Reasoning · Grade 2-1 Cryptarithms and Magic Squares
Problem
The nine numbers total 45, and sharing that across three rows confirms each line is 15.
Sharing the total 45 equally among 3 rows gives 15 each -- the same way you split a total into equal groups.
2.NBT.B.6Guess And CheckEvery row must total 15, because the nine numbers add to 45 and the three rows share that total equally.
The three rows use every number once and none twice, so the three row totals put together are exactly the total of all nine numbers.
Three equal rows making 45 is the same statement as three times the row total being 45, so dividing recovers the row total.
5 appears in the most trios summing to 15, and the center sits on four lines — so 5 belongs there.
Listing every 'three numbers that make 15' shows 5 is the busiest number, so it sits where the most lines cross.
2.OA.B.2Make A Systematic ListAcross the center, facing pairs must add to 10: 1&9, 2&8, 3&7, 4&6.
Numbers on opposite sides of 5 must balance to 10, so they pair up as small-with-large.
2.OA.C.3Look For A PatternEvens in the corners and odds on the edges gives 2 9 4 / 7 5 3 / 6 1 8, and all eight lines make 15.
After placing the pairs, you just add up each row, column, and diagonal to make sure they all hit 15.
2.NBT.B.6Guess And CheckThis only needs Grade 2 adding and a little even/odd sense -- sharing 45 into three fifteens does the heavy lifting!