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Math Standards of Learning
The 34 standards represented in this section relates to the knowledge, skills and disposition required for students to develop mathematical competency and to gain understanding of fundamental ideas in arithmetic, measurement, geometry, probability, data analysis, statistics, and algebra. The element represented in each standard is in keeping with the National Council for the Teaching of Mathematics (2000) position that math instruction should enable students to engage in critical thinking activities and to communicate mathematically. Also integrated in the standards for The Belize High School are the expectations described in the Ministry of Education Resource Guide for Lower Secondary School, the learning expectations outlined in the CSEC syllabi and the SAT. Note, the code M represents the math standards in this subsection.
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Area 1: Algebra
M 1: Interpret and solve multistep linear equations and inequalities
M 2: Represent and evaluate verbal quantitative situations algebraically
M 3: Understand and justify steps used in simplifying expressions and solving equations and inequalities
M 4: Use various representations such as matrices to organize and manipulate data
M 5: Apply the laws of exponents to perform operations
M 6: Understand and effectively factor first and second degree binomials and trinomials
M 7: Solve quadratic equations both algebraically and graphically
M 8: Understand and explain field properties, axioms of equality and inequality
M 9: Accurately add, subtract, multiply, divide, and simplify rational expressions, including complex fractions
M 10: Accurately add, subtract, multiply, divide, and simplify radical expressions containing positive rational numbers and variables and expressions containing rational exponents
M 11: Interpret and solve absolute value equations and inequalities graphically and algebraically
M 12: Understand, identify and factor polynomials representing the difference of squares, perfect square trinomials, the sum and difference of cubes, and general trinomials.
M 13: Select, justify, and apply a technique to solve a quadratic problem
M 14: Understand and solve equations containing rational expressions and equations containing radical expressions algebraically and graphically
M 15: Recognize and explain and recognize multiple representations of functions (linear, quadratic, absolute value, step, and exponential functions)
Knowledge
1. Write linear equations and inequalities
2. Explain and use concrete objects, pictorial representations to represent math concepts
3. Identify properties of real numbers, equality and inequality
4. Interpret data from business, industrial and consumer situations
5. Explain and use tabular, symbolic, graphical, verbal, and physical representations to analyze a given set of data
6. Identify integral exponents and use scientific notation when appropriate
7. Identify and interpret properties of order that are valid for the set of real numbers and its subsets, complex numbers, and matrices
8. Explain and write radical expressions as expressions containing rational exponents and vice versa
9. Identify the value of a function for a given element in its domain
10. Explain and use graphic illustrations to assist in investigations of functions
11. Describe using graphs, the relationships between the solution of an equation, zero of a function, x-intercept of a graph, and factors of a polynomial expression
12. Represent problem situations with a system of linear equations
13. Identify and solve nonlinear systems of equations, including linear-quadratic and quadraticquadratic, algebraically and graphically
14. Recognize the general shape of polynomial, exponential, and logarithmic functions
15. Identify the properties of arithmetic and geometric properties
16. Identify conic sections (circle, ellipse, parabola, and hyperbola) from equations
Skills
1. Apply skills from linear equations to solve practical problems
2. Use graphing calculators to confirm algebraic solutions
3. Choose appropriate computational technique
4. Apply cognitive skills and use calculators to solve math problems
5. Use graphing calculator to investigate changes
6. Find the values of a function for elements in its domain
7. Locate the zeros of the function both algebraically and with a graphing calculator
8. Sketch graphs of conic sections, using transformations
9. Collect and analyze data to make predictions and solve practical problems
Attitudes and Disposition
1. Value the use of algebraic functions in authentic activities
2. Perform operations on complex numbers and express the results using mathematical terms
Area 2: Geometry
M 16: Identify the converse, inverse, and contra positive of a conditional statement
M 17: Investigate and examine congruence and relationships between geometrical shapes
M 18: Understand and solve practical problems involving right-angled triangles by using the Pythagorean Theorem, properties of special right triangles, and right-angled triangle trigonometry
M 19: Apply deductive reasoning to investigate and prove properties of quadrilaterals
