Page 11 - Math_Genius_V1.0_C6_Flipbook

E:\Working\Focus_Learning\Math_Genius-6\Open_Files\01_Chapter_1\Chapter_1
\ 07-Nov-2024 Bharat Arora Proof-8 Reader’s Sign _______________________ Date __________

So, what does ‘pattern’ actually mean?

If we focus only on mathematical context, a pattern can be described as a repeated design or
recurring sequence of numbers, geometrical shapes, etc., which is followed by a specific rule.
Do you still remember the multiplication tables, you have learnt as a toddler?

2 × 1 = 2 5 × 1 = 5 12 × 1 = 12
Maths Talk
2 × 2 = 4 5 × 2 = 10 12 × 2 = 24
What do you notice in
2 × 3 = 6 5 × 3 = 15 12 × 3 = 36 the multiplication tables?
-------------- --------------- ----------------- Discuss with your friends.
So, is there any need to
2 × 10 = 20 5 × 10 = 50 12 × 10 = 120 explore mathematical patterns?

Multiplication tables are the simplest mathematical patterns.
Let’s explore a mathematical pattern first before discussing its need. Suppose in the farewell
ceremony of your school, students from your class are called on the stage. Let’s assume there are
some steps on the stairs, and you are directed to come on stage either by climbing 1 step each
time or jumping a maximum of 2 steps at a time.
If there is only 1 step, then you can reach the stage in 1 way.

If there are 2 steps, then you can reach the stage in 2 ways – either climbing
1 step at a time or jumping 2 steps and reaching the stage.

If there are 3 steps, then you can reach the stage in 3 ways.
1 + 1 = 2

3 = 1 + 1 + 1 = 2 + 1 = 1+ 2
If there are 4 steps, then you can reach on the stage in 5 ways.

4 = 1 + 1 + 1 + 1 = 2 + 2 = 2 + 1 + 1 = 1 + 1 + 2 = 1 + 2 + 1
How will you reach on stage if there are 5 steps?

You can check below that it can be done in 8 ways.

5 = 1 + 1 + 1 + 1 + 1 = 2 + 2 + 1 = 2 + 1 + 2 = 1 + 2 + 2 = 1 + 1 + 2 + 1 = 1 + 1 + 1 + 2
= 2 + 1 + 1 + 1 = 1 + 2 + 1 + 1

9 Patterns in Mathematics