Objective:

Students will generate and simplify equivalent expressions using properties of operations and solve word problems. They will discuss how variables in math problems relate to variables in coding and the significance of data representation in real-world contexts.

Materials Needed:

• Paper, pencils

• Pre-designed word problems involving rational coefficients

• Whiteboards or chart paper for group collaboration

Steps:

• Introduction: 

  • Review how to generate equivalent expressions using properties of operations (distributive property, combining like terms, etc.). 

  • Introduce real-world word problems requiring students to write and simplify expressions.

• Group Activity: 

  • In groups, students will work through multi-step word problems that require them to add, subtract, and factor linear expressions. 

  • Each group will present their solutions and explain how they used different forms of expressions to simplify their process.

• Discussion on Variables: 

  • Discuss how variables in math and computer science both represent values. 

  • Students will brainstorm how a computer program could be written to automate these calculations using clearly defined variables.

• Reflection: 

  • Lead a class discussion on the importance of organizing and representing data clearly in both math problems and computational algorithms.

Equity and Access:

Provide word problems of varying difficulty levels, ensuring that all students have an entry point into the activity. Support struggling students with additional scaffolds, such as partially completed problems.

Real-World Application:

Discuss how online shopping platforms use algorithms to calculate costs, taxes, and discounts, linking this process back to the simplification of expressions.

CS Practice(s):

• Developing and Using Abstractions: Students draw connections between variables in math expressions and variables in programming.

• Communicating about Computing: Students explain how rewriting expressions helps clarify problem-solving processes, both in manual calculations and in algorithms.

Standard(s):

• CA CCSS Mathematics 7.EE.1

• CA CS 6-8.AP.11

Objective:

Students will use Pencil Code, p5.js, Scratch, or other coding platforms to write programs that solve multi-step word problems involving rational numbers, using variables and basic arithmetic operations to explore real-world mathematical scenarios.

Materials Needed:

• Computers 

• Pre-designed word problems involving rational numbers

• Coding tutorials for beginners (optional)

Steps:

• Introduction: 

  • Students review a multi-step word problem, such as calculating the total cost of an item after applying a tax rate and discount. 

  • Show how the problem can be broken down into steps and introduce a web editor or coding platform as a tool to automate this process.

• Group Activity: 

  • Students work in pairs to write a program in a web editor or coding platform. 

  • They define variables like price, discount, and tax_rate, and write functions that perform the necessary calculations (e.g., total cost = price + price * tax_rate - discount). 

  • Students use basic arithmetic operators and console output to display the results of their program.

• Testing and Refining: 

  • Students test their programs by changing the values of their variables to see how different inputs (e.g., higher tax rates or different discount amounts) impact the final calculation. 

  • Encourage them to troubleshoot any errors and refine their code to ensure it handles various inputs accurately.

• Reflection: 

  • Students reflect on how using code to automate a math problem can simplify calculations, making it easier to handle real-world scenarios where variables like price and tax can change.

Equity and Access:

Provide starter code templates and step-by-step guides for students who need additional support. Encourage students to collaborate with peers, ensuring all group members contribute to the programming process.

Real-World Application:

Discuss how similar automated systems are used in retail stores and online shopping to calculate totals with tax and discounts, demonstrating how coding is applied to everyday tasks.

CS Practice(s):

• Creating Computational Artifacts: Students write programs in a web editor that perform automated calculations based on real-world math problems.

• Testing and Refining Computational Artifacts: Students test their code with different inputs, making adjustments to ensure accuracy and functionality.

Standard(s):

• CA CCSS Mathematics 7.EE.1

• CA CS 6-8.AP.11