Reasoning · Grade 2-1 Finding Numbers That Fit Conditions
Problem
Across grid (1), the triples with middle digit 8 or 9 are 391, 186.
The tens place is the middle of three left-to-right cells, so I just look at the middle digit.
2.NBT.A.1Make A Systematic ListIn a left-to-right triple the middle cell is the tens digit, so the condition can be tested by looking at that one cell.
Three cells read in order are hundreds, tens and ones, so a cell's position in the triple is what decides which place it holds.
The horizontal triples and the vertical triples are separate families with nothing in common, so each can be swept on its own and the finds added.
Down the columns only 593 survives — 378 has a 7, and one triple starts with 0.
Reading down a column, the middle cell is still the tens digit; 7 itself does not count because it must be greater than 7.
2.NBT.A.1Eliminate PossibilitiesSo grid (1) gives 186, 391, 593.
Gathering every kept triple from both directions gives the full answer.
2.NBT.A.1Make A Systematic ListAcross grid (2), the triples adding to 5 are 212, 230.
Adding three small digits is a quick mental sum, so I test each triple in turn.
2.OA.B.2Make A Systematic ListDown the columns the third one hits twice: 113, 131.
The same digit-sum test runs down the columns; two neighboring triples in column 3 both total 5.
2.OA.B.2Make A Systematic ListSo grid (2) gives 113, 131, 212, 230.
Collecting every triple that totals 5 from both directions completes the list.
2.OA.B.2Make A Systematic ListWith only 16 triples per grid, listing every row and column triple in order lets you catch them all without missing any!