Magic Triangle: Balance All Three Sides to One Target Sum
Drag the numbers 1 through 6 onto the corners and edges, then keep swapping until every side adds to the same total. Each attempt trains you to hold three running sums in mind and reason toward a shared goal.
Guessing Corners Stalls Out: Their Total Must Be a Multiple of Three
Shuffling numbers at random rarely lands a balanced triangle, because the three corner cells decide everything before you touch a single edge. Add all of 1-6 and you get 21; since each corner counts toward two sides, three equal sides force the corner numbers to total a multiple of three. Put 1, 2, and 3 in the corners (total 6) and each side lands on a target sum of 9; slide the 3 out and drop the 5 in so the corners read 1, 3, 5 (total 9) and every side jumps to a target sum of 10. Try corners of 1, 2, and 4 (total 7) and no swap of the edge numbers will ever even them out. Checking that corner total first turns blind swapping into a quick filter you can run in your head.
Spotting a Multiple of Three Grows Number Sense in Grades 3-5
The puzzle picks up right after students learn to add three single-digit numbers fluently (1.OA.A.2) and pushes that skill into a reason-first habit: before moving pieces, decide whether a corner trio can work by testing it against the multiple-of-three rule. That is early divisibility and structure thinking—the same judgment behind checking whether an answer is reasonable in two-step problems (3.OA.D.8) and the multi-step word problems of fourth grade (4.OA.A.3). Re-adding each side after a swap keeps addition within 20 sharp.
Three Skills Practiced in Magic Triangle
- adding three values to a target sum
- recognizing that one node can belong to two constraints
- using elimination and organized trials
Teacher and Parent Note
Ask the student to mark why corner values have more influence than middle positions. Record all three side sums after each swap and use the table to decide whether the move reduced the imbalance.