Stmaryhigh.com



Rationale

To provide students with the opportunity to further their knowledge, skills, and attitudes related to Mathematics.

The focus of the Mathematics Curriculum:

❖ Using Mathematics to confidently solve problems

❖ Using Mathematics to better understand the world around us

❖ Communicating

Content Strands in the Mathematics Curriculum

❖ Overall and specific expectations in Mathematics are organized into eight strands, which are the eight major areas of knowledge and skills in the Mathematics Curriculum. and reasoning mathematically

❖ Appreciating and valuing Mathematics

❖ Making connections between Mathematics and its applications

❖ Becoming mathematically literate and using Mathematics to participate in, and contribute to society

A. Number Theory E. Relations, Functions and Graphs

B. Measurement F. Statistics and Probability

C. Geometry and Trigonometry G. Consumer Arithmetic

D. Algebra H. Vectors and Matrices

Process Strands in the Mathematics Curriculum

The mathematical process expectations are to be integrated into student learning associated with all the content strands.

▪ Communicating – communicate mathematical thinking visually, orally and in writing; using mathematical vocabulary and appropriate representations to express their understanding.

▪ Problem Solving – develop and apply problem-solving strategies to solve problems and conduct investigations to help improve mathematical understanding.

▪ Connecting – connect mathematical ideas to other concepts in Mathematics, to everyday situations and to other disciplines (e.g., other curriculum areas, daily life, current events, art and culture, sports).

▪ Reasoning and Proving – develop and apply reasoning skills (e.g., recognition of relationships, generalization through inductive reasoning, use of counter-examples) to justify conclusions and construct mathematical arguments.

▪ Selecting Tools and Computational Strategies – select and use technologies as tools to investigate mathematical ideas and to solve problems.

▪ Reflecting – demonstrate reflection to help clarify understanding by: assessing the effectiveness of strategies and processes used; proposing alternative approaches; judging the reasonableness of results; and verifying solutions.

Roles and Responsibilities in Mathematics Education

Students’ Responsibilities

1) View Mathematics as a language that helps them to organize and understand their world.

2) Build on personal experiences and prior learning to understand mathematical concepts and apply them to real life.

3) Participate actively, think critically and communicate effectively about mathematical reasoning and solutions.

4) Use technology, literature and connections to other disciplines to better understand Mathematics and support mathematical literacy.

5) Seek extra help, extracurricular activities and other assistance to ensure success in Mathematics.

Teachers’ Responsibilities:

1) Develop appropriate instructional strategies to help students achieve the curriculum expectations.

2) Create supportive classrooms to facilitate students attaining high standards and developing mathematical literacy.

3) Plan lessons to accommodate students with varying learning needs, abilities and interests.

4) Use effective teaching strategies, available materials, tools and technologies to engage students in learning Mathematics.

5) Challenge student to think critically, communicate their understanding and solve problems.

6) Use formative and summative assessments to monitor student achievement and adjust instruction.

Parents’ Responsibilities:

1) To become familiar with the curriculum, know what is being taught in each grade and what their child is expected to learn.

2) To discuss schoolwork with their child, to communicate with teachers, and to ask relevant questions about their child’s progress in Mathematics.

3) To provide their child with the necessary materials and tools to promote the learning of Mathematics.

4) To encourage the child to complete assignments completely and on time.

|Unit 1, 6 weeks September week1 October week2 |

|Topic/Sub-topic |Objectives |Learning activities |Resources |Assessment |

|Consumer Arithmetic |Students should be able to: | | | |

| |1. solve problems involving: | |Worksheets | |

| |(a) salaries and wages; |Individual research |Projector / catalogues |Worksheet on: |

|The Consumer: Working and Earning paying |Discuss some sources of income: | |Worksheet |Salaries and Wages and commission |

|taxes |full or part-time employment to an employer; | |CSEC past paper questions | |

|Salaries |self-employment ( trade, profession, informal vending) | |Textbook –Vol-2 |Income tax and sales tax |

|Wages |formal business ventures (concept of entrepreneurship) | | | |

|Commissions | |Discussing and analyzing different advertisements from | |Profit and loss, Discount and Hire |

