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
• Solve 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 , and
• 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) to centimetres

b) to metres

c) to millimetres

Worked Example 3

Convert between metric units of length:

a) to metres

b) to kilometres

c) to centimetres

Worked Example 4

Find the perimeter when all side lengths are known:

a) a rectangle with side lengths and

b) a triangle with side lengths

Worked Example 5

Find the perimeter when all side lengths are known:

a) a pentagon with side lengths

b) a square with side length

Worked Example 6

Find the unknown side length when the perimeter is known:

a) a rectangle has perimeter and one pair of sides is each. Find the other side length

b) a triangle has perimeter and two sides are and . 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) to centimetres

b) to metres

c) to millimetres

Problem 3

Convert between metric units of length:

a) to metres

b) to kilometres

c) to centimetres

Problem 4

Find the perimeter when all side lengths are known:

a) a rectangle with side lengths and

b) a triangle with side lengths

Problem 5

Find the perimeter when all side lengths are known:

a) a pentagon with side lengths

b) a square with side length

Problem 6

Find the unknown side length when the perimeter is known:

a) a rectangle has perimeter and one pair of sides is each. Find the other side length

b) a triangle has perimeter and two sides are and . Find the third side

Exercises

Understanding and Fluency

Exercise 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 ______

Exercise 2.

Convert between metric units of length:

a) to centimetres

b) to metres

c) to millimetres

d) to kilometres

Exercise 3.

Convert between metric units of length:

a) to metres

b) to centimetres

c) to millimetres

d) to kilometres

Exercise 4.

Find the perimeter of each shape:

a) a triangle with sides

b) a rectangle with side lengths and

c) a square with side length

Exercise 5.

Find the perimeter of each shape:

a) a pentagon with sides

b) a rectangle with side lengths and

c) an irregular quadrilateral with sides

Exercise 6.

Find the unknown side length when the perimeter is known:

a) a triangle has perimeter and two sides are and

b) a rectangle has perimeter and one pair of sides is each

c) a quadrilateral has perimeter and three sides are

Exercise 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

Exercise 8.

Solve each:

a) A rectangle has side lengths and . Find its perimeter

b) A shape has perimeter and three known sides of and . Find the fourth side

c) Convert to centimetres, then state the perimeter of a square with that side length

Reasoning

Exercise 9.

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

Exercise 10.

A student says that the perimeter of a rectangle with side lengths and is . Explain the mistake.

Exercise 11.

Noah says that converting to centimetres gives . Is he correct? Explain.

Exercise 12.

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

Exercise 13.

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

Problem-solving

Exercise 14.

A garden is shaped like a rectangle with length and width . Find its perimeter.

Exercise 15.

A triangular sign has side lengths and . Find its perimeter.

Exercise 16.

A square frame has perimeter . Find the length of one side.

Exercise 17.

A running track boundary is long. Write this length in metres.

Exercise 18.

A quadrilateral has perimeter . Three sides are and . Find the fourth side.

Exercise 19.

A rectangular playground has perimeter . Its length is . 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

Next: 120r. Review Circles and Circumference