High School Math A & B

High School Math A & B

Some Manipulatives

Algebra tiles Mirrors or miras Volume demonstration kits
Dice Spinners Measuring tools
Geometric models Geoboards Compasses
Tessellation tiles Tessellation tiles PentaBlocks

Calculators will be required for use on Math A and B assessments. Scientific calculators are required for the Math A
Regents examinations. Graphing calculators that do not allow for symbolic manipulation will be required for the Math B
Regents examination and will be permitted (not required) for the Math A Regents examination starting in June 2000.

The Math A exam may include any given topic listed in the Core Curriculum with any performance indicator. The content
includes most of the topics in the present Course I and a selection of topics from Course II. Programs other than
Course I and II could be used as long as all the performance indicators and topics in the curriculum are part of the program.
Examples of assessment items for Math A have been provided for most performance indicators. The items were
taken from the 1997 pilot test and 1998 Test Sampler. Suggestions for classroom activities are substituted for any performance
indicator that was not included in the sample test.

The Math B exam may include any given topic listed in the Core Curriculum with any performance indicator. Programs
other than Course II and III could be used as long as the performance indicators and topics mentioned are part of the
program. Since there is no Math B exam at this time, no assessment items have been included for Math B. Suggestions
for possible classroom activities or problems are given instead to provide clarification of most performance indicators.

Math A

Key Idea 1
Mathematical Reasoning

Students use mathematical reasoning to analyze mathematical situations,
make conjectures, gather evidence, and construct an argument.

1A. Construct valid arguments. • Truth value of compound sentences
(conjunction, disjunction, conditional,
related conditionals such as
converse, inverse, and contrapositive,
and biconditional).
• Truth value of simple sentences
(closed sentences, open sentences
with replacement set and solution
set, negations).
See Assessment Example 1A.
1B. Follow and judge the validity of
• Truth value of compound
See Assessment Example 1B.

Key Idea 2
Number and Numeration

Students use number sense and numeration to develop an understanding of the
multiple uses of numbers in the real world , the use of numbers to communicate
mathematically, and the use of numbers in the development of mathematical

2A. Understand and use rational and irrational
• Real numbers including irrational
numbers such as non-repeating
decimals, irrational roots, and pi.
See Assessment Example 2A.
2B. Recognize the order of real numbers. • Rational approximations of irrational
See Assessment Example 2B.
2C. Apply the properties of real numbers to
various subsets of numbers.
• Properties of real numbers including
closure, commutative, associative,
and distributive properties ,
and inverse and identity elements.
See Classroom Idea 2C.

Key Idea 3

Students use mathematical operations and relationships among them to understand

3A. Use addition, subtraction, multiplication,
division, and exponentiation with real
numbers and algebraic expressions.
Signed numbers .
Use of variables : order of operations
and evaluating algebraic
expressions and formulas.
• Addition and subtraction of polynomials:
combining like terms and
fractions with like denominators .
• Multiplication of polynomials:
powers, products of monomials
and binomials, equivalent fractions
with unlike denominators, and
multiplication of fractions.
• Simplification of algebraic expressions.
• Division of polynomials by monomials .
• Operations with radicals: simplification,
multiplication and division,
and addition and subtraction.
• Scientific notation.
• Simplification of fractions.
• Division of fractions.
• Prime factorization.
• Factoring: common monomials ,
binomial factors of trinomials .
Difference of two squares .
See Assessment Example 3A.
3B. Use integral exponents on integers and
algebraic expressions.
• Powers: positive, zero, and
negative exponents .
See Assessment Example 3B.
3C. Recognize and identify symmetry and
transformations on figures.
• Intuitive notions of line reflection ,
translation, rