Objective:

Students will understand the relationship between the radius, circumference, and area of a circle through hands-on activities. They will develop and follow a procedure to draw circles with different radii, applying mathematical concepts to solve problems related to circle geometry.

Materials Needed:

• String or compass

• Rulers

• Large paper or chart paper

• Markers

Steps:

• Introduction:

  • Begin by reviewing the formulas for the area (A = πr²) and circumference (C = 2πr) of a circle. 

  • Ask students, “What happens to the area and circumference when we change the radius?” 

  • Explain that students will use simple tools to draw circles of varying sizes and explore how changing the radius affects the properties of the circle.

• Group Activity:

  • In pairs, students will use string or a compass to draw circles. 

  • They will choose different radii, measure the radius, and calculate the circle's area and circumference. 

  • Each group will follow a step-by-step procedure they create for drawing circles using the chosen radius, ensuring that each circle is accurate.

• Testing and Refining:

  • After drawing their circles, students will compare the results and check whether the calculated area and circumference match the dimensions of the drawn circles. 

  • If the measurements seem off, students will refine their procedures to ensure accuracy.

• Presentation and Discussion:

  • Each group will present their circles and explain how changing the radius affected the area and circumference. 

  • The teacher will lead a discussion on how the manual process of drawing and measuring circles is similar to using a procedure with parameters in programming. 

  • For example, defining the radius as a parameter allows the same "circle-drawing" procedure to create circles of different sizes in programming.

Equity and Access:

Provide tools like pre-cut string lengths for students needing assistance with the procedure. Pair students with varying levels of understanding to ensure collaboration and support.

Real-World Application:

Relate the lesson to how architects and engineers use geometric principles when designing structures that require precise measurements, such as circular windows or towers.

CS Practice(s):

• Recognizing and Defining Computational Problems: Students develop and refine a procedure for drawing circles, applying computational thinking to geometric concepts.

Standard(s):

• CA CCSS Mathematics 7.G.4

• CA CS 6-8.AP.14

Objective:

Students will use p5.js, pencil code, App Lab, or another coding platform to create a reusable procedure that draws circles with varying radii. By defining the radius as a parameter, students will explore how altering this parameter affects the circle's size and how functions improve code modularity and reusability.

Materials Needed:

Computers or tablets with access to p5.js

Pre-written template with basic code for drawing shapes

Steps:

• Introduction:

  • Start by discussing the relationship between a circle's radius, area, and circumference. 

  • Explain that in coding, students can create a reusable function to draw circles of various sizes by changing the radius as a parameter. 

  • Demonstrate how to set up a simple function to draw a circle in a coding platform.

• Group Activity:

  • In pairs, students will open their coding environment and use the ellipse() function in p5.js to draw a circle. 

  • They will then define a new function called drawCircle(radius) that takes the radius as an input and uses it to create circles of different sizes.

• Testing and Refining:

  • After creating their drawCircle function, students will test it by calling the function with different radius values. 

  • They will refine their code to ensure that the function produces correct results and displays circles of the appropriate size.

• Presentation and Discussion:

  • Each pair will share their code with the class, explaining how the radius parameter works within the drawCircle function. 

  • The teacher will guide a discussion on how creating procedures with parameters makes code more modular and easier to reuse, relating this back to the geometric concept of circle dimensions.

Equity and Access:

Provide pre-written code templates for students who need extra support with coding. Pair students with different levels of programming experience to ensure that all students can participate fully.

Real-World Application:

Connect the activity to how game developers use functions with parameters to generate shapes and objects of various sizes in digital environments. Discuss how this principle of modularity applies across different fields like software development and graphic design.

CS Practice(s):

• Recognizing and Defining Computational Problems: Students define a procedure that draws circles of varying sizes based on a radius parameter.

• Testing and Refining Computational Artifacts: Students test their functions and adjust the parameters to create the desired output.

Standard(s):

• CA CCSS Mathematics 7.G.4

• CA CS 6-8.AP.14