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Smart Charts - Tally Marks

Grade 4CBSE

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

🔑Concepts

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Data Collection: Data is a collection of information or facts, such as numbers, names, or measurements. A 'Smart Chart' is a visual way to organize this data into tables so we can analyze it and answer questions easily.

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Tally Marks: Tally marks are vertical lines used to keep track of counts. Each single vertical stroke ∣| represents 11. For example, the number 33 is represented by three vertical lines ∣∣∣|||.

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The Bundle of Five: To make counting large numbers easier, we group tally marks in sets of 55. After drawing four vertical lines ∣∣∣∣||||, the 55th line is drawn as a diagonal stroke across them. This creates a visual 'bundle' or 'gate' shape that represents exactly 55 items.

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Skip Counting: Tally marks allow for fast counting of large data sets. Because each bundle equals 55, we can skip-count by fives (5,10,15,…5, 10, 15, \dots) and then add the individual lines that are left over.

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Frequency: Frequency refers to how many times a particular item or value occurs in the data. In a Smart Chart, the 'Frequency' or 'Number' column displays the numerical total of the tally marks for each category.

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Smart Chart Structure: A frequency table or Smart Chart usually contains three columns: the first for the Item Name (e.g., Favorite Fruits), the second for the Tally Marks (visual bundles), and the third for the Frequency (the numerical total).

📐Formulae

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

Category Frequency=(Number of Bundles×5)+Remaining Single Marks\text{Category Frequency} = (\text{Number of Bundles} \times 5) + \text{Remaining Single Marks}

Grand Total=Sum of all category frequencies\text{Grand Total} = \text{Sum of all category frequencies}

💡Examples

Problem 1:

During a nature walk, Priya saw 1313 butterflies. How would she represent this number using tally marks in a Smart Chart?

Solution:

Step 1: Divide the total count by 55 to find the number of bundles. 13÷5=213 \div 5 = 2 bundles with a remainder of 33. \ Step 2: Draw 22 bundles of five (each bundle consists of four vertical lines and one diagonal line crossing them). \ Step 3: Draw 33 single vertical lines next to the bundles to represent the remaining count. \ Final Tally: Two bundles and three single lines.

Explanation:

We group the 1313 butterflies into sets of 55 to make them easier to count at a glance. Two full bundles make 1010, and adding the 33 single lines gives the total of 1313.

Problem 2:

A Smart Chart for favorite snacks shows the following: \ Biscuits: ∣∣∣∣|||| \ Chips: 22 bundles of five and 44 single lines \ Fruit: 11 bundle of five and 11 single line. \ Calculate the total number of children who participated in the survey.

Solution:

Step 1: Calculate the frequency for Biscuits. 44 single marks =4= 4. \ Step 2: Calculate the frequency for Chips. (2×5)+4=10+4=14(2 \times 5) + 4 = 10 + 4 = 14. \ Step 3: Calculate the frequency for Fruit. (1×5)+1=5+1=6(1 \times 5) + 1 = 5 + 1 = 6. \ Step 4: Add all frequencies together to find the grand total: 4+14+6=244 + 14 + 6 = 24.

Explanation:

To find the total number of children, we first convert the tally marks for each snack into their numerical values (frequencies) and then sum those values together.