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Note that the number of classes given for each topic is not including tests. Unit 1 and 2 should be tested together, and unit 13 will not necessarily include a test at all. Where possible the tests should be cumulative ( so the test on unit 9 should include unit 7 and 8 in it ) as the final assessment for this course is cumulative.
There are investigations in almost every chapter of the Haese and Harris textbook. Doing some of these investigations or assigning them as homework will help prepare our students for their projects next year.
Vocabulary is a big part of this course. Having a vocabulary wall, or a "word a week" might be one way to help the students learn the necessary vocabulary.
Many of the word problems in this course are possible SAT questions. Since many 11th grade students will be taking their SAT's, good examples of these word problems will help them tremendously.
The amount of time students are allotted for questions on their IB exams are usually indicated by the number of points the question is worth. A small amount of points for something like 'standard deviation' indicates the use of the calculator is expected. Unlike the SL and HL courses, the calculator is an important part of the final exam. Students are expected to be very familiar with their calculators.
UnitTopicsResources/Ideas#1 Number sets and properties
( 3 classes)- Set language
- Number sets
- Exponential notation
- Factors of natural numbers
- Multiples of natural numbers
- Order of operationsChapter 1 in Haese and Harris
- This information should mostly be review. We allow a 'soft opening' into the course because of the people who start the year late.
- Students find the number sets particularly tricky and will forget them immediately. Reviewing these sets as the year progresses will help the students immensely (since these sets are nearly always tested).#2 Measurement
( 4 classes )- Time
- Temperature
- Imperial standard units
- Standard form (Scientific notation)
- Rounding numbers
- Significant figures
- Accuracy of measurement
- Error and percentage errorChapter 2 in Haese and Harris
- Our students have difficulty with the imperial units because of their unfamiliarity.
- On last year's final exam more than 50% of the students lost marks because of significant figures and rounding errors.
- Error and percent error are no longer absolute values.#3 Linear and Exponential Algebra
( 8 classes )- Algebra substitution
- Linear equations
- Fractional equations
- Formula rearrangement
- Simultaneous equation
- Index notation and laws
- Exponential equations
- Problem solvingChapter 6 in Haese and Harris
- Useful to show the students how to solve these equations on their calculators.
- Students are not expected to know logarithms. They may be a convenient way to solve exponential equations, but too tricky for the students.
- Simultaneous equations are often used with word problems, and are one of the few 'presumed knowledge' topics which is always tested.#4 Coordinate Geometry
( 7 classes )- Distance formula
- Gradient/Slope
- Applications of gradients
- Midpoints
- Vertical and horizontal lines
- Graphing lines
- Midpoints and perpendicular bisectorsChapter 7 in Haese and Harris
- Showing students how to solve a lot of these problems graphically is a good idea. Also should point out the relationship between the distance formula and Pythagoras.
- Using the midpoint and distance formula to 'prove' facts about polygons drawn in the coordinate plane is a good exercise. For example: prove ABCD is a rhombus (given the coordinates of ABCD).#5 Quadratic Algebra
( 6 classes )- Products and expansions
- Factorizations of quadratic expressions
- Quadratic equations
- Completing the square
- Optional: The quadratic formula
- Problem solvingChapter 8 in Haese and Harris
- Show the students how to solve these equations on their calculator (either graphically or using the solver).
- The word problems here for our students are really difficult so numerous examples are a good idea.
- The quadratic formula is optional but some students find the easiest way to solve straight forward equations.
- Students are expected to be able to solve by factoring, but working backward from the solution found using a different method is acceptable.#6 Sequences and Series
( 8 classes )- Sequences of numbers
- Arithmetic sequences
- Geometric sequences
- Series
- Growth and decayChapter 12 in Haese and Harris
- Students find the relationship between n and EMBED Equation.DSMT4 to be difficult.
- Make sure to use the notation and terminology that is similar to the formula sheet.
