Statistics and data: maths lessons by year

What's taught, year by year

The steps in statistics and data, in the order children usually meet them. Years are named as in Australia; the ages are a guide.

Sort objects into groups by colour, shape or size. Put a mixed collection into groups that share one feature and say what the rule was.

Sort, count each group and say which has most or fewest. Count the objects in each sorted group and compare the groups using most, fewest and the same.
Ask a simple question and collect the answers. Ask classmates a question with a few possible answers (yes/no, favourite colour) and keep track of each reply.
Show data with real objects and drawings. Line up objects or drawings in rows, one for each answer, so the groups can be compared at a glance.

Use Venn and Carroll diagrams to sort. Sort items into a Venn diagram or a two-way Carroll diagram using one or two yes/no rules.
Record counts with tally marks. Make tally marks in fives to record answers and turn each tally into a number.
Read and make a picture graph (one picture = one). Draw one symbol for each item in a picture graph and read how many are in each category.
Answer how many more and how many in total from a graph. Use a picture graph to find totals and the difference between two categories.

Organise data in a simple table. Turn a list or tally into a table with a row for each category and its count.
Make a block graph or bar graph counting in ones. Build a bar or block graph with a labelled axis that goes up in ones and read it back.
Picture graphs where one picture stands for 2, 5 or 10. Read and draw picture graphs with a key where each symbol is worth more than one, including half symbols.
Make a dot plot of whole-number data. Place a dot above a number line for each value and spot where the data bunches up.

Read and draw bar graphs with scales of 2, 5 and 10. Draw a bar graph with a title, labels and an even scale, and read values that fall between gridlines.
Solve one- and two-step problems from bar graphs and tables. Use a graph or table to answer questions that need adding, subtracting or comparing values.
Category data and number data. Tell apart data that are words or groups (favourite fruit) from data that are numbers (number of pets).
Investigation step 1: pose a statistical question and plan. Write a question that expects different answers, decide who to ask and how to record the data.
Investigation step 2: collect and organise the data. Gather data with a survey or observation, then sort it into a tally, table or list ready to graph.
Investigation step 3: analyse the graph and write a conclusion. Describe what the display shows, answer the original question and say what you would do differently.
Line plots of measurements in halves and quarters. Measure objects to the nearest half or quarter unit and show the measurements on a line plot.

Counted data and measured data (discrete and continuous). Decide whether data come from counting or measuring and what that means for the graph.
Choose the best graph for a set of data. Compare displays of the same data and explain which one shows the comparison most clearly.
Find the mode: the most common value. Identify the value or category that appears most often in a list, table or graph.
Read line graphs that show change over time. Read values from a time-series line graph and describe when it rises, falls or stays the same.
Make a graph with a spreadsheet. Enter a small data set into a spreadsheet and produce a labelled column or line graph.

Draw a line graph from a table. Plot points from a table of values over time, join them with straight lines and label both axes.
Read and complete two-way tables. Use a table sorted two ways (for example year group and favourite sport) to find and total values.
Compare two groups with side-by-side bar graphs. Draw and read grouped bar graphs to compare two groups across the same categories.
Group measurements into intervals. Sort measured data into equal class intervals in a frequency table and graph them as a frequency diagram.
Check data for mistakes and unusual values. Spot recording errors and values far from the rest, and decide whether to keep, fix or question them.
Describe the shape and spread of a data set. Say where data clusters, whether it is spread out or bunched, and whether it is lopsided.
Find the range of a data set. Subtract the smallest value from the largest to describe how spread out the data are.
The mean as a fair share (levelling out). Share out unequal stacks equally so each has the same amount, and link that to the mean.
Read pie charts with simple fractions. Read a pie chart split into halves, quarters and tenths and work out how many each slice stands for.
Read waffle diagrams (100-square displays). Read a 10 by 10 grid display to find the fraction or percentage each category takes up.

Calculate the mean: add then divide. Find the mean by totalling the values and dividing by how many there are, and find a missing value from a known mean.
Find the median: the middle value. Order the data and find the middle value, including when there is an even number of values.
Choose the best average: mean, median or mode. Compare the three averages for a data set and explain which one describes it best.
Draw pie charts using angles. Turn each category's share into degrees of a full turn and draw the pie chart with a protractor.
Scatter graphs: is there a relationship?. Plot pairs of values on a scatter graph and describe whether one tends to rise as the other rises.
Box plots and the interquartile range. Find the quartiles of a data set and draw a box plot to show its middle half.
Mean absolute deviation. Measure spread by finding how far, on average, each value sits from the mean.
Investigate a question that compares two groups. Run a full enquiry cycle comparing two groups, using displays and averages to back up the conclusion.
Judge claims made with data in the news. Check a graph or statistic from the media for misleading scales, small samples or unsupported claims.