Reasoning · Grade 2-1 Ancient Numbers
Problem
The labels 1, 2, 4, 8 each double the one before, so four cells make every number 0 to 15 in exactly one way.
Doubling (skip-counting that grows 1, 2, 4, 8) is an easy pattern to spot, and it guarantees one clean way to build each number.
2.NBT.A.2Look For A PatternFor 7 the 8 is too big, so take 4 leaving 3, then 2 and 1: 1, 2, 4.
Grabbing the biggest piece that still fits, then the next, is the same greedy idea kids use to make an amount with coins.
1.NBT.C.4Make A Systematic ListTaking the biggest cell that still fits, then the next, builds 7 out of the doubling pieces 1, 2, 4, 8 without ever needing a piece twice.
The shaded cells are pieces that must add back to the target exactly, so building a number is choosing a set of pieces whose total is the number.
Each piece is worth double the one before it, so it is worth more than every smaller piece put together and can never be replaced by them.
Bundling a fixed number of smaller units into one bigger unit is the same idea that makes ten ones a ten, only here the bundle is two.
For 10 take 8, leaving 2, which the 2 fills exactly: 2 and 8.
10 is just one ten, and 8 + 2 = 10 is a friendly make-ten fact second graders know by heart.
1.NBT.C.4Make A Systematic ListFor 13 take 8, leaving 5, then 4 and 1: 1, 4, 8.
Checking 8 + 4 + 1 = 13 by adding the chosen pieces back makes sure no cell was missed.
1.NBT.C.4Make A Systematic List15 is every label added together, so shade all four cells.
When the target equals the full total, every cell must be shaded - a quick check at the top of the range.
1.NBT.C.4Make A Systematic ListPick the biggest label that still fits, then the next - and 1, 2, 4, 8 let you build every number up to 15!