| Full lesson | Create for a teacher a set of content for giving a lesson, beginning with the lesson plan. Each new block of materials must begin with an H1 heading (other subheaders must be H2, H3, etc). When you describe required pictures, write those descriptions in curly brackets, for example: {A picture of a triangle} |
| Which subject | Mathematics |
| What topic | Solving problems involving area of composite figures using the headings below:Get Started: Students must complete independently upon entering the classroom. Brain Break: What activity? When will it occur? Set A Purpose: Explicit statement of the Lesson Objective and Essential Question(s) Build Engagement: What strategy will you use to establish personal or life relevance with learners and connection to the Purpose and Learning Objective? Activate Prior Knowledge: What activity will you use to connect students to their prior knowledge? Direct Instruction w/ Modeling: What information will you explain and model? How will you do that? Guided Practice: What activities will you use for students to demonstrate their initial understanding of the learning objective (LO)? Checks for Understanding: What will you as |
| What length (min) | 60 |
| What age group | Year or Grade 6 |
| Class size | 25 |
| What curriculum | 6th grade math south carolina standards using math nation textbook |
| Include full script | |
| Check previous homework | |
| Ask some students to presents their homework | |
| Add a physical break | |
| Add group activities | |
| Include homework | |
| Show correct answers | |
| Prepare slide templates | |
| Number of slides | 15 |
| Create fill-in cards for students | |
| Create creative backup tasks for unexpected moments |
Mathematics
Solving Problems Involving Area of Composite Figures
Year/Grade 6
60 minutes
25
6th Grade Math South Carolina Standards
| Step Number | Step Title | Length | Details |
|---|---|---|---|
| 1 | Get Started | 5 min | Students will complete a brief warm-up activity involving basic area calculations independently. |
| 2 | Brain Break | 5 min | Quick stretching activity with a focus on shapes (e.g., students make shapes with their bodies). |
| 3 | Set A Purpose | 5 min | Teacher will clearly state the lesson objectives and essential questions related to composite figures. |
| 4 | Build Engagement | 5 min | Share a real-life scenario (e.g., designing a garden) that requires calculating the area of composite figures. |
| 5 | Activate Prior Knowledge | 5 min | Students will complete a quick review quiz on the area of basic shapes (squares, rectangles, circles). |
| 6 | Direct Instruction w/ Modeling | 10 min | Teacher will explain the steps to find the area of composite figures, modeling examples on the whiteboard. |
| 7 | Guided Practice | 10 min | Students work in groups of 4 to solve a composite figure problem using printable cards and materials provided. |
| 8 | Checks for Understanding | 5 min | Teacher will circulate to randomly check what students filled out on their cards, providing feedback. |
| 9 | Assign Homework | 5 min | Homework assigned without students presenting; instructions will be shared for them to complete at home. |
| 10 | Closing | 5 min | Recap the lesson, addressing any remaining questions regarding solving area of composite figures. |
"Good morning, everyone! Today we’re going to jump right into our warm-up activity. I want each of you to take out a piece of paper and a pencil. For the next five minutes, I will give you a few basic area calculations to work on independently. Please find the area of the following shapes:
Make sure to show all your work. You have five minutes! Begin now!"
"Alright class, let’s take a quick break! Stand up and stretch out. I want you to create different shapes with your bodies. Try to make a square, a triangle, and a circle with your classmates. You have two minutes to create as many shapes as you can! Ready? Go!"
"Wonderful job, everyone! Please take your seats. Today, we will focus on solving problems involving the area of composite figures. By the end of our lesson, you will be able to calculate the area of these complex shapes and apply your skills to real-world problems. Our essential questions today are: How can we apply the concept of area to solve real-world problems? What strategies can we use to break down composite figures into simpler shapes? Keep these questions in mind as we move along."
"Let’s get engaged! I want you to imagine designing your own garden. This garden has various sections—a rectangular patch for vegetables, a circular area for flowers, and a small storage shed that is shaped like a square. To create this garden, you will need to calculate the total area of all these sections combined. This is a perfect example of how we can apply our knowledge of area to real-life situations!"
