Data Handling and Symmetry: Class 6 Study Guide
Graphs help us see data at a glance, and symmetry describes balance in shapes.
Data is information collected to answer a question. We record it with a tally chart (one stroke for each, crossed at five) and show it in a pictograph (a picture stands for a number) or a bar graph (bars of equal width with an even scale). Always read the key or the scale.
A shape has line symmetry if a line divides it into two halves that fold exactly on top of each other. The line is a line of symmetry.
Lines of symmetry
| Shape | Lines of symmetry |
|---|---|
| Square | 4 |
| Rectangle | 2 |
| Equilateral triangle | 3 |
| Isosceles triangle | 1 |
| Regular hexagon | 6 |
| Circle | Infinitely many |
| Letter H | 2 |
| Letter A | 1 |
Reading a graph
In a pictograph where one picture stands for 5 students, 4 pictures mean 20 students. In a bar graph, read the height of the bar against the scale. To find how many more, subtract. To find the total, add all the bars.
What does one symbol mean?
Use the scale.
Subtract to find the difference.
With the unit.
Making a graph
Choose a title and a scale that fits the largest number. Draw equal-width bars with equal gaps. Label both axes. Colour or shade the bars neatly. A clean graph is easy to read.
Worked examples and common mistakes
Example: How many lines of symmetry does a rectangle have? Two. Example: A bar reaches 35 on a scale of 5s. The value is 35. Common mistakes: giving a rectangle four lines of symmetry (its diagonals are not lines of symmetry), and using a scale that is uneven.
Check your understanding: model answers
1. Three. 2. So the reader knows what the data is about. 3. 35 students.
✨ Key Takeaways
- A tally chart collects data.
- Pictographs and bar graphs need a key or scale.
- A line of symmetry folds a shape onto itself.
- A circle has infinitely many lines of symmetry.
💬 Questions for Discussion & Reflection
- How many lines of symmetry does an equilateral triangle have?
- Why does a graph need a title?
- In a pictograph, one star is 10 students. How many students are 3½ stars?