Reasoning · Grade 4-1 Large Numbers
Problem
The counts 2, 3, 5 in 235 are exactly its digits.
Matching the number of copies of a symbol against each digit is the same expanded-form thinking used to write 235 as 200 + 30 + 5.
4.NBT.A.2Look For A PatternIn 1340 and 63008 a 0 digit shows no symbol.
In our system 0 is a placeholder that keeps the other digits in the right columns; when every symbol already carries its own value, nothing has to hold a place.
4.NBT.A.2Look For A PatternThe Egyptian system needs no symbol for zero, because every symbol already carries its own value instead of relying on its position.
In our numerals a digit's worth comes from which bundle it counts, so an empty bundle still needs a mark to hold the other digits in their columns.
When each symbol names a fixed amount, the numeral is just those amounts added together, and leaving one out simply adds nothing.
2054 is 2 lotus, 5 heel, 4 stroke.
Writing the number in expanded form first means each term of the sum turns straight into one group of repeated symbols.
4.NBT.A.2Make A Systematic List30530 is 3 finger, 5 rope, 3 heel.
The two 0 digits do real work in our numeral 30530 but disappear completely in the Egyptian one, which is the clearest sign that the two systems store value in different ways.
4.NBT.A.2Make A Systematic ListAdding back gives 2054 and 30530.
Because the system is purely additive, reading a numeral backwards is the same work as writing it — a free check.
4.NBT.A.2Analyze The UnitsBreak the number into thousands, hundreds, tens and ones first — then any picture-number system is just counting out that many of each stamp!