Equal Cuts Reference Sheet
Part 1 • Halves Family Grades 3–5 • Math Reference
Equal Cuts Reference Sheet
THE 1/2 BENCHMARK
Different Numbers • Same Amount
Fraction Strips Alignment Wall
Follow the red dashed line down the center!
1/2 Line
1 Whole
1/2
1/2
1/4
1/4
1/4
1/4
1/6
1/6
1/6
1/6
1/6
1/6
1/8
1/8
1/8
1/8
1/8
1/8
1/8
1/8
1/10
1/10
1/10
1/10
1/10
1/10
1/10
1/10
1/10
1/10
Proof 1 • Factor ×2
1
2
=
2
4
Visual Strip Match: 2 fourths = 1 half
1/2
1/4
1/4
Multiply Top & Bottom
1 × 2
2 × 2
= 2/4
Proof 2 • Factor ×3
1
2
=
3
6
Visual Strip Match: 3 sixths = 1 half
1/2
1/6
1/6
1/6
Multiply Top & Bottom
1 × 3
2 × 3
= 3/6
Proof 3 • Factor ×4
1
2
=
4
8
Visual Strip Match: 4 eighths = 1 half
1/2
1/8
1/8
1/8
1/8
Multiply Top & Bottom
1 × 4
2 × 4
= 4/8
Proof 4 • Factor ×5
1
2
=
5
10
Visual Strip Match: 5 tenths = 1 half
1/2
1/10
1/10
1/10
1/10
1/10
Multiply Top & Bottom
1 × 5
2 × 5
= 5/10
The Golden Rule: Multiply or divide the top and bottom by the same number to find an equivalent fraction.
1/2 = 2/4 = 3/6 = 4/8 = 5/10
Part 2 • Visual Strip Matches Grades 3–5 • Math Reference
Thirds, Fourths & Twelfths
EQUIVALENCE PROOFS
Matched Lengths • Resized Pieces
Thirds, Fourths & Twelfths Strip Guide
Compare how pieces subdivide evenly
1 Whole
1/3
1/3
1/3
1/4
1/4
1/4
1/4
1/12
1/12
1/12
1/12
1/12
1/12
1/12
1/12
1/12
1/12
1/12
1/12
Match 1 • Factor ×3
3
4
=
9
12
Visual Strip Match: 9 twelfths = 3 fourths
1/4
1/4
1/4
1/12
1/12
1/12
1/12
1/12
1/12
1/12
1/12
1/12
Multiply Top & Bottom
3 × 3
4 × 3
= 9/12
Match 2 • Factor ×4
1
3
=
4
12
Visual Strip Match: 4 twelfths = 1 third
1/3
1/12
1/12
1/12
1/12
Multiply Top & Bottom
1 × 4
3 × 4
= 4/12
Match 3 • Factor ×2
2
3
=
4
6
Visual Strip Match: 4 sixths = 2 thirds
1/3
1/3
1/6
1/6
1/6
1/6
Multiply Top & Bottom
2 × 2
3 × 2
= 4/6
Match 4 • Factor ×3
1
12
=
3
36
Visual Micro-Slice Match: 3 thirty-sixths = 1 twelfth
1/12
1/36
1/36
1/36
Multiply Top & Bottom
1 × 3
12 × 3
= 3/36
Key Takeaway: When you cut each piece into smaller equal slices, the shaded area stays identical!
3/4 = 9/12 • 1/3 = 4/12 • 2/3 = 4/6 • 1/12 = 3/36
