One touch, one number
To count a group of things, touch each one once and say one number as you touch it: 1, 2, 3, and on. The last number you say tells you how many there are. Count the ducks on a pond, and if the last number is 7, there are 7 ducks.
Two slips spoil a count: touching the same thing twice, and missing one out. When things are in a jumble, move each one aside or cross it off once it has its number. Then nothing is counted twice and nothing is left out.
One more, one fewer
The counting numbers always come in the same order, and each one is one more than the number before it. After 7 comes 8, because 7 and 1 more is 8. So when one more duck lands on the pond, there is no need to count all the ducks again: the new total is the next number.
It works the other way too. The number just before 8 is 7, so when one button falls off a coat that had 8, there are 7 left. On a number line every number has its own place, smallest on the left. A step to the right is one more, and a step to the left is one fewer.
Each step to the right on the number line adds 1, and each step to the left takes 1 away.
Worked example: Ducks Counted One by One, Then One More Duck
Question There are 7 ducks on a pond. Mei touches each duck once as she counts. (a) What is the last number Mei says? (b) One more duck comes to the pond. How many ducks are there now?
1.Draw one counter for each duck, all in a row.
One counter is one duck. There are 7 counters in a row. 2.Touch each counter once and count: 1, 2, 3, 4, 5, 6, 7.
Touch each counter once and say one number for each: 1, 2, 3, 4, 5, 6, 7. 3.(a) The last number Mei says is 7. There are 7 ducks.
(a) The last number Mei says is 7. There are 7 ducks. 4.(b) Draw one more counter. The number after 7 is 8, so 7 + 1 = 8. There are 8 ducks now.
(b) One more duck comes. The number after 7 is 8, so 7 + 1 = 8 ducks.
Answer: (a) 7; (b) 8 ducks
Common mistakes
- Touching one duck two times and saying 8 in part (a). Each duck gets one number only, so touch each duck once.
- Counting all the ducks again from 1 in part (b) and losing your place. You know there are 7, so one more is the next number, 8.
Worked example: Buttons on a Coat, One Falls Off
Question Sam has 8 buttons on his coat. (a) One button falls off. How many buttons are on the coat now? (b) Then one more button falls off. How many buttons are on the coat now?
1.Draw 8 counters in a row for the 8 buttons. Write the numbers 1 to 8 under them.
One counter is one button. The numbers 1 to 8 are under the 8 counters. 2.One button falls off. Cross out the last counter, the one with 8 under it.
One button falls off, so the last counter is crossed out. 3.(a) The number just before 8 is 7. There are 7 buttons on the coat now.
(a) The number just before 8 is 7. There are 7 buttons on the coat. 4.(b) Cross out one more counter. The number just before 7 is 6. There are 6 buttons on the coat now.
(b) One more counter is crossed out. The number just before 7 is 6. There are 6 buttons on the coat.
Answer: (a) 7 buttons; (b) 6 buttons
Common mistakes
- Saying 9 in part (a). The button falls off, so there are fewer buttons, and the number goes back to 7.
- Saying 7 again in part (b). Two buttons have gone now, so go back one more number, from 7 to 6.