Objective:

Students will use ratio tables and graphs to analyze and represent proportional relationships in real-world scenarios and explore the limitations and tradeoffs of relying on technology for these computations.

Materials Needed:

• Paper, graph paper, and pencils

• Real-world ratio examples (recipes, distance-time problems)

• Calculators (optional for checking calculations)

Steps:

• Introduction: 

  • Begin by explaining ratios and proportional relationships. 

  • Use real-world examples like scaling recipes or calculating travel distances to set the context.

• Group Activity: 

  • Students will work in small groups to create ratio tables and graphs for the given real-world problems. 

  • For example, they will calculate unit rates such as miles per hour or cost per item and graph the proportional relationship.

• Discussion on Technology: 

  • Lead a class discussion on how computers use algorithms to automate these types of proportional calculations in tools like Google Maps or online shopping platforms. 

  • Discuss the tradeoffs between speed and accuracy, as well as where human oversight might be needed.

• Presentation and Reflection: 

  • Each group presents their ratio tables and graphs. 

  • They will also share reflections on how computers handle proportional calculations and where potential errors or misinterpretations might arise.

Equity and Access:

Provide examples with different levels of complexity and allow students to choose tasks based on their comfort level with ratios and graphing. Offer graphing templates for students who need additional support.

Real-World Application:

Relate this lesson to the ways proportional relationships are used in real life, such as in online navigation tools or scaling recipes for different-sized groups.

CS Practice(s):

• Recognizing and Defining Computational Problems: Students identify how real-world proportional problems can be translated into computational algorithms.

• Communicating about Computing: Students discuss how computers handle proportional relationships and the potential issues that arise without human oversight.

Standard(s):

• CA CCSS Mathematics 7.RP.2

• CA CS 6-8.IC.20

Objective:

Students will use spreadsheets to automate the creation of ratio tables and proportional graphs, exploring the tradeoffs between relying on technology for calculations and the need for human accuracy checks.

Materials Needed:

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

• Real-world ratio problems (e.g., recipes, distance-time problems)

Steps:

• Introduction: 

  • Introduce proportional relationships and explain how spreadsheets can be used to model these. 

  • Demonstrate how to set up a ratio table and create a formula for calculating unit rates in a spreadsheet.

• Group Activity: 

  • Students work in pairs to input data from real-world ratio problems into the spreadsheet. 

  • They will calculate unit rates and graph the proportional relationships using the spreadsheet’s graphing function. 

  • Encourage them to experiment with different quantities and ratios to see how the graph changes.

• Discussion on Technology: 

  • Facilitate a discussion about how using a spreadsheet simplifies the calculation process but also presents tradeoffs. 

  • Discuss the importance of human oversight in ensuring that formulas and data are correct and how automation can sometimes lead to errors if not checked.

• Presentation and Reflection: 

  • Groups will present their spreadsheet graphs and explain how they used formulas to calculate unit rates. 

  • They will reflect on the benefits and drawbacks of relying on technology for these types of proportional problems.

Equity and Access:

Provide step-by-step guides or templates for students who are unfamiliar with spreadsheets. Allow for differentiated tasks, with simpler or more complex proportional problems based on students’ experience levels.

Real-World Application:

Link the use of spreadsheets to common real-world applications, such as business cost calculations, budgeting, or online shopping tools that calculate costs based on quantity.

CS Practice(s):

• Creating Computational Artifacts: Students use spreadsheets to create computational artifacts that solve proportional problems.

• Testing and Refining Computational Artifacts: Students test their spreadsheet formulas to ensure accuracy and refine them as needed.

Standard(s):

• CA CCSS Mathematics 7.RP.2

• CA CS 6-8.IC.20