Principles of IGCSE MATHEMATICS

The content themes or topics should include, but not be limited to, the following:

• Number Sense

• Algebra

• Functions

• Geometry

• Transformations and vectors

• Geometrical measurement

• Coordinate geometry

• Trigonometry

• Probability

• Statistics

Major Concepts/Skills:

The purpose of this course is to enable students to develop their mathematical knowledge, as well as oral, written, and practical skills; read mathematics and write and talk about the subject in a variety of ways; carry out calculations and understand the significance of the results obtained; apply mathematics in everyday situations and develop an understanding of the part that mathematics plays in the world around them; solve problems, present the solutions clearly, and check and interpret the results; develop an understanding of mathematical principles; recognize when and how a situation may be represented mathematically; identify and interpret relevant factors and, where necessary, select an appropriate mathematical method to solve the problem; use mathematics as a means of communication with emphasis on the use of clear expression; develop an ability to apply mathematics in other subjects, particularly science and technology; develop the ability to reason logically, to classify, to generalize, and creative work arising from mathematical ideas; develop their mathematical abilities by considering problems and conducting individual and cooperative inquiry and experiment, including extended pieces of work of a practical and investigative kind; appreciate the interdependence of different branches of mathematics; acquire a foundation appropriate to their further study of mathematics and of other disciplines.

IGCSE Syllabus: IGCSE Mathematics (US) 0444

MAT099 Principles of IGCSE Mathematics

Scope & Sequence:

Unit Outline, Synopsis & Projected Time

Unit 1: Numeracy

Develops an understanding of number relationships and simplifying numerical expressions.

6 weeks

Unit 2: Ratios, Percents, and Interests

Connects ratios and percents to solve application problems relating to percents and interest.

5 weeks

Unit 3: Solving Equations

A look at solving one variable and multivariable equations and basic systems of equations. Includes evaluating formulas.

6 weeks

Unit 4: Angles and Polygons

Introduction to angles, lines, and polygons. Multiple properties are applied to find the measure of angles given in a variety of contexts.

5 weeks

Unit 5: Coordinate Geometry

Explores lengths, slopes, graphing lines, and writing equations of lines.

5 weeks

Unit 6: Probability and Statistics

Develops and understanding of representation and interpretation of data and probability.

4 weeks

Constructions Project I

Introduction to making geometric constructions using a compass and straightedge.

1 week

Unit 1: Numeracy

Learning Goal: The learner will understand how to classify and perform operations with real numbers, roots and exponents, and find factors and multiples of numbers.

Objectives: TLW - 1.1 Classify real numbers and compare integers and numbers with decimals using correct inequality symbols.

Notes and Examples

● As Rational, Irrational, Integers and Natural.

Ex: Complete using the correct inequality symbol

-5 ____ 4 , 3.05 ____ 3.2

Ex: True or false? If false, correct the statement

-3 < -5 , 3.060 = 3.0

Projected Time

3 days

AZCCRS

A1.N-RN.B.3

Syllabus

1.1

Objectives: TLW - 1.2 Apply integer rules for adding, subtracting, multiplying and dividing.

Notes and Examples

● Problems should include only one step.

Ex: 4+(-8), -5-(-3), (-2)(4), (-8)/(-2)

Projected Time

5 days

AZCCRS

6.EE.A.2

Syllabus

1.2

Objectives: TLW - 1.3. Perform operations with integers and using the correct order of operations including application problems.

Notes and Examples

● Problems should not exceed 3 steps.

Ex: Simplify: , , 4-9-2+5

Ex: Find the range of temperatures in a week given a table.

Projected Time

5 days

AZCCRS

6.EE.A.2

Syllabus

1.2

Objectives: TLW - 1.4. Find the multiples, factors, LCM and GCF of numbers and

determine if they are prime

Notes and Examples

● Use divisibility rules to scaffold this objective.

● Use numbers less than or equal to 20 for multiples and less than or equal to 100 for factors

Projected Time

5 days

AZCCRS

6.NS.B.4

Syllabus

1.3

Objectives: TLW - 1.5 Simplify and perform operations on numerical expressions using rules of exponents.

Notes and Examples

● Write numbers from exponential to expanded form and vice versa

● Convert numbers with negative exponents into fractions

● Re-write numbers with the same base using product, quotient, power, and zero exponent rules

● convert to and from scientific notation

Projected Time

5 days

AZCCRS

8.EE.A1

Syllabus

1.7

Objectives: TLW - 1.6 Calculate square roots and cube roots.

