Space, Measurement & Data
Data Handling: Graphs and Introduction to Probability
Grade 4 · Grade 5 · Grade 6
- ✓By the end of this lesson students will be able to collect and organise data using tally marks and tables.
- ✓By the end of this lesson students will be able to represent data using pictographs and bar graphs, and interpret information from them.
- ✓By the end of this lesson students will be able to describe the likelihood of events using appropriate vocabulary.
- ✓By the end of this lesson students will be able to identify possible outcomes of simple events and express probability as a fraction.
- ✓By the end of this lesson students will be able to draw conclusions and make comparisons based on presented data.
Key concepts
Data handling is about collecting, organising, representing, and interpreting information (data). We use data handling to understand things better and make decisions.
To collect data, we can ask questions or observe. We then organise this data using tally marks and tables. A tally mark ( | ) represents one item, and every fifth tally mark is drawn across the previous four ( |||| ) to make counting easier.
A pictograph uses pictures or symbols to represent data. Each picture or symbol stands for a certain number of items, which is explained in the 'key'. Pictographs must have a title and labels.
A bar graph uses bars of different lengths or heights to show data. The length or height of each bar represents the quantity of an item. Bar graphs must have a title, labels for both axes (horizontal and vertical), and a clear scale on the numerical axis.
A pie chart is a circle divided into sectors, where each sector represents a part of the whole. The size of each sector shows the proportion of that part. For Grades 4-6, we mainly focus on interpreting simple pie charts, understanding that bigger slices mean more.
Interpreting data means looking at the organised or represented data (like a graph) and understanding what it tells us. We can find the most popular item, the least popular, compare different items, and draw conclusions.
Probability is about how likely something is to happen. We use words to describe the chance of an event occurring.
We describe the likelihood of an event using words like:\n- 'Impossible': It cannot happen.\n- 'Unlikely': It probably will not happen.\n- 'Equally likely': It has the same chance of happening or not happening (e.g., a 50/50 chance).\n- 'Likely': It probably will happen.\n- 'Certain': It will definitely happen.
An 'outcome' is a possible result of an event. For example, when you flip a coin, the outcomes are 'heads' or 'tails'. We can express probability as a fraction: (Number of favourable outcomes) / (Total number of possible outcomes).
Key facts to remember
- 1Data handling involves collecting, organising, representing, and interpreting data.
- 2Tally marks are used to count items, with every fifth mark crossing the previous four.
- 3Pictographs use pictures and a key to show data.
- 4Bar graphs use bars to represent quantities, requiring a title, labelled axes, and a scale.
- 5Always read the 'key' in a pictograph and the 'scale' on a bar graph carefully.
- 6Probability describes how likely an event is to happen.
- 7Words like 'impossible', 'unlikely', 'equally likely', 'likely', and 'certain' are used to describe likelihood.
- 8The probability of an event can be expressed as a fraction: (Number of favourable outcomes) / (Total number of possible outcomes).
Worked examples
Example 1
A Grade 5 class voted for their favourite fruit. Here are the results:\nApple: 8 votes\nBanana: 10 votes\nOrange: 6 votes\nGrape: 4 votes\n\n1. Organise this data into a tally table.\n2. Draw a bar graph to represent this data.
Answer
1. **Tally Table:**\n | Fruit | Tally Marks | Frequency |\n |---------|-------------|-----------|\n | Apple | |||| ||| | 8 |\n | Banana | |||| |||| | | 10 |\n | Orange | |||| | | 6 |\n | Grape | |||| | 4 |\n\n2. **Bar Graph:** (Imagine a bar graph with the following features)\n * **Title:** Favourite Fruits of Grade 5 Class\n * **Vertical Axis (y-axis):** Number of Votes (Scale: 0, 2, 4, 6, 8, 10)\n * **Horizontal Axis (x-axis):** Fruit (Labels: Apple, Banana, Orange, Grape)\n * **Bars:**\n * Apple: Bar height up to 8\n * Banana: Bar height up to 10\n * Orange: Bar height up to 6\n * Grape: Bar height up to 4
Remember to always include a title, labels for both axes, and a clear scale on your bar graphs.
Example 2
Look at the pictograph below showing the number of books read by four friends in a month.\n\n**Books Read in a Month**\nThabo: 📚📚📚📚\nSipho: 📚📚📚📚📚📚\nLindi: 📚📚📚\nZola: 📚📚📚📚📚\n\n**Key:** 📚 = 2 books\n\n1. How many books did Sipho read?\n2. Who read the fewest books?\n3. How many more books did Thabo read than Lindi?
Answer
1. Sipho read 12 books.\n2. Lindi read the fewest books.\n3. Thabo read 2 more books than Lindi.
Always check the 'key' in a pictograph carefully, as one symbol might represent more than one item.
Example 3
Describe the likelihood of the following events using the words: 'impossible', 'unlikely', 'equally likely', 'likely', 'certain'.\n\n1. The sun will rise tomorrow.\n2. You will roll a 7 on a standard six-sided die (numbered 1 to 6).\n3. You will get 'heads' when flipping a fair coin.\n4. It will rain in the desert next week.
Answer
1. Certain\n2. Impossible\n3. Equally likely\n4. Unlikely
Think about all the possible outcomes and how often the specific event you are looking for occurs.
Common mistakes
- ✗Forgetting to include a title, axis labels, or a scale on graphs.
- ✗Misinterpreting the 'key' in a pictograph, especially when one symbol represents more than one item.
- ✗Drawing bars of different widths or with unequal spacing in a bar graph.
- ✗Confusing 'unlikely' with 'impossible' or 'likely' with 'certain'.
- ✗Not considering all possible outcomes when determining the likelihood of an event.
Exam tips
- ★Read the question carefully to understand what data needs to be collected or what information needs to be extracted from a graph.
- ★When drawing graphs, use a ruler and pencil. Ensure all parts (title, labels, scale, bars/pictures) are clear and accurate.
- ★Always check the 'key' for pictographs and the 'scale' for bar graphs before answering questions.
- ★When dealing with probability, list all possible outcomes first to help determine the likelihood or the fraction.
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