The Art of Estimation

It was a weekend and my son was helping me re-organize the cupboards in his bedroom. That’s when we found his piggy bank. It was quite heavily filled with a lot of coins. He was very happy and wanted to find out how much money he has.

“Let me open it and count how much money I have” said my son.

“How about telling me that without counting?” I asked.

“How can I tell without counting? How do I know?” exclaimed my son.

“Give it a guess. Just try.” I wanted him to try.

“What if it is wrong?” He resisted coming up with a number. It took me some time to convince him that not all answers need to be exactly correct and sometimes a “GOOD ENOUGH” answer is acceptable.

Estimation – according to John A. Van de Walle, a Maths education researcher – is a higher-level skill that requires students to be able to conceptualize and mentally manipulate numbers. Estimation is a skill that we use everyday intuitively, be it during shopping where we want to know roughly how much money we need to pay, or planning a journey where we want to know approximately when we will reach the destination.

Estimation is a combination of mental Maths and logical reasoning. Teaching estimation to students is different from any other topic in Mathematics. Students know that there is a right answer to each Mathematical problem. But in estimation there is no right or wrong answer. How good or how close the estimate is to the actual is the key. Here, I share some of the techniques that can be used while teaching estimation.

– Never compare estimate to a right answer. This makes the student actually calculate instead of estimate, in order to get a correct answer. Always give a range of best estimates.

– Give some hints to compare. If the activity is to estimate the height of the wall, the hint could be that your ruler is 30 cm long. Now the students start thinking how many such rulers need to be stacked, to scale the height of the wall.

– Depending on the age group of the student group, change the range of best estimates. For kindergarten students it can be a wide range, for higher grade students the range can be narrow.

– Let the students write their estimates and explain how they have arrived at that number. By doing so, students get exposed to different logical methods of estimation.

– Always ask students to estimate the answer first before doing numerical calculations. E.g.:  while calculating 523 x 61, if a student’s final answer is 366, they should sense something is wrong. This is because while estimating they would have rounded the numbers to nearest hundreds and tens. So 500 x 60 = 30000. They can go over their calculations again and correct them.

On the whole, estimation can be fun and makes one mentally active. To sharpen this skill, one needs a lot of practice. Encourage students to estimate whatever they encounter in real life. How many candies should you buy for your birthday party? What time should you start from your home, to reach your friend’s house at 4:00 pm? How long is a train? How heavy is an elephant?

I will conclude with a small exercise for your brain. Estimate how many people are required to stand one on top of the other to reach the height of Mount Everest? Let us see whose estimate is CLOSE ENOUGH!

-Jyothi Giri, Facilitator, BRAINSTARS

Further Reading

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