Information Processing — Class 4 Mathematics (Samacheer Kalvi)
TN State Board (Samacheer Kalvi) Class 4 Mathematics, Unit 6. Systematic listing, representing data in bar graphs, and representing data in pie charts. Taught in September.
1. Systematic listing
Some questions ask you to find all the possibilities, not just one. Guessing will always miss a few. The cure is to be systematic: fix one thing, run through every choice for the rest, then move on.
From the book. Using the digits 5, 3, 7 and 1, how many two-digit numbers can you make without repeating a digit?
Fix the tens digit and list every possible ones digit:
| Tens digit | Numbers formed |
|---|---|
| 5 | 53, 57, 51 |
| 7 | 75, 73, 71 |
| 3 | 35, 37, 31 |
| 1 | 15, 13, 17 |
Four choices for the first digit, and three left for the second, giving 12 two-digit numbers. Notice the count: 4 × 3 = 12.
Clothes. With 2 pants and 4 shirts, every pant can go with every shirt, so there are 2 × 4 = 8 ways to dress.
Medals. Three sprinters A1, A2 and A3 finish a race and take gold, silver and bronze. Gold can go to any of the 3, silver to either of the 2 left, bronze to the last one: 3 × 2 × 1 = 6 possible results.
The habit to build is ordering your list. Written in order, a missing case shows up as a gap.
2. Bar graphs
A bar graph shows numbers as bars. Taller bar, bigger number — you can compare at a glance without reading a single digit.
Every bar graph needs three things: a scale up the side, a label under each bar, and bars of equal width.
Here is a cricket score card from the book:
| Player | Score |
|---|---|
| Kannan | 60 |
| Rohit | 40 |
| Babu | 50 |
| Ramu | 10 |
Drawn as a bar graph with a scale in tens, Kannan's bar is the tallest and Ramu's the shortest. To read one off, follow the top of the bar across to the scale.
Questions on a bar graph usually ask for the highest value, the lowest value, two equal values, or the difference between two bars. For the last one, read both and subtract: Kannan and Ramu differ by 60 − 10 = 50 runs.
3. Pie charts
A pie chart is a circle cut into slices. Each slice shows a part of the whole, and the bigger the slice, the bigger the share.
A bar graph is best for comparing separate amounts. A pie chart is best for showing how one total is divided up.
From the book. An ice cream parlour's varieties are shown as a pie chart: Vanilla 50, Chocolate 30, Pista 20.
- How many varieties in all? 50 + 30 + 20 = 100
- Vanilla alone? 50
- Chocolate and pista together? 30 + 20 = 50
So vanilla fills half the circle, and the other two together fill the other half.
From the book. There are 60 students in a class. Half of them eat idly, so that is 30 students. Of the remaining 30, half eat something else, which is 15, and 15 are left. A pie chart makes those halves and quarters visible as slices.
4. When one unit stands for many
Suppose 60 children voted for their favourite subject. Drawing 60 separate steps up the side of a bar graph would be unreadable. Instead we let one unit on the scale stand for several children.
Choosing the scale is a judgement:
| Data range | Sensible scale |
|---|---|
| 0 to 50 | 1 unit = 5 |
| 0 to 100 | 1 unit = 10 |
The scale must be big enough to fit the largest value on the page, and it must stay the same all the way up the axis.
Whichever scale you pick, label both axes — the categories along the bottom and the counts up the side — and give the graph a title.
The same idea applies to a pictograph, where one picture stands for several items. If the key says one symbol = 5 children, then 4 symbols mean 4 × 5 = 20 children, not 4.
Read the key before you read anything else. A pictograph answered without checking the key is almost always wrong.
5. Modelling with a route map
A route map is a drawing of places and the paths that join them. It leaves out everything that does not matter, such as how wide the roads are, and keeps only what you need: which places are connected, and how far apart they are.
Suppose a route map joins a house, a school, a library, a playground and a computer centre. Two questions can be answered straight off the map.
Is there a path at all? Two places are connected if you can trace a route from one to the other, even if you have to pass through other places on the way. If no line reaches a place, you cannot get there by these paths.
Which route is shortest? Usually more than one route joins two places. List every route from start to finish, add up the distances along each, and compare the totals.
| Route from school to house | Distance |
|---|---|
| School to house directly | 900 m |
| School to library to house | 400 m + 600 m = 1,000 m |
| School to playground to computer centre to house | 300 m + 250 m + 500 m = 1,050 m |
The direct route of 900 m is the shortest and the third route of 1,050 m is the longest. Notice that the shortest route is not always the one with fewest stops, so the distances have to be added rather than guessed.
6. Worked examples
Example 1. How many three-digit numbers can be formed from 9, 7 and 2 without repeating a digit?
Solution: 3 × 2 × 1 = 6, namely 972, 927, 792, 729, 297 and 279.
Example 2. In the bar graph of a student's marks, the highest bar is Maths and the lowest is Tamil. What does that mean?
Solution: The student scored most in Maths and least in Tamil.
Example 3. A bar graph shows 40 marks in English and 70 in Science. How many more marks in Science?
Solution: 70 − 40 = 30 marks.
Example 4. In the ice cream pie chart, how many more vanilla than pista?
Solution: 50 − 20 = 30.
Example 5. With 3 shirts and 3 pants, how many outfits are possible?
Solution: 3 × 3 = 9 outfits.
Example 6. Two dice-like cards show 4 and 6. List all the two-digit numbers formed without repetition.
Solution: 46 and 64, so 2 numbers. Here 2 × 1 = 2.
7. Practice
- Write all the two-digit numbers that can be made from 2, 5 and 8 without repeating a digit. How many are there?
- With 3 caps and 2 bags, how many pairs can be chosen?
- In the cricket score card above, who scored the most and who the least?
- What is the difference between Babu's and Rohit's scores?
- In the ice cream pie chart, how many chocolate and vanilla together?
- Which is better for showing how a total is divided up, a bar graph or a pie chart?
- Three friends line up for a photograph. In how many orders can they stand?
- A bar graph has equal-height bars for Tamil and English at 60 each. What does that tell you?
- A pictograph key says one symbol = 5 children. How many children do 4 symbols show?
- Data runs from 0 to 100. What scale would you choose for a bar graph?
- Name the two things every axis of a bar graph must have.
- On the route map above, how much longer is the route through the library than the direct route from school to house?
- Two places on a route map have no line joining them, directly or through any other place. Can you travel between them using the map?
8. Answers
- 25, 28, 52, 58, 82, 85 — six numbers, since 3 × 2 = 6.
- 3 × 2 = 6 pairs.
- Kannan scored most (60) and Ramu least (10).
- 50 − 40 = 10 runs.
- 30 + 50 = 80.
- A pie chart.
- 3 × 2 × 1 = 6 orders.
- The student scored the same marks in both subjects.
- 4 × 5 = 20 children.
- 1 unit = 10.
- A label saying what it shows, and a consistent scale.
- 1,000 m - 900 m = 100 m longer.
- No. If no path connects them, the two places are not connected on that map.
9. Summary
- List possibilities systematically: fix one item, run through the rest, and keep the list in order so gaps show.
- Choosing one from each of two groups gives (first count) × (second count) possibilities.
- Arranging 3 different things in order gives 3 × 2 × 1 = 6 arrangements.
- A bar graph compares separate amounts; taller means bigger. It needs a scale, labels and equal bar widths.
- To compare two bars, read both values and subtract.
- A pie chart shows how one whole is divided; the bigger the slice, the bigger the share.
- Ice cream chart totals: 50 + 30 + 20 = 100 varieties.
