Counting backward

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Children count backwards from a "high" number. What "high" is depends on the children. Whatever the children can count forwards to they should learn to count backwards from (though they do not have to count all the way to zero if they start at a high number). As we start at a high number and count to a lower one, we can also start our hands at a high position and gradually move them lower, reaching the floor by "zero." And we start our voices loud enough and gradually get softer until we're just whispering by zero.

Planning ahead, so that we save enough room to get to zero (not reaching the floor too quickly) is part of “feeling” the numbers: we are not just reciting sounds, but keeping track of roughly how far we’ve gone and how far we have to go.


Setup of the activity

This particular time, we started with the A, B, C song (see high and low notes) before counting backward.

"A, B" are low notes in the song.

By the time we reach "E, F" we're reaching very high!

Now we're back at the desks, counting backward from 30. This time, instead of changing pitch as we count, we change dynamics, getting softer as we reach the lower numbers.

We start high for 30.

We're at about 20 now.

We're getting below 10, ready to touch the floor at 0.


Purpose: Being competent at counting backwards aids subtraction even when children are not using it directly to subtract. Being able to make it successfully across the decades (… 51, 50, 49, for example, or 32, 31, 30, 29) helps students understand the structure of the place value system so that when they are asked to subtract 4 from 900, they know to back off to 890 (from 90 to 89 in their heads) and can use the pairs-to-10 that they’ve over-learned to get the answer 896. If I make it sound too “easy” here, it is, in fact, that easy. A few particular selected skills—the list found on Think Math! website, in this case—help children go very far very fast.

The purpose of softening the voice is partly to accord with “smaller number, smaller voice” and develop attention to musical dynamics. It also serves another purpose: Without that special directive, children have a tendency to scream the countdown from 10 to 0 and follow with a “blast off!” To avert the noise, we replace it with something else that requires their planning and control: lowering the voice (but not too quickly) and lowering the hands (but not too quickly!).

Counting backwards is a good "warm up" exercise in the beginning of a lesson, or a "cool down" after coming in from recess. Counting backwards from 30 to 0 can also be timed so that children get the sense of how long a second is, and how long a half minute is.

On their own

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