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Student printable

Picture Equation Balance Puzzles

Solve each balance puzzle. Remember: matching shapes have matching values, and a balanced scale means both sides are equal. This student sheet does not include answers or worked steps.

Need solutions? Use the separate adult answer key.

Canonical examples

Example 1: One unknown — remove known units

Easy
2 circles + 3 unit cubes = 13 unit cubes
What is the value of 1 circle?
Expression: circle
Answer: ____________________

Example 2: Known substitution — two shapes

Medium
3 triangles + 2 squares = 18 unit cubes
1 square = 3 unit cubes
What is the value of 1 triangle?
Expression: triangle
Answer: ____________________

Example 3: Two equations, two unknowns

Medium
2 stars + 1 moon = 13 unit cubes
1 star + 2 moons = 14 unit cubes
What is star + moon?
Expression: star + moon
Answer: ____________________

Example 4: Equivalent groups / ratio challenge

Medium
2 diamonds = 3 circles
1 diamond + 1 circle = 20 unit cubes
What is diamond - circle?
Expression: diamond - circle
Answer: ____________________

Example 5: Three-picture challenge

Challenge
2 hexagons + 1 triangle = 16 unit cubes
1 triangle + 2 circles = 14 unit cubes
1 hexagon + 1 circle = 11 unit cubes
What is hexagon + triangle + circle?
Expression: hexagon + triangle + circle
Answer: ____________________

Generated practice set

Easy practice puzzle

Seed: student-sheet-easy-1
Easy
4 circles + 5 unit cubes = 33 unit cubes
What is the value of 1 circle?
Expression: circle
Answer: ____________________

Easy practice puzzle

Seed: student-sheet-easy-2
Easy
4 circles + 3 unit cubes = 31 unit cubes
What is the value of 1 circle?
Expression: circle
Answer: ____________________

Medium practice puzzle

Seed: student-sheet-medium-1
Medium
2 stars + 3 moons = 31 unit cubes
1 moon = 7 unit cubes
What is the value of 1 star?
Expression: star
Answer: ____________________

Medium practice puzzle

Seed: student-sheet-medium-2
Medium
4 triangles + 2 moons = 42 unit cubes
1 moon = 3 unit cubes
What is the value of 1 triangle?
Expression: triangle
Answer: ____________________

Challenge practice puzzle

Seed: student-sheet-challenge-1
Challenge
2 squares + 1 diamond = 25 unit cubes
1 diamond + 2 stars = 25 unit cubes
1 square + 1 star = 16 unit cubes
What is square + diamond + star?
Expression: square + diamond + star
Answer: ____________________

Challenge practice puzzle

Seed: student-sheet-challenge-2
Challenge
2 moons + 1 diamond = 25 unit cubes
1 diamond + 2 hexagons = 13 unit cubes
1 moon + 1 hexagon = 10 unit cubes
What is moon + diamond + hexagon?
Expression: moon + diamond + hexagon
Answer: ____________________