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Plant Spacing worksheet

Grades 7–8 · CCSS 8.G.B.7

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

1.
Problem 1.
- Bed length: 10 ft
- Bed width: 4 ft
- Plant spacing (center to center): 14 in
- Layout: Triangular (offset rows)
Find: Plants that fit
Answer
2.
Problem 2.
- Bed length: 8 ft
- Bed width: 4 ft
- Plant spacing (center to center): 10 in
- Layout: Square grid (rows and columns)
Find: Plants that fit
Answer
3.
Problem 3.
- Bed length: 10 ft
- Bed width: 4 ft
- Plant spacing (center to center): 14 in
- Layout: Square grid (rows and columns)
Find: Plants that fit
Answer
4.
Problem 4.
- Bed length: 8 ft
- Bed width: 3 ft
- Plant spacing (center to center): 13 in
- Layout: Square grid (rows and columns)
Find: Plants that fit
Answer
5.
Problem 5.
- Bed length: 10 ft
- Bed width: 6 ft
- Plant spacing (center to center): 10 in
- Layout: Triangular (offset rows)
Find: Plants that fit
Answer
6.
Problem 6.
- Bed length: 13 ft
- Bed width: 4 ft
- Plant spacing (center to center): 12 in
- Layout: Square grid (rows and columns)
Find: Plants that fit
Answer
7.
Problem 7.
- Bed length: 10 ft
- Bed width: 4 ft
- Plant spacing (center to center): 11 in
- Layout: Square grid (rows and columns)
Find: Plants that fit
Answer
8.
Problem 8.
- Bed length: 10 ft
- Bed width: 3 ft
- Plant spacing (center to center): 11 in
- Layout: Square grid (rows and columns)
Find: Plants that fit
Answer
9.
Problem 9.
- Bed length: 12 ft
- Bed width: 3 ft
- Plant spacing (center to center): 15 in
- Layout: Square grid (rows and columns)
Find: Plants that fit
Answer
10.
Problem 10.
- Bed length: 12 ft
- Bed width: 3 ft
- Plant spacing (center to center): 13 in
- Layout: Square grid (rows and columns)
Find: Plants that fit
Answer