"Now, let’s activate some of your prior knowledge! I will hand out a quick review quiz with a few questions on the area of basic shapes such as squares, rectangles, and circles. This will help us recall what we’ve learned so far. You will have five minutes to complete the quiz. Ready? Let’s get started!"
"Great job on the quiz! Now, let’s move on to our direct instruction. I’m going to explain how to find the area of composite figures. Composite figures are made up of two or more shapes, and we can find their area by breaking them down into smaller, simpler shapes.
Let’s look at this example on the whiteboard. Here’s a composite figure made up of a rectangle and a semicircle. First, I’ll calculate the area of the rectangle. (Writes dimensions on the board) Then, I’ll calculate the area of the semicircle. Finally, I’ll add both areas together to find the total area of the composite figure.
Does everyone see how we can approach this? If you have questions, ask me now!"
"Now it’s your turn! I’m going to divide you into groups of four, and you will work together to solve a composite figure problem. I have provided printable cards with different examples for each group. Use your markers and graph paper if you need to. Give it a go, and I will circulate around to assist. You have ten minutes!"
"Time is up! I want to see what you all have come up with. I will be walking around the room to check your printable cards and make sure you filled in your work. Don’t be afraid to ask me any questions. I’m here to help!"
"Great work today, everyone! For homework, I want you to complete the exercise in your Math Nation textbook on pages 120-122 about the area of composite figures. Be sure to follow the instructions carefully! You will not be presenting this in class, but please bring it completed for review next lesson. Any questions about the homework before we move on?"
"Let’s recap what we learned today. We explored how to calculate the area of composite figures and applied this concept to real-life scenarios like designing a garden. Remember to think about how you can deconstruct complex shapes into simpler ones when calculating area. Before we finish, does anyone have any remaining questions or need clarification on anything we covered? Alright, fantastic work today. Have a wonderful day!"
| Slide number | Image | Slide content |
|---|---|---|
| 1 | {Image: Students working on math problems} | - Introduction to area calculations - Shapes for calculations: square, rectangle, circle - Encourage showing all work - Time given: 5 minutes |
| 2 | {Image: Students stretching and moving} | - Quick brain break activity - Create shapes with bodies: square, triangle, circle - Time given: 2 minutes |
| 3 | {Image: Teacher explaining a lesson} | - Purpose of the lesson: Area of composite figures - Essential questions: - How can we apply area in real-world problems? - Strategies for breaking down shapes |
| 4 | {Image: Garden design with various sections} | - Engage students' imagination with garden design - Shapes to include: rectangular patch, circular area, square shed - Real-world application of area calculations |
| 5 | {Image: Review quiz paper} | - Activate prior knowledge - Quick review quiz on basic shapes: squares, rectangles, circles - Time given: 5 minutes |
| 6 | {Image: Teacher demonstrating on whiteboard} | - Introduction to composite figures - Breakdown method for calculating area - Example: Rectangle + semicircle - Encouragement for questions |
| 7 | {Image: Students working in groups} | - Guided practice session in groups - Solve composite figure problems with provided examples - Materials: markers, graph paper - Time given: 10 minutes |
| 8 | {Image: Teacher checking students' work} | - Check for understanding - Walking around to assess group work - Encouragement for questions and providing help |
| 9 | {Image: Math textbook with dog-eared pages} | - Assignment of homework - Complete textbook exercise on pages 120-122 - Reminder to follow instructions carefully - No presentation required |
| 10 | {Image: Recap notes on a chalkboard} | - Recap of the lesson - Topics covered: Area of composite figures and real-life applications - Reminder on deconstructing complex shapes |
| 11 | {Image: Students raising hands} | - Open floor for questions - Clarify any concepts that need further explanation - Encouragement to engage with the material |
| 12 | {Image: Classroom closing for the day} | - Summary of the day’s learning activities - Acknowledgment of students’ efforts - Farewell and wish for a wonderful day |
| 13 | {Image: Decorative shapes on a graph paper} | - Visual representation of composite figures - Encourage creativity in area calculations - Diverse shapes and their significance in design |
| 14 | {Image: Group discussions in a classroom} | - Importance of collaboration in learning - Discussing various approaches to solve composite figure problems - Learning from peers |
| 15 | {Image: Classroom celebration with students} | - Closing remarks and motivational note - Celebrate completion of a challenging topic - Reminder to apply learning in future math activities |
Calculate the area of a composite figure that consists of a rectangle measuring 6 cm by 4 cm and a triangle with a base of 4 cm and a height of 3 cm. Show your work.
