NCERT Smart Charts: CBSE Class 3 Maths Chapter 13

What are Smart Charts and Data?

A smart chart is a visual tool that helps us present information in a clear and organized format. When we collect facts, votes, or counts of things, we call this raw information data. If you just write down a long list of numbers, it can be very confusing to read. Smart charts solve this problem by converting numbers into visual representations.

In Class 3, we focus on two main ways of organizing data:

1. Tally Charts: Using straight tally marks to bundle counts into groups of five.
2. Pictographs: Using simple pictures or drawings to represent quantities of items.

These charts make comparing things super easy! By looking at a smart chart, you can instantly tell which item is the most common, which is the least, and the total count of all items combined.

How to Make Tally Marks Step-by-Step

1. Draw standing lines for numbers 1 to 4 — For each item you count, draw one standing vertical line (|). For example, 1 is shown as '|', 2 is shown as '||', 3 is shown as '|||', and 4 is shown as '||||'.
2. Cross on the 5th count to make a bundle — When you reach the number 5, do not draw a fifth standing line. Instead, draw a diagonal slash across the first four lines to close the bundle. This bundle represents exactly 5 items and makes counting by fives very easy later!
3. Start a new bundle for counts above 5 — For the 6th item, start a new standing line right next to your bundle of 5. For example, 7 is drawn as one bundle of five plus two standing lines next to it.

Solved Examples of Smart Charts

• Example 1: Class 3 students voted for their favorite fruits. The collected tallies are: Mangoes (One bundle of 5 and 3 standing lines), Apples (One bundle of 5), and Bananas (4 standing lines). Let us count them! Mangoes = 5 + 3 = 8 votes. Apples = 5 votes. Bananas = 4 votes. Total votes = 8 + 5 + 4 = 17 votes. Mango is the most popular fruit because it has the highest number of tallies.
• Example 2: In a pictograph showing books read by students, 1 book picture represents 3 actual books read. If Rohit has 4 book pictures next to his name, how many real books did he read? Since 1 picture = 3 books, we multiply: 4 pictures × 3 books = 12 real books. Rohit read 12 books.

Smart Tips for Solving Chart Problems

Always pay attention to the Key at the bottom of a pictograph! Sometimes, 1 picture doesn't mean just 1 item; it could represent 2, 5, or even 10 items. For tally marks, remember that a fully crossed group is always worth 5, so you can count them quickly by skip-counting by 5s!

Practice Questions with Solutions

• Q: Draw the tally marks for the number 13. A: Step 1: We know that tally marks are grouped in bundles of 5. Step 2: Divide 13 into groups of 5. We get two groups of 5 (which is 10) and 3 leftover lines. Step 3: Draw two crossed bundles of 5, followed by 3 single vertical lines. Final answer: [<s>||||</s>] [<s>||||</s>] |||
• Q: A toy store chart shows toy cars sold on Monday. The key says: 1 Toy Car Picture = 2 real toy cars. If the chart has 6 pictures, how many toy cars were sold? A: Step 1: Count the number of pictures, which is 6. Step 2: Look at the key: 1 picture = 2 real toy cars. Step 3: Multiply the number of pictures by the value of each picture: 6 × 2 = 12. Final answer: 12 toy cars were sold.
• Q: Sania saw different colored butterflies in her garden: Red = 4, Yellow = 9, Blue = 2. Which color butterfly did she see the most, and what is the difference between the highest and lowest count? A: Step 1: Identify the counts: Red = 4, Yellow = 9, Blue = 2. Step 2: Compare the numbers. 9 is the highest count, which belongs to Yellow. 2 is the lowest count, which belongs to Blue. Step 3: Calculate the difference: 9 - 2 = 7. Final answer: Yellow butterflies were seen the most. The difference between the highest and lowest count is 7.
• Q: Look at these tally marks: [<s>||||</s>] ||||. What number does this represent? A: Step 1: Identify the bundled group: [<s>||||</s>] represents 5. Step 2: Count the single lines next to the bundle: |||| represents 4. Step 3: Add them together: 5 + 4 = 9. Final answer: The tally marks represent the number 9.

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