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.
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.
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.”
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:
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.
Each step adds exactly one dot:
Even counts split into pairs with nothing left over. We jump two dots at a time:
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:
Patterns can use shapes, not only dots. Watch the pictures repeat:
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 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 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.
You can count higher than ten on your fingers — people use place value. Ten single dots can be thought of as one group of ten. Ten groups of ten make one hundred.
The number 47 means 4 tens and 7 ones — forty-seven dots, without drawing every dot one by one.
The world is huge. Counting every grain of sand on a beach one by one would take forever, so we use big number words to talk about amounts we cannot easily picture dot by dot. They matter because governments, scientists, and shops all work with large totals.
| Word | How we write it | Why it matters |
|---|---|---|
| hundred | 100 | About how many people fit in a big sports field; pages in a long novel. |
| thousand | 1,000 | Steps you might walk in a long hike; students in a large school district. |
| million | 1,000,000 | People in a large city; dollars in a national budget line item. |
| billion | 1,000,000,000 | World population is several billion; stars in our galaxy are hundreds of billions. |
Each big word is one thousand times the word before (ten hundreds make a thousand; one thousand thousands make a million). We bundle in tens and thousands so we can compare and add without losing track.
Use the tools below: count dots, add and multiply, share equally, and zoom from one dot up to a billion to see how big numbers compare.