Reasoning · Grade 5-2 Foundations of Magic Squares
Problem
Comparing neighbours cancels the shared number.
The equals sign means the two sides weigh the same, so taking the identical shared number off each side keeps them balanced — that is the whole idea, and the three-circle Example lets you see it before the five-circle chain arrives.
1.OA.D.7Solve An Easier Related ProblemThe second and third give 4.
This pair is the right place to start because covering B leaves only one letter, C, in the equation — no other unknown is in the way.
4.OA.A.3Draw A DiagramComparing two neighbouring circles lets the numbers they share be struck out, leaving one letter behind.
The two circle totals are equal, so removing the same shared numbers from both sides keeps the statement true.
Each circle total is its numbers added together, so what is left after the shared ones go is exactly the numbers that differ.
The third and fourth give 1.
Each neighbouring pair is its own little problem, and covering the shared number always leaves exactly one letter, so the pairs can be solved in any order.
4.OA.A.3Identify SubproblemsThat makes the common total 11.
Once any one circle has all its numbers filled in, that circle simply tells you the common total, and the rest of the puzzle becomes ordinary addition.
2.NBT.B.5Draw A DiagramThe end circles take 8 and 9.
The two end circles hold just two numbers each, so once the common total is known each one is a single subtraction.
4.OA.A.3Identify SubproblemsAll five circles total 11.
Adding up all five circles at the end is quick and catches any slip, because a single wrong entry would break at least one of the five totals.
2.NBT.B.5Draw A DiagramWhen two circles share a number, cover it up — whatever is left on each side still has to balance!