Understanding fractions (age 7+)

Activities to try

1. 1

   Maths proofreader's bench: fix the almost-right statements

   Why it works: A written mathematical statement should be readable by anyone without guesswork; a dropped unit, a missing decimal place, or a swapped term can change the meaning a reader takes from it, so following shared conventions is an act of communication, not a nitpick.

   1. Work through a set of statements that are almost right and repair each one: '£3.5' (a price), '35' (a length), 'the top number is the denominator', and '7 + 5 = 12 + 3'.
   2. Submit each statement first as it is written — the sloppy version — to a reader that acts only on what is written and may misread nonstandard notation, then submit the repaired version and compare what the reader does with each. For example, when the two-decimal-place convention is dropped, a reader could misread '£3.5' as three pounds and five pence (£3.05) and short-change the customer; writing '£3.50' removes that ambiguity.
   3. Repair the price to '£3.50', add 'cm' to the 35, and rewrite the fraction sentence as 'the top number is the numerator', checking it against a fraction bar where the numerator counts the shaded parts.
   4. Decide whether '7 + 5 = 12 + 3' is true, and state why the equals sign means 'is the same as' rather than 'here comes the answer'.
   5. Proofread each finished statement by asking 'could someone misunderstand this?'
2. 2

   Dialogue with a literal reader

   Why it works: Precision repairs can come from seeing a listener try to act on exactly what was written or said; the child supplies the convention that prevents the misreading and says why it matters.

   1. Give notation to a character (a shopkeeper or robot) who acts only on what is written and may misread nonstandard notation: writing '£3.5' lets the character show how it could be misread as three pounds five pence (£3.05), even though £3.5 strictly equals £3.50, and writing '35' with no unit leaves the character unable to tell whether cm, m or mm is meant, so it cannot act correctly.
   2. Correct the notation in response to what the character does: fix £3.5 to £3.50, add the missing unit, and name the numerator and denominator correctly when asked for fraction words.
   3. Explain to the character why the corrected version removes the confusion.
3. 3

   Spot-the-error and write-it-correctly screener

   Why it works: Recognising and rewriting common notation slips builds fluency and shows which conventions are not yet automatic.

   1. Work through short items that present units, money, and fraction-vocabulary slips (e.g. '35' for a length, '£3.5', '£3.50p', 'the top number is the denominator') and either flag the error or rewrite the statement correctly.
   2. For each flagged item, write the corrected version.