|(d)Income tax |Money earned: |catalogues based on hire purchase versus the cash price. |Scientific calculator |Purchase |

|(sales tax) |distinction between wage and salary; | | | |

| |computation of regular wage for a fixed | | |Simple and compound interest and |

| |time, at a fixed rate; |Discussion of the terms | |Depreciation |

|Trading: Buying and selling transactions |computation of monthly or yearly salary |Discussion of past paper questions | | |

| |commission at agreed rate | | | |

|Profit and loss |total income over a specified time and | |Utility bills |Currency conversion worksheet and |

|Discounts |average income per week/month over a | | |Utility bills |

|Hire purchase |given time | |Shopping bills | |

| |(vi) additional wages for | | | |

|Money Management |- ‘overtime’ work ( time & half and | | | |

|Simple and Compound interest |double time rates); | | | |

|Appreciation and depreciation |- tips and computation of extra wages; |Discussing and analyzing selected utility bills. | | |

|Currency conersion |(vii) understanding and use of concepts: | | | |

| |- gross and net pay, | | | |

| |- deductions, allowances | | | |

| |- taxable income, | | | |

| |- income tax | | | |

| | | | |In class unit test |

| |2. calculate: | | |( multiple choice and mixed short |

| |(a) profit | | |answer questions) |

| |(b) loss; |Discussion of terms | | |

| |(c) percentage profit | | | |

| |(d) percentage loss; | | | |

| |3. express a profit, loss, discount, | | | |

| |markup and purchase tax, as a | | | |

| |percentage of some value; | | | |

| |4. solve problems involving marked | | | |

| |price, selling price, cost price, profit, | | | |

| |loss or discount; | | | |

| | | | | |

| |5. solve problems involving payments by installments as in the case of hire purchase solve | | | |

| |problems involving simple | | | |

| |interest; | | | |

| |Principal, time, rate, amount. | | | |

| |6. solve problems involving | | | |

| |compound interest; |Discussions of terms | | |

| |Formulae may be used in computing compound | | | |

| |interest. The use of calculators is encouraged. | | | |

| |7. solve problems involving | | | |

| |appreciation and depreciation; | | | |

| |8. solve problems involving | | | |

| |Currency conversion and utility bills. | | | |

| | | | | |

| | | | | |

|UNIT Two (6 Weeks) |

|Topic/Sub-topics |Objectives |Learning Activities |Resources |Assessments |

|Geometry and Trigonometry |Students should be able to: | | | |

| | | | | |

|Trigonometry ratios |Solve questions involving right-angled triangles using the trigonometric ration sine, cosine and |Representing worded problems by means of|Laptop |Trigonometric ratio work sheet |

|Review Grade 9 Sub-topics |tangent. |diagrams |Projector | |

| | |Practice related question from CSEC past|Worksheet | |

| | |paper |CSEC past paper questions | |

|Sine Rule and Cosine Rule | | |Textbook –Vol-2 |Trigonometric Rules Test |

| |Prove the sine rule. |Discussion on how to determine the |Scientific calculator | |

| |Determine when to use the sine rule |bearing of a point from another | | |

| |Use sine rule to solve non-right angle triangles. |Representing worded problems by means of|Compass | |

| |Use the cosine rule to solve non-right angle triangles |diagrams |Ruler | |

| |Use sine rule and cosine rule to solve problems involving triangles. |Practice related question from CSEC past| |Bearings Class work |

| | |paper | | |

| | | | | |

| | | | | |

|Bearing | | | | |

| |Represent the relative position of two points given the bearing of one point with respect to the | | | |

| |other. | | | |

| |Determine the bearing of one point relative to another point given the positions of the points. | | | |

| |Apply the sine and cosine rules to solve problems involving bearings. | | | |

| |Solve practical problems involving heights and distances in three dimensional situations. | | | |

