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Right Angle, Right Area!

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Lesson Plan

Right Angle, Right Area!

Students will be able to recall and apply formulas to calculate the area of rectangles and right triangles.

Understanding area is crucial for many real-world applications, from designing a room to planning a garden. This lesson provides essential geometry skills.

Audience

6th Grade Students

Time

30 minutes

Approach

Direct instruction, guided practice, and independent application.

Materials

Smartboard or Projector, Slide Deck: Right Angle, Right Area!, Warm-Up: Shape Up!, Worksheet: Area Adventure, Answer Key: Area Adventure, and Cool-Down: Quick Area Check

Prep

Teacher Preparation

10 minutes

Step 1

Introduction & Warm-Up

5 minutes

  • Display the Warm-Up: Shape Up! on the board or distribute copies.
    - Have students complete the warm-up, activating prior knowledge about shapes.
    - Briefly discuss their responses, focusing on identifying rectangles and triangles.

Step 2

Direct Instruction: Area of Rectangles

8 minutes

  • Present the first few slides of the Slide Deck: Right Angle, Right Area! explaining the concept of area and the formula for rectangles (Area = length × width).
    - Go through example problems together, emphasizing units.

Step 3

Direct Instruction: Area of Right Triangles

8 minutes

  • Continue with the Slide Deck: Right Angle, Right Area!, introducing the concept that a right triangle is half of a rectangle.
    - Explain the formula for right triangles (Area = 1/2 × base × height).
    - Work through example problems, connecting them to the rectangle examples.

Step 4

Guided Practice & Independent Work

7 minutes

  • Distribute the Worksheet: Area Adventure.
    - Guide students through the first few problems, offering support.
    - Allow students to work independently on the remaining problems.
    - Circulate to provide individual assistance and check for understanding.

Step 5

Cool-Down & Wrap-Up

2 minutes

  • Distribute the Cool-Down: Quick Area Check.
    - Students complete the cool-down as an exit ticket.
    - Briefly review the main concepts, reminding students of the formulas learned.
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Slide Deck

Welcome! Let's Talk Area!

What is Area?

  • The amount of space inside a 2D shape.
  • Measured in square units (like square inches, square centimeters).

    Think: How much carpet do you need for a room?

Welcome students and introduce the day's topic: understanding the area of shapes. Briefly review what 'area' means (the space inside a 2D shape).

Area of a Rectangle

Formula:

Area = Length × Width

Example:
A rectangle is 5 cm long and 3 cm wide.
Area = 5 cm × 3 cm = 15 square cm (or 15 cm²)

Introduce rectangles. Explain that the area of a rectangle is found by multiplying its length by its width. Show the formula and an example.

Area of a Right Triangle

A Right Triangle is Half a Rectangle!

Area = 1/2 × Base × Height

Example:
A right triangle has a base of 6 inches and a height of 4 inches.
Area = 1/2 × 6 in × 4 in = 12 square inches (or 12 in²)

Introduce right triangles. Explain that a right triangle is essentially half of a rectangle. Illustrate this visually if possible. Show the formula for a right triangle.

Practice Time!

Quick Check:

  1. What is the formula for the area of a rectangle?
  2. What is the formula for the area of a right triangle?

Ready for some practice?

Review both formulas and provide a quick check for understanding. Ask students to verbalize the formulas or identify parts of a given shape.

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Warm Up

Shape Up! Warm-Up

Instructions: Look at the shapes below.

  1. What do you notice about each shape?
  2. Do you know what these shapes are called?
  3. Can you think of where you might see these shapes in the real world?

Shape A

Rectangle










Shape B

Right Triangle










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Worksheet

Area Adventure: Rectangles and Right Triangles

Instructions: Calculate the area for each shape below. Remember to include your units!

Part 1: Rectangles

  1. A rectangle has a length of 8 cm and a width of 4 cm.
    What is its area?






  2. Find the area of a square with sides of 6 meters.






  3. A rectangular garden is 10 feet long and 5 feet wide.
    What is the area of the garden?






Part 2: Right Triangles

  1. A right triangle has a base of 7 inches and a height of 6 inches.
    What is its area?






  2. Find the area of a right triangle with a base of 12 cm and a height of 5 cm.






  3. A triangular flag has a base of 3 feet and a height of 4 feet.
    What is the area of the flag?






Part 3: Challenge!

  1. A rectangular room is 9 meters long and 7 meters wide. If you want to carpet half of the room with a special rug, what is the area of the rug?












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Answer Key

Area Adventure: Answer Key

Part 1: Rectangles

  1. A rectangle has a length of 8 cm and a width of 4 cm. What is its area?

    • Thought Process: The formula for the area of a rectangle is Length × Width. I need to multiply 8 cm by 4 cm.
    • Answer: 8 cm × 4 cm = 32 cm²

  2. Find the area of a square with sides of 6 meters.

    • Thought Process: A square is a special type of rectangle where length and width are equal. So, the formula is side × side. I need to multiply 6 meters by 6 meters.
    • Answer: 6 m × 6 m = 36 m²

  3. A rectangular garden is 10 feet long and 5 feet wide. What is the area of the garden?

    • Thought Process: The formula for the area of a rectangle is Length × Width. I need to multiply 10 feet by 5 feet.
    • Answer: 10 ft × 5 ft = 50 ft²

Part 2: Right Triangles

  1. A right triangle has a base of 7 inches and a height of 6 inches. What is its area?

    • Thought Process: The formula for the area of a right triangle is 1/2 × Base × Height. I need to multiply 1/2 by 7 inches and then by 6 inches.
    • Answer: 1/2 × 7 in × 6 in = 21 in²

  2. Find the area of a right triangle with a base of 12 cm and a height of 5 cm.

    • Thought Process: The formula for the area of a right triangle is 1/2 × Base × Height. I need to multiply 1/2 by 12 cm and then by 5 cm.
    • Answer: 1/2 × 12 cm × 5 cm = 30 cm²

  3. A triangular flag has a base of 3 feet and a height of 4 feet. What is the area of the flag?

    • Thought Process: The formula for the area of a right triangle is 1/2 × Base × Height. I need to multiply 1/2 by 3 feet and then by 4 feet.
    • Answer: 1/2 × 3 ft × 4 ft = 6 ft²

Part 3: Challenge!

  1. A rectangular room is 9 meters long and 7 meters wide. If you want to carpet half of the room with a special rug, what is the area of the rug?
    • Thought Process: First, find the total area of the rectangular room (Length × Width). Then, divide that area by 2 to find the area of the rug that covers half the room.
    • Answer:
      • Area of room = 9 m × 7 m = 63 m²
      • Area of rug = 63 m² / 2 = 31.5 m²
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Cool Down

Quick Area Check

Instructions: Answer the following questions to show what you learned today.

  1. What is the formula for the area of a rectangle?



  2. What is the formula for the area of a right triangle?



  3. Calculate the area of a rectangle with a length of 7 cm and a width of 3 cm.



  4. Calculate the area of a right triangle with a base of 8 inches and a height of 5 inches.



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