Objective:
The main objective of the video is that the learners will be able to explain why an expression cannot be divided by zero and to recognize what values of a variable are non-permissible for an algebraic expression.
The content of the video is to meet the requirements for Outcome P20.3 in the Pre-Calculus 20 curriculum:
Expand and demonstrate understanding of rational expressions and equations (up to and including degree 2 numerators and denominators) including:
- equivalent forms of expressions
- operations on expressions
- solving equations that can be simplified to linear or quadratic equations.
More specifically, the video is to meet indicators P20.3b and P20.3c
P20.3b - Verify, with explanation, whether or not a given value is permissible for a given rational expression.
P30.3c - Develop, explain, and apply strategies for determining the non-permissible values of a rational expression.
Also, the project aligns with the the philosophy behind the new mathematics curriculum encouraging students to make decisions based upon their prior learning (dividing), ability to develop number sense (does it make sense to divide by zero?), logical thinking (finding non-permissible values of the denominator by sight and by factoring), and their understanding of mathematics as human endeavor will also be considered in the planning behind the material presented.
Needs Assessment:
The new mathematics curriculum requires that students not memorize mathematical principles but understand mathematical concepts. Students typically have a difficult time with the topic of division and their reliance on algorithms and lack of understanding of the concept becomes very evident in Pre-Calculus 20.
The principle of dividing by 0 is introduced in Pre-Calculus 20 and is a major component in Pre-Calculus 30 and Calculus 30. The intent is to present the students with a learning resource early on that will help them to understand the concept by using a simple, real-life example acted out on film. The purpose of the video is to help understand the facts that 0/# = 0 and that #/0 = undefined.
The video will show learners using a dramatic re-enactment what dividing by zero means using an example such as withdrawing money from a bank, relating the current topic to their prior knowledge. After that, the students will apply the principle of dividing by zero by recognizing non-permissible values of the denominator. The aim is to introduce new vocabulary such as “non-permissible values of the denominator”, “infinity versus undefined”, and “vertical asymptote” in an introductory fashion.
Audience Analysis:
The intended audience is primarily for Pre-Calculus 20 students in grade 11. I would like to design the video in such a way, however, that it can be used in teachable moments in grades 9 or 10 when students wonder why dividing a number by 0 in their calculator gives them an error. At this point the instructor could show the video to the grade 9 or 10 students and stop before the discussion on non-permissible values starts.
The introductory dramatic portion would be acted out in such a way that a student would require minimal knowledge of “pre-calculus” principles in order to understand the topic. The issue is that many texts over-complicate this topic by introducing mathematical jargon right away. The intent is to hook the students with a humorous yet accurate depiction as to why an expression cannot be divided by 0.
Another target audience for the video are adult learners going back to school learning pre-calculus after a long period away from mathematics. A real-life demonstration explaining how you cannot divide by zero would also be beneficial to mature learners who lack confidence in understanding somewhat difficult concepts.
Content:
The video will be 5 - 10 minutes long and feature myself as well as extras who are yet to be determined. The video will be filmed at Clavet School after school hours.
The video will include a dramatic explanation as to what happens when a person goes into a bank and makes withdrawls in their account until the account is empty. The second scenario will explain what happens if a person goes into a bank but takes no money out - driving home the relationship to dividing by 0. The third scenario will describe what happens when 0 is divided by any other number (except 0, a topic saved for Calculus 30).
The video will explain why students need to learn this topic (in order to draw complicated graphs later on). A graph will be used to explain why the result of dividing by zero is referred to as being undefined (rather than “infinity”) but graphing is not the main purpose of the video. The concept will then be applied to an algebraic principle called “non-permissible values of the denominator”. The students will then algebraically apply the principle to find non-permissible values in rational expressions. The instructor (myself) will give explanations either directly, by voice-over, or by other participants. In order to turn a somewhat dry topic into something a bit lighter, various filming techniques, angles, computer-generated graphics, and humour will be used. Parts of the video will be reportorial style narrative as well.
Evaluation:
Supplementary activities such as a worksheet will be provided as an exercise to go along with the video activity.
Costs
No extra costs are to be associated with making the video.
Renting a facility will not be an issue since I will be using Clavet School, where I work to film.
Regarding to talent costs, I will be using volunteers or members from ETAD 879.6 as potential extras. Consent and release forms as appropriate will be distributed and collected.