M 20: Understand, investigate and solve practical problems involving properties of angles, arcs, chords, tangents, and secants
M 21: Understand the properties of, construct and bisect line segments
M 22: Use visual representations to illustrate, compare and contrast two and three- dimensional figures
M 23: Use formulae for surface area and volume of three-dimensional objects to solve practical Problems
Knowledge
1. Interpret, investigate and use formulae for finding distance, midpoint, and slope
2. Determine whether a figure has been translated, reflected or rotated
3. Identify various types of angles and their properties
4. Identify and explain the properties of mathematical figures/shapes
5. Identify, describe and construct line segments
Skills
1. Translate a short verbal argument into symbolic form
2. Use Venn diagrams to represent sets of relationships
3. Use pictorial representations such as those generated by computer software
4. Use algebraic and coordinate methods and deductive proofs
5. Apply mathematical principles/skills to prove theories
6. Express solutions in radical form or as a decimal
7. Explain and prove properties of quadrilaterals, using algebraic and coordinate methods
8. Measure interior and exterior angles of polygons
9. Use tessellations and tiling problems to make connections to art structure and nature scale drawings
10. Use drawings, blueprints, or computer simulations to represent geometric figures
Attitudes and Disposition
- Solve practical problems involving complementary, supplementary, and congruent angles
Area 3: Trigonometry
M 24: Understand and use the definitions of the six trigonometric functions to find the sine, cosine, tangent, cotangent, secant, and cosecant of an angle in standard position
M 25: Understand and identify the value of trigonometric function
M 26: Understand and explain using a calculator the value of any trigonometric function and inverse trigonometric function
M 27: Understand, identify, create, and solve practical problems involving triangles using the trigonometric functions, the Pythagorean Theorem, the Law of Sines, and the Law of Cosines
Knowledge
1. Identify a given point, other than the origin, on the terminal side of the angle
2. Properties of the unit circle and definitions of circular functions
3. State the domain and the range of the function
4. Determine the amplitude, period, phase shift, and vertical shift
5. Identify the domain and range of the inverse trigonometric functions and recognize the graphs of these functions
Skills
1. Independently calculate the values of the trigonometric functions of special angles and their related angles
2. Convert radians to degrees and vice versa
3. Verify basic trigonometric identities and make substitutions, using the basic identities
4. Sketch the graph of a function by using transformations for at least a one-period interval
5. Solve trigonometric equations that include both infinite solutions and restricted domain solutions and solve basic trigonometric inequalities
6. Use graphing utilities to solve equations, check for reasonableness of results, and verify algebraic solutions
Area 4: Probability and Statistics
M 28: Analyze numerical characteristics of univariate data sets to describe patterns and departure from patterns, using mean, median, mode, variance, standard deviation, interquartile range, range, and outliers
M 29: Analyze scatterplots to identify and describe the relationship between two variables
M 30: Find and interpret linear correlation
M 31: Analyze categorical data to describe patterns and departure from patterns
M 32: Understand and describe various methods of data collection including surveys, experiments, and observational study
M 33: Plan and conduct various types of statistical experiments
M 34: Describe and identify properties of a normal distribution and apply the normal distribution to determine probabilities
Knowledge
l. Identify and analyze graphical displays of data, including dotplots, stemplots, and histograms
2. Identify and use central tendency, spread, clusters, gaps, and outliers
3. Describe and analyze the center and spread of various sets of data
4. Identify shape; strength of relationship; clusters; positive, negative, or no association; outliers; and influential points of scatterplots
5. Identify marginal frequency and relative frequencies
6. Identify and use randomization, and measurement of experimental error
7. Identify and describe two or more events as complementary, dependent, independent, and/or mutually exclusive
8. Identify conditional probabilities
9. Develop, interpret, and apply the binomial probability distribution for discrete random variables
11. Identify random variables as independent or dependent
12. Find the mean and standard deviations for sums and differences of independent random variables
13. Identify the meaning of sampling distribution
Skills
1. Use technology to create graphical displays
2. Use technology to calculate statistics
3. Use residual plots to assess linearity
Attitude and Disposition
1. Demonstrate mastery of mathematical content consistent with the school curriculum and contemporary needs
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