Collect, organise and present information using pictographs and bar graphs.
Data are collected observations or values, such as classmates’ favourite colours or measurements. Before collecting data, decide the question and what counts as one response. Record answers consistently so that categories do not overlap or become unclear. A tally table helps count responses without losing track; group tallies in fives when appropriate, then write the total. Organising raw information makes it easier to compare categories and answer questions. Check that every response is included exactly once and that the total matches the number of observations collected.
A pictograph represents counts using pictures or symbols. Its key tells how many items each symbol stands for. If one symbol represents 2 students, then 4 symbols represent 8 students. Half-symbols may be needed when the key permits them and the data total is not a whole multiple of the key value. Always read the key before comparing bars or symbols. A pictograph is attractive and accessible, but the key must be clear; without it, the picture count can be misunderstood.
A bar graph uses bars to show values for categories. The categories are placed along one axis and the scale of counts along the other. Bar heights or lengths represent the values, while spaces between bars make categories distinct. To read a bar graph, identify the title, labels and scale before reading a bar. Compare bar lengths to find the largest or smallest category, and use the scale to find the exact value. A graph with uneven or unlabeled scale intervals can mislead readers, so inspect the axis carefully.
Begin with a suitable question and organised data. Draw and label two axes, place categories at equal intervals, and choose a scale that fits the largest value. Mark equal intervals on the numerical axis and label them accurately. Draw bars of equal width, leaving equal gaps, and make each height match its value. Include a title and units when relevant. The scale need not always count by ones; it can count by twos, fives or tens if the data range requires it, provided the interval is consistent.
A graph should be attractive without distorting information. Keep the scale consistent and the bars proportional to the values. Avoid decorative pictures or 3-D effects that make one category appear larger than its data justify. Use readable labels, a meaningful title and sufficient contrast. If two graphs are compared, make sure their scales are understood; different scales can make similar data look very different. Good data presentation helps the reader see the evidence rather than steering the reader toward an unsupported conclusion.
Example 1: A tally count of 7 can be recorded as one group of five plus two extra marks. Example 2: If one pictograph symbol equals 4 books and a category has 3 symbols, the category represents 3×4 = 12 books. Example 3: In a bar graph with intervals of 2, a bar reaching the fifth interval represents 10, not 5. Common mistakes include forgetting the key, starting the numerical axis at an unlabeled value, changing the scale interval halfway through, and comparing bar heights before checking the axis labels. Always cross-check totals against the original data.
| Idea | How to use it | Check |
|---|---|---|
| Identify the rule | Describe what changes and what remains fixed. | Test more than one example. |
| Choose a representation | Use a diagram, number line, table or equation. | Labels and units are clear. |
| Explain the answer | Show the operation and each step. | The result fits the question. |
Example A. Read the question and name the relevant mathematical idea. Write the information given before choosing an operation. This prevents a familiar-looking number from being used in the wrong way.
Example B. Show the calculation in small steps. For example, when a calculation involves a product and a sum, compute the product first if the expression requires it, then add. Keep intermediate values visible so an arithmetic slip can be found.
Example C. Check the result using a second representation where possible: estimate it, draw a model, use a number line, or substitute it back into the original relationship. A check is especially useful when a question involves units, scale, direction or a geometric condition.
How many items each symbol represents.
The title, axis labels and scale.
They help record and count responses systematically.
An inconsistent or unclear scale.
Data Handling and Presentation builds mathematical understanding through careful observation and clear representations. Identify the key quantities, shapes or relationships before choosing a method. Use diagrams, tables, number lines or equations to make thinking visible. Show calculations in order and keep labels and units consistent. Check whether the result satisfies the definition or rule in the question. Explain the result in a sentence so another learner can follow the reasoning.