A park is designed in the shape of an L, which consists of a rectangle measuring 10 m by 4 m and another rectangle measuring 6 m by 3 m. What is the total area of the park? Show all calculations.
A school playground is divided into a square sandbox with sides of 5 ft, a circular swing area with a radius of 3 ft, and a rectangular slide area that is 2 ft by 4 ft. What is the total area of the playground? Make sure to present your work.
You are planning to paint a mural on a wall that is made up of a rectangular section measuring 8 ft by 5 ft and a semicircular section with a radius of 3 ft. What is the total area that will be painted? Provide a step-by-step calculation.
A garden design includes a rectangular vegetable patch (4 m by 3 m), a circular flower bed (radius 2 m), and a triangular herb section with a base of 3 m and a height of 4 m. Calculate the total area of the garden. Outline your work clearly.
Area of rectangle = 6 cm 4 cm = 24 cm². Area of triangle = (1/2) base height = (1/2) 4 cm * 3 cm = 6 cm². Total area = 24 cm² + 6 cm² = 30 cm².
Area of first rectangle = 10 m 4 m = 40 m². Area of second rectangle = 6 m 3 m = 18 m². Total area = 40 m² + 18 m² = 58 m².
Area of sandbox = 5 ft 5 ft = 25 ft². Area of swing area = π (3 ft)² ≈ 28.27 ft². Area of slide area = 2 ft * 4 ft = 8 ft². Total area = 25 ft² + 28.27 ft² + 8 ft² ≈ 61.27 ft².
Area of rectangle = 8 ft 5 ft = 40 ft². Area of semicircle = (1/2) π * (3 ft)² ≈ 14.13 ft². Total area = 40 ft² + 14.13 ft² ≈ 54.13 ft².
Area of vegetable patch = 4 m 3 m = 12 m². Area of flower bed = π (2 m)² ≈ 12.57 m². Area of triangle = (1/2) 3 m 4 m = 6 m². Total area = 12 m² + 12.57 m² + 6 m² ≈ 30.57 m².
| Question | Answer |
|----------------------------------------------------------------------------------------------|--------|
| What is the area of a square with a side length of 4 cm? | |
| How do you calculate the area of a rectangle that is 3 cm by 5 cm? | |
| What is the formula to find the area of a circle with a radius of 2 cm? | |
| How can we apply the concept of area to solve real-world problems? | |
| What strategies can we use to break down composite figures into simpler shapes? | |
| If you design a garden with a rectangular patch for vegetables and a circular area for flowers, how would you find the total area? | |
| What shapes make up a composite figure, and how do you find its area? | |
| Can you explain the process of finding the area of a composite figure? | |
| What was the main focus of today's lesson on area? | |
| How does working in groups help when solving composite figure problems? | |If you were to design a park instead of a garden, what new shapes would you include, and how would you calculate the area for each section?
Can you think of an object in your home that has a composite shape? Describe it and how you would calculate its area.
How would you explain the process of finding the area of a composite figure to someone who has never learned about it before?
Imagine you have a composite figure that includes a triangle and a trapezoid. What steps would you take to find the total area of this figure?
Why do you think understanding area in a real-world context, like designing a garden, is important? Can you think of other real-life situations where area calculations are necessary?