| |

| |

| |

|UNIT Three (9 Weeks) |

|Topic/Sub-topics |Objectives |Learning Activities |Resources |Assessments |

|Algebra | | | | |

|Review Grade 9 Sub-topics |. | | | |

| |solve quadratic equations | | | |

| |algebraically by | | | |

| |Formula, methods of factoring and completing the square. | | | |

| | | | | |

| | | | | |

| |Solve a pair of equations in two variables when one equation is quadratic or non-linear and the other | | | |

| |is linear | | | |

| |rewrite a quadratic | | | |

| |expression in the form | | | |

| |a(x + h)2 + k | | | |

| | | | | |

| |Represent direct and indirect variation symbolically | | | |

| | | | | |

| |Solve problems involving direct variation and inverse variation | | | |

| | | | | |

| | | | | |

| | | | | |

|Relations, Functions and Graphs | | | | |

|Relations |Explain concepts associated with relations: |Discussion of the terms | | |

| |Concept of a relation |Practice evaluating functions from past |Projector | |

| |Types of relations |papers and textbook |Laptop | |

| |Examples and non-examples of relations | |Textbook | |

| |Domain, range, image, co-domain | |CSEC Past papers | |

| | | |Worksheets | |

| |Represent a relation in various ways: | |Textbook- Vol 1&2 | |

| |Set of ordered pairs | | | |

| |Arrow diagrams | | | |

| |Graphically | | | |

| |Algebraically | | | |

| | | | | |

| |State the characteristics that define a function | | | |

| |Concept of a function | | | |

| |Examples and no-examples of functions | | | |

| | | | | |

|Functions |Use functional notation |Discuss the method of solution for | | |

| |For example [pic] |selected questions | | |

| | |Practice past paper questions in pairs | | |

| |Distinguish between a relation and a function |Have students present answer and explain| | |

| |Ordered pairs |the mode of solution | | |

| |Arrow diagram | | | |

| |Graphically (vertical line test) |Have the students draw and interpret | | |

| | |linear graphs | | |

| |Draw and interpret graphs of linear functions | | | |

| |Concept of linear function | | | |

| |Types of linear function (y = c; x = k; y = mx + c; where m, c and k are real numbers) | | | |

| | | | | |

| |Determine the intercepts of the graph of linear functions | | | |

| |x-intercepts and y-intercepts | | | |

| |Graphically and algebraically | | | |

| | | | | |

| |Determine the gradient of a straight line | | | |

| |Concept of slope | | | |

| | |Discussion on application and use of | | |

| |Determine the equation of a straight line |linear programming in real life | | |

|Gradient |The graph of the line | | | |

| |The co-ordinates of two points on a line | | | |

| |The gradient and one point on the line | |Graph board | |

| |One point on the line and its relationship to another line | |Graphmatica | |

| | | |Graph leaves | |

| |Solve problems involving the gradient of parallel and perpendicular lines | |Worksheets | |

| | | |CSEC Past paper questions | |

| |Determine from co-ordinates on a line segment | |Textbook- Vol 2 | |

| |The concept of magnitude or length |Review steps of completing the squares | | |

| |The concept of midpoint |of a quadratic function | | |

| |The length | | | |

| |The co-ordinates of the midpoint |Class discussion on interpreting a | | |

| | |quadratic graph given | | |

| |Solve graphically a system of two linear equations in two variables | | | |

| | |Have students draw graphs of quadratic | | |

| |Represent the solution of linear inequalities in one variable using: |functions given | | |

| |Set Notation | | | |

| |The number line | | | |

| |Graph |Discussion of physics base worded | | |

| | |situations relates to speed, time and | | |

| |Draw a graph to represent a linear inequality in two variables |acceleration | | |

| | | | | |

| | | | | |

| |Use linear programming techniques to solve problems involving two variables | | | |

