Number

Counting and Cardinality

Junior Infants · Senior Infants · 1st Class · 2nd Class

✓By the end of this lesson students will be able to count forwards and backwards to 20.
✓By the end of this lesson students will be able to count forwards and backwards to 100.
✓By the end of this lesson students will be able to demonstrate one-to-one correspondence when counting objects.
✓By the end of this lesson students will be able to recognise and write numerals from 0 to 10.
✓By the end of this lesson students will be able to recognise and write numerals from 0 to 100.

Key concepts

Counting

Counting is saying numbers in order, like 1, 2, 3, 4, 5. We use counting to find out how many things there are in a group. When we count, we say one number for each object.

Cardinality

When you count a group of things, the last number you say tells you the total number of things in that group. This is called cardinality. For example, if you count five apples, the number 'five' tells you how many apples there are in total.

One-to-one Matching (or Correspondence)

One-to-one matching means giving one number to one thing, or pairing one thing with exactly one other thing. When you count, you must point to each object only once and say only one number for it.

Numerals

Numerals are the special pictures or symbols we use to write numbers down. For example, '3' is the numeral for the number three, and '42' is the numeral for the number forty-two.

Key facts to remember

1Counting helps us to know 'how many' items are in a group.
2When we count a group of objects, the last number we say tells us the total amount (cardinality).
3We must count each object only once and assign it only one number word (one-to-one correspondence).
4Numbers can be counted forwards (getting bigger) and backwards (getting smaller).
5Numerals are the written symbols we use to represent numbers.
6A number line can help us to see numbers in order and count forwards or backwards.

Worked examples

Example 1

Count the number of blue squares. (Imagine 🟦🟦🟦🟦🟦🟦🟦)

IPoint to the first square and say 'one'.

IIPoint to the second square and say 'two'.

IIIPoint to the third square and say 'three'.

IVPoint to the fourth square and say 'four'.

VPoint to the fifth square and say 'five'.

VIPoint to the sixth square and say 'six'.

VIIPoint to the seventh square and say 'seven'.

Answer

There are 7 blue squares.

The last number you said, 'seven', tells you how many squares there are in total.

Example 2

Count forwards from 18 to 23.

IStart by saying 'eighteen'.

IIThen say the next number: 'nineteen'.

IIIThen say the next number: 'twenty'.

IVThen say the next number: 'twenty-one'.

VThen say the next number: 'twenty-two'.

VIThen say the next number: 'twenty-three'.

Answer

18, 19, 20, 21, 22, 23.

When counting forwards, the numbers get bigger. When counting backwards, the numbers get smaller.

Example 3

Look at the numeral: 65. What number is this?

ILook at the first digit, '6'. This means six tens.

IILook at the second digit, '5'. This means five units.

IIIPut the tens and units together to read the number.

Answer

Sixty-five.

The position of a digit in a numeral tells us its value (e.g., whether it's tens or units).

Common mistakes

✗Skipping numbers or saying numbers out of order when counting.
✗Counting an object more than once, or missing an object when counting a group.
✗Not understanding that the last number counted represents the total number of items (cardinality error).
✗Confusing similar-looking numerals, such as '6' and '9' or '12' and '21'.
✗Starting to count a set of objects from a number other than 'one' (e.g., starting at 'two' by mistake).

Exam tips

★Always point to each object as you count it to ensure you count each one only once.
★Practise counting forwards and backwards every day, starting from different numbers.
★Look carefully at the numeral to make sure you know what number it represents.
★Use a number line or a hundred square to help you count forwards and backwards, especially for larger numbers.

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