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Smart Charts - Tally Marks

Grade 3CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Tally marks are a quick way of recording and counting data in groups of 55. Instead of writing long numbers, we use small vertical lines to keep track of items one by one.

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For the numbers 1,2,3,1, 2, 3, and 44, we draw simple vertical lines. For example, 11 is represented by ∣\mid, 22 is represented by ∣∣\mid\mid, 33 is represented by ∣∣∣\mid\mid\mid, and 44 is represented by ∣∣∣∣\mid\mid\mid\mid.

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When we reach the number 55, we do not draw a fifth vertical line. Instead, we draw a diagonal line across the first four vertical lines. This creates a 'bundle' or 'gate' shape that is easy to identify as exactly 55.

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Counting in groups of 55 makes it much faster to find the total. If you see three bundles and two single lines, you can skip-count: 5,10,155, 10, 15 and then add the two extra lines to get 1717.

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A Smart Chart is a table used to organize this data. It usually contains three columns: the name of the item (e.g., 'Color of Car'), the Tally Marks column where lines are drawn, and the 'Number' or 'Frequency' column where the total is written in digits.

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Data interpretation involves looking at the completed tally chart to answer questions, such as which item appeared the most (highest count) or the least (lowest count), and finding the total number of items collected by adding all the frequencies together.

📐Formulae

Value of 1 Bundle=5\text{Value of 1 Bundle} = 5

Total Count=(5×Number of Bundles)+Number of Individual Lines\text{Total Count} = (5 \times \text{Number of Bundles}) + \text{Number of Individual Lines}

Total Data Points=Sum of all Frequencies\text{Total Data Points} = \text{Sum of all Frequencies}

💡Examples

Problem 1:

In a fruit basket, there are 88 Apples, 55 Bananas, and 33 Oranges. Represent this data using tally marks.

Solution:

  1. For Apples: Since the count is 88, we draw one bundle of 55 (four vertical lines with one diagonal slash) and 33 extra vertical lines. Result: ∣∣∣∣∣∣∣\cancel{\mid\mid\mid\mid} \mid\mid\mid
  2. For Bananas: Since the count is 55, we draw exactly one bundle of 55 (four vertical lines with one diagonal slash). Result: ∣∣∣∣\cancel{\mid\mid\mid\mid}
  3. For Oranges: Since the count is 33, we draw 33 vertical lines. Result: ∣∣∣\mid\mid\mid

Explanation:

We break each number down into groups of five and remainders. 8=5+38 = 5 + 3, 5=55 = 5, and 3=33 = 3 to determine the tally structure.

Problem 2:

A student recorded the number of blue pens in a box using these tally marks: ∣∣∣∣∣∣∣∣∣∣\cancel{\mid\mid\mid\mid} \cancel{\mid\mid\mid\mid} \mid\mid. How many blue pens are there in total?

Solution:

Step 1: Count the number of complete bundles. There are 22 bundles. Step 2: Multiply the number of bundles by 55: 2×5=102 \times 5 = 10. Step 3: Count the individual vertical lines. There are 22 lines. Step 4: Add the bundle total and the individual lines: 10+2=1210 + 2 = 12. Final Answer: There are 1212 blue pens.

Explanation:

To solve this, we use skip-counting by 55 for the bundles and then add the remaining single marks to get the final frequency.