Shop Class Math

Foundations workbook

Even when school math doesn’t click.

Nine short lessons · 45 exercises · worked answer key

Write your answers on paper, or use this alongside the interactive course. Educational practice only; not construction specifications or certification.

1. Fractions

Same-size pieces, simple addition

The bottom number tells you the size of each piece. The top number counts the pieces. To add fractions with the same denominator, add only the top numbers.

Two 1/8-inch pieces make 1/4 inch.

  1. Join a 1/16-inch spacer and a 1/16-inch spacer. What is their total thickness in inches?

    Answer: ____________________

  2. Join a 2/16-inch spacer and a 2/16-inch spacer. What is their total thickness in inches?

    Answer: ____________________

  3. Join a 3/16-inch spacer and a 3/16-inch spacer. What is their total thickness in inches?

    Answer: ____________________

  4. Join a 4/16-inch spacer and a 4/16-inch spacer. What is their total thickness in inches?

    Answer: ____________________

  5. Join a 5/16-inch spacer and a 5/16-inch spacer. What is their total thickness in inches?

    Answer: ____________________

2. Tape measures

Feet and inches speak the same language

Convert feet to inches by multiplying by 12. Then add the leftover inches. On a tape, count the equal spaces between whole-inch marks—not the marks themselves.

A half inch is 8/16. A quarter is 4/16.

  1. A measurement is 3 feet 1 inches. How many inches is that?

    Answer: ____________________

  2. A measurement is 4 feet 2 inches. How many inches is that?

    Answer: ____________________

  3. A measurement is 5 feet 3 inches. How many inches is that?

    Answer: ____________________

  4. A measurement is 6 feet 4 inches. How many inches is that?

    Answer: ____________________

  5. A measurement is 7 feet 5 inches. How many inches is that?

    Answer: ____________________

3. Area & materials

Area first. Extra material second.

For a rectangle, multiply length by width using the same units. Apply the extra-material percentage to that area, not separately to both dimensions.

Square feet measure area; feet measure length.

  1. A rectangular floor is 6 ft by 9 ft. Allow 10% extra material. How many square feet should you budget for?

    Answer: ____________________

  2. A rectangular floor is 7 ft by 10 ft. Allow 10% extra material. How many square feet should you budget for?

    Answer: ____________________

  3. A rectangular floor is 8 ft by 11 ft. Allow 10% extra material. How many square feet should you budget for?

    Answer: ____________________

  4. A rectangular floor is 9 ft by 12 ft. Allow 10% extra material. How many square feet should you budget for?

    Answer: ____________________

  5. A rectangular floor is 10 ft by 13 ft. Allow 10% extra material. How many square feet should you budget for?

    Answer: ____________________

4. Read a tape

Read the spaces, not the ticks

This tape divides one inch into sixteen equal spaces. Start at zero. The longest middle mark is one half; quarter marks divide the inch into four equal lengths.

Count from the zero mark. This practice drawing is not a physical ruler.

  1. Read the marked position on this one-inch tape. Give your answer in inches.01 in

    Answer: ____________________

  2. Read the marked position on this one-inch tape. Give your answer in inches.01 in

    Answer: ____________________

  3. Read the marked position on this one-inch tape. Give your answer in inches.01 in

    Answer: ____________________

  4. Read the marked position on this one-inch tape. Give your answer in inches.01 in

    Answer: ____________________

  5. Read the marked position on this one-inch tape. Give your answer in inches.01 in

    Answer: ____________________

5. Decimal inches

Fractions and decimals are two labels

Divide the numerator by the denominator to turn a fraction into a decimal. Keep the unit: inches remain inches.

0.5 inch is not five inches. The decimal point matters.

  1. Convert 1/8 inch to decimal inches.

    Answer: ____________________

  2. Convert 2/8 inch to decimal inches.

    Answer: ____________________

  3. Convert 3/8 inch to decimal inches.

    Answer: ____________________

  4. Convert 4/8 inch to decimal inches.

    Answer: ____________________

  5. Convert 5/8 inch to decimal inches.

    Answer: ____________________

6. Perimeter

Go around the outside

Perimeter is the total distance around a shape. A rectangle has two equal lengths and two equal widths.

Trim around an edge uses length; flooring uses area.

