One more and one less

Why this exists

The counting words are not just a chant: each word names a group exactly one bigger than the word before it. So when one thing is added, the count is the next word, and when one thing is taken away, the count is the word before, with no need to count the whole group again. These four days build that link with cube towers and stones, line the towers up into a staircase, and end with groups the child cannot see, up to twenty.

The child should already know that the last word said tells how many.

Day 1: One more cube

You need: about 12 snap-together cubes (linking cubes or plastic bricks).

Build a tower of 4 cubes with the child and count it together: “one, two, three, four. Four cubes.” Hold up one more cube and say, “I am going to put one more on top. How many will there be?” Let the child guess, snap it on, and then count to check.

Ask, “What number comes after four when we count? How many cubes are in the tower now?” Both answers are “five”. That is the idea of the day: one more cube makes the count the next counting word.

Practice.

1. A tower of 2 cubes, and one more goes on. Answer: 3 cubes, the word after “two”.
2. A tower of 6 cubes, and one more goes on. Answer: 7 cubes.
3. A tower of 9 cubes, and one more goes on. Answer: 10 cubes.
4. Build a tower of 5, then put one more on while the child’s eyes are closed. “How many now?” Answer: 6. A child who says it without counting from one has the idea.

Day 2: One less stone

You need: about 10 smooth stones (or large dry beans) and a small dish.

Lay 6 stones in a row and count them together. Then take the last stone away and drop it in the dish. Ask, “How many stones are left? What word comes just before six?”

Both answers are “five”. Taking one away moves the count back one word. Count the row to check, then take away one more and ask again.

Practice.

1. 4 stones, take one away. Answer: 3, the word before “four”.
2. 8 stones, take one away. Answer: 7.
3. 3 stones, take one away. Answer: 2.
4. 1 stone, take one away. How many are left? Answer: 0, none. One less than one is zero.

Day 3: The cube staircase

You need: the snap-together cubes from Day 1, enough for 10 towers (about 55 cubes, or build fewer towers).

Build a tower of 1 cube. Then ask, “Make a tower with one more.” The child builds 2. Then one more than that, and so on, standing each tower to the right of the one before. The towers make a staircase, and each step goes up by one cube.

Point to a tower and ask, “Which tower has one more cube than this one? Which has one less?” The child points right for one more and left for one less, and says the number.

Practice.

1. Which tower is one more than the tower of 3? Answer: the tower of 4, just to its right.
2. Which tower is one less than the tower of 5? Answer: the tower of 4, just to its left.
3. The staircase in the picture stops at 6. Build the next tower. Answer: 7 cubes, one more than 6.
4. With the staircase built up to 10, which tower is one less than the tallest? Answer: the tower of 9.

Day 4: One more and one less without looking

You need: a small box with a lid and about 20 stones or cubes.

Count 11 stones together and put them in the box. Close the lid. Let the child watch you drop in one more. Ask, “How many are in the box now?” The child cannot see them, so the only way to know is the counting words: one more than eleven is twelve. Open the box and count to check. Do the same with one taken out.

Then play “What comes next, what comes before?” with no objects: say a number up to 20 and the child says one more and one less.

Practice.

1. 14 in the box, one taken out. Answer: 13.
2. 17 in the box, one more dropped in. Answer: 18.
3. 20 in the box, one taken out. Answer: 19.
4. “What is one more than ten? One less than ten?” Answer: 11 and 9.

Exercises

1. How many cubes are in the tower? How many would there be with one more cube on top? How many with one cube taken off?
2. There are 16 crackers on a plate, and Rosa eats one. How many crackers are on the plate now?

Where this goes next

One more and one less are the first steps of counting on and counting back, where a child starts from a known amount and keeps counting instead of going back to one. One more is the simplest case of adding by joining, and one less the simplest case of taking away. The staircase, where each step is one bigger, is the idea behind comparing two numbers and, later, the evenly spaced The number line.