Information Processing — Class 3 Mathematics (Samacheer Kalvi)
TN State Board (Samacheer Kalvi) Class 3 Mathematics. Tally marks, frequency tables and bar graphs.
1. Counting things as they happen
Suppose you stand at the school gate and count vehicles going past. You cannot stop to write "17" each time, because the next vehicle is already coming.
Tally marks solve this. Draw one stroke for each thing you count, and bundle them in fives.
- 1 is one stroke
- 2 is two strokes
- 3 is three strokes
- 4 is four strokes
- 5 is four strokes with a fifth stroke drawn across them, diagonally
Then 6 is a crossed bundle plus one more stroke, 7 is a bundle plus two, and so on.
The crossing stroke matters. Five separate strokes are just as hard to count as any other row of lines. The whole point of the diagonal is that you can then count the bundles in fives and add the leftovers, which is far faster and much harder to get wrong.
2. From tally marks to a table
Once the counting is finished, tidy the marks into a frequency table. Frequency simply means how many.
| Fruit | Tally | Frequency |
|---|---|---|
| Apple | two bundles and two | 12 |
| Banana | one bundle and three | 8 |
| Mango | three bundles | 15 |
| Orange | two bundles | 10 |
The total is 12 + 8 + 15 + 10 = 45 children.
3. Reading a bar graph
A bar graph turns the table into a picture, so the biggest and smallest can be seen at a glance.
- The horizontal axis carries the categories: apple, banana, mango, orange.
- The vertical axis carries the count: 0, 5, 10, 15.
- The scale says what one square is worth, for example one square = one child.
To read a value, find the top of the bar and follow it across to the vertical axis.
The tallest bar is the largest category and the shortest bar the smallest. To compare two categories, subtract the shorter from the taller.
4. Drawing a bar graph fairly
Three rules keep a bar graph honest.
Every bar must be the same width. A wider bar looks like more even when the count is the same.
The gaps between bars must be equal. Uneven gaps make some bars look crowded and others important.
The vertical axis must start at 0. Starting at 8 instead of 0 would make a bar of 10 look twice a bar of 9, when the real difference is one child.
5. Worked examples
Example 1. A tally row shows two crossed bundles and three single strokes. What is the count?
Two bundles are 2 × 5 = 10, plus 3 more, so the count is 13.
Example 2. From the fruit table above, how many more children chose mango than banana?
15 − 8 = 7 children.
Example 3. In the fruit table, which fruit was chosen least, and what fraction of the 45 children chose mango?
Banana was least, with 8. Mango was chosen by 15 of 45 children, which is one third.
Example 4. A bar graph of favourite sports shows cricket 20, football 14, hockey 9. How many children were surveyed, and how many more chose cricket than hockey?
Total = 20 + 14 + 9 = 43 children. Cricket beats hockey by 20 − 9 = 11.
6. Practice
- Write the tally marks for 9 and for 17, describing the bundles.
- A tally row has three crossed bundles and one single stroke. What is the count?
- Using the fruit table, what is the total number of children?
- Using the fruit table, how many more chose apple than banana?
- Name the two axes of a bar graph and say what each one carries.
- Why must all the bars in a bar graph be the same width?
- A classmate draws a bar graph whose vertical axis starts at 10. Why is this unfair?
7. Answers
- 9 is one crossed bundle and four strokes. 17 is three crossed bundles and two strokes.
- 3 × 5 + 1 = 16.
- 12 + 8 + 15 + 10 = 45.
- 12 − 8 = 4.
- The horizontal axis carries the categories; the vertical axis carries the count.
- Because a wider bar looks like a larger count even when it is not, which misleads the reader.
- Small differences near the bottom get cut off, so a bar of 12 looks twice a bar of 11 when the real gap is one.
8. Summary
- Tally marks record counts as they happen, bundled in fives with the fifth stroke crossing.
- Without the crossing stroke the bundles cannot be counted quickly, which defeats the purpose.
- A frequency table lists each category with its count; the total is the sum of all counts.
- In a bar graph the horizontal axis carries categories and the vertical axis carries counts.
- The tallest bar is the largest category; compare two categories by subtracting.
- Bars must have equal width and equal gaps, and the vertical axis must start at 0.
