119r. Review Perimeter and Metric Length Units

Learning Intentions

• To understand that perimeter is the distance around a shape and is measured in one dimensional units, such as kilometres, metres, centimetres and millimetres
• convert between different metric units of length
• find the perimeter of a shape when its individual side lengths are known
• find an unknown side length of a shape when its perimeter is known

Pre-requisite Summary

• Know that length measures distance in one dimension
• Know common metric units of length: kilometres, metres, centimetres and millimetres
• Understand that $1\text{ km}=1000\text{ m}$, $1\text{ m}=100\text{ cm}$ and $1\text{ cm}=10\text{ mm}$
• Be able to add and subtract whole numbers and decimals accurately
• Know that the sides of a shape can be measured and combined
• Understand that a shape may have equal sides or different side lengths
• Be able to read labelled side lengths from a diagram
• Understand that solving for an unknown length may require subtraction

Worked Examples

Worked Example 1

State the meaning of perimeter and identify an appropriate unit:

a) the distance around a garden
b) the distance around a book
c) the distance around a country

Worked Example 2

Convert between metric units of length:

a) $3\text{ m}$ to centimetres
b) $450\text{ cm}$ to metres
c) $7\text{ cm}$ to millimetres

Worked Example 3

Convert between metric units of length:

a) $2.5\text{ km}$ to metres
b) $3600\text{ m}$ to kilometres
c) $84\text{ mm}$ to centimetres

Worked Example 4

Find the perimeter when all side lengths are known:

a) a rectangle with side lengths $8\text{ cm}$ and $5\text{ cm}$
b) a triangle with side lengths $6\text{ m},7\text{ m},9\text{ m}$

Worked Example 5

Find the perimeter when all side lengths are known:

a) a pentagon with side lengths $4\text{ cm},6\text{ cm},5\text{ cm},3\text{ cm},7\text{ cm}$
b) a square with side length $9\text{ mm}$

Worked Example 6

Find the unknown side length when the perimeter is known:

a) a rectangle has perimeter $30\text{ cm}$ and one pair of sides is $8\text{ cm}$ each. Find the other side length
b) a triangle has perimeter $21\text{ m}$ and two sides are $7\text{ m}$ and $5\text{ m}$. Find the third side

Problems

Problem 1

State the meaning of perimeter and identify an appropriate unit:

a) the distance around a playground
b) the distance around a phone
c) the distance around a suburb

Problem 2

Convert between metric units of length:

a) $5\text{ m}$ to centimetres
b) $320\text{ cm}$ to metres
c) $9\text{ cm}$ to millimetres

Problem 3

Convert between metric units of length:

a) $1.8\text{ km}$ to metres
b) $2400\text{ m}$ to kilometres
c) $95\text{ mm}$ to centimetres

Problem 4

Find the perimeter when all side lengths are known:

a) a rectangle with side lengths $10\text{ cm}$ and $4\text{ cm}$
b) a triangle with side lengths $5\text{ m},8\text{ m},11\text{ m}$

Problem 5

Find the perimeter when all side lengths are known:

a) a pentagon with side lengths $3\text{ cm},4\text{ cm},6\text{ cm},5\text{ cm},2\text{ cm}$
b) a square with side length $12\text{ mm}$

Problem 6

Find the unknown side length when the perimeter is known:

a) a rectangle has perimeter $26\text{ cm}$ and one pair of sides is $6\text{ cm}$ each. Find the other side length
b) a triangle has perimeter $24\text{ m}$ and two sides are $9\text{ m}$ and $6\text{ m}$. Find the third side

Exercises

Understanding and Fluency

1. Complete each statement:
   a) Perimeter is the distance ______ a shape
   b) Perimeter is measured in ______-dimensional units
   c) Suitable units for perimeter include kilometres, metres, centimetres and ______

2. Convert between metric units of length:
   a) $4\text{ m}$ to centimetres
   b) $600\text{ cm}$ to metres
   c) $11\text{ cm}$ to millimetres
   d) $3000\text{ m}$ to kilometres

