgeon, J. & Hansen, A. (2011). Measures. In S. Hansen (Ed.), Children’s errors in mathematics: Understanding common misconceptions in primary schools
(2nd ed.) (pp. 99-121). Exeter, England: Learning Matters.
Education Services Australia. (n.d.) Curriculum. Retrieved from http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=1
Haylock, D. (2014). Mathematics explained for primary teachers. London, England: SAGE Publications.
Lehrer, R., Jaslow, L., & Curtis, C. (2013). Developing an understanding of measurement in the elementary grades. In D. Clements & G. Bright (Eds.), Learning and teaching measurement: 2003 yearbook (pp. 100-121). Reston, VA: The National Council of Teachers of Mathematics.
McDonough, A., Cheeseman, J., & Ferguson, S. (2013). Young children's emerging understandings of the measurement of mass. Australasian Journal of
Early Childhood 38(4), 13-20. Retrieved from http://search.informit.com.au.ezproxy1.acu.edu.au/fullText;dn=200348;res=AEIPT
NRICH. (n.d.). Socks. Retrieved from http://nrich.maths.org/content/id/11218/Socks.pdf
Suh, J. (n.d.). Finding perimeter and area. Retrieved from http://illuminations.nctm.org/lesson.aspx?id=2176
TES Australia. (2013). Early childhood maths activities. Retrieved from http://www.tesaustralia.com/ResourceDetail.aspx?storyCode=6024949&
Van de Walle, J., Karp, K., & Bay-Williams, J. (2014). Elementary and middle school mathematics teaching developmentally (8th ed.). Essex, England: Pearson Education.