NCERT Class 7 Ganita Prakash 2 Chapter 07 Finding the Unknown PDF Download

Chapter 7: Finding the Unknown

7.1 Find the Unknowns

Unknown Weights

We have a weighing scale that behaves as follows. The numbers represent same units of weight:

[Figure: Two weighing scale examples showing balanced weights, See in your textbook]

? Find the unknown weights in the following cases:

[Figure 7.1: A weighing scale showing objects with weights to find, See in your textbook]

[Figure 7.2: A weighing scale showing objects with weights to find, See in your textbook]

[Figure 7.3: A weighing scale showing objects with weights to find, See in your textbook]

[Figure 7.4: A weighing scale showing objects with weights to find, See in your textbook]

[Figure 7.5: A weighing scale showing objects with weights to find, See in your textbook]

[Figure 7.6: A weighing scale showing objects with weights to find, See in your textbook]

[Figure 7.7: A weighing scale showing objects with weights to find, See in your textbook]

[Figure 7.8: A weighing scale showing objects with weights to find, See in your textbook]

Math Talk

? Discuss the answers with your classmates. Give reasons why you think your answer is right.

? Find the unknown weight of the sack in the following cases. In Fig. 7.10, all the sacks have the same weight.

[Figure 7.9: A weighing scale with sacks and weights to find, See in your textbook]

[Figure 7.10: A weighing scale with multiple sacks and weights to find, See in your textbook]

[Hint: If we remove equal weights from both the plates, will the weighing scale still be balanced? Remove one sack from each plate for Fig. 7.10.]

Teacher's Note

When you remove the same weight from both sides of a balanced scale, it stays balanced. This is a key idea you will use many times: whatever you do to one side of a balance, do the same to the other side to keep it even. Try this with the sack problems - remove one sack from each plate and see what you get.

[Figure 7.11: A weighing scale with sacks and weights to find, See in your textbook]

[Figure 7.12: A weighing scale with sacks and weights to find, See in your textbook]

[Hint: Can you remove objects so that the sacks are only on one plate?]

Let us find an unknown value in a different setting.

Matchstick Pattern

Consider this sequence of matchstick arrangements.

[Figure: Matchstick patterns numbered 1, 2, 3, and 4 showing triangular arrangements, See in your textbook]

Recall that we have studied this sequence in an earlier chapter.

Teacher's Note

Look at how the matchstick pattern grows: each new triangle adds three more matchsticks. If you can spot the pattern of growth, you can find the number of matchsticks in any arrangement without drawing it - that is exactly what "finding the unknown" means in sequences.

Key Points

• A balanced weighing scale shows that the weights on both sides are equal. When you remove the same amount from both sides, the scale stays balanced.
• To find an unknown weight on a balanced scale, remove weights from both sides equally until the unknown is alone on one plate.
• Patterns in sequences can help you find unknown values without counting every item - look for how the pattern grows from one step to the next.
• Different problems can be solved using different strategies; comparing your method with a classmate's helps you learn new ways to think.

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