Venue Price Faceoff

Overview

Students act as event planners comparing two venue pricing plans. They build input-output tables, graph each linear relationship, identify the break-even point, and use equations and written evidence to recommend a plan for different event budgets. The lesson builds on recognizing slope, intercepts, and linear relationships.

Learning intentions

Students will be able to:

• Create equations in two variables from verbal pricing descriptions.
• Construct tables and graph linear relationships with labeled axes and appropriate scales.
• Find and interpret the break-even point for two pricing plans.
• Compare functions represented by equations, tables, graphs, and written descriptions.
• Justify a recommendation using mathematical evidence.

Success criteria

• I can define variables and write an equation for each venue plan.
• I can make an accurate table and graph with labeled axes and scales.
• I can explain what the intersection point means in the event-planning context.
• I can use calculations and written reasoning to recommend a plan for a specific budget.

Curriculum links

• Creating equations in two or more variables to represent relationships between quantities and graphing them on labeled coordinate axes.
• Recognizing situations in which one quantity changes at a constant rate per unit interval.
• Constructing linear functions from descriptions and tables.
• Comparing properties of functions represented algebraically, graphically, numerically, and verbally.

Lesson structure (30 minutes)

1. 0–4 min · Hook and predict. Display the opening question from the event-planning introduction deck: “Which venue is cheaper for a small event—and will that always be true?” Present two plans: Venue A charges a $300 rental fee plus $20 per guest; Venue B charges a $700 rental fee plus $10 per guest. Students predict which plan they would choose for 10 and 80 guests, explaining their initial thinking to each other.

2. 4–9 min · Build the models. Use the equation modeling slides to define (x) as number of guests and (y) as total cost. Guide students to write (y=20x+300) for Venue A and (y=10x+700) for Venue B. Students identify the rate of change and starting value in each equation, then calculate one value for each plan. Check that they understand why guest count is the input and cost is the output.

3. 9–16 min · Tables and graphs. Distribute the venue comparison worksheet. Students complete tables for 0, 10, 20, 40, 60, 80, and 100 guests, then graph both plans on the same coordinate grid. The teacher pauses to check axis labels, scale, plotted points, and whether each line begins at the correct y-intercept. Students use different colors or symbols and describe how the lines differ.

4. 16–21 min · Find the break-even point. Show the break-even prompt in the graphing and break-even slides. Students inspect their graph to estimate where the lines intersect, then solve (20x+300=10x+700) to verify the result. They find (x=40) and (y=1{,}100), and explain: at 40 guests, both venues cost $1,100; below 40 guests Venue A is cheaper, while above 40 guests Venue B is cheaper.

5. 21–27 min · Budget recommendations. Assign each student one scenario on the venue comparison worksheet: a 25-guest event with a $900 budget, or an 80-guest event with a $1,600 budget. Students calculate both costs, decide whether each plan fits the budget, and write a recommendation using at least two forms of evidence: an equation, table value, graph feature, or break-even interpretation. Students then present their recommendations to each other, challenging one calculation or asking for clarification.

6. 27–30 min · Plenary and exit check. Use the discussion and exit prompt to ask, “Why can the cheaper plan change as the number of guests increases?” Each student completes the final section of the venue comparison worksheet: “For 50 guests, which venue is cheaper, and by how much? Explain how you know.” Review answers immediately and address any misconception about slope, intercept, or the intersection.

Resources

• the event-planning introduction deck
• the venue comparison worksheet
• Graph paper or coordinate-grid worksheet
• Pencils, rulers, and two colored writing tools
• Calculator or approved graphing technology
• Whiteboard and markers
• Optional document camera for displaying student graphs

Assessment

• During modeling, ask students to explain the meaning of the coefficient and constant in each equation; listen for correct interpretations of rate and fixed fee.
• Check tables and graphs for accurate substitutions, labeled axes, consistent scales, and correctly plotted lines.
• Collect the worksheet exit response. Proficiency requires a correct comparison for 50 guests and a written explanation connected to an equation, table, graph, or break-even point.

Differentiation

• Provide a partially completed table, labeled axes, and the sentence frame “The coefficient of (x) represents ___, while the constant represents ___” for students who need support.
• Let students use a calculator or graphing tool after writing the equations, while requiring them to explain what the graph shows.
• For language support, preview “fixed fee,” “per guest,” “total cost,” “budget,” and “break-even,” and allow students to rehearse explanations orally before writing.
• For students ready for more challenge, ask them to determine the guest range in which each plan fits a $1,200 budget and justify the answer with an inequality.