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Shoe Size worksheet

Grades 6–7 · CCSS 6.EE.A.2.c

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- What do you know?: UK size
- UK size: 8
Find: EU size
Answer
2.
Problem 2.
- What do you know?: US men's size
- US men's size: 11
Find: EU size
Answer
3.
Problem 3.
- What do you know?: US women's size
- US women's size: 7
Find: EU size
Answer
4.
Problem 4.
- What do you know?: Foot length
- Foot length: 22 cm
Find: EU size
Answer
5.
Problem 5.
- What do you know?: US men's size
- US men's size: 7
Find: EU size
Answer
6.
Problem 6.
- What do you know?: EU size
- EU size: 38
Find: EU size
Answer
7.
Problem 7.
- What do you know?: EU size
- EU size: 40
Find: EU size
Answer
8.
Problem 8.
- What do you know?: Japanese size (cm)
- Japanese size: 22 cm
Find: EU size
Answer
9.
Problem 9.
- What do you know?: US men's size
- US men's size: 12
Find: EU size
Answer
10.
Problem 10.
- What do you know?: EU size
- EU size: 48
Find: EU size
Answer

Answer key: Shoe Size worksheet

1. EU size: 42
1. UK sizes run 1 below US men's, so foot length = (UK size + 23) ÷ 3
  $\frac{8 + 23}{3}$ $= 10.333333 in$
2. Each US size is a third of an inch, so US men's = 3 × foot length (in) − 22. Women's adds 1.5, and UK takes away 1
  $3 \times 10.333333 - 22$ $= 9$
3. EU = 1.5 × (foot length in cm + 1.6933 cm of extra room in the shoe)
  $1.5 \times (26.246667 + 1.6933)$ $= 41.91$
4. Round the EU size to the nearest half size
  $EU size$ $= 42$
2. EU size: 44.5
1. Foot length from a US men's size: (size + 22) ÷ 3 inches
  $\frac{11 + 22}{3}$ $= 11 in$
2. Each US size is a third of an inch, so US men's = 3 × foot length (in) − 22. Women's adds 1.5, and UK takes away 1
  $3 \times 11 - 22$ $= 11$
3. EU = 1.5 × (foot length in cm + 1.6933 cm of extra room in the shoe)
  $1.5 \times (27.94 + 1.6933)$ $= 44.45$
4. Round the EU size to the nearest half size
  $EU size$ $= 44.5$
3. EU size: 37.5
1. US women's sizes run 1.5 above men's, so take that off first. Then foot length = (men's size + 22) ÷ 3
  $\frac{7 - 1.5 + 22}{3}$ $= 9.166667 in$
2. Each US size is a third of an inch, so US men's = 3 × foot length (in) − 22. Women's adds 1.5, and UK takes away 1
  $3 \times 9.166667 - 22$ $= 5.5$
3. EU = 1.5 × (foot length in cm + 1.6933 cm of extra room in the shoe)
  $1.5 \times (23.283333 + 1.6933)$ $= 37.465$
4. Round the EU size to the nearest half size
  $EU size$ $= 37.5$
4. EU size: 35.5
1. Convert the foot length to inches (1 in = 2.54 cm)
  $\frac{22 cm}{2.54}$ $= 8.661417 in$
2. Each US size is a third of an inch, so US men's = 3 × foot length (in) − 22. Women's adds 1.5, and UK takes away 1
  $3 \times 8.661417 - 22$ $= 3.984252$
3. EU = 1.5 × (foot length in cm + 1.6933 cm of extra room in the shoe)
  $1.5 \times (22 + 1.6933)$ $= 35.54$
4. Round the EU size to the nearest half size
  $EU size$ $= 35.5$
5. EU size: 39.5
1. Foot length from a US men's size: (size + 22) ÷ 3 inches
  $\frac{7 + 22}{3}$ $= 9.666667 in$
