1. Counting & Numbers to 20
KindergartenEvery big idea in math starts with counting. In this chapter we count things we can touch, learn what a number really means, and put numbers in order — all the way up to 20.
What a number really is
A number tells us how many. When we count a group of things, we touch or point to one object for each number word, in order, without skipping or repeating. That is called one-to-one counting. The very last number we say is the total — how many there are.
Numbers have a fixed order. 1 comes before 2, 2 comes before 3, and so on, all the way to 20:
Each number also has a written symbol called a numeral — like "7" — that stands for that many things, no matter what the things are: 7 apples, 7 claps, 7 stars.
Why counting carefully matters
If you skip a number, or count the same toy twice, you get the wrong total — and that matters, like when you are counting cookies to make sure everyone at the party gets one! Careful, one-for-one counting is the whole secret.
Numbers also let us compare. Line up 7 blocks in one row and 5 blocks in another, right next to each other — you can see that 7 is more than 5 without even counting again. That is the idea of more, less, and equal (the same).
Hands-on: count your own treasures
Gather 12 small things — buttons, spoons, toy cars, anything nearby.
- Line them all up in a row so none are hiding behind another.
- Touch each one and say the next number out loud, starting at "1."
- The last number you say is how many there are in total — that should be 12.
- Now split them into two piles and count each pile. Add the two piles together in your head and check it matches 12.
Answer: there are 12 objects in total, however you split the pile.
Test your understanding
What number comes right after 9?
10. After we finish counting single things "1" through "9," the very next number starts a new pair of digits: 10. It means "one group of ten, and zero extra."
Which is more: 7 apples or 5 apples?
7 apples is more, because when counting up, 7 comes after 5. You can check by lining up both groups side by side — the row of 7 has extra apples left over once the row of 5 runs out.
Is zero a number?
Yes! Zero means "none at all." If a jar has no cookies in it, the number of cookies is 0. It is a real, useful number — it just tells you the group is empty.
What number comes between 14 and 16?
15. Counting in order: …13, 14, 15, 16, 17… — 15 sits exactly one step after 14 and one step before 16.
How the ideas connect
Every key idea in this chapter, branching from the core concept — use it to see the whole picture at a glance.
The key facts, visualised
Worked problems, step by step
Follow each solution line by line, then try to reproduce it on paper before moving on.
Example 1How many apples are in a row of 4 apples?
- Touch each apple and say a number
- Say one, two, three, four
- The last number said is four
Example 2Which group has more: 3 stars or 5 stars?
- Count the first group: 1, 2, 3
- Count the second group: 1, 2, 3, 4, 5
- 5 comes after 3, so 5 is more
Now you try
Work each one out first, then tap to reveal the worked answer.