You're playing a board game: your counter is on square 7, you roll a
3, and you hop forward — 8, 9, 10. That's
counting on, and it's how we add without starting all over again. Counting back the
same way lets you take away — handy for scores, steps and change.
When you count, you don't
always have to begin at 1. You can pick up the count from
any number you like — 5, 27,
anywhere. The numbers carry on in the same order wherever you join them.
Picture a number line.
Counting on is walking to the right, one step at a time, saying each
number as you land on it — the numbers get bigger. Counting back is turning
round and walking to the left — the numbers get smaller.
Start at 7 and count on three: you say
8, 9, 10 and land on 10. Start at
7 and count back three: you say 6, 5, 4 and land
on 4. Each word you say is one hop along the line.
Press play, then replay it: each time a marker drops onto a fresh starting number, hops
forward a few steps (counting on), then turns around and hops back a few
steps (counting back), reading aloud every number it lands on.
Three worked examples
Every count is the same move: put your finger on the start, then hop one place per number you say.
-
Count on 4 from 6. Hop right
four times, saying 7, 8, 9, 10. You land on
10.
-
Count back 3 from 9. Hop left
three times, saying 8, 7, 6. You land on 6.
-
Count on 5 from 20. You don't
have to start at one — begin at 20 and hop right five times:
21, 22, 23, 24, 25. You land on 25.
This is the bridge to addition
and subtraction:
adding is just counting on, and taking away is just counting back. So
6 + 4 means "start at 6, count on
4" — which is the first example, landing on 10.
And 9 - 3 means "start at 9, count back
3" — the second example, landing on 6.
The number you start on is not a hop — you say it silently in your head, then start
counting from the next one.
- To count on 3 from 5, say
6, 7, 8 and land on 8.
Don't recount the 5 (saying 5, 6, 7 lands you
one short, on 7).
- To count back 2 from 8, say
7, 6 and land on 6 — not
8, 7.
A frog sits on lily pad 4 and hops three pads forward:
5, 6, 7 — splash, splash, splash. It lands on pad
7. That is counting on 3 from
4. Each hop is one number, and the frog never lands on its own starting pad
again — it leaves it behind on the very first hop.
When a rocket launches, the crew count back:
10, 9, 8, 7, 6, 5, 4, 3, 2, 1 — blast off! That is counting back, one
step at a time along the number line, all the way down to 1 (and then
0: lift-off). Counting back is just counting on in reverse, so the numbers
get smaller as you go.