2. Each US size is a third of an inch, so US men's = 3 × foot length (in) − 22. Women's adds 1.5, and UK takes away 1
  $3 \times 9.666667 - 22$ $= 7$
3. EU = 1.5 × (foot length in cm + 1.6933 cm of extra room in the shoe)
  $1.5 \times (24.553333 + 1.6933)$ $= 39.37$
4. Round the EU size to the nearest half size
  $EU size$ $= 39.5$
6. EU size: 38
1. EU sizes count steps of 2/3 cm along the shoe form, which is a bit longer than the foot. So foot length = EU ÷ 1.5 − 1.6933 cm
  $\frac{38}{1.5} - 1.6933$ $= 23.64 cm$
2. Convert to inches (1 in = 2.54 cm)
  $\frac{23.64}{2.54}$ $= 9.307087 in$
3. Each US size is a third of an inch, so US men's = 3 × foot length (in) − 22. Women's adds 1.5, and UK takes away 1
  $3 \times 9.307087 - 22$ $= 5.92126$
4. EU = 1.5 × (foot length in cm + 1.6933 cm of extra room in the shoe)
  $1.5 \times (23.64 + 1.6933)$ $= 38$
5. Round the EU size to the nearest half size
  $EU size$ $= 38$
7. EU size: 40
1. EU sizes count steps of 2/3 cm along the shoe form, which is a bit longer than the foot. So foot length = EU ÷ 1.5 − 1.6933 cm
  $\frac{40}{1.5} - 1.6933$ $= 24.973333 cm$
2. Convert to inches (1 in = 2.54 cm)
  $\frac{24.973333}{2.54}$ $= 9.832021 in$
3. Each US size is a third of an inch, so US men's = 3 × foot length (in) − 22. Women's adds 1.5, and UK takes away 1
  $3 \times 9.832021 - 22$ $= 7.496063$
4. EU = 1.5 × (foot length in cm + 1.6933 cm of extra room in the shoe)
  $1.5 \times (24.973333 + 1.6933)$ $= 40$
5. Round the EU size to the nearest half size
  $EU size$ $= 40$
8. EU size: 35.5
1. A Japanese size is the foot length in cm. Convert it to inches for the US and UK formulas
  $\frac{22}{2.54}$ $= 8.661417 in$
2. Each US size is a third of an inch, so US men's = 3 × foot length (in) − 22. Women's adds 1.5, and UK takes away 1
  $3 \times 8.661417 - 22$ $= 3.984252$
3. EU = 1.5 × (foot length in cm + 1.6933 cm of extra room in the shoe)
  $1.5 \times (22 + 1.6933)$ $= 35.54$
4. Round the EU size to the nearest half size
  $EU size$ $= 35.5$
9. EU size: 45.5
1. Foot length from a US men's size: (size + 22) ÷ 3 inches
  $\frac{12 + 22}{3}$ $= 11.333333 in$
2. Each US size is a third of an inch, so US men's = 3 × foot length (in) − 22. Women's adds 1.5, and UK takes away 1
  $3 \times 11.333333 - 22$ $= 12$
3. EU = 1.5 × (foot length in cm + 1.6933 cm of extra room in the shoe)
  $1.5 \times (28.786667 + 1.6933)$ $= 45.72$
4. Round the EU size to the nearest half size
  $EU size$ $= 45.5$
10. EU size: 48
1. EU sizes count steps of 2/3 cm along the shoe form, which is a bit longer than the foot. So foot length = EU ÷ 1.5 − 1.6933 cm
  $\frac{48}{1.5} - 1.6933$ $= 30.306667 cm$
2. Convert to inches (1 in = 2.54 cm)
  $\frac{30.306667}{2.54}$ $= 11.931759 in$
3. Each US size is a third of an inch, so US men's = 3 × foot length (in) − 22. Women's adds 1.5, and UK takes away 1
  $3 \times 11.931759 - 22$ $= 13.795276$
4. EU = 1.5 × (foot length in cm + 1.6933 cm of extra room in the shoe)
  $1.5 \times (30.306667 + 1.6933)$ $= 48$
5. Round the EU size to the nearest half size
  $EU size$ $= 48$