Mental Maths helps in strengthening your ‘number sense’. One becomes more aware of how numbers ‘play’ – an important aspect to be learned because maths is something that builds on itself. Students who are not so flexible in splitting and combining the numbers in easier ways, not only get baffled executing the standard algorithms in their heads but often yield incorrect results, without any clue of its inaccuracy.

Mental Maths strategies relieves the students of the computational part of mathematics, thus enabling them to focus towards the bigger mathematical idea under consideration.

Besides, Mental Maths also helps in developing the confidence of students and it is also an excellent way to stimulate your brain. I start my session daily with a 10-minute Mental Math activity. Following three problems were posed to them, one after the other, to solve mentally.

**Problem-1**

How much is 9.8 x 2.5 ?

Kanchan says,

I will consider the numbers as 98 and 25. Further, lets round up 98 as 100. So now, 25 times 100 gives 2500. But I have taken 2 times 25 more..

So, 98 x 25 = 2500 – 50 = 2450

Now, since I had multiplied each of the two given numbers by 10, the obtained product will be 100 times more than the desired one. Hence the actual answer will be 2450 / 100 = 24.5

Rohit said,

I know that 2.5 x 4 = 10 … So if I am increasing one factor by 4 , then I will have to decrease the other by 4…. i.e. I need to find 9.8 / 4

Now., I know that 25 x 4 = 100 and so, 24 x 4 = 96…..

Hence 24.5 x 4 = 98

Hence 2.45 x 4 = 9.8 i.e. 9.8 / 4 = 2.45

Now, the problem 9.8 x 2.5 becomes 2.45 x 10 = 24.5

Tanvi said,

Lets ignore the decimal points. So the problem is 98 x 25

Now, 98 x 100 = 9800

So, 98 x 25 = 9800 / 4 = Half of Half of 9800 = Half of 4900 = Half of 4800 + Half of 100 = 2400 + 50 = 2450

Now, with the same reason what Kanchan gave, we will have to decrease the product by factor of 100.

So, 9.8 x 2.5 = 2450 / 100 = 24.5

**Problem-2**

What is 12.5 x 8.5

**Student-1:** Ignore the decimal points. So the problem becomes 125 x 85.

125 x 85 = 125 x 100 – 125 x 20 + 125 x 5

= 12500 – 2500 + 625

= 10000 + 625 = 10625

Divide the answer by 100 to get 106.25

I asked him how did he calculate 125 x 5 = 625 in his head…

He replied, “Sir, I know that 125 is 5 x 5 x 5. Further multiplying it by 5 means 5 x 5 x 5 x 5 = 25 x 25 which I knew is 625.”

**Student-2:** I considered 12.5 as 125. Now, 125 x 8 = 1000. Then, 125 x 0.5 means half of 125 = 62.5…. So we get 1062.5….. Now we divide this answer by 10 as we have worked with 125 instead of 12.5 …. This gives 106.25

**Student-3:**

12 x 8 = 96

12 x 0.5 = 6

0.5 x 8 = 4

0.5 x 0.5 = 0.25

So answer is 96 + 10.25 = 106.25

**Student-4:**

12.5 x 8 = 100

12.5 x 0.5 = 6.25

So the answer is 106.25

**Student-5:**

Sir, we can use the trick of multiplying two numbers ending in 5…

125 x 85 = [ (12 x 8) + (12 + 8)/4 ] x 100 + 25 = 96 + 10 + 25 = 10625

Divide the answer by 100 to get 106.25

**Problem-3**

How much is 644 / 14 without using Long division method?

**Student-1:**

I know 70 / 14 = 5

So, 700 / 14 = 50

Now, 700 – 644 = 56 and 56 / 14 = 4

So, the answer is 50 – 4 = 46

**Student-2:**

I know 560 is divisible by 14. (14 x 40 = 560)

So 644 – 560 = 84

Now, 84 / 14 = 6

So the answer is 40 + 6 = 46

**Student-3:**

14 x 40 = 560

14 x 50 = 700

Since 644 is between 560 and 700… So, answer is going to be between 40 and 50

Now, 644 ends in 4.. So if 14 x some number ends in 4, then that some number should end in 1 or 4… But 560 + 14 cannot be equal to 644… So 560 + 14 x 6 will give 644…. So answer is 40 + 6 = 46

1) How would you solve these 3 problems mentally?

2) How about your students/ children?

3) What are your views about the approaches used by these students?

4) What are your views about the language used by them to communicate their reasoning?

Waiting for your responses…

How can students be guided towards discovery by asking the right questions, so that they are able to discover and correct mistakes on their own? Some answers may be found in the various stories and Maths conversations recorded in my blog.

Email-id: rupesh.gesota@gmail.com

Blog: www.rupeshgesota.blogspot.in

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Blog & photos: Rupesh Gesota, Maths Educator, Mumbai for Comet Media Foundation