Counting a set of objects
How does a child count a set of up to twenty things without skipping one or counting one twice?
Where you are 23 in Counting and cardinality
When you reach for it
Counting a set means giving each object exactly one counting word, in order, so that no object is skipped and none gets two words. Up to ten a child can often do this by eye and by habit; between eleven and twenty the sets get big enough that keeping track becomes the real work, and the words themselves change shape. Reach for it once a child can say the counting words to twenty and has met one word for each object with small sets.
Each day below takes about fifteen minutes. Every count this week is between eleven and twenty.
Day 1: The words past ten
You need: about 15 toy cars, or any small things that can stand in a line along the edge of a table.
Line the cars up along the table edge while the child watches. Count them together, touching each one: “one, two, ... ten.” Then slow down and keep going: “eleven, twelve, thirteen.” Point out that the words after ten sound different. “Eleven” and “twelve” are new words, and from “thirteen” on, each word ends in “teen”. The touching does not change: one car, one word.
Ask, “Which car got the word eleven? Which one got twelve?” Then, “What was the last word?”
Practice.
- Touch and count the counters in the picture above. Answer: 13; the last counter gets “thirteen”.
- Line up 11 cars and count them. Answer: 11; the word right after “ten” is “eleven”.
- Line up 12 crackers and count them. Answer: 12, with “eleven” and “twelve” on the last two.
- Line up 15 cars and count them. Answer: 15; the words after ten are “eleven, twelve, thirteen, fourteen, fifteen”.
Day 2: Counting in a circle
You need: about 16 small toy animals, a sock, and a paper plate with 13 buttons.
Sit the animals in a circle on the floor. Ask the child to count them. A circle has no first or last animal, so it is easy to go around past the start and count some animals again. Show the fix: lay the sock next to one animal before starting. Count from that animal, go around, and stop at the animal just before the sock.
Ask, “How did you know when to stop?” The answer you want is something like “when I got back to the sock”.
Practice.
- Count the counters in the ring above, starting at the hollow one. Answer: 15.
- Sit 16 animals in a circle, put the sock by one, and count. Answer: 16; the count stops just before the sock comes around again.
- Set the 13 buttons around the rim of the plate and count them, with no sock this time. Answer: 13; the child picks a first button and keeps a finger beside it, so they know where to stop.
Day 3: Rows of rows
You need: an empty egg carton (two rows of 6), 12 cotton balls, and 20 crayons.
Have the child put one cotton ball in each cup of the carton, then count the cotton balls. With two rows there is a new place to slip: the end of the first row. Show the child how to count along the top row, keep a finger on the last one, and carry the count on into the next row: “six” at the end of the top row, then “seven” at the start of the bottom row. The count does not start again at “one”.
Ask, “Where did you start the second row? What word did you say there?”
Practice.
- Count the counters in the picture above, row by row. Answer: 18; the second row starts at “seven” and the third at “thirteen”.
- Count the cotton balls in the egg carton. Answer: 12, one in each cup.
- Lay 20 crayons in two rows of 10 and count them. Answer: 20; the second row starts at “eleven”.
Day 4: Counting a loose pile
You need: a tray, about 20 pieces of dry pasta, a strip of paper, and a pencil.
Pour pasta onto the tray. In a loose pile, nothing tells the child which piece comes next, so they need a way to separate the counted pieces from the uncounted ones. Here is one: lift each piece onto the paper strip as you say its word, so the counted ones end up in a line. On a picture, where nothing can move, the child makes a small pencil mark on each one as it is counted. A scattered picture is the hardest case: kindergarten expects it only up to about 10 things, so a picture of 14 is a stretch, and the marks are what make it possible.
Then count the same pile a second time, or have someone else count it. Ask, “Did we get the same number? If not, how can we find out which one is right?” Counting again slowly, together, settles it.
Practice.
- Count the counters in the picture above, marking each one. Answer: 14.
- Pour 15 pieces of pasta on the tray and count them by moving each onto the strip. Answer: 15.
- You and the child each count the same pile of 20 pieces of pasta. Answer: both counts are 20; if the counts differ, count together slowly to find the slip.
Exercises
- Ask the child to count the counters in the picture. The count runs past ten, so listen for the words after “ten” and watch how the child keeps each counted one apart from the rest.
- Set out blocks in two rows, 9 in the top row and 8 in the bottom row. Ask the child to count them. How many blocks are there, and what word goes on the first block of the bottom row?
Answers
- 19 counters. Each counter gets one word, from “one” to “nineteen”. A child who has it marks or touches each counter once, keeps going past “ten” with “eleven, twelve, ...”, and does not stop or start over at the edge of the picture.
- 17 blocks. The top row ends at “nine”, so the bottom row starts at “ten” and ends at “seventeen”. A child who has it carries the count on into the second row instead of starting again at “one”.
Where this goes next
Once the last word of a count is understood to name the whole set, the child has the last word tells how many. Counting the other way around, picking out a set of a given size from a bigger pile, is counting out a given number. Counting the teen numbers leads to seeing thirteen as ten and three, and larger piles are counted faster by grouping them into tens. Two counted sets put together are the start of addition, and saying which object came first, second and third is ordinal numbers.