01
Digits as separate numbers
23 + 40 becomes 27 or 63 depending on which digits get added.
Topic hub
Place value
The value of a digit depends on where it sits — ones, tens, tenths. Children struggle when they still see 34 as ‘three and four’ rather than 3 tens and 4 ones, and the same crack reappears later in decimals.
Why this concept matters
Regrouping, decimals, and any multi-digit operation sit on this picture. It is the most expensive Class 2 idea to leave half-built.
Misconceptions, in the order we see them
02
Borrowing as crossing out
The ten that was broken cannot be pointed to.
03
Zeros are empty, not a place
100 − 7 and 0.07 both become mysteries.
Which classes cover this
Related: Fractions · Decimals · Percentages · Ratio and proportion · Integers
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