| | | | | |

| | | | | |

| | | | | |

| |Derive composite functions | | | |

| |Composite function for example, fg, f2 given f and g | | | |

| |Non-commutativity of composite functions (fg [pic] gf) | | | |

| | | | | |

| |State the relationship between a function and its inverse | | | |

| |The concept of the inverse of a function | | | |

| | | | | |

|Composite Functions |Derive the inverse of a function | | | |

| |f-1, (fg)-1 | | | |

| | | | | |

| |Evaluate f(a), f-1(a), fg(a), (fg)-1(a) where a [pic] | | | |

|Inverse Functions | | | | |

| |Use the relationship (fg)-1=g -1f -1 | | | |

| | | | | |

| |Draw and interpret graphs of a quadratic function to determine: | | | |

| |The elements of the domain that have a given image | | | |

| |The image of a given element in the domain | | | |

| |The maximum or minimum value of the function | | | |

| |The equation of the axis of symmetry | | | |

| |The interval of the domain for which the elements of the range may be greater than or less than a | | | |

| |given point | | | |

|Concepts of Gradient of a curve at a point, |An estimate of the value of the gradient at a given point | | | |

|tangent, turning point. Roots of the equation. |Intercepts of the function | | | |

| | | | | |

| |Determine the axis of symmetry, maximum and minimum value of a quadratic function expressed in the | | | |

| |form a(x + h)2 + k | | | |

| | | | | |

| |Sketch graph of quadratic function expressed in the form a(x + h)2 + k and determine number of roots | | | |

| | | | | |

| |Draw and interpret the graphs of other non-linear functions | | | |

| | | | | |

| |Draw and interpret distance-time graphs and speed-time graphs (straight line only) to determine: | | | |

| |Distance | | | |

| |Time | | | |

| |Speed | | | |

| |Magnitude of acceleration | | | |

|Statistics |Unit 4 | | | |

| |differentiate between sample | | | |

| |and population attributes; | | | |

| |Sample statistics and population parameters. | | | |

| |2. construct a frequency table | | | |

| |for a given set of data; | | | |

| |Discrete and continuous variables. | | | |

| |Ungrouped and grouped data. | | | |

| |3. determine class features for a | | | |

| |given set of data; | | | |

| |Class interval, class boundaries, class limits, class | | | |

| |midpoint, class width. | | | |

| |4. construct statistical diagrams; Pie charts, bar charts, line graphs, histograms with | | | |

| |bars of equal width and frequency polygons. | | | |

| |5. determine measures of central | | | |

| |tendency for raw, ungrouped | | | |

| |and grouped data; | | | |

| |Ungrouped data: mean, median and mode | | | |

| |Grouped data: modal class, median class and the | | | |

| |estimate of the mean. | | | |

| |6. determine when it is most | | | |

| |appropriate to use the mean, | | | |

| |median and mode as the | | | |

| |average for a set of data; | | | |

| |Levels of measurement (measurement scales): | | | |

| |nominal, ordinal, interval and ratio. | | | |

| |Sets with extreme values or recurring values. | | | |

| |7. determine the measures of | | | |

| |dispersion (spread) for raw, | | | |

| |ungrouped and grouped data; | | | |

| |Range, interquartile range and semi-interquartile | | | |

| |range; estimating these measures for grouped data. | | | |

| |8. use standard deviation to | | | |

| |compare sets of data; | | | |

| |No calculation of the standard deviation will be | | | |

| |required. | | | |

| |9. draw cumulative frequency | | | |

| |curve (Ogive); | | | |

| |Appropriate scales for axes. | | | |

| |Class boundaries as domain. | | | |

| |10. analyse statistical diagrams; Finding the mean, mode, median, range, quartiles, | | | |

| |interquartile range, semi-interquartile range; trends | | | |

| |and patterns. | | | |

| |11. determine the proportion or | | | |

| |percentage of the sample | | | |

| |above or below a given value | | | |

| |from raw data, frequency | | | |

| |table or cumulative | | | |

| |frequency curve; | | | |

| |12. identify the sample space for | | | |

| |simple experiment; | | | |

| |Including the use of coins, dice and playing cards. | | | |

| |The use of contingency tables. | | | |

| |13. determine experimental and | | | |

| |theoretical probabilities of | | | |

| |simple events; and, | | | |

| |The use of contingency tables. | | | |

| |Addition for exclusive events; multiplication for | | | |

| |independent events. | | | |

| |14. make inference(s) from | | | |

| |statistics. | | | |

| | | | | |

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