Parentheses Puzzle
A puzzle: insert parentheses into 1 + 2 × 3 + 4 × 5 + 6 × 7 + 8 to get as many different totals as possible, with worked examples.
Use this cartoon
Free for classrooms, worksheets, slides and other non-commercial use under CC BY-NC 4.0, with credit to Ben Orlin.
Cartoon by Ben Orlin, Math with Bad Drawings. https://cartoons.mathwithbaddrawings.com/2017-01-02-parentheses-puzzle/ (CC BY-NC 4.0)Transcript
"How many totals can you achieve, just by adding parentheses?"
1 + 2 × 3 + 4 × 5 + 6 × 7 + 8
[for example...] (1+2)×3+4×5+6×7+8; 1+2×(3+4)×5+6×7+8; 1+2×3+4×(5+6)×7+8; (1+2×3+4×5+6)×7+8; (1+2×3+4×5+6)×(7+8); 1+2×(3+4)×(5+6)×7+8; (1+2×3+4)×5+6×7+8; 1+2×3+4×(5+6×7+8); (1+2×3+4)×(5+6×7+8) etc.!