Notes and Examples

● Mentally calculate square roots of perfect squares 1 - 144

● Mentally calculate cube roots of perfect cubes 1 - 125

● Compute non-perfect roots using calculators.

● Convert numbers with fractional exponents to radicals and vice versa

● Connect roots to area of a square

ex: if a square has an area of 54.76 units, what is the measure of each side?.

ex: what is the cube root of 64?

Projected Time

3 days

AZCCRS

8.EE.A.2

Syllabus

1.8

Unit 1 Summary:

Days for review, remediation and assessment

4 days

Total projected time to complete the unit:

30 days - 6 weeks

Unit 2: Ratios, Percents, and Interest

Learning Goal: The learner will understand how to use ratios, percents and interest calculations to solve application problems.

Objectives: TLW - 2.1 Round numbers correctly

Notes and Examples

● Use decimal places and significant figures

● Students should consider whether the answer is reasonable in the context

Projected Time

3 days

AZCCRS

8.NS.A.2

Syllabus

1.9

Objectives: TLW - 2.2 Perform operations on fractions.

Notes and Examples

● Simplifying, multiply, divide, add and subtract proper and improper fractions

● Mixed numbers included

Projected Time:

4 days

AZCCRS

7.NS.A1

7.NS.A2

Syllabus

1.2

Objectives: TLW - 2.3 Simplify ratios and divide given quantities into assigned ratios.

Notes and Examples

● Simplify ratios: Ex:

Ex: Inheritance :- $1200 divided on the ratio 1:2:3.

Projected Time

3 days

AZCCRS

7.RP.A.1

Syllabus

1.4

Objectives: TLW - 2.4 Be able to solve proportions.

Notes and Examples

● Proportions simple applications

Ex: 2 cup of milk must be added for 8 pancakes, how many pancakes can be made with 20 cups of milk?

● Inverse proportions

Ex: 2 cup of milk must be added for 8 pancakes, how many cups of milk will be needed to make 32 pancakes?

● Include unit conversions

Ex: If 1 dollar is 17 pesos, how many pesos are there in 48 dollars.

Projected Time

5 days

AZCCRS

7.RP.A.2

Syllabus

1.4

Objectives: TLW - 2.5 Calculate percents and perform conversions between percentages, decimals, and fractions.

Notes and Examples

Ex: What is 30% of 45?

Ex: Convert between all three forms

Projected Time:

4 days

AZCCRS

6.RP.A.3

Syllabus

1.5

Objectives: TLW - 2.6 Solve application problems involving percent increase and decrease.

Notes and Examples

● Include direct increase and decrease problems

● Do NOT include reverse percentages

Projected Time:

3 days

AZCCRS

7.RP.A.3

Syllabus

1.6

Unit 2 Summary

Days for review, remediation and assessment

3 days

Total projected time to complete the unit

25 days - 5 weeks

Unit 3: Solving Equations

Learning Goal: The learner will simplify expressions and solve linear equations.

Objectives: TLW - 3.1 Simplify variable expressions.

Notes and Examples

● Identify terms, factors and coefficients

● Combine like terms and distributive property (expanding parentheses).

● Simplify expressions – multi-step including parentheses with no exponents.

Projected Time:

6 days

AZCCRS

A1.A-APR.A.1

Syllabus

2.7

2.8

Objectives: TLW - 3.2 Create Variable Expressions

Notes and Examples

● Create and simplify expressions involving perimeter, area and linear relationships.

Ex. Justin had a $500 operation. Nursing care costs $170 for each day he is in the hospital. Write an expressions for the total cost of his surgery and nursing care.

Projected Time:

3 days

AZCCRS

A1.A-SSE.A.1

Syllabus

2.3

Objectives: TLW - 3.3 Solve linear equations .

Notes and Examples

● Include fractional expressions with one denominator

● Multi-step including expanding parentheses

● Multi-step including combining like terms

● Multi-step including equations with variables on both sides

● Limit equations to no more than 4 steps

Ex: 4(x+3) = 9 - 2x

Projected Time

8 days

AZCCRS

A1.A-CED.A.1

A1.A-REI.A1

A1.A-REI.B.3

Syllabus

2.3

Objectives: TLW - 3.4 Rearrange and evaluate formulae.

Notes and Examples

● No exponents when manipulating formulae (Ex: solve for r )

● Exponents when evaluating for a given variable (Ex: when x = –3 and y = 4, find the value of xy 2.)

Projected Time

5 days

AZCCRS

A1.A-CED.A.4

Syllabus

2.5

Objectives: TLW - 3.5 Solve simple systems of linear equations in two variables algebraically.

