Which is the best estimate of

You know what it’s like when you ask children to ‘estimate’… there’s always a problem. Children want to give you the ‘right‘ answer – nothing else will do! So they resist guessing, and simply calculate their answer. But there is a way around this problem…

One useful technique is to ask children to come up with not one, but two estimates. Given a calculation, the children need to create one estimate that they know is larger, and one that is smaller than the answer!

There’s no hiding place now. We need two estimates that potentially zero in on the actual answer.

A little maths game

Here’s a simple little game using a set of digit cards, some counters and paper that could be used to help children refine their ability to ‘estimate’.

Write calculation function on a post-it note or piece of paper (in this case we chose multiplication). This is placed on the table. Now a set of 1-9 digit cards is mixed, and one player chooses the top three cards and a deals them out around the function marker:

At this point the cards are face-down. All players pick up a pencil and a piece of paper.

When everyone is ready the three cards are turned over and all of the players have to estimate the product of the two numbers as quickly as they can.

No written calculations allowed here, just estimates!

As was mentioned above, we don’t want one estimate. We want two.

All of the players need to choose a number they feel would be close to the actual answer but a little too large, and one they feel would be close, but a little smaller than the actual answer. They write these estimates on the paper and place them face down in front of them, and take it in turns to explain their thinking.

From the above numbers, for example, Ben suggested that:

7 x 28 is similar to 7 x 30, and since 7 x 3 was 21,

This gave him a large estimate of 210

7 x 28 could be thought of as 7 x 25, and since 7 x 20 is 140 and 7 x 5 is 35…

this game him a small estimate of 175

Next, a calculator is used to find the actual product. Finally, everyone shares their estimates and discuss how they created them.  The player who made the most reasonable two estimates wins a counter.

Play the game until one person has 4 counters.

We were playing this at home so used what we had available; a set of Phase 10 Cards
(we removed the 10, 11 and 12 cards), but any maths number cards, such as our mathsticks number cards, (or even playing cards) could be used instead.

 If you find this teaching idea useful please let others know about mathsticks.

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you have a maths activity or idea that has worked well for you?

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