Ordinal numbers

Why this exists

The words first, second, third, fourth and so on name a place in a line, not an amount. “Four” tells how many things are in a group; “fourth” points at one single thing, the one that gets the word “four” when you count along the line from its start. So a line needs a start before its places mean anything, and these three days build that: naming places, telling a place from an amount, and seeing that the start of the line decides who is first.

A child should already be able to count a set of objects and know that the last word said tells how many. Keep every line at ten or fewer.

Day 1: First, second, third

You need: 5 small toys (stuffed animals or toy cars), a block or a book to be the “door”.

Put the door on the table and line the toys up from it, one after another. Say, “The line starts at the door. This one is next to the door, so it is first.” Touch the next toy: “This one is second.” Then “third”, “fourth”, “fifth”. Point out that the place words sound like the counting words, except “first”, “second” and “third”, which have their own names.

Ask, “Who is first? Who is third? Point to the fifth one.” Then let the toys take turns going through the door, and ask before each one goes, “Which one goes now? First, second, or third?”

Practice. Use the picture. The line starts at the flag.

1. Which shape is first? Answer: the dark circle, the one next to the flag.
2. Which shape is third? Answer: the triangle.
3. What place is the dark square in? Answer: fourth.
4. Which shape is last, and what place is it? Answer: the open circle, in fifth place.
5. Line up 4 toys and have the child name each place out loud. Answer: “first, second, third, fourth”, one place word for each toy.

Day 2: Fourth is one thing, four is a group

You need: about 10 blocks or counters, one of them a different color.

Make a line of 6 blocks starting at the door, with the odd-colored block in the fourth spot. Ask, “What place is the odd block in?” Let the child touch and say “first, second, third, fourth”. Then ask, “How many blocks are there?” The answer is 6, found by counting all of them.

Now put the two words side by side. Say, “Hand me three blocks”, then put them back and say, “Hand me the third block.” The first time the child hands you a group of 3. The second time the child hands you one block, the one in the third place. The same counting along the line finds both, but “three” keeps all the blocks counted, and “third” keeps only the last one touched.

Practice.

1. In the picture, what place is the dark counter in? Answer: fourth.
2. How many counters are in the picture? Answer: 6.
3. How many counters come before the dark one? Answer: 3, the first, second and third.
4. Line up 7 blocks. “Hand me 5 blocks.” Then, “Hand me the fifth block.” Answer: a group of 5 blocks the first time, a single block the second time.
5. Sam is fifth in line for the slide. How many children are before him? Answer: 4, the ones in places first to fourth.

Day 3: Where the line starts, and on to tenth

You need: 10 toy cars (or 10 counters), a strip of tape for a finish line.

Line up all 10 cars facing the finish line. The car nearest the finish line is first, so the line starts there. Name every place together, all the way out: first, second, third, fourth, fifth, sixth, seventh, eighth, ninth, tenth. The last car in a line of ten is tenth, just as the last word in a count of ten is “ten”.

Then move the finish line to the other end and turn every car around. Ask, “Who is first now?” The car that was last is first, and the car that was first is last. Nothing moved except the start, so a place always depends on which end the line starts from. On a picture, look for the start before naming any place.

Practice. In this picture, the flag is on the right.

1. What place is the dark counter in? Answer: seventh, counting from the flag on the right.
2. A child counts from the left end and says “fourth”. What went wrong? Answer: the child started at the wrong end; this line starts at the flag.
3. How many counters are there, and what place is the one at the far left? Answer: 10 counters, and the far left one is tenth.
4. 5 cars race, and the blue car is second. Then the race turns around and goes back the other way. What place is the blue car now? Answer: fourth. From the new start, the old fifth car is first, the old fourth is second, the old third is third, and the old second is fourth.
5. Say all the place words from first to tenth. Answer: first, second, third, fourth, fifth, sixth, seventh, eighth, ninth, tenth.

Exercises

1. The line starts at the flag. What place is the dark counter in? How many counters come after it?
2. Ava is third in a line of 9 children. How many children are before her, and how many are after her?

Where this goes next

Places in a line come back on the The number line, where each number has its own spot and the spots run in order from a start. Words that say where something is, like above and beside, are Position words: above, below, beside, in front of, behind. The place words lean on the counting words of Number names, numerals and zero, which is why “fourth” sounds like “four”.