  1. A rectangular frame is 4 ft wide and 8 ft long. What is its perimeter in feet? Ignore joints and cutting loss.

    Answer: ____________________

  2. A rectangular frame is 5 ft wide and 9 ft long. What is its perimeter in feet? Ignore joints and cutting loss.

    Answer: ____________________

  3. A rectangular frame is 6 ft wide and 10 ft long. What is its perimeter in feet? Ignore joints and cutting loss.

    Answer: ____________________

  4. A rectangular frame is 7 ft wide and 11 ft long. What is its perimeter in feet? Ignore joints and cutting loss.

    Answer: ____________________

  5. A rectangular frame is 8 ft wide and 12 ft long. What is its perimeter in feet? Ignore joints and cutting loss.

    Answer: ____________________

7. Material packs

Buy enough whole packages

Divide the needed quantity by coverage per package. If a fraction remains, buy the next whole package. Include the material allowance before this step.

Always read actual package coverage. Do not add the same allowance twice.

  1. You need 13 sq ft of flooring, including your allowance. Each box covers 20 sq ft. How many whole boxes must you buy?

    Answer: ____________________

  2. You need 26 sq ft of flooring, including your allowance. Each box covers 20 sq ft. How many whole boxes must you buy?

    Answer: ____________________

  3. You need 39 sq ft of flooring, including your allowance. Each box covers 20 sq ft. How many whole boxes must you buy?

    Answer: ____________________

  4. You need 52 sq ft of flooring, including your allowance. Each box covers 20 sq ft. How many whole boxes must you buy?

    Answer: ____________________

  5. You need 65 sq ft of flooring, including your allowance. Each box covers 20 sq ft. How many whole boxes must you buy?

    Answer: ____________________

8. Volume

From surface to space

Rectangular volume is length times width times depth. All three measurements must use the same units before multiplication.

One cubic yard is 27 cubic feet. These are geometry exercises, not construction specifications.

  1. A rectangular container is 3 ft long, 3 ft wide and 2 ft deep. What is its volume in cubic feet?

    Answer: ____________________

  2. A rectangular container is 4 ft long, 3 ft wide and 2 ft deep. What is its volume in cubic feet?

    Answer: ____________________

  3. A rectangular container is 5 ft long, 3 ft wide and 2 ft deep. What is its volume in cubic feet?

    Answer: ____________________

  4. A rectangular container is 6 ft long, 3 ft wide and 2 ft deep. What is its volume in cubic feet?

    Answer: ____________________

  5. A rectangular container is 7 ft long, 3 ft wide and 2 ft deep. What is its volume in cubic feet?

    Answer: ____________________

9. Scale drawings

Small drawing, real dimensions

A scale describes the relationship between a drawing and the real object. Divide the drawing measurement by the drawing amount that represents one real unit.

Check the stated scale and print size. Resizing an image changes its measured scale.

  1. A drawing uses 1/4 inch to represent 1 foot. A line measures 2 inches on the drawing. How many real feet does it represent?

    Answer: ____________________

  2. A drawing uses 1/4 inch to represent 1 foot. A line measures 3 inches on the drawing. How many real feet does it represent?

    Answer: ____________________

  3. A drawing uses 1/4 inch to represent 1 foot. A line measures 4 inches on the drawing. How many real feet does it represent?

    Answer: ____________________

  4. A drawing uses 1/4 inch to represent 1 foot. A line measures 5 inches on the drawing. How many real feet does it represent?

    Answer: ____________________

  5. A drawing uses 1/4 inch to represent 1 foot. A line measures 6 inches on the drawing. How many real feet does it represent?

    Answer: ____________________

Worked answer key

Fractions

  1. Both pieces use sixteenths, so add the numerators: 1 + 1 = 2. Keep the denominator: 2/16 inch (0.125 inch).
  2. Both pieces use sixteenths, so add the numerators: 2 + 2 = 4. Keep the denominator: 4/16 inch (0.25 inch).
  3. Both pieces use sixteenths, so add the numerators: 3 + 3 = 6. Keep the denominator: 6/16 inch (0.375 inch).
  4. Both pieces use sixteenths, so add the numerators: 4 + 4 = 8. Keep the denominator: 8/16 inch (0.5 inch).
  5. Both pieces use sixteenths, so add the numerators: 5 + 5 = 10. Keep the denominator: 10/16 inch (0.625 inch).

Tape measures

  1. Each foot contains 12 inches. Multiply 3 × 12 = 36, then add 1: 37 inches.
  2. Each foot contains 12 inches. Multiply 4 × 12 = 48, then add 2: 50 inches.
  3. Each foot contains 12 inches. Multiply 5 × 12 = 60, then add 3: 63 inches.
  4. Each foot contains 12 inches. Multiply 6 × 12 = 72, then add 4: 76 inches.
  5. Each foot contains 12 inches. Multiply 7 × 12 = 84, then add 5: 89 inches.

