Session 29: Perimeter word problems

 

Introduction activity (10 minutes)

1. Engage students: Ask, “What do you think ‘perimeter’ means?”

2. Hook Question: “If you walked all the way around your backyard, what are you measuring?” (Introduce the idea of perimeter.)

3. Define Perimeter: The distance around a 2D shape.

4. Show visuals of different shapes and identify their sides.

Main Activity(Activity (70 minutes):

Teach formulas: (10 minutes)

Rectangle: P = 2(l + w)

Square: P = 4 × side

Triangle: P = a + b + c

Use real-life examples: (15 minutes)

1.Fencing a garden  -Problem: Rectangle Garden 

Sarah wants to put a fence around her rectangular garden. The length of the garden is 8 meters and the width is 5 meters.

Question:

What is the total length of fencing Sarah needs?

Answer:

Perimeter = 2 × (Length + Width) = 2 × (8 + 5) = 2 × 13 = 26 meters 

2.Square Chalkboard  Problem:

A chalkboard in the classroom is square and each side measures 5 feet.

Question:

What is the total length of trim needed to go around the board?

Answer:

Perimeter = 4 × 5 = 20 feet

3 Triangle

.A triangle has sides that measure 6 cm, 7 cm, and 5 cm. What is the perimeter?

Solution:

Perimeter = 6 + 7 + 5 = 18 cm

Independent Practices (25 minutes )

Rectangle Problem

1.A rectangle has a length of 8 cm and a width of 5 cm. What is its perimeter?

Solution:

Perimeter = 2 × (length + width)

= 2 × (8 + 5) = 2 × 13 = 26 cm

 Square Problem

1.Each side of a square is 9 meters. What is the perimeter of the square?

Solution:

Perimeter = 4 × side = 4 × 9 = 36 meters

 Square Tile

One square floor tile has sides that measure 30 cm.

Question: What is the perimeter of the tile?

Answer:

Perimeter = 4 × 30 = 120 cm

C. Triangle Problem

1.A triangle has sides that measure 6 cm, 7 cm, and 5 cm. What is the perimeter?

Solution:

Perimeter = 6 + 7 + 5 = 18 cm

2. Triangular Flower Bed

A triangular flower bed has three sides that measure 7 feet, 9 feet, and 6 feet.

Question: What is the total length of the fencing needed for the flower bed?

Answer:

Perimeter = 7 + 9 + 6 = 22 feet

5. Irregular Shape Problem

A shape has sides measuring 3 cm, 4 cm, 5 cm, 2 cm, and 6 cm. What is the total perimeter?

Solution:

Perimeter = 3 + 4 + 5 + 2 + 6 = 20 cm

6. Missing Side Problem

A rectangle has a length of 14 m. The perimeter is 46 m. What is the width?

Solution:

Perimeter = 2 × (length + width)

46 = 2 × (14 + width)

46 = 28 + 2 × width

46 - 28 = 18

2 × width = 18 → width = 9 meters

Game Time  (20 minutes)

Instruction -

• Ask the children what they see in the farmhouse.
• Give them only the questions you have given them, and explain the questions in a way that will lead them to the answer.
• These problems should be divided into 4 papers and given to each group.
• Divide them into four groups and give the same topics to two groups..

1. Group 1 - farm house
2. Group 2 - classroom
3. Group 3- farm house 
4. Group 4- classroom 

Farmhouse related problems 

1. Fencing or Walls

Problem: You want to fence the entire perimeter of your farmhouse which is 100m long and 60m wide.

Question: How much fencing is needed?

Solution: Perimeter = 2 × (100 + 60) = 320 മീറ്റർസ്

2. Gates

Problem: You plan to install a gate on each side of a square farmhouse (each side 75 meters).

Question: What is the distance between each gate if equally spaced?

Solution: Perimeter = 4 × 75 = 300 meters

Distance between gates = 300 ÷ 4 = 75 meters

3. Paths or Roads

Problem: A walking path is to be laid around the edge of the farmhouse (perimeter = 280 meters).

Question: If it costs ₹50 per meter to build the path, what is the total cost?

Solution: 280 × 50 = ₹14,000

4. Animal Pens or Shelters

Problem: You plan to build 3 animal pens along one 90-meter side of the perimeter, spaced equally.

Question: How long is each pen (if no space between)?

Solution: 90 ÷ 3 = 30 meters per pen

5. Hedges or Trees

Problem: You are planting trees every 10 meters along a 240-meter perimeter.

Question: How many trees do you need?

Solution: 240 ÷ 10 = 24 trees

6. Water Channels or Ditches

Problem: You want to dig a drainage ditch along the full perimeter (300 meters).

Question: How much digging is required?

Solution: 300 meters of ditch

Classroom related problems 

1. Walls

Problem: The classroom is rectangular, with a length of 8 meters and a width of 6 meters.

Question: What is the perimeter of the classroom?

Solution:

Perimeter = 2 × (8 + 6) = 2 × 14 = 28 meters

2. Doors

Problem: There are 2 doors in the classroom, each measuring 1.5 meters wide. If the total perimeter of the classroom is 28 meters,

Question: What is the total width of the doors compared to the perimeter?

Solution:

Total width of doors = 2 × 1.5 = 3 meters

The doors take up 3 meters of the perimeter.

3. Windows

Problem: There are 4 windows, each 2 meters wide, placed along the perimeter of the classroom.

Question: What is the total width of all the windows?

Solution:

Total width of windows = 4 × 2 = 8 meters

4. Blackboard/Whiteboard

Problem: The classroom has a whiteboard that is 3 meters wide. If you want to place a frame around the whiteboard,

Question: What is the perimeter of the frame?

Solution:

Perimeter = 2 × (3 + 1) = 2 × 4 = 8 meters (assuming a 1-meter height for the whiteboard).

5. Decorations or Charts

Problem: You plan to hang charts along 3 walls, with each wall being 5 meters long.

Question: What is the total length of the walls where charts will be hung?

Solution:

Total length = 3 × 5 = 15 meter

The team that completes the problems first will win

Review Questions (5 minutes):

 

Follow up Task (5 minutes):

Home Work

Rectangle Garden

Lena is planting a rectangular garden that is 9 meters long and 6 meters wide.

Question: How much fencing will she need to go around the garden?

Answer:

Perimeter = 2 × (9 + 6) = 2 × 15 = 30 meters

Expected learning outcome 

Knowledge building

1. Formulas for Perimeter
2. Definition of Perimeter
3. Properties of Shapes

Skill building

1. Reading and Understanding Word Problems
2. Calculation Accuracy
3. Choosing the Right Formula