Answer key: Plant Spacing worksheet

1. Plants that fit: 24
1. Convert the bed to inches (1 ft = 12 in) so it matches the spacing
  $10 \times 12 by 4 \times 12$ $= 120 by 48 in$
2. Count the plants along the length: divide by the spacing and round down. The end plants sit half a spacing from the edge
  $\frac{120}{14}$ $= 8.5714$ $= rounded down: 8$
3. Staggered rows sit closer together. The gap is the height of a triangle with equal sides, about 0.866 × the spacing
  $14 \times \frac{\sqrt{3}}{2}$ $= 12.1244 in$
4. Count the rows that fit across the width, keeping half a spacing clear at each edge
  $\frac{48 - 14}{12.1244} + 1$ $= rounded: 3$
5. Every second row shifts over half a spacing, so it may hold one fewer plant
  $\frac{120}{14} - 0.5$ $= rounded down: 8$
6. Add up the plants: 2 full rows of 8, plus 1 shifted rows of 8
  $2 \times 8 + 1 \times 8$ $= 24$
2. Plants that fit: 36
1. Convert the bed to inches (1 ft = 12 in) so it matches the spacing
  $8 \times 12 by 4 \times 12$ $= 96 by 48 in$
2. Count the plants along the length: divide by the spacing and round down. The end plants sit half a spacing from the edge
  $\frac{96}{10}$ $= 9.6$ $= rounded down: 9$
3. Count the rows across the width the same way: divide by the spacing and round down
  $\frac{48}{10}$ $= 4.8$ $= rounded down: 4$
4. Multiply the plants in each row by the number of rows
  $9 \times 4$ $= 36$
3. Plants that fit: 24
1. Convert the bed to inches (1 ft = 12 in) so it matches the spacing
  $10 \times 12 by 4 \times 12$ $= 120 by 48 in$
2. Count the plants along the length: divide by the spacing and round down. The end plants sit half a spacing from the edge
  $\frac{120}{14}$ $= 8.5714$ $= rounded down: 8$
3. Count the rows across the width the same way: divide by the spacing and round down
  $\frac{48}{14}$ $= 3.4286$ $= rounded down: 3$
4. Multiply the plants in each row by the number of rows
  $8 \times 3$ $= 24$
4. Plants that fit: 14
1. Convert the bed to inches (1 ft = 12 in) so it matches the spacing
  $8 \times 12 by 3 \times 12$ $= 96 by 36 in$
2. Count the plants along the length: divide by the spacing and round down. The end plants sit half a spacing from the edge
  $\frac{96}{13}$ $= 7.3846$ $= rounded down: 7$
3. Count the rows across the width the same way: divide by the spacing and round down
  $\frac{36}{13}$ $= 2.7692$ $= rounded down: 2$
4. Multiply the plants in each row by the number of rows
  $7 \times 2$ $= 14$
5. Plants that fit: 92
1. Convert the bed to inches (1 ft = 12 in) so it matches the spacing
  $10 \times 12 by 6 \times 12$ $= 120 by 72 in$
2. Count the plants along the length: divide by the spacing and round down. The end plants sit half a spacing from the edge
  $\frac{120}{10}$ $= 12$ $= rounded down: 12$
3. Staggered rows sit closer together. The gap is the height of a triangle with equal sides, about 0.866 × the spacing
  $10 \times \frac{\sqrt{3}}{2}$ $= 8.6603 in$
4. Count the rows that fit across the width, keeping half a spacing clear at each edge
  $\frac{72 - 10}{8.6603} + 1$ $= rounded: 8$
5. Every second row shifts over half a spacing, so it may hold one fewer plant
  $\frac{120}{10} - 0.5$ $= rounded down: 11$
6. Add up the plants: 4 full rows of 12, plus 4 shifted rows of 11
  $4 \times 12 + 4 \times 11$ $= 92$
6. Plants that fit: 52
1. Convert the bed to inches (1 ft = 12 in) so it matches the spacing
  $13 \times 12 by 4 \times 12$ $= 156 by 48 in$
2. Count the plants along the length: divide by the spacing and round down. The end plants sit half a spacing from the edge
  $\frac{156}{12}$ $= 13$ $= rounded down: 13$
3. Count the rows across the width the same way: divide by the spacing and round down
  $\frac{48}{12}$ $= 4$ $= rounded down: 4$
4. Multiply the plants in each row by the number of rows
  $13 \times 4$ $= 52$
7. Plants that fit: 40
1. Convert the bed to inches (1 ft = 12 in) so it matches the spacing
  $10 \times 12 by 4 \times 12$ $= 120 by 48 in$
2. Count the plants along the length: divide by the spacing and round down. The end plants sit half a spacing from the edge
  $\frac{120}{11}$ $= 10.9091$ $= rounded down: 10$
3. Count the rows across the width the same way: divide by the spacing and round down
  $\frac{48}{11}$ $= 4.3636$ $= rounded down: 4$
4. Multiply the plants in each row by the number of rows
  $10 \times 4$ $= 40$
8. Plants that fit: 30
1. Convert the bed to inches (1 ft = 12 in) so it matches the spacing
  $10 \times 12 by 3 \times 12$ $= 120 by 36 in$
2. Count the plants along the length: divide by the spacing and round down. The end plants sit half a spacing from the edge
  $\frac{120}{11}$ $= 10.9091$ $= rounded down: 10$
3. Count the rows across the width the same way: divide by the spacing and round down
  $\frac{36}{11}$ $= 3.2727$ $= rounded down: 3$
4. Multiply the plants in each row by the number of rows
  $10 \times 3$ $= 30$
9. Plants that fit: 18
1. Convert the bed to inches (1 ft = 12 in) so it matches the spacing
  $12 \times 12 by 3 \times 12$ $= 144 by 36 in$
2. Count the plants along the length: divide by the spacing and round down. The end plants sit half a spacing from the edge
  $\frac{144}{15}$ $= 9.6$ $= rounded down: 9$
3. Count the rows across the width the same way: divide by the spacing and round down
  $\frac{36}{15}$ $= 2.4$ $= rounded down: 2$
4. Multiply the plants in each row by the number of rows
  $9 \times 2$ $= 18$
10. Plants that fit: 22
1. Convert the bed to inches (1 ft = 12 in) so it matches the spacing
  $12 \times 12 by 3 \times 12$ $= 144 by 36 in$
2. Count the plants along the length: divide by the spacing and round down. The end plants sit half a spacing from the edge
  $\frac{144}{13}$ $= 11.0769$ $= rounded down: 11$
3. Count the rows across the width the same way: divide by the spacing and round down
  $\frac{36}{13}$ $= 2.7692$ $= rounded down: 2$
4. Multiply the plants in each row by the number of rows
  $11 \times 2$ $= 22$