How to teach expanded form

Grade 2 to Grade 5

Expanded form writes a number as the sum of the value of each digit, so 347 becomes 300 + 40 + 7. It makes place value visible and is the bridge between reading a number and understanding what its digits are worth. Standard form is just the normal way of writing it (347).

How to teach it

1. Build the number first with base-ten blocks or place-value counters so each digit's value is concrete.
2. Write each digit's value under a place-value chart: the 3 is 300, the 4 is 40, the 7 is 7.
3. Add them with plus signs to make the expanded form: 300 + 40 + 7.
4. Practise both directions , number to expanded form, and expanded form back to a standard number.
5. Show what happens with a zero: 508 is 500 + 8 (the zero tens are left out).

Common mistakes

• Writing the digits instead of their values (3 + 4 + 7 instead of 300 + 40 + 7).
• Including a zero place (500 + 0 + 8 instead of 500 + 8).
• Losing the place value of a middle zero when going back to standard form.