Movie parts

Purpose

The purpose of this unit is to engage students in applying their knowledge and understanding of fractions, decimals, and percentages when identifying and generalising a linear trend.

Students develop these skills, related to Multiplicative Thinking and Patterns and Relationships (e.g. understanding of proportion), in the context of film and television program timing.

Achievement Objectives
NA4-3: Find fractions, decimals, and percentages of amounts expressed as whole numbers, simple fractions, and decimals.
AO elaboration and other teaching resources
NA4-9: Use graphs, tables, and rules to describe linear relationships found in number and spatial patterns.
AO elaboration and other teaching resources
Specific Learning Outcomes

  • Apply knowledge of rates and ratios, and reasoning with linear proportions, to solve problems involving time.

  • Find and describe a rate of change for given data from a linear trend. 

  • Find and describe a linear trend.

Opportunities for Adaptation and Differentiation

The learning opportunities in this unit can be differentiated by providing or removing support to students, and by varying the task requirements. Ways to differentiate include:

  • roaming and supporting students in a variety of groupings to ensure they understand the task at hand, the skills needed to succeed, and can apply these skills in a suitable process
  • varying the amount of structured scaffolding and guided teaching you provide to students when investigating new tasks
  • providing opportunities for students to create their own problems, perhaps as word problems related to a shared, relevant context (e.g. advertisements they have seen on TV)
  • providing extended opportunities for students to revise and apply learning from throughout the unit
  • modelling the application of ideas at every stage of the unit
  • strategically organising students into pairs and small groups in order to encourage peer learning, scaffolding, and extension
  • allowing the use of calculators to reduce the cognitive load required in each task
  • working alongside individual students (or groups of students) who require further support with specific areas of knowledge or activities (e.g. identifying a rule, creating a graph).

The context of film and television is likely to be relevant to your students. However, the relevance of this learning can be enhanced by connections being made to literacy learning (e.g. the film used in a film study unit), to a topical event or subject, and to students’ cultures, interests, and lived experiences (e.g. by using a relevant, meaningful film).

The relevance of this learning can also be enhanced with the inclusion of key vocabulary from your students' home languages. For example, te reo Māori kupu such as pāpātanga (rate), ōwehenga (ratio), pānga rārangi (linear relationship), wā (time), pāpātanga o te whiti (rate of change), and ia (trend) might be introduced in this unit and then used throughout other mathematical learning.

Structure

Following the introductory session, each subsequent session in the unit is composed of four sections: Introducing Ideas, Building Ideas, Reinforcing Ideas, and Extending Ideas. It is recommended that you work through the first two of this sections with the whole class, before providing time for students to explore the latter two stages. This exploration might be structured as students working in small groups, students working alongside the teacher (perhaps until understanding is demonstrated), students working independently, or as students working in a variety of flexible groupings. Consider what structure will best suit, and respond to, the needs of your class, as demonstrated in the first stage of each session. 

Importantly, students should have multiple opportunities to, throughout and at the conclusion of each session, compare, check, and discuss their ideas with peers and the teacher, and to reflect upon their ideas and developed understandings. These reflections can be demonstrated using a variety of means (e.g. written, digital note, survey, sticky notes, diagrams, marked work, videoed demonstration) and can be used to inform your planning for subsequent sessions.

Required Resource Materials
  • Clips of relevant films, short films, TV commercials, 
  • Calculators
  • Graphing software
Activity

Introductory session

This session is intended to motivate students towards the context of filmmaking, and to inform teachers of students' knowledge and understanding. Students' engagement in this session can be increased by using it to complement the viewing of a relevant film (e.g. perhaps as part of a film study unit). Alternatively, you might find a relevant short film to show the class at the start of the lesson. These films will be used in this session, session two, and can be revisited in session six.

  1. After viewing the film, explain to students: An expert in filmmaking, Michael Hauge, suggests that most Hollywood movies follow the same structure. He says there are five turning points that occur in the same place in each film. These are:
  • The opportunity, occurs when the film is 10% of the way through.
  • The change of plans, occurs when the film is 25% of the way through.
  • The point of no return, occurs when the film is 50% of the way through.
  • The major set back, occurs when the film is 75% of the way through,
  • The climax, occurs when the film is 90% of the way through.
     