- The relationship between geometric series and compound interest should be handled in the Financial mathematics unit.
- Show students how to solve some problems using the table feature of their calculator.#7 The Rule of Pythagoras
( 5 classes )- EMBED Equation.DSMT4
- Pythagoras and 3 dimensional figures
- The converse of the Pythagorean theorem
- Bearings and navigation
- Pythagoras in 3D
- Problem solvingChapter 4 in Haese and Harris
- This is review for most of the students.
- Focus on understanding the 3D diagrams.
- Lots of word problem examples are a good idea here.#8 Numerical Trigonometry
( 6 classes )- Right angled trigonometry
- RAT in 3D
- Areas of triangles
- Cosine rule
- Sine rule
- Problem solvingChapter 10 in Haese and Harris
- SOHCAHTOA
- Lots of word problem examples.
- Ambiguous case of the Sine law is NOT part of the IB curriculum.#9 Perimeter, Area and Volume
( 4 classes )- Conversion of units
- Perimeter
- Area
- Compound figures
- Surface area
- Volume
- Density
- Problem solvingChapter 11 in Haese and Harris
- Students find conversion of units difficult, especially when the units are for area or volume.
- Show students how to break down the formulae for cones and cylinders for problems with 'open' ends.
- Word problems are tricky for the students here so lots of examples are a good idea.#10 Sets and Venn diagrams
( 5 classes )- Set builder notation
- Union and intersection of sets
- Complements of sets
- Venn diagrams
- Problem solvingChapter 3 in Haese and Harris
- The notation for union and intersection of sets comes from chapter 1 first unit.
- Students find the shading of Venn diagrams tricky. There are some useful web applets out there try http://unitorganizer.com/javascript/venndiagrams/
- Word problems tricky here, lots of examples are a good idea.#11 Financial Mathematics
( 5 classes )- Foreign exchange
- Simple interest
- Compound interest
- Depreciation
- Loans
- Inflation
- Using the calculator
- Problem solvingChapter 13 in Haese and Harris
- To help students with foreign exchange, focus not on the multiplication or division required, but on recognizing the relative values of the currency so the students understand if their answer is reasonable.
- Vocabulary here is tricky for some students.
- Students often have difficulty substituting the correct values into the compound interest equation.
- Make sure students know how to use the Financial mathematics application on their calculator. This is expected of them for the IB exam.#12 Exponential and Trigonometric functions
( 10 classes )- Evaluating exponential functions/expressions
- Graphing exponential functions
- Exponential growth/decay
- Periodic functions
- The graphs of Sine and Cosine
- Modelling using exponential, Sine and Cosine functions
- Equations involving Sine and Cosine
- Problem solvingChapter 16 in Haese and Harris
- Lots of scope to include fun investigations and experiments in this chapter.
- This is one of the best chapters for introducing modelling which is useful for students' projects next year.
- Using Geogebra for graphing the functions is good, and this is an excellent unit for learning how to use the program. Many students find this superior to using their calculators. Note that they still need to know how to use their calculators to solve some numerical problems.
- Word problems are difficult here so lots of examples are a good idea.#13 Descriptive Statistics
( 6 classes )- Describing data and types of variables
- Presenting and interpreting data
- Frequency distribution tables
- Outliers
- Measuring the spread of data
- Box-and-whisker plots
- Standard deviation
- Statistics on the calculator
- Problem solving/InvestigationChapter 5 in Haese and Harris
- This final chapter should be assessed using the investigation on page 154/155 of the Haese and Harris textbook. This will help prepare them for their projects next year, should they choose a statistics project. The assessment criteria for this sample project should match those of the IB Mathematical Studies project.
- Students will be familiar with most of the material in this chapter and so will be over-confident. They will not have understood the nuances of the material, so some complex examples should be chosen to highlight these nuances.
- Students MUST be able to use their calculator efficiently to do these problems, they are never expected to work any of these out by hand (with the possible exception of some word problems involving the mean).
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