Area & materials

  1. Area = 6 × 9 = 54 sq ft. Ten percent extra = 5.4 sq ft. Total = 59.4 sq ft. This exercise assumes a 10% allowance; actual projects vary.
  2. Area = 7 × 10 = 70 sq ft. Ten percent extra = 7 sq ft. Total = 77 sq ft. This exercise assumes a 10% allowance; actual projects vary.
  3. Area = 8 × 11 = 88 sq ft. Ten percent extra = 8.8 sq ft. Total = 96.8 sq ft. This exercise assumes a 10% allowance; actual projects vary.
  4. Area = 9 × 12 = 108 sq ft. Ten percent extra = 10.8 sq ft. Total = 118.8 sq ft. This exercise assumes a 10% allowance; actual projects vary.
  5. Area = 10 × 13 = 130 sq ft. Ten percent extra = 13 sq ft. Total = 143 sq ft. This exercise assumes a 10% allowance; actual projects vary.

Read a tape

  1. Each small interval is 1/16 inch. Count 1 intervals from zero: 1/16 inch = 0.0625 inch.
  2. Each small interval is 1/16 inch. Count 2 intervals from zero: 2/16 inch = 0.125 inch.
  3. Each small interval is 1/16 inch. Count 3 intervals from zero: 3/16 inch = 0.1875 inch.
  4. Each small interval is 1/16 inch. Count 4 intervals from zero: 4/16 inch = 0.25 inch.
  5. Each small interval is 1/16 inch. Count 5 intervals from zero: 5/16 inch = 0.3125 inch.

Decimal inches

  1. A fraction means division. 1 ÷ 8 = 0.125 inch. The measurement stays the same; only the notation changes.
  2. A fraction means division. 2 ÷ 8 = 0.25 inch. The measurement stays the same; only the notation changes.
  3. A fraction means division. 3 ÷ 8 = 0.375 inch. The measurement stays the same; only the notation changes.
  4. A fraction means division. 4 ÷ 8 = 0.5 inch. The measurement stays the same; only the notation changes.
  5. A fraction means division. 5 ÷ 8 = 0.625 inch. The measurement stays the same; only the notation changes.

Perimeter

  1. Add all four sides: 4 + 8 + 4 + 8 = 24 ft. Perimeter is length around the edge, not area.
  2. Add all four sides: 5 + 9 + 5 + 9 = 28 ft. Perimeter is length around the edge, not area.
  3. Add all four sides: 6 + 10 + 6 + 10 = 32 ft. Perimeter is length around the edge, not area.
  4. Add all four sides: 7 + 11 + 7 + 11 = 36 ft. Perimeter is length around the edge, not area.
  5. Add all four sides: 8 + 12 + 8 + 12 = 40 ft. Perimeter is length around the edge, not area.

Material packs

  1. 13 ÷ 20 = 0.65 boxes. You cannot buy a partial box, so round UP to 1. Do not add the allowance again.
  2. 26 ÷ 20 = 1.3 boxes. You cannot buy a partial box, so round UP to 2. Do not add the allowance again.
  3. 39 ÷ 20 = 1.95 boxes. You cannot buy a partial box, so round UP to 2. Do not add the allowance again.
  4. 52 ÷ 20 = 2.6 boxes. You cannot buy a partial box, so round UP to 3. Do not add the allowance again.
  5. 65 ÷ 20 = 3.25 boxes. You cannot buy a partial box, so round UP to 4. Do not add the allowance again.

Volume

  1. Use matching units. Length × width × depth = 3 × 3 × 2 = 18 cubic feet. Area covers a surface; volume fills a space.
  2. Use matching units. Length × width × depth = 4 × 3 × 2 = 24 cubic feet. Area covers a surface; volume fills a space.
  3. Use matching units. Length × width × depth = 5 × 3 × 2 = 30 cubic feet. Area covers a surface; volume fills a space.
  4. Use matching units. Length × width × depth = 6 × 3 × 2 = 36 cubic feet. Area covers a surface; volume fills a space.
  5. Use matching units. Length × width × depth = 7 × 3 × 2 = 42 cubic feet. Area covers a surface; volume fills a space.

Scale drawings

  1. Four quarter-inch sections fit in one inch. Each section represents one foot: 2 × 4 = 8 feet. This assumes the drawing has not been resized.
  2. Four quarter-inch sections fit in one inch. Each section represents one foot: 3 × 4 = 12 feet. This assumes the drawing has not been resized.
  3. Four quarter-inch sections fit in one inch. Each section represents one foot: 4 × 4 = 16 feet. This assumes the drawing has not been resized.
  4. Four quarter-inch sections fit in one inch. Each section represents one foot: 5 × 4 = 20 feet. This assumes the drawing has not been resized.
  5. Four quarter-inch sections fit in one inch. Each section represents one foot: 6 × 4 = 24 feet. This assumes the drawing has not been resized.