Year Level: Year 3
ACARA Outcomes:
Chance- Conduct chance experiments, identify and describe possible outcomes and recognise variation in results (ACMSP067).
Data representation and interpretation- Collect data, organise into categories and create displays using lists, tables, picture graphs and simple column graphs, with and without the use of digital technologies (ACMSP069).
Proficiency Strands:
Understanding includes connecting number representations with number sequences, partitioning and combining numbers flexibly, representing unit fractions, using appropriate language to communicate times, and identifying environmental symmetry.
Fluency includes recalling multiplication facts, using familiar metric units to order and compare objects, identifying and describing outcomes of chance experiments, interpreting maps and communicating positions.
Problem Solving includes formulating and modelling authentic situations involving planning methods of data collection and representation, making models of three-dimensional objects and using number properties to continue number patterns.
Reasoning includes using generalising from number properties and results of calculations, comparing angles, creating and interpreting variations in the results of data collections and data displays.
Prior Knowledge: Year 2
Chance- Identify practical activities and everyday events that involve chance. Describe outcomes as ‘likely’ or ‘unlikely’ and identify some events as ‘certain’ or ‘impossible’ (ACMSP047).
Data representation and interpretation- Identify a question of interest based on one categorical variable. Gather data relevant to the question (ACMSP048).
Collect, check and classify data (ACMSP049).
Create displays of data using lists, table and picture graphs and interpret them (ACMSP050).
Learning Objectives:
Students are able to confidently conduct chance experiments and list possible outcomes. They carry out simple data investigations for categorical variables.
Misconceptions to Consider:
- Students may become confused with probability and fractions.
- Language or cultural barriers must be considered before planning lessons.
- The concept that the students must understand in order to understand this topic is that some events, such as the probability of picking a certain skittle is varied due to the amount of each colour there is.
- Students may think that the outcome of one event affects the outcome of the next, e.g. flipping a coin and it landing on heads doesn't mean it will land on tails the next time flipped.
References:
Australiancurriculum.edu.au, (2015). Mathematics Foundation to Year 10 Curriculum by rows - The Australian Curriculum v7.3. [online] Available at: http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=1#level3 [Accessed 23 Mar. 2015].
Clements, D. H., & Sarama, J. (2004). Learning trajectories in mathematics education. Mathematical Thinking and Learning, 6(2), 81-89.
Probability – more, less or equally likely to happen. (n.d.). Retrieved March 23, 2015, from Math 4 Children Plus: http://www.math4childrenplus.com/probability-more-less-or-equally-likely-to-happen/
Probability Game for Kids. (n.d.). Retrieved March 23, 2015, from Kids Maths Games Online: http://www.kidsmathgamesonline.com/numbers/probability.html
Warner, M. (2015). Probability Cards . Retrieved March 23, 2015, from Teaching Ideas: http://www.teachingideas.co.uk/maths/probabilitycards.htm
Sarama, J., & Clements, D. _2009. Teaching maths in the primary grades: The learning trajectories approach. Young Children, 64_2_, 63-65. Accessed 10/3.
ACARA Outcomes:
Chance- Conduct chance experiments, identify and describe possible outcomes and recognise variation in results (ACMSP067).
Data representation and interpretation- Collect data, organise into categories and create displays using lists, tables, picture graphs and simple column graphs, with and without the use of digital technologies (ACMSP069).
Proficiency Strands:
Understanding includes connecting number representations with number sequences, partitioning and combining numbers flexibly, representing unit fractions, using appropriate language to communicate times, and identifying environmental symmetry.
Fluency includes recalling multiplication facts, using familiar metric units to order and compare objects, identifying and describing outcomes of chance experiments, interpreting maps and communicating positions.
Problem Solving includes formulating and modelling authentic situations involving planning methods of data collection and representation, making models of three-dimensional objects and using number properties to continue number patterns.
Reasoning includes using generalising from number properties and results of calculations, comparing angles, creating and interpreting variations in the results of data collections and data displays.
Prior Knowledge: Year 2
Chance- Identify practical activities and everyday events that involve chance. Describe outcomes as ‘likely’ or ‘unlikely’ and identify some events as ‘certain’ or ‘impossible’ (ACMSP047).
Data representation and interpretation- Identify a question of interest based on one categorical variable. Gather data relevant to the question (ACMSP048).
Collect, check and classify data (ACMSP049).
Create displays of data using lists, table and picture graphs and interpret them (ACMSP050).
Learning Objectives:
Students are able to confidently conduct chance experiments and list possible outcomes. They carry out simple data investigations for categorical variables.
Misconceptions to Consider:
- Students may become confused with probability and fractions.
- Language or cultural barriers must be considered before planning lessons.
- The concept that the students must understand in order to understand this topic is that some events, such as the probability of picking a certain skittle is varied due to the amount of each colour there is.
- Students may think that the outcome of one event affects the outcome of the next, e.g. flipping a coin and it landing on heads doesn't mean it will land on tails the next time flipped.
References:
Australiancurriculum.edu.au, (2015). Mathematics Foundation to Year 10 Curriculum by rows - The Australian Curriculum v7.3. [online] Available at: http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=1#level3 [Accessed 23 Mar. 2015].
Clements, D. H., & Sarama, J. (2004). Learning trajectories in mathematics education. Mathematical Thinking and Learning, 6(2), 81-89.
Probability – more, less or equally likely to happen. (n.d.). Retrieved March 23, 2015, from Math 4 Children Plus: http://www.math4childrenplus.com/probability-more-less-or-equally-likely-to-happen/
Probability Game for Kids. (n.d.). Retrieved March 23, 2015, from Kids Maths Games Online: http://www.kidsmathgamesonline.com/numbers/probability.html
Warner, M. (2015). Probability Cards . Retrieved March 23, 2015, from Teaching Ideas: http://www.teachingideas.co.uk/maths/probabilitycards.htm
Sarama, J., & Clements, D. _2009. Teaching maths in the primary grades: The learning trajectories approach. Young Children, 64_2_, 63-65. Accessed 10/3.