Measurement, Space & Statistics
Data and Chance
Year 3 · Year 4
- ✓By the end of this lesson students will be able to collect and organise data using tally marks.
- ✓By the end of this lesson students will be able to create and interpret tables, pictographs, and column graphs.
- ✓By the end of this lesson students will be able to compare different data displays to answer questions.
- ✓By the end of this lesson students will be able to describe outcomes of chance experiments using terms like 'likely', 'unlikely', 'certain', 'impossible', and 'even chance'.
Key concepts
Data is information we collect about something. We can collect data about our favourite colours, how many pets people have, or what kind of weather we have each day.
Tally marks are a quick way to count things. We draw a vertical line for each item, and for every fifth item, we draw a diagonal line across the previous four. This makes it easy to count in groups of five.
A table is a way to organise data in rows and columns. It helps us to see information clearly and compare different pieces of data.
A pictograph uses pictures or symbols to show data. Each picture usually represents a certain number of items, and this is explained in a 'key'.
A column graph uses columns (or bars) to show data. The height of each column tells us how much of something there is. Column graphs have a title, labels for the axes, and a scale.
Chance is about how likely something is to happen. We use special words to describe how likely an event is.
These are terms we use to describe the likelihood of an event:\n- **Certain:** Something that will definitely happen. (e.g., The sun will rise tomorrow.)\n- **Likely:** Something that probably will happen, but not definitely. (e.g., It is likely to rain in winter.)\n- **Even Chance:** Something that has an equal chance of happening or not happening. (e.g., Flipping a coin and getting heads.)\n- **Unlikely:** Something that probably will not happen, but it's still possible. (e.g., It is unlikely to snow in Queensland in summer.)\n- **Impossible:** Something that cannot happen at all. (e.g., A fish will fly.)
Key facts to remember
- 1Data is information we collect.
- 2Tally marks help us count and organise data in groups of five.
- 3Tables organise data in rows and columns for clarity.
- 4Pictographs use pictures, and column graphs use columns, to show data visually.
- 5Always include a title and labels for graphs, and a key for pictographs.
- 6Chance describes how likely an event is to happen.
- 7The terms for describing chance are: Impossible, Unlikely, Even Chance, Likely, and Certain.
- 8'Even chance' means something has an equal chance of happening or not happening.
Worked examples
Example 1
The column graph below shows the favourite fruits of students in Year 3.\n\n[Imagine a column graph here with fruits on the horizontal axis: Apple, Banana, Orange, Pear, Grapes. And number of students on the vertical axis: 0 to 10. The columns show: Apple: 8 students, Banana: 10 students, Orange: 5 students, Pear: 3 students, Grapes: 6 students]\n\na) Which fruit is the most popular?\nb) How many students chose Orange as their favourite?\nc) How many more students chose Apple than Pear?
Answer
a) Banana\nb) 5 students\nc) 5 more students
Always check the labels on the axes and the title of the graph.
Example 2
A group of Year 4 students recorded the number of sunny and cloudy days in a week:\nMonday: Sunny\nTuesday: Sunny\nWednesday: Cloudy\nThursday: Sunny\nFriday: Sunny\nSaturday: Cloudy\nSunday: Sunny\n\na) Create a tally chart and a table to show this data.\nb) Create a pictograph using the data, where each sun symbol (☀️) represents 1 sunny day and each cloud symbol (☁️) represents 1 cloudy day.
Answer
a)\n**Weather in a Week**\n| Weather | Tally | Number of Days |\n|---------|---------|----------------|\n| Sunny | |||| | | 5 |\n| Cloudy | || | 2 |\n| Rainy | | 0 |\n\nb)\n**Weather in a Week**\nSunny: ☀️☀️☀️☀️☀️\nCloudy: ☁️☁️\nRainy:\nKey: ☀️ = 1 day, ☁️ = 1 day
Always include a title and a key for pictographs.
Example 3
A bag contains 5 red marbles, 1 blue marble, and 4 yellow marbles. If you pick one marble without looking, describe the chance of picking:\na) A red marble\nb) A green marble\nc) A blue marble\nd) A marble that is not blue
Answer
a) Likely\nb) Impossible\nc) Unlikely\nd) Likely
Think about how many favourable outcomes there are compared to the total number of outcomes.
Common mistakes
- ✗Forgetting to include a title for graphs or a key for pictographs.
- ✗Not reading the scale on a column graph correctly, leading to incorrect interpretations.
- ✗Miscounting tally marks, especially when there are many items to count.
- ✗Confusing 'likely' with 'certain' or 'unlikely' with 'impossible'.
- ✗Not considering all possible outcomes when describing the chance of an event.
Exam tips
- ★Read the question carefully to understand what data you need to find or what type of graph to create.
- ★When interpreting graphs, always look at the title, axis labels, and key first to understand the information.
- ★Use a ruler to draw straight lines for column graphs to make them clear and accurate.
- ★When describing chance, think about the total number of possibilities and how many of those possibilities match the event you are describing.
- ★Double-check your tally counts and any calculations you make from the data.
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