20までの数と数え方

When you count objects, touch each one and say one number for it (one-to-one correspondence). The last number you say is how many there are altogether. Moving the objects around does not change how many there are: 7 apples are still 7 apples whether they are in one row or two rows.

Zero is the number that means 'none'.

As well as counting on in ones, you can count in twos and in tens. Counting in twos goes $2,4,6,8,10$; counting in tens goes $0,10,20$. Practise starting from any number, and also counting back in ones and in tens.

The numbers you say when you count in twos from 0, $0,2,4,6,\dots$, are the even numbers; the numbers in between, $1,3,5,7,\dots$, are the odd numbers.

To decide which of two numbers is greater, think of the counting sequence (0, 1, 2, 3, …): the number that comes later is greater. Between $14$ and $17$, $17$ comes later, so it is the greater number. You also practise putting several numbers in order, from smallest or from greatest.

Numbers from 11 to 20 are easier to understand as 'ten and some more': $13$ is $10$ and $3$, and $18$ is $10$ and $8$.

In the Cambridge Primary Mathematics (0096) curriculum framework, Stage 1 covers counting objects from 0 to 20 (1Nc.01), recognising small groups up to 10 without counting (1Nc.02), estimating up to 20 and checking by counting (1Nc.03), counting on in ones, twos or tens and back in ones and tens (1Nc.04), and even and odd numbers as 'every other number' (1Nc.05). Reading and writing numbers (1Ni.01), zero as 'none' (1Np.01), and comparing and ordering numbers from 0 to 20 (1Np.03) are also Stage 1.