Notes and Examples

● By substitution or elimination (focus on one method only)

● If using substitution, give at least one equation is already solved for a variable.

Ex: y= 2x + 4

2x+3y=20

Projected Time

4 days

AZCCRS

A1.A-REI.C.5

Syllabus

2.6

Unit 3 Summary

Days for review, remediation and assessment

4 days

Total projected time to complete the unit

30 days - 6 weeks

Objectives: TLW - Unit 4: Angles and Polygons

Learning Goal: Students will work with the properties of angles, triangles, and polygons to find the angle measurements.

Objectives: TLW - 4.1. Use angle relationships to find missing angles.

● Define angles (acute, obtuse, right, reflex)

● Explore measuring angles with protractor

● Include vertical angles, angles on a line (supplementary), angles around a point, and complementary angles

● Include problems that require basic algebraic equations:

Projected Time

7 days

AZCCRS

G.G-CO.C.9

G.G-CO.C.10

Syllabus

4.1

4.4

Objectives: TLW - 4.2 Find missing angles created by parallel lines and transversals.

Notes and Examples

● Include alternate and corresponding angles.

● Use previous angle relationships in 4.1

● Include problems that require basic algebraic equations.

Projected Time

5 days

AZCCRS

G.G-CO.C.9

G.G-CO.C.10

Syllabus

4.2

4.4

Objectives: TLW - 4.3 Find missing angles in triangles and quadrilaterals using the Angle Sum Theorem.

Notes and Examples

● Include classify triangles by angles and sides (acute, obtuse, right, ) (isosceles, equilateral, scalene)

● Connect Angle Sum Theorem to the sum of angles in a quadrilateral is 360

● Find the number of lines of symmetry of triangles and quadrilaterals

Projected Time

5 days

AZCCRS

G.G-CO.C.9

G.G-CO.C.10

Syllabus

4.1

4.4

Objectives: TLW - 4.4 Classify and find interior and exterior angles of polygons.

Notes and Examples

● Classify polygons as regular or irregular and name them using sides (triangle, quadrilateral, pentagon, hexagon, octagon)

● Classify quadrilaterals as square, rectangle, rhombus or trapezoid

● Sum of exterior angles is 360

● Use the sum of interior angle formula to find missing angles in regular polygons.

● Use supplementary angles to find individual exterior angles of regular polygons

Projected Time

5 days

AZCCRS

G.G-CO.C.9

G.G-CO.C.10

Syllabus

4.1

4.4

Unit 4 Summary

Days for review, remediation and assessment

3 days

Total projected time to complete the unit

25 days - 5 weeks

Objectives: TLW - Unit 5: Coordinate Geometry

Learning Goal: The learner will understand how to find lengths and points on a line given a ratio, graph and generate equations of lines, and solve systems of equations.

Objectives: TLW - 5.1 Use the Pythagorean Theorem to find the side lengths of right triangles.

Notes and Examples

● Radical solutions need not be simplified but students should be encouraged to estimate radicals based on their knowledge of perfect squares.

Projected Time

3 days

AZCCRS

G.G-SRT.C.8

Syllabus

8.1

Objectives: TLW - 5.2 Locate points and calculate the distance and midpoint between two points.

Notes and Examples

● Plot points and write the coordinates of points in the cartesian plane.

● Find the distance between two points given a diagram

● Find the midpoint of a line segment given a diagram

Projected Time

4 days

AZCCRS

G.G-GPE.B.6

G.G-GPE.B.7

Syllabus

7.1

7.2

7.3

Objectives: TLW - 5.3 Calculate the slope of a line given a graph or 2 coordinates.

Notes and Examples

● Include zero and undefined slopes.

Projected Time

4 days

AZCCRS

8.EE.B.6

Syllabus

7.4

Objectives: TLW - 5.4 Graph linear equations using a table of values.

Notes and Examples

● Complete the table using an equation

● Graph the line given the table

● Identify x and y-intercepts

● Complete the table using the graph of a line

Projected Time

3 days

AZCCRS

A1.A-CED.A.2

Syllabus

7.5

Objectives: TLW - 5.5 Graph the line of an equation given in y = mx+b

Notes and Examples

● Develop meaning and use y = mx + b. Start with y = ax and have students explore changing a and adding a b using graphical technology (desmos)

● Include graphing lines that are parallel to given line through a point.

Projected Time

5 days

AZCCRS

A1.A-CED.A.2

Syllabus

7.5

Objectives: TLW - 5. 6 Write the equation of a line in slope intercept form.

