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# Activity: Cell phone pricing plans

## Purpose

Compare and contrast cell phone pricing plans using linear algebraic models.

Learning to model real-life situations using mathematics, making assumptions, and simplifying the situation in order to model it.

## Achievement objectives

• NA6-7 Relate graphs, tables, and equations to linear, quadratic, and simple exponential relationships found in number and spatial patterns.

## Indicators

• Demonstrates understanding of linear relationships.
• Makes connections between representations such as number patterns, tables, equations and graphs.
• Identifies and uses key features including gradient and intercepts.

## Specific learning outcomes

Students will be able to:

• recognise the structure of linear relations in the formula, table, and graph
• understand and apply gradient and intercept to sketch and interpret straight lines
• understand that the gradient is the variable cost and y-intercept is a fixed cost in the formula, table, and graph
• understand intersection of lines is where both equations have the same charge for the same number of minutes
• link written information, formula, graph, and table to the situation
• generate written information, formulae, graphs, and tables
• make connections between the increment in the table, the gradient of the graph, and formula
• recognise parallel lines have the same gradients in the formula and graph, and the tables have the same increments.

## Diagnostic snapshot(s)

See in 'planned learning experiences' for information regarding diagnostic activity.

## Planned learning experiences

Rich starter/diagnostic activity
(This information will be used for the following activities.)

The purpose of this starter is to generate the plans to model, co-constructing the work with the students. The idea is to move from these concrete plans to the abstract ideas of linear relations.

1. As a group, find three cell phone plans that would best meet your needs (text, calls, data, etc).
2. State criteria/priorities/considerations for a cell phone plan. For example, the teacher could model this using an example of buying a house: price range, location, number of bedrooms, bath rooms, sun, not a leaky home etc.
3. Students present their three plans with pros and cons and a final decision on which one they would select and why. (Possible: have students debate their preferences.)

The students will see the complexity of the situations and appreciate the need to build simpler models to analyse the situation. (This is how mathematical modelling works.)

Building simple models
Look at calls and texts by themselves.

Question: How can we represent these plans so we can compare them?

Desired result: written information, formula, table, and graph:

• Consider fixed rates (horizontal lines).
• Understand and apply gradient and intercept to sketch and interpret straight lines.
• Understand that the gradient is the variable cost and y-intercept is a fixed cost in the formula, table, and graph.
• Link written information, formula, graph, and table to the situation.
• Generate written information, formulae, graphs, and tables.
• Make connections between the increment in the table, the gradient of the graph, and formula.

Compare simple models
Start with a simple model such as comparing a fixed rate with variable rates.

• Understand intersection of lines is where both plans have the same charges.
• Recognise parallel lines have the same gradients in the formula and graph, and the tables have the same increments.

How do we recognise linear relationships in written information, formula, graph, and table?

Building more complex models
(Combining text and calls, or other.)

Linking to other contexts that use linear modelling.

What other things are like cell phone plans:

• Tax rate
• Parcel post (bulk rate)
• Taxi fares
• Hire purchase

• Economics or personal finance
• Financial literacy

### Extension ideas

Recognise arithmetic sequences as examples of linear patterns.

## Planned assessment

This teaching and learning activity could lead towards assessment in the following achievement standard:

## Spotlight on

### Pedagogy

• Creating a supportive learning environment:
• Listening to and accepting all student responses as part of the learning process.
• Being aware of literacy implications of mathematical and statistical tasks.
• Enhancing the relevance of new learning:
• Providing appropriate levels of challenge.
• Encouraging students to explain their thinking.
• Facilitating shared learning:
• Appropriate groupings of students.
• Students working in groups.

### Key competencies

• Using language, symbols and texts:
• Process and communicate mathematical ideas.
• Relating to others:
o Work as a group, understand others thinking, accept and value differing viewpoints, negotiating meaning.

### Values

Students will be encouraged to value:

• innovation, inquiry, and curiosity, by thinking critically, creatively, and reflectively
• community and participation for the common good.

### Planning for content and language learning

• Begin with context embedded tasks which make the abstract concrete:
• How can I put these concepts into a concrete context?
• Provide multiple opportunities for authentic language use with a focus on students using academic language:
• Is the language focus on key language?
• Do I make sure the students have many opportunities to notice and use new language?
• Reinforce vocabulary of linear relationships via student discussion.

Digital learning objects

## Connections

• Lovitt, C., & Clarke, D. (1992). Algebra walk. MCTP professional development package: Activity bank volume 1 (p. 213). Carlton, Victoria: Curriculum Corporation.