3. Convert between metric units of length:
   a) $2.4\text{ km}$ to metres
   b) $750\text{ mm}$ to centimetres
   c) $8.5\text{ cm}$ to millimetres
   d) $4500\text{ m}$ to kilometres

4. Find the perimeter of each shape:
   a) a triangle with sides $3\text{ cm},4\text{ cm},5\text{ cm}$
   b) a rectangle with side lengths $9\text{ m}$ and $2\text{ m}$
   c) a square with side length $7\text{ mm}$

5. Find the perimeter of each shape:
   a) a pentagon with sides $5\text{ cm},5\text{ cm},4\text{ cm},6\text{ cm},3\text{ cm}$
   b) a rectangle with side lengths $12\text{ cm}$ and $7\text{ cm}$
   c) an irregular quadrilateral with sides $8\text{ m},6\text{ m},5\text{ m},9\text{ m}$

6. Find the unknown side length when the perimeter is known:
   a) a triangle has perimeter $18\text{ cm}$ and two sides are $5\text{ cm}$ and $7\text{ cm}$
   b) a rectangle has perimeter $40\text{ m}$ and one pair of sides is $11\text{ m}$ each
   c) a quadrilateral has perimeter $25\text{ cm}$ and three sides are $4\text{ cm},6\text{ cm},8\text{ cm}$

7. Choose the best metric unit for each perimeter:
   a) the perimeter of a coin
   b) the perimeter of a classroom
   c) the perimeter of a football field
   d) the perimeter of a state

8. Solve each:
   a) A rectangle has side lengths $6.5\text{ cm}$ and $3.5\text{ cm}$. Find its perimeter
   b) A shape has perimeter $32\text{ cm}$ and three known sides of $9\text{ cm},7\text{ cm}$ and $6\text{ cm}$. Find the fourth side
   c) Convert $2.75\text{ m}$ to centimetres, then state the perimeter of a square with that side length

Reasoning

9. Explain why perimeter is measured in units such as centimetres or metres, not in square units.

10. A student says that the perimeter of a rectangle with side lengths $8\text{ cm}$ and $5\text{ cm}$ is $13\text{ cm}$. Explain the mistake.

11. Noah says that converting $3\text{ m}$ to centimetres gives $3000\text{ cm}$. Is he correct? Explain.

12. Explain why knowing the perimeter and the other side lengths allows you to find a missing side length.

13. A student adds only the different side lengths of a rectangle and says that is the perimeter. Describe the error.

Problem-solving

14. A garden is shaped like a rectangle with length $14\text{ m}$ and width $9\text{ m}$. Find its perimeter.

15. A triangular sign has side lengths $45\text{ cm},38\text{ cm}$ and $52\text{ cm}$. Find its perimeter.

16. A square frame has perimeter $48\text{ cm}$. Find the length of one side.

17. A running track boundary is $2.5\text{ km}$ long. Write this length in metres.

18. A quadrilateral has perimeter $36\text{ cm}$. Three sides are $8\text{ cm},11\text{ cm}$ and $9\text{ cm}$. Find the fourth side.

19. A rectangular playground has perimeter $54\text{ m}$. Its length is $16\text{ m}$. Find its width.

Potential Misunderstandings

• Students may think perimeter means the space inside a shape rather than the distance around it
• Students may confuse one-dimensional units for perimeter with square units used for area
• Students may forget to include all sides when finding a perimeter
• Students may add only the different side lengths of a rectangle instead of all four sides
• Students may use the wrong conversion factor when changing between metric units
• Students may confuse converting to a smaller unit with dividing instead of multiplying
• Students may confuse converting to a larger unit with multiplying instead of dividing
• Students may subtract incorrectly when finding a missing side from a known perimeter
• Students may forget that equal sides in shapes such as squares and rectangles must be counted correctly
• Students may choose an unrealistic unit for a given object, such as kilometres for a book