  1. Pose the following scenario to students: A group of students are planning to make a 24 minute film about a very short boy who, wants to go to the school dance, but is too shy to ask a short girl he is keen on outright so leaves a note in her locker, but then finds out they got the wrong locker and a different, very tall girl accepts the invitation. The climax is on the night of the dance, whether the short boy turns up to take his tall date to the dance or not. This scenario could be adapted to be of increased relevance to your students. Consider how the events in the proposed film reflect on the cultural diversity, interests, and lived experiences that are relevant to your class. The proposed film should have 5 elements (opportunity, change of plans, point of no return, major set back, and climax) with each comprising the proportions mentioned in point 1.
     
  2. As a class, use the Hauge model to plan the the 24 minute sequence. Discuss:
  • How many sections are there separated by the turning points?
  • What is the ratio of the sections of film separated by the turning points?
  • How could the structure of a film, with these five turning points be represented graphically.
  • If a feature film of two hours followed the same structure, when would each of the five turning points occur?
  • In reality, the turning points take time to unfold. Is there room in a short film for the five turning points?
  • Sometimes a film is criticised because ‘nothing ever happens’ or because it was ‘long and drawn out’. Discuss how the film may be structured, in terms of its turning points, if such criticism is justified.

Following this discussion, consider your students' demonstrated capability to manage percentages and find and express a ratio. In turn, this will allow you to locate students on the Multiplicative Thinking learning progression.

Session two

This session focuses on using rates and ratios, and reasoning with linear proportions, to solve a problem.

Introducing Ideas

  1. Pose the following task to students: Use the 5 turning point model for the structure of a film to identify how long a film will run for if the ‘change of plan’ occurs 20 minutes into the film. Remind students of the 5 turning point model is:
  • The opportunity, occurs when the film is 10% of the way through.
  • The change of plans, occurs when the film is 25% of the way through.
  • The point of no return, occurs when the film is 50% of the way through.
  • The major set back, occurs when the film is 75% of the way through,
  • The climax, occurs when the film is 90% of the way through.
  1. Discuss:
  • The structure is given as a percentage. How could this be used to show the number of minutes?
  • What proportion of the film has run when the change of plan occurs (20 minutes in)?

Building Ideas

  1. Pose the following task to students: Use the 5 turning point model for the structure of a film to say how long a film will run for in each of the following scenarios:
  • the ‘opportunity’ occurs 6 minutes into the film.
  • the ‘change of plan’ occurs 15 minutes into the film.
  • the ‘point of no return’ occurs 30 minutes into the film.
  • the ‘major set back’ occurs 45 minutes into the film.

Reinforcing Ideas

  1. Pose the following task to students: Use the 5 turning point model for the structure of a film to say how long a film will run for  in each of the following scenarios:
  • the ‘opportunity’ occurs 15 minutes into the film.
  • the ‘change of plan’ occurs 21 minutes into the film.
  • the ‘point of no return’ occurs 37 minutes into the film.
  • the ‘major set back’ occurs one hour into the film.

Extending Ideas

  1. Pose the following task to students: Use the 5 turning point model for the structure of a film to say how long a film will run for  in each of the following scenarios:
  • the ‘opportunity’ occurs 15 minutes before the ‘change of plan’.
  • the ‘change of plan’ occurs 21 minutes before the ‘point of no return’.
  • the ‘point of no return’ occurs 37 minutes after the ‘opportunity’.
  • the ‘major set back’ occurs one hour after the ‘opportunity’.

Session three

This session focuses on using rates and proportions to solve a time problem.

Introducing Ideas

  1. Pose the following task to students: One hour of television viewing time typically has only 14 minutes, 15 seconds of commercials. If there are three ad breaks in thirty minutes of television viewing and an average of five commercials per break, what is the average (mean) length of a commercial?  
  2. Discuss:
  • Summarise what we know from the problem.
  • What is the best way to go about solving this problem?  

Building Ideas

  1. Pose the following task to students: One hour of television viewing time typically has only 14 minutes, 15 seconds of ads. 
  • How many ads of 15 s can fit into this time? 
  • Is it possible to fill this time with only ads that are 30 seconds long?

Reinforcing Ideas

  1. Pose the following task to students: One hour of television viewing time typically has only 14 minutes, 15 seconds of ads. 
  • How many ads of 45 s can fit into this time?
  • If some ads are 45 s and some are 20 s, find at least two different ways that a combination of 45 s and 20 s ads could fit into the 14 minutes and 15 seconds of commercial time. 

Extending Ideas

  1. Pose the following task to students: One hour of television viewing time typically has only 14 minutes, 15 seconds of ads (advertisements). 
  • If some ads are 45 s and some are 20 s, find as many different ratios of 45 s to 20 s ads that could fit into the 14 minutes and 15 seconds of commercial time.