Notes and Examples

● Write the equation in y=mx+b given the graph a line, slope and y-intercept, or the two coordinates (use point slope form or substituting an ordered pair to find b)

● Write the equation parallel to a line but passing through a given point.

Projected Time

4 days

AZCCRS

A1.A-CED.A.2

8.EE.B.6

G.G-GPE.B.5

Syllabus

7.5

7.6

Unit 5 Summary

Days for review, remediation and assessment

3 days

Total projected time to complete the unit

25 days - 5 weeks

Unit 6: Probability and Statistics

Learning Goal: Students will understand data through use of probability and measures of statistics.

Objectives: TLW - 6.1 Define and find the experimental probability of an event. (all based on observation NOT calculations)

Notes and Examples

● Find the probability of an event as a fraction, decimal, and percent

Ex: Have a bag with 10 marbles in 3 colors. Draw 20 samples and have students estimate the exact mix of the colors.

● Significance of the value of probability and using it to make decisions

● Understand P(event) = 1 - P(not occurring)

● Understand the difference between fair and unfair ex. uneven spinners

● Understand that relative probably is an estimate of probability

Projected Days

3 days

AZCCRS

A1.S-CP.A.1

A1.S-CP.A.2

Syllabus

9.1

9.2

Objectives: TLW - 6.2 Find expected number of occurrences.

Notes and Examples

● Calculate the theoretical probability of simple events (dice and cards)

● Specifically the relationship between theoretical probability and actual outcomes.

Ex: Set up a variety of probability experiments that have a theoretic probability. Get each group of five pairs to work on one experiment. Work out the theoretic probability and the experimental probability for 100 goes. Compare the theoretic and the experimental probability and pool the results of the group to get 500 results. Discuss the outcomes for the different experiments and when the theoretic and experimental converge.

Projected Time

4 days

http://www.cimt.org.uk/resources/help/h10prob1.pdf

http://www.cimt.org.uk/resources/help/h10prob2.pdf

AZCRS

A1.S-CP.A.2

Syllabus

9.3

Objectives: TLW - 6.3 Read, interpret, and create graphs and tables

Notes and Examples

● Be able to read information on graphs of different types

● Use frequency charts to collect data both continuous and discrete

● Be able to create the following charts using the correct guidelines

○ Compound bar charts, dot plots, line graphs, pie charts, and simple frequency distributions.

● Use different representations of the same data.

Projected Time

7 days

http://www.cimt.org.uk/resources/help/h6data1.pdf

http://www.cimt.org.uk/resources/help/h6data2.pdf

AZCCRS

A1.S-ID.A.1

A1.S-ID.B.6

Syllabus

10.1

10.2

10.3

10.8

Objectives: TLW - 6.4 Find measures of central tendency.

Notes and Examples

● Find mean, median, mode, and range with discrete data

● Continuous data and tables are NOT required (optional)

Projected Time

3 days

AZCCRS

A1.S-ID.A.2

Syllabus

10.4

Unit 6 Summary

Days for review and assessment

3 days

Total projected time to complete the unit

20 days - 4 weeks

Constructions Project I

Learning Goal: The learner will make formal geometric constructions with compass and straightedge only.

Objectives: TLW - 1. Copy a segment, copy an angle, and copy a triangle.

Projected Time

1 day

https://www.youtube.com/watch?v=OLCRsYuBqWg

AZCCRS

G.G-CO.D.12

G.G-CO.D.13

Syllabus

4.5

Objectives: TLW - 2. Bisect a segment and bisect an angle.

Projected Time

1 day

AZCCRS

G.G-CO.D.12

G.G-CO.D.13

Syllabus

4.5

Objectives: TLW - 3. Construct perpendicular lines and perpendicular bisectors.

Projected Time

1 day

https://www.youtube.com/watch?v=XXI60B3m70Y

AZCCRS

G.G-CO.D.12

G.G-CO.D.13

Syllabus

4.5

Objectives: TLW - 4. Construct triangles with side measures given or congruent to a given segment and a square.

Notes and Examples

● An initial segment is given to be used as one of the sides of the triangle or square.

Projected Time

1 day

AZCCRS

G.G-CO.D.12

G.G-CO.D.13

Syllabus

4.5

Project Summary

Days for review and assessment

1 day

Total projected time to complete the unit

5 days - 1 week

### Requested competency code:

- Math

Need more on what level of IGCSE Mathematics is being requested. All cambridge courses include IGCSE Mathematics I & II have already been previously reviewed and courses are listed on Cambridge pre-approve course list. https://courseapproval.asu.edu/files/CambridgeCourseEvaluation.pdf