School name / Meridian School / School code / 922775
Name of the DP subject / Math SL 1, Math SL 2
Level
(indicate with X) / Standard completed in two years / Standard completed in one year*
Higher / Standard completed in two years / X / Standard completed in one year*
Standard completed in two years / Standard completed in one year*
Name of the teacher who completed this outline / Mark Rogers / Date of IB training / 23/6/2012 - 26/6/2012
Date when outline was completed / 9/7/2012 / Name of workshop
(indicate name of subject and workshop category) / FLIBS - Cat. 1
* All Diploma Programme courses are designed as two-year learning experiences. However, up to two standard level subjects,excluding languages ab initio and pilot subjects, can be completed in one year, according to conditions established in the Handbook of procedures for the Diploma Programme.
- Course outline
–Use the following table to organize the topics to be taught in the course. If you need to include topics that cover other requirements you have to teach (for example, national syllabus), make sure that you do so in an integrated way, but also differentiate them using italics. Add as many rows as you need.
–This document should not be a day-by-day accounting of each unit. It is an outline showing how you will distribute the topics and the time to ensure that students are prepared to comply with the requirements of the subject.
–This outline should show how you will develop the teaching of the subject. It should reflect the individual nature of the course in your classroom and should not just be a “copy and paste” from the subject guide.
–If you will teach both higher and standard level, make sure that this is clearly identified in your outline.
Topic/unit(as identified in the
IB subject guide)
State the topics/units in the order you are planning to teach them. / Contents / Allocated time / Assessment instruments to be used / Resources
List the main resources to be used, including information technology if applicable.
One class is / minutes.
90
In one week there are / classes.
2
Year 1 / Circular Functions and Trigonometry: 1st 9-weeks /
- The Unit Circle
- Trig ratios
- Pythagorean Identity
- Circular Functions
- Solving Trig equations
- Triangles in Trig
Functions and Equations: 2nd 9-weeks /
- Function Notation
- Technology & Graphing
- Transformations
- Quadratics
- Reciprocal and Rational
- Exponential & Logarithmic
Vectors: 3rd 9-weeks /
- Vector representation & manipulation
- Scalar products, Perpendicular/Parallel
- Vector equations and Angles
- Coincidence & Intersection
Algebra: 4th 9-weeks /
- Sums, series, and their ties to Calculus
- Exponents and Logarithms
- Binomial theorem and Pascal’s Triangle
Year 2 / Calculus: 1st and 2nd 9-weeks /
- Limits
- Derivatives
- Maximum and Minimum
- Integration
- Definite Integrals
- Application of Calculus
Statistics and Probability: 3rd and 4th 9-weeks /
- Data presentation for samples
- Measuring data
- Cumulative frequency
- Correlation
- Experimental vs. Theoretical
- Conditional Probability and Independent Events
- Discrete Random Samples
- Binomial Distribution
- Normal Curve
Internal Assessment: From 4th 9-weeks Year 1 to 2nd 9-weeks Year 2 /
- Topic Investigation
- Initial Draft
- Final Draft
- IB internal assessment requirement to be completed during the course
Briefly explain how and when you will work on it. Include the date when you will first introduce the internal assessment requirement to your students, the different stages and when the internal assessment requirement will be due.
As a class, we will begin exploring topics in April 2015 which corresponds to the second of four Math SL semesters. I will encourage them to list stimuli on their desks describing real-world activities or subjects that interest them. If a student struggles to find a stimulus, I will provide a range of topics to assist. During this initial exploration, students will review sample internal assessments from years passed in order to investigate the assessment criteria.From one selected stimulus, the student will then branch foci around that selected stimulus to help narrow down an explorable topic. At this point, the student will create an outline to help organise the focus of their internal assessment. By May of 2015, Math SL students will all have the outlines completed in order for drafting to begin on their summer holidays.
In September of 2015, which corresponds to the third of four Math SL semesters, students will have an opportunity to self-assess their work in order to create a more polished draft. These drafts will be given to me for review. I will have individual meetings with each students to discuss their drafts and provide further commentary for improvement.
By November of 2015, students will have a finished draft for me to mark.
- Links to TOK
You are expected to explore links between the topics of your subject and TOK. As an example of how you would do this, choose one topic from your course outline that would allow your students to make links with TOK. Describe how you would plan the lesson.
Topic / Link with TOK (including description of lesson plan)Statistics and Probability: Conditional Probability and Independent Events / Given the idea that disease testing cannot be 100% accurate, what are the ethical implications for giving these tests and stating a certain degree of sensitivity?
Engage: Students will see medically applicable scenarios of different diseases and the implications of false positives and false negatives. Examples will include STDs, Lyme disease, and cancer. Students’s emotional centres will ignite with the thought of disease testing as the primary way of knowing.
Explore: Students will conduct an experiment idiosyncratic of our school where a disease outbreak occurs and medical testing occurs. Students will “test” others for the disease, find those infected, then calculate false positives and false negatives. Students will use reasoning as a primary way of knowing during this testing.
