Numbers, Operations and Relationships

Every digit in a number has a value that depends on its position. This is called place value. Moving one place to the left makes a digit ten times bigger.

We use four columns for four-digit numbers. Each column has its own colour — learn these colours because we use them in every example below:

The number shown in the table is 4 327. The 4 sits in the Thousands column, so it is worth 4 000. The 3 sits in the Hundreds column, so it is worth 300. The 2 sits in the Tens column, so it is worth 20. The 7 sits in the Units column, so it is worth 7.

We can write this in expanded notation — splitting the number to show the value of every digit:

4 327  =  4 000  +  300  +  20  +  7

Counting forwards means adding the same number each time to get the next number. Counting backwards means subtracting the same number each time. The number you add or subtract is called the interval.

Counting in 1s — add 1 each time:

1 → 2 → 3 → 4 → 5   (each number is 1 more than the one before it)

Counting in 10s — add 10 each time:

10 → 20 → 30 → 40 → 50   (each number is 10 more than the one before it)

Counting in 100s — add 100 each time:

100 → 200 → 300 → 400 → 500   (each number is 100 more than the one before it)

Counting in 1 000s — add 1 000 each time:

1 000 → 2 000 → 3 000 → 4 000 → 5 000   (each number is 1 000 more than the one before it)

To count backwards, use the same intervals but subtract each time instead of adding.

We use three symbols to compare numbers:

• <   means less than  — example: 3 < 7  (3 is less than 7)
• >   means greater than  — example: 7 > 3  (7 is greater than 3)
• =   means equal to  — example: 5 = 5

💡 Memory trick: The open mouth of < or > always points towards the bigger number — like a hungry crocodile that always wants to eat the bigger meal!

Follow these steps when comparing any two numbers:

Step 1 — Count the digits. More digits = bigger number. A 4-digit number is always bigger than a 3-digit number.

Step 2 — If both numbers have the same number of digits, compare the thousands digits first. The bigger thousands digit means the bigger number.

Step 3 — If the thousands digits are equal, compare the hundreds digits. If those are equal too, compare the tens digits. If those are also equal, compare the units digits.

Sometimes we do not need an exact number — we need a number that is close enough and easy to work with. We call this rounding off.

There is one simple rule for rounding:

• If the deciding digit is 0, 1, 2, 3 or 4 — round down (the digit in the column you are rounding to stays the same)
• If the deciding digit is 5, 6, 7, 8 or 9 — round up (add 1 to the digit in the column you are rounding to)

The deciding digit is the digit just to the right of the column you are rounding to. Here is which digit to look at:

• Rounding to the nearest 10 — look at the units digit (the blue column). Replace the units digit with 0.
• Rounding to the nearest 100 — look at the tens digit (the green column). Replace the tens and units digits with 0.

A number line is a straight line with numbers written on it at equal spaces. The numbers always increase from left to right — smaller numbers are on the left and larger numbers are on the right.

The equal spaces between the numbers are called intervals. If a number line goes from 0 to 1 000 with marks at every 100, the interval is 100.

Some numbers fall exactly on a mark. Others fall between two marks. To find where a number sits between two marks:

• Look at the two marks on either side of your number.
• If your number is exactly in the middle, it is the halfway point.
• To calculate the halfway point: add the two marks together and divide by 2.