Session 29: Perimeter word problems

Introduction activity (15 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

Direct Instruction (30minutes):

Teach formulas:

Rectangle: P = 2(l + w)

Square: P = 4 × side

Triangle: P = a + b + c

Use real-life examples:

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 Flower Bed 

Tom is fencing a square flower bed. Each side of the flower bed is 6 feet long.

Question:

How many feet of fencing does he need?

Answer:

Perimeter = 4 × side = 4 × 6 = 24 feet

3.Bordering a classroom board Problem:Rectangular Board 

Ms. Lee wants to put a border around her classroom bulletin board. The board is 6 feet long and 4 feet high.

Question:

How many feet of border does she need?

Answer:

Perimeter = 2 × (6 + 4) = 2 × 10 = 20 feet

4.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

Independent Practice 

Guided Practice (45 minutes )

A. Rectangle Problem

Question:

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

2. 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

3. Picture Frame

A rectangular picture frame is 12 inches long and 8 inches wide.

Question: How many inches of decorative ribbon are needed to wrap around the frame?

Answer:

Perimeter = 2 × (12 + 8) = 2 × 20 = 40 inches

B. Square Problem

Question:

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

Solution:

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

3. 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

Question:

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

Question:

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

Question:

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

Follow up task -30 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..

Group 1 - farm house

Group 2 - classroom

Group 3- farm house 

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 മീറ്റർസ്

The team that completes the problems first will wiplan 

Expected learning outcome 

1. Understanding Perimeter: Students will learn to calculate the perimeter of different objects in a classroom, like walls, desks, and windows.

2. Real-World Application: Students will apply perimeter concepts to solve practical problems, such as measuring space for furniture or determining material needs.