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Data and chance in primary school maths: how to help at home
What children learn about data and chance from Foundation to Year 6, why chance starts in Year 3, and simple ways to practise graphs and probability at home.
Read the guideKey points
Data work starts in Foundation, where children "collect, sort and compare data represented by objects and images" [1]. Chance does not appear until Year 3 [2][3][4].
In Year 3 children describe events as "likely" or "unlikely" and some as "certain" or "impossible", and run repeated chance experiments [4].
By Year 6 children place probabilities on a scale of 0 to 1 or 0 to 100 per cent and critique statistical claims made in the media [7].
Research with Australian primary students found predictions from a data table improved markedly between Year 3 and Year 4, while explanations lagged behind [8].
What do children learn, year by year?
Data and chance are the parts of primary maths parents notice least: they produce fewer worksheets than number work and less homework than times tables. They also show up most often in adult life, in weather forecasts, sports statistics, health advice and advertising claims. This guide traces what the Australian Curriculum expects year by year, then sets out practical ways to help at home.
The curriculum separates two strands: Statistics covers collecting, representing and interpreting data, and Probability covers chance and likelihood.
In Foundation, children "collect, sort and compare data represented by objects and images" in response to investigative questions about familiar situations [1].
In Year 1, children "acquire and record data for categorical variables in various ways" and represent it "using one-to-one displays" [2], meaning one sticker, block or square for each item counted.
In Year 2, data is gathered "through surveys, observation, experiment and using digital tools", sorted into lists and tables, and children create different graphical representations and compare their features [3].
Year 3 is where numerical data arrives: children acquire data "for categorical and discrete numerical variables", record it in frequency tables and spreadsheets, and conduct guided statistical investigations [4]. Chance also begins. Children "identify practical activities and everyday events involving chance", describe outcomes as "likely" or "unlikely", identify some as "certain" or "impossible" explaining reasoning, and conduct repeated chance experiments, recording the results and discussing the variation [4].
In Year 4, children use many-to-one pictographs and column graphs, analyse "the effectiveness of different displays or visualisations" and discuss the shape of distributions [5]. In chance, they order outcomes by likelihood and begin to identify independent or dependent events [5].
In Year 5, data work extends to nominal and ordinal categorical variables, interpreting line graphs representing change over time, and planning statistical investigations [6]. In chance, children list the outcomes of experiments involving equally likely outcomes "and compare to those which are not equally likely", then use frequency to estimate likelihoods [6].
In Year 6, children compare data sets "in terms of mode, range and shape", and identify "statistically informed arguments presented in traditional and digital media", critiquing the methods and conclusions [7]. Probabilities are placed on "numerical scales of 0-1 or 0%-100%" using fractions, percentages and decimals, and children run simulations with more and more trials, discussing "the effect on variation of increasing the number of trials" [7].
Two things stand out. Chance language is formal from the start: certain, impossible, likely and unlikely are curriculum terms, not loose description. And the Year 6 media work is as much a reading skill as a maths one.
What do children find difficult?
Australian research gives a useful picture of the data side. Oslington, Mulligan and Van Bergen followed 44 students at one metropolitan Sydney school from Year 3 into Year 4, asking them to predict monthly maximum temperatures from a data table [8]. The share making at least ten reasonable predictions out of twelve rose from 54 per cent to 87 per cent, and the share whose drawn representations reorganised the data rather than copying it rose from 19 per cent to 71 per cent [8]. Explanations improved more slowly: those coordinating the rows and columns of the table rose only from 15 per cent to 36 per cent [8]. This was one cohort at one relatively advantaged school, so the figures describe those students rather than children generally.
On the chance side, a study of 776 pupils aged 9 to 12 in Cyprus used tree diagrams to test probabilistic thinking. On one such question, 68 per cent correctly judged which outcome was more likely, yet across the whole sample only a handful of pupils could calculate a probability at all, and about one in six explained their answer using subjective reasons such as the length of a path rather than the number of possible outcomes [9]. The data were collected in 2000 in a different school system, so the figures are indicative rather than Australian. The pattern will be familiar to teachers: children often reach the right answer about likelihood for the wrong reason.
How can you help at home?
Collect real data, in small amounts. The Mathematics Hub, funded by the Australian Government Department of Education, advises families that "travelling, shopping, cooking and making are all great times to talk about numbers, measurements, shapes" [10]. Rainfall for a week, travel times to school, or the colours of cars in a car park are enough. Because the curriculum works through investigative questions, decide what you want to find out before counting anything.
Ask what the display hides. Once a graph is drawn, the useful question is not only which bar is tallest. Ask what the graph does not tell you, whether a different display would show it better, and whether the answer would change with more data. That matches the Year 4 expectation of analysing how effective a display is [5].
