Place value explained for parents and teachers
Place value is the idea that a digit's worth depends on its position. In 3,405 the 4 is not four but four hundred. Nearly every written method in primary maths depends on it, from column addition to long division and decimals, so time spent here pays back for years.
Why it is hard
Pupils can read and write numbers long before they understand them. They may say "three four zero five" and write 3405 without knowing that the zero holds the tens place open. Mistakes such as writing 'three hundred and forty' as 30040 show a rule learned from the words rather than the structure.
Build it with objects
Use ones as single cubes, tens as rods of ten and hundreds as flats. Trading ten ones for a ten, and a ten for ten ones, teaches the exchange that underlies carrying and borrowing. Place value counters on a chart help later: a counter in the tens column is worth ten. Make the move from objects to counters to digits slowly.
Use the number line
A number line shows size. Ask pupils to place 450 between 400 and 500, then to find a number closer to 400 than 450. Zooming into a section between 3,400 and 3,500 shows the same structure at a smaller scale. This also leads naturally into rounding and estimating.
Say it in several ways
Practise partitioning: 3,405 is 3,000 plus 400 plus 5, and also 34 hundreds and 5 ones. Flexible partitioning is what lets pupils subtract across zeros or multiply by tens. Ask for a number that is 100 more, 10 less and 1000 more, and notice which digits change.
Extend to decimals
The same system continues to the right of the point: tenths, hundredths and thousandths, each ten times smaller. Pupils who see 0.45 as four tenths and five hundredths rarely say that 0.45 is bigger than 0.5 because 45 is bigger than 5. Compare decimals on a number line and with money to firm up the idea. The decimals topics for Year 5, Grade 5 and Australian Year 5 give practice.
Common slips and fixes
Reversing digits, ignoring zeros as placeholders, and ordering numbers by their first digit alone are common. A quick check: ask the pupil to read their answer aloud and to say what each digit stands for. Where a slip repeats, build a place value chart on the sheet using a text block.
Sheet ideas
For beginners, use missing-number questions such as "3,000 + __ + 5 = 3,405". For a stretch, ask pupils to make the largest and smallest numbers from four digit cards, then to find the difference. Set the difficulty to match the stage and mix in rounding for variety.
Build one in the editor, or see how place value sits in each country's curriculum on the year levels guide.