Me -

**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

Me - Excellent. Any other way?

Rohit says,

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

Me - Fantastic. Any other way?

Tanvi says,

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

-----

1) How would you solve this problem 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?

5) Why do you feel these students were able to solve this problem, this way?

Waiting for your responses...

Regards

Rupesh Gesota

PS: These students hail from the marathi medium municipal school in navi-mumbai. To know more about the maths enrichment program being run with them, check the website www.supportmentor.weebly.com

Excellent post!

ReplyDeleteThat's an awesome discussion. All approaches seem fine to me.. Different ppl, different styles. All the best

ReplyDeleteI completed it by rounding 9.8 up to 10 and then multiplying by 2.5. So 10 X 2.5 is 25. Then I had to subtract the extra which was 0.2 x 2.5 = 0.5. Thus 25 - 0.5 = 24.5.

ReplyDeleteI'm not sure what age these children are but I think it's great they all have different methods of mental computation. They obviously have a strong undrstanding of place value and the ability to partition numbers and understand the compensation strategy. I only teach grade 1 but we are already working on developing a strong understanding of partitioning numbers and place value so they can mentally computation addition and usbtraction questions involving three digit numbers.

Great to see children deploying concepts of Partitioning / Compensation.

ReplyDeleteMental Math

9.8 × 2.5

{(9.8 × 10) ÷ 2} ÷ 2

{98 ÷ 2} ÷ 2

49 ÷ 2

24.5

Wonderful to see that there is no linear approach to getting the right answer being followed in your session Rupesh. Your approach has obviously allowed them to open their heads like a parachute and explore the computation on their own whilst arriving at the right answer.Such approaches are crucial to developing an intrinsic interest in the subject as opposed to turning it into a dreaded and boring maths session! My daughter would have opted to approach it in the way that has been "taught"to her in school..but I will take this to her and give her the option of approaching it in her own way and see what happens:)

ReplyDeleteI found the enthusiasm with which the children have engaged themselves infectious and from their language,to me, it appears that they are thinking and thinking without preconditions...which is huge.

Thanks for sharing Rupesh.

I did (98x25)/100 = 98/4= ((98)/2 )/2 = 49/2 = 24.5

ReplyDeleteI do number talks on Every Wednesday. Students love it.

What you are doing is awesome!

So nice to see so many methods to the same problem. I used Kanchan's approach in my mind. Great work.

ReplyDeleteThis is what I did mentally:

ReplyDeleteChange 9.8 to 10 and 2.5 to 2. So 10x2 = 20. Now we need to subtract 0.2 of 2 which is 0.4. So 20-0.4 = 19.6. Now we just need to add half of 9.8 (because we had changed 2.5 to 2). Half of 9.8 = 4.9. So 19.6 + 4.9 = 24.5 (this also can be done by adding 5 to 19.6 and then just subtract 0.1 from it)

Amazing! It's so nice to read your post ... Absolutely love the way you challenge children to look beyond one way of looking at the problem...

ReplyDeleteI did this - consider 9.8 as 10 ? It's simply (9.8 + 0.2). Then 10 × 2.5 = 25. Further 25 - 0.50 = 24.50 (?). Since I added (0.2 × 2.5 = 0.50) this amount so I must subtract it.

ReplyDeleteI really amazed to see your student responses & I appreciate them. After reading Your blog I feel involved in finding new things , approaches..