Look around you. How many birds? How many cups? You can answer by counting — pointing at one thing at a time until everything has been pointed at. This chapter uses pictures of dots to stand for real things, like marbles or fingers.

What is counting?

To count is to touch (or point at) each object once. Say a word for each touch: “one, two, three…” The last word tells you how many there are.

Try it on your fingers: one finger up for each thing you counted. If every object has a finger, the number of fingers matches the number of objects.

Zero

When there is nothing to point at, we write 0 and say zero. An empty plate, no toys in the box — zero dots:

(none)

Zero comes before one when we count: first nothing, then one, then two, and so on.

Remember

Zero means “none here,” not “forgot to count.”

Numbers 1 to 10

Each number has a digit (the symbol), a word, and a picture of dots — one dot for each thing you counted.

Digit Word Dots
1 one
2 two
3 three
4 four
5 five
6 six
7 seven
8 eight
9 nine
10 ten

Which group has more dots — the bigger picture wins:

7 more
4 fewer

Patterns

A pattern is when something repeats or grows the same way each time. You can often guess what comes next if you look at the pictures.

One more dot each time

Each step adds exactly one dot:

  1. 1
  2. 2
  3. 3
  4. 4
  5. 5
The pictures keep growing: 6 dots, then 7, all the way to 10 — one new dot every time.

Two dots at a time (even numbers)

Even counts split into pairs with nothing left over. We jump two dots at a time:

  1. 0 none
  2. 2
  3. 4
  4. 6
  5. 8
  6. 10
Each picture has one more pair of dots than the picture before. Every dot has a buddy.

One extra dot (odd numbers)

Odd counts also grow by two dots each step, but there is always one dot left alone — it does not fit in a pair. Look for the single dot in orange:

  1. 1
  2. 3
  3. 5
  4. 7
  5. 9
The lonely dot stays while the pairs grow: next would be 11 — five pairs and one dot by itself.

Circle, square, circle, square…

Patterns can use shapes, not only dots. Watch the pictures repeat:

  1. circle
  2. square
  3. circle
  4. square
  5. circle
  6. square
  7. next?
After a square comes a circle. The shapes take turns, over and over.

Addition

Addition means putting two groups together. Three dots and four more dots make seven dots in one big group. We write 3 + 4 = 7.

Adding

Start with the first group, then place the second group beside it and count all the dots.

Multiplication

Multiplication is many equal groups. Three bags with two sweets each is the same as three pairs of dots. We write 3 × 2 = 6 — “three groups of two.”

You can lay the dots in a rectangle: 3 rows with 2 dots in each row fills a block of 6 dots.

Division

Division is about sharing equally or making equal groups. If 12 biscuits are shared among 4 friends, each friend gets the same number. We write 12 ÷ 4 = 3 — “twelve split into four equal piles gives three in each pile.”

Division is the partner of multiplication. If 3 × 4 = 12, then 12 ÷ 3 = 4 and 12 ÷ 4 = 3. One picture of dots can answer both kinds of question.

Fair shares

When every pile has the same number of dots, the share is fair. If dots are left over, the total does not split evenly — those extras are the remainder.