Use the chance words precisely. When something is certain or impossible, say so in those words. When your child says something always happens, ask whether it is certain or just likely. This builds the vocabulary the Year 3 curriculum asks for [4].
Run the experiment more than once. Rolling a die ten times, then sixty times, and comparing the results is what Year 6 asks children to do with simulations [7]. It is also the quickest way to counter the common belief that a run of one outcome makes the opposite outcome due.
Read one claim together. A single advertisement or headline containing a percentage is enough for the Year 6 skill of critiquing statistical arguments [7]. Ask who was surveyed, how many people, and what is being compared.
Keep practice short and regular. Printable worksheets for data (/worksheets/maths/topic/data) and chance (/worksheets/maths/topic/chance), with answer keys, are free at /worksheets/maths. For the year-level expectations behind all of this, see what the curriculum expects in each year (/learn/is-my-child-on-track), and for the related strand, measurement in Years 3 to 6 (/learn/measurement-years-3-to-6-how-to-help-at-home).
How Noooli can help
Noooli publishes free printable maths worksheets for Kindergarten to Year 6, with answer keys and no sign-up, at /worksheets/maths. There is also short daily maths practice of about ten minutes, aligned to the Australian Curriculum, with progress parents can see. Noooli is also on the App Store and Google Play: get the app (/free/app).
References
1. Queensland Curriculum and Assessment Authority, "Australian Curriculum v9.0 mathematics: Prep achievement standard and content description alignment". https://www.qcaa.qld.edu.au/downloads/aciqv9/mathematics/curriculum/ac9_maths_prep_as_cd_alignment.pdf
2. Queensland Curriculum and Assessment Authority, "Australian Curriculum v9.0 mathematics: Year 1 alignment". https://www.qcaa.qld.edu.au/downloads/aciqv9/mathematics/curriculum/ac9_maths_yr1_as_cd_alignment.pdf
3. Queensland Curriculum and Assessment Authority, "Australian Curriculum v9.0 mathematics: Year 2 alignment". https://www.qcaa.qld.edu.au/downloads/aciqv9/mathematics/curriculum/ac9_maths_yr2_as_cd_alignment.pdf
4. Queensland Curriculum and Assessment Authority, "Australian Curriculum v9.0 mathematics: Year 3 alignment". https://www.qcaa.qld.edu.au/downloads/aciqv9/mathematics/curriculum/ac9_maths_yr3_as_cd_alignment.pdf
5. Queensland Curriculum and Assessment Authority, "Australian Curriculum v9.0 mathematics: Year 4 alignment". https://www.qcaa.qld.edu.au/downloads/aciqv9/mathematics/curriculum/ac9_maths_yr4_as_cd_alignment.pdf
6. Queensland Curriculum and Assessment Authority, "Australian Curriculum v9.0 mathematics: Year 5 alignment". https://www.qcaa.qld.edu.au/downloads/aciqv9/mathematics/curriculum/ac9_maths_yr5_as_cd_alignment.pdf
7. Queensland Curriculum and Assessment Authority, "Australian Curriculum v9.0 mathematics: Year 6 alignment". https://www.qcaa.qld.edu.au/downloads/aciqv9/mathematics/curriculum/ac9_maths_yr6_as_cd_alignment.pdf
8. Oslington, G. R., Mulligan, J. and Van Bergen, P., "The development of predictive reasoning in Grades 3 through 4", in Leong, Y. H. et al. (eds), Excellence in Mathematics Education: Foundations and Pathways, Mathematics Education Research Group of Australasia, 2021, pages 305 to 312. https://files.eric.ed.gov/fulltext/ED616268.pdf
9. Lamprianou, I. and Afantiti Lamprianou, T., "The probabilistic thinking of primary school pupils in Cyprus: the case of tree diagrams", University of Manchester, data collected 2000. https://files.eric.ed.gov/fulltext/ED501002.pdf
10. Mathematics Hub, "Families", Education Services Australia for the Australian Government Department of Education. https://www.mathematicshub.edu.au/families/
Common questions
When do children start learning about chance in Australian primary schools?
Chance first appears as its own strand in Year 3, where children describe events as likely, unlikely, certain or impossible, and conduct repeated chance experiments. Foundation to Year 2 covers collecting, sorting and displaying data, but contains no probability content at all.
What is the difference between statistics and probability in primary maths?
Statistics is about collecting, displaying and interpreting data, which starts in Foundation. Probability is about how likely something is, which starts in Year 3. By Year 6 children express probabilities on a scale from 0 to 1 or 0 to 100 per cent.
How can I help my child with graphs at home?
Collect a small set of real data together, such as weather or travel times, then ask your child to choose a display and explain what it shows. Asking what the graph does not tell you is as useful as asking them to read values from it.
