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\ 07-Nov-2024 Bharat Arora Proof-8 Reader’s Sign _______________________ Date __________

Practice Time 1B

1. Some tokens bearing a number, as shown alongside. Sort out
the numbers that can be kept in the following categories. (You 25 66 81
may take a number more than once if required).
100 28 35
(a) Even numbers ....................................................................
(b) Odd numbers ....................................................................... 64 49 10 55
(c) Triangular numbers .............................................................
15 27
(d) Square numbers ..................................................................

(e) Cubic numbers ....................................................................
(f) Pentagonal numbers ............................................................
(g) Hexagonal numbers .............................................................

2. Draw some triangular number patterns in your notebook. Show that every hexagonal number is also
a triangular number.

3. Name four polygonal numbers with the number of sides less than or equal to 6. Draw them with the
help of colourful bindis.

4. You have noticed that 36 is both a square number and a triangular number. Arrange 36 dots on a
page making a triangle and a square. Can you find another square number that is also a triangular
number?
5. Can you think of pictorial ways to visualise power of a number? Here is one illustration of the power of 2.

1 2 4 8 16
Draw a similar illustration of the power of 3 in your notebook.

6. What happens when you add consecutive centred hexagonal numbers, i.e., 1, 1 + 7, 1 + 7 + 19, ...?
What sequence do you get? Explain it using a pictorial representation of dots.

Relations among Number Sequences

Numbers are interrelated. Can you establish a relation between two types of numbers such as
square numbers and triangular numbers?
(a) Triangular numbers and Square numbers

1 + 3 = 4 3 + 6 = 9 6 + 10 = 16

The sum of two consecutive triangular numbers makes a square number.

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