Session four

This session focuses on finding and describing a rate of change for given data from a linear trend.

Introducing Ideas

  1. Pose the following task to students: One hour of tv viewing time typically has 14 minutes, 15 seconds of commercials. 
  • Five years ago, television viewing averaged 13 minutes and 30 seconds of commercial time per hour.
  • Ten years ago, television viewing averaged 12 minutes and 45 seconds of commercial time per hour.
  • Describe the rate of change of commercial time, per hour of television viewing over the past ten years.  
  1. Discuss:
  • Is the commercial time increasing or decreasing?
  • What is the difference in the time spent on commercials during an hour of TV ten years ago, five years ago, now?
  • What is the rate of change in the time spent on commercials during an hour of TV?

Building Ideas

  1. Pose the following task to students: Using the data on the typical amount of time over an hour of television time given to commercials, find the average amount of programme time in an hour of television viewing:
  • now
  • five years ago
  • ten years ago.  

Reinforcing Ideas

  1. Pose the following task to students: Using the data on the typical amount of time over an hour of television time given to commercials: 
  • Find the change in average amount of programme time in an hour of television viewing between now and ten years ago.  
  • Find the rate of change, per year, of average amount of programme time in an hour of television viewing between now and ten years ago.

Extending Ideas

  1. Pose the following task to students: Using the data on the typical amount of time over an hour of television time given to commercials, write a rule to find the expected average amount of programme time in an hour of television viewing x number of years from now.

Session five

This session focuses on finding and describing a linear trend.

Introducing Ideas

  1. Pose the following task to students: Fifty years ago, the average length of a TV program promotional ad was one minute. Since then, the shortest length of such TV ads has decreased at a rate of one second per year.
  • What was the average length of a TV program promotional ad twenty years ago?
  1. Discuss:
  • Summarise what we know from the problem.
  • If a pattern is decreasing, how is this shown in the rate?
  • What would this pattern look like on a graph?

Building Ideas

  1. Pose the following task to students: The average length of a tv program promotional ad was one minute and since then, the shortest length of such TV ads has decreased at a rate of one second per year. Use this information to complete the table below:
Years ago302520151050
Average length of a tv promo ad       

Reinforcing Ideas

  1. Pose the following task to students: Construct a graph to show the the average length of a TV program promotional ad, given that fifty years ago, it was one minute and that the shortest length of such tv ads has decreased at a rate of one second per year. Use the graph to find the average length of a tv program promotional ad: 
  • Five years ago
  • today
  • In five years’ time. 

Extending Ideas

  1. Pose the following task to students: Write a rule to describe the average length of a TV program promotional ad for any given year over the last fifty years.
  • Can the average length of a TV program promotional ad continue to fall at the same rate (one second per year)? Why/ why not?

Session six

This session focuses on finding and describing a linear trend.

Introducing Ideas

  1. Pose the following task to students: Thirty years ago, the average length of a feature film was 108 minutes. The average length of feature films has been increasing at a steady rate so that now it is 130 minutes. At what rate (in minutes per year) is the average length of feature film increasing?

Discuss:

  • How did you find this rate?
  • Is it likely that the length of feature films will always been increasing at this rate? Why/ why not?
  • Is it likely that the length of feature films have always been increasing at this rate? Why/ why not?

Building Ideas

  1. Pose the following task to students: Thirty years ago, the average length of a feature film was 108 minutes. Now, the average length of a feature film is 130 minutes. Use this information to complete the table below:
Years ago302520151050
Average length of a feature film       

Reinforcing Ideas

  1. Pose the following task to students: Construct a graph to show the the average length of a feature film given that it has been increasing at a steady rate from 108 minutes thirty years ago, to 130 minutes today. Use your graph to find the average length of a feature film: 
  • Five years ago
  • today
  • In five years’ time. 

Extending Ideas

  1. Pose the following task to students: Write a rule to describe the average length of a feature film over the last 30 years.
  2. Using this rule, what would you expect the average length of a feature film to have been in 1980?
Home Link

Dear families and whānau,

Recently we have been investigating ratios, rates, percentages, graph construction, linear proportions, and trends and rules, in the context of film and television program timing. This week, your child has been asked to apply one of the tasks from our learning sessions to a television programme or film watched at home. Ask them to share their learning with you.

Printed from https://nzmaths.co.nz/resource/movie-parts at 8:12pm on the 25th April 2024