Objective: 

Students will apply their understanding of linear equations to test whether two points lie along a line defined by a linear function. They will use compound conditions to analyze relationships between points, the slope, and the line, developing logical thinking skills.

Materials Needed:

Graph paper

Pencils

Linear equations and points for students to test

Steps:

• Introduction: 

  • Introduce the concept of linear equations and their graphical representations. 

  • Explain that students will work in pairs to test whether two points lie on a line defined by a linear equation using compound conditions.

• Group Activity: 

  • In pairs, students will be given a linear equation (e.g., y = 2x + 1) and two points. 

  • They will calculate the slope between the two points and compare it to the slope of the given line. 

  • Then, they will substitute the coordinates of the points into the linear equation to check if both satisfy the equation. 

  • They will combine these conditions to conclude whether the points lie on the line.

• Testing and Refining: 

  • Students will work through several examples and test their calculations. 

  • If discrepancies arise, they will review their compound conditions to ensure both the slope and the equation are being considered correctly.

• Presentation and Discussion: 

  • Each pair will share their findings, explaining how they used compound conditions to determine whether the points lay on the line. 

  • Lead a class discussion about how logical reasoning and conditionals are used in mathematics to evaluate multiple factors at once.

Equity and Access: 

Provide graphing tools and step-by-step guides for students who need extra support with plotting points and calculating slope. Pair students of different ability levels to encourage collaborative learning.

Real-World Application: 

Relate the activity to how engineers and architects use coordinate systems and slope calculations to ensure that structures align correctly and follow a specified design.

CS Practice(s):

• Developing and Using Abstractions: Students simplify the problem by using compound conditions to check multiple criteria for determining if points lie on a line.

• Recognizing and Defining Computational Problems: Students identify the relationships between points, slope, and the linear equation and use conditional reasoning to solve the problem.

Standard(s):

• CA CCSS Mathematics 8.EE.7a

• CA CS 6-8.AP.12

Objective:

Students will program robots to move along a path defined by a linear equation, using compound conditionals to determine if the robot can move between two points that lie on the line. They will develop control structures and conditionals in their robot code, iteratively testing and refining their programs.

Materials Needed:

• Robots (e.g., LEGO EV3, Sphero, VEX, etc.)

• Grid layout on the floor or a large graphing mat

• Devices for coding (e.g., tablets, computers)

• Robot programming software

Steps:

• Introduction: 

  • Begin by reviewing how linear equations represent a line and how points are used to determine if they lie on that line. 

  • Introduce the robot task: Students will program their robots to move along a line defined by a linear equation using conditional logic to test if the points the robot moves through lie on the line.

• Group Activity: 

  • In small groups, students will program their robots to move along a grid representing a coordinate plane. They will input a linear equation (e.g., y = 2x + 1) and then write code that moves the robot between two points. Compound conditionals will ensure the robot only follows the line if the two points meet the conditions of both the slope and the equation.

• Creating and Coding: 

  • Students will develop control structures and conditionals in their robot programming environment. For example, they will code the robot to calculate the slope between two points and verify that both points satisfy the linear equation using an AND conditional. 

  • If the points satisfy both conditions, the robot will move along the line; otherwise, it will stop or display an error message.

• Testing and Refining: 

  • Once students have written their programs, they will test their robots on the grid to see if they can successfully move along the line between two points. 

  • If the robot deviates from the path or stops incorrectly, students will debug their code by adjusting their conditionals or recalculating the slope. 

  • They will also test how changes in variables, such as slope or intercept, affect the robot’s movement.

• Presentation and Discussion: 

  • Each group will present their programmed robot’s journey along the grid, explaining how they used compound conditionals in their code to ensure the robot moved only if the points satisfy the equation of the line. 

  • Lead a class discussion on how the compound conditionals helped ensure the accuracy of the robot’s movement, and how similar logic is applied in real-world robotic programming for navigation.

Equity and Access:

Provide pre-programmed robots or partial code templates for students who may need additional support. Offer hands-on guidance to ensure that all students are able to participate, and pair students with varying experience levels to foster collaboration.

Real-World Application:

Connect this lesson to real-world applications where robots and drones use conditional programming for navigation, such as mapping terrain or delivering packages. Emphasize how robots rely on complex conditionals to follow specific paths and avoid obstacles.

CS Practice(s):

• Creating Computational Artifacts: Students create robot code that models movement along a linear equation by implementing compound conditionals.

• Testing and Refining Computational Artifacts: Students iteratively test their robot’s movement and refine their code to ensure accuracy when navigating the grid.

Standard(s):

• CA CCSS Mathematics 8.EE.7a

• CA CS 6-8.AP.12