Explanation: Students will explain the math behind their ability to decipher the results as well as interview those who received “false negatives” and “false positives” to gauge their emotional reactions.
Elaboration: Students will apply this new knowledge to other types of diseases, run statistical analyses, and look for articles describing people who have suffered through false positives and false negatives along with the harm caused by the incorrect prognosis.
Evaluation: Students will assess their knowledge by balancing the existence of false negatives and false positives with the benefits inherent of testing. Their expertise will be gauged when they record themselves teaching the mathematical and ethical areas of knowledge from this lesson to the online community.
- International mindedness
Every IB course should contribute to the development of international mindedness in students. As an example of how you would do this, choose one topic from your outline that would allow your students to analyse it from different cultural perspectives. Briefly explain the reason for your choice and what resources you will use to achieve this goal.
Topic / Contribution to the development of international mindedness (including resources you will use)Functions and Equations: Exponential and Logarithmic / Exponential functions almost categorically rely on empirical data in order for students to completely understand the topic. One of my favourite, real-world applicable examples of exponential functions lies in its usefulness in predicting populations. I will foster international mindedness by using human population growth in Europe, Africa, and Asia with comparisons throughout. In addition to learning the underlying mathematical concepts behind Exponential Functions, students in my class will understand the similarities and differences among our neighbours in different continents.
I will require data going back 300 hundred years in each of the three continents as well as the individual countries. This is available in country and continent specific census data. I will also tie this lesson into the concept of Exponential Regression seen in Statistics, so we will be using Ti-84 plus graphing calculators as a resource. Students can export this data to a computer spreadsheet and compare their interpolations and extrapolations with expert analysis from around the globe.
- Development of the IB learner profile
Through the course it is also expected that students will develop the attributes of the IB learner profile. As an example of how you would do this, choose one topic from your course outline and explain how the contents and related skills would pursue the development of any attribute(s) of the IB learner profile that you will identify.
Topic / Contribution to the development of the attribute(s) of the IB learner profileCalculus: Derivatives / Because of the perceived and actual difficulty surrounding this topic, students will automatically feel as if they are in the role of a risk-taker. One assessment I will utilise when introducing this topic is in the form of a student-created, online tutorial video. Students will research, practice, devise, film, edit, and publish a video that shows them teaching a lesson on Derivatives.
Given that a student would have just been introduced to this concept, they will see this as a definite risk. Conquering their self-created lesson in this format will develop them as a communicator and encourage them to continue taking risks in the future. Because students will be working with their peers both within the classroom and across the world, they also become open-minded with an increased appreciation for internationalism.
- Resources
Describe the resources that you and your student will have to support the subject. Indicate whether they are sufficient in terms of quality, quantity and variety. Briefly describe what plans are in place if changes are needed.
Technology: Ti-84 plus (class set sufficient for student use): Ti-84 plus has native features allowed on the external assessment that will assist students. The most important, “Catalog Help,” explains calculator functions to students in plain language and will be a great help to my IB students.MacBook (1/3:1 computer to student ratio is sufficient): MacBooks allow my students access to a bevy of online resources, advanced spreadsheet computing power, and graphical representations of numbers.
Video Cameras (2 per grade are sufficient for filming): Video Cameras give my students opportunities to practice, teach, film, and edit short tutorial videos. This resource allow my students to become experts in content areas and gain exposure to IB Math in different ways.
Editing Software and Equipment (MacBooks have native, high-quality editing software): This resource will give students ancillary mathematical skills related to technology. They will edit the movies and tutorial videos made for math class and share with the class.
iPads (1/3:1 iPad to student ratio is sufficient): This provides an alternative to the MacBook and provides more technology resources to our students. Students also create mathematical apps related to our IB Math SL curriculum.
Reference Materials: Mathematical Ideas by Miller, Heeren, and Hornsby (1 book used as teacher resource is sufficient); Mathematics Standard Level for the IB Diploma by Smedley and Wiseman (class set sufficient for student use); Mark Rogers’s real-world applicable problems (I create math problems related to my past experience as an entrepreneur)
People: Rick Fernandez (administrative assistance); Sue Cox and Kay Williams (IB Math SL trainers); Lucia Harvilchuck (IB TOK trainer). All personnel sufficient for success.
Contingency Plans: In the event we need to change, our status as a charter school allows for the ability to be nimble. Our resources have been sufficient to see students succeed, but additional fundraising boosted our MYP resources by more than $20k. Due to our community support, quality staff, and ability to execute changes quickly as a charter school gives me every reason to believe we will succeed no matter the circumstances.
ASSESSMENT WEIGHTING
EXTERNAL / ASSESSMENT / Percentage / Timeframe / Ways Students Will PreparePaper 1 / 40% / 4th Semester / Released IB Non-calculator questions, teacher-prepared assessments,
Paper 2 / 40% / 4th Semester / Released IB Calculator questions, teacher-prepared assessments
TOTAL / 80%
INTERNAL / ASSESSMENT
Mathematical / Exploration / 20% / 2nd and 3rd Semester / Sample Internal Assessments from past years, topic investigation, initial drafts, student-instructor meeting
TOTAL / 20%
1