Electricity

Which generator should the business owner choose?

Use your understanding of data and representational forms to help a business owner decide which generator is best for running a food truck.

Grade

Duration

40 mins

Type

Group work

Overview

Your class will use limited data to make initial recommendations about the purchase of a generator for a small business. Students then determine which representational form would be the most helpful, then use additional information and data to refine and confirm their initial recommendations

Instructions

What you'll need

"Choosing the best generator" worksheet, one for each student
"Generator data" handout, one for each group
"Determining the best ways to represent data" worksheet, one for each student
"Choosing the best generator" slideshow
Digital projector and screen

Organize students into pairs and provide each student with a copy of the "Choosing the best generator" worksheet and each group with a copy of the "Generator data" handout. Briefly review the challenge and then invite groups to use the data about the generators from the handout to make an initial recommendation to the food truck owner: Which generator should food truck owner purchase?
Invite groups to share their initial recommendations and thinking with the class.
Ask your students to suggest other mathematical representations or forms that could be used to present the data needed to make the recommendation (they should suggest algebraic equations and graphs). Use their suggestions to co-develop or present the criteria for determining the best form. The criteria would include:

Understandable: makes trends in the data easy to see and understand
Comparable: makes the cost of generators easy to compare
Informative: provides the information needed to make a decision

Organize your students into small groups (2-4 students) and provide each student with a copy of the "Determining the best ways to represent data" worksheet. Briefly explain that their task is to decide which representative form would be the best for helping the food truck owner make the decision.
Prompt groups to rate the two algebraic equations. Remind groups to use the criteria to guide their thinking, and to support their decisions with mathematical evidence.
Bring up the "Choosing the best generator" slideshow. Show slides 3 and 4, and ask groups to rate the two graphs (green = graph 1; blue = graph 2). Remind groups to use the criteria to guide their thinking, and to support their decisions with mathematical evidence.
Show slides 5 and 6. Briefly review the information with students, and then ask groups to decide which representative form would be the best for helping the food truck owner make the decision. Encourage groups to share their decisions and thinking with the class.
Encourage students to individually revisit the "Choosing the best generator" worksheet and their initial recommendations about the purchase of the generators. Invite them to make revisions and additions based on their new learning.
To conclude the activity, ask students to suggest how the ideas and concepts from this activity could be used by other people in the province. For example, students might suggest that the information could be used to prepare households for emergencies, or by remote communities needing back-up power sources.

Curriculum Fit

Math 11

Big Idea

Optimization informs the decision-making process in situations involving extreme values.

Content

Graphical analysis (using technology only)
- Quadratic functions (characteristics including end behaviour, max/min; vertex; symmetry and intercepts)
- Systems of equations including linear with linear; linear with quadratic; and quadratic with quadratic)
- Optimization (maximizing and minimizing quantities in authentic contexts)

Curricular competencies

Reasoning and modelling

Explore, analyze, and apply mathematical ideas using reason, technology, and other tools
Estimate reasonably and demonstrate fluent, flexible, and strategic thinking about numbers
Model with mathematics in situational contexts
Think creatively and with curiosity and wonder when exploring problems

Understanding and solving

Develop, demonstrate and apply mathematical understanding through inquiry and problem-solving
Visualize to explore and illustrate mathematical concepts and relationships
Apply flexible and strategic approaches to solve problems
Solve problems with persistence and a positive disposition

Communicating and representing

Use mathematical vocabulary and language to contribute to discussions in the classroom
Explain and justify mathematical ideas and decisions in many ways
Represent mathematical ideas in concrete, pictorial, and symbolic forms
Take risks when offering ideas in classroom discourse

Connecting and reflecting

Reflect on mathematical thinking
Connect mathematical concepts with each other, other areas, and personal interests
Use mistakes as opportunities to advance learning

Assessments

Assess your students’ ability to:

Use their understanding of the properties of quadratics to gather evidence and assess the various representational forms;
Use criteria to assess the representational forms (for example, it is more informative; more easily understood to see the details visually; and easier to compare by finding the points of intersection to solve the problem in the given context).
Self-correct and extend their thinking from the beginning of the lesson to the end
Use appropriate vocabulary and representational forms to make recommendations when considering quadratics (e.g., max/min, x-intercepts, vertex, symmetry)
Pay close attention to appropriate details

Students’ final recommendations to the owner of the food truck could also be used as an “exit ticket” to gather assessment evidence of learning.

Teaching Notes

This lesson will work best if students had previously learned about the properties of quadratics, and the various representations of quadratic functions.
Ensure students recognize the necessary restrictions placed on graphs; tables of value; equations within real world contexts.
Highlight how different measures of power; watts vs MWs, are used in the additional information and in the table of values and graphs. Support student with conversions if necessary.
Encourage students to make assumptions where necessary (for example, size of food truck)
Avoid telling students that they should solve Systems of Equations to address the problem; allow students to make this connection when they receive the graphs (and algebraic solution if you wish the students to do this) to solve for points of intersection.