Place value and number system: maths lessons by year

Sheets only, lesson coming

Comparing numbers: Which number is bigger, which is smaller, and how we can tell.
Ordering numbers: Putting numbers in order, from smallest to largest and back.
Understanding place value: What each digit is worth: ones, tens, hundreds and more.
Building numbers with place value: Making a number from tens and ones, and splitting it up again.

The steps in place value and number system, in the order children usually meet them. Years are named as in Australia; the ages are a guide.

Teen numbers are ten and some more. Show numbers 11 to 19 as one ten and some ones using ten frames or blocks.
Tens and ones in two-digit numbers. Say how many tens and ones are in a two-digit number and the value of each digit.
Partition two-digit numbers into tens and ones. Split a two-digit number into tens and ones, e.g. 47 = 40 + 7.
Compare two-digit numbers with < > =. Use tens and ones to decide which number is bigger and write it with <, > or =.
Place numbers on a number line to 100. Find and mark numbers on a number line or number track up to 100.
Find 10 more and 10 less. Add or take one ten from a number to 100 and see only the tens digit change.
Round to the nearest 10. Round a two- or three-digit number to the nearest ten.

Partition two-digit numbers in different ways. Split a number in non-standard ways, e.g. 45 = 30 + 15, using blocks.
Estimate where a number sits on a number line. Place a number on a line marked only at its ends, e.g. 0 to 100.
Hundreds, tens and ones. Say the value of each digit in a three-digit number.
Read and write numbers to 1000. Read and write three-digit numbers in numerals, words and expanded form.
Zero as a place holder. Explain what a zero digit does in numbers like 205 and 250.
Regroup: ten tens make a hundred. Exchange 10 ones for a ten and 10 tens for a hundred, and rename numbers.
Compare and order three-digit numbers. Use place value to compare and order numbers to 1000.
Find 100 more and 100 less. Add or take one hundred from a three-digit number and see the hundreds digit change.

Round to the nearest 100. Round a three-digit number to the nearest hundred.
Thousands: place value in four-digit numbers. Say the value of each digit in a four-digit number.
Read, write, compare and order numbers to 10 000. Read, write and order four- and five-digit numbers.
Place larger numbers on a number line. Find and estimate positions of 3- and 4-digit numbers on lines with different scales.
Estimate answers by rounding. Round numbers first to make a quick estimate and check if an answer is sensible.
Read Roman numerals to 12. Read I to XII, as on a clock face, and see how the symbols combine.
Count back through zero to negative numbers. Continue counting backwards past zero, e.g. 2, 1, 0, -1, -2.

Round to the nearest 1000. Round four-digit numbers to the nearest thousand.
Each place is ten times the place to its right. See that a digit moved one place left is worth ten times as much.
Place value to 100 000. Read, write and give the value of digits in numbers to 100 000.
Read Roman numerals to 100. Read and write Roman numerals from I to C.

Read, write and order numbers to 1 000 000. Read, write, compare and order numbers up to one million.
Count in powers of 10 from any number. Count forwards and backwards in steps of 10, 100, 1000, 10 000 and 100 000.
Round to the nearest 10 000 and 100 000. Round numbers up to one million to a given power of ten.
Negative numbers in real life. Use negative numbers for temperatures, depths and money owed.
Read Roman numerals to 1000 and years. Read Roman numerals to M and read years written in them.

Numbers to 10 000 000. Read, write, order and compare numbers up to ten million.
Compare and order negative numbers. Use a number line to order and compare positive and negative numbers.
Calculate differences across zero. Find the gap between a negative and a positive number, e.g. from -4 to 7.