Objective:

Students will use number lines and diagrams to represent and solve addition and subtraction problems involving rational numbers, while exploring the tradeoffs of how computers store and represent these numbers.

Materials Needed:

• Paper and pencils

• Number line templates

• Real-world scenarios involving rational numbers (e.g., temperature changes, financial transactions)

Steps:

• Introduction: 

  • Explain the concepts of adding and subtracting rational numbers using a number line, and relate these concepts to real-world examples, such as temperature changes or balancing a checkbook.

• Group Activity: 

  • In small groups, students will solve problems involving rational numbers, representing their solutions on a number line. 

  • They will describe situations where opposite quantities combine to make 0.

• Discussion on Technology: 

  • Lead a discussion about how computers represent rational numbers (fractions, decimals) as binary data. 

  • Discuss the limitations of computer representations, including rounding errors and precision issues.

• Presentation and Reflection: 

  • Each group presents their solutions and number lines. 

  • The class reflects on the tradeoffs between using technology for calculating rational numbers and the need for human understanding and oversight in certain scenarios.

Equity and Access:

Provide number line templates and real-world problems with varying levels of complexity so students can work at their own pace and comfort level.

Real-World Application:

Connect this lesson to real-world financial literacy (e.g., tracking spending and savings) and how digital systems like online banking handle rational numbers through addition and subtraction.

CS Practice(s):

• Recognizing and Defining Computational Problems: Students explore how the representation of numbers in computers can lead to errors and how those errors can impact real-world applications.

• Communicating about Computing: Students discuss how computers handle rational numbers differently from humans and the potential consequences of these differences.

Standard(s):

• CA CCSS Mathematics 7.NS.3

• CA CS 6-8.DA.7

• CA CS 6-8.IC.20

Objective:

Students will use spreadsheet tools to solve problems involving multiplication and division of rational numbers and explore how changing variables can affect the outcome of computations.

Materials Needed:

• Computers with access to spreadsheet software (Google Sheets, Excel)

• Real-world scenarios (e.g., tax calculations, discount applications, financial projections)

Steps:

• Introduction: 

  • Introduce how to use a spreadsheet to perform operations with rational numbers, including multiplication and division. 

  • Demonstrate how to input real-world data and apply formulas to automate calculations.

• Group Activity: 

  • Students work in pairs to input data into the spreadsheet and solve problems involving rational numbers, such as calculating tax, discounts, and balances. 

  • They will also explore how changing variables, such as interest rates, affects the overall outcome.

• Discussion on Technology: 

  • Facilitate a discussion about the benefits and limitations of using spreadsheets to handle rational number operations. 

  • Emphasize the importance of accuracy when inputting data and interpreting results.

• Presentation and Reflection: 

  • Each group presents their spreadsheet and explains how they used formulas to calculate and analyze real-world data. 

  • They reflect on the tradeoffs of automating calculations versus manual problem-solving.

Equity and Access:

Provide step-by-step guides for students who are new to spreadsheets, and allow for differentiated tasks, with simpler or more complex problems based on experience.

Real-World Application:

Link this activity to real-world applications such as budgeting, financial planning, and how businesses calculate costs, taxes, and profits using spreadsheets.

CS Practice(s):

• Creating Computational Artifacts: Students use spreadsheet software to create a computational artifact that automates the process of solving rational number problems.

• Testing and Refining Computational Artifacts: Students modify their spreadsheets by changing variables and observe the effects on the outcomes.

Standard(s):

• CA CCSS Mathematics 7.NS.3

• CA CS 6-8.DA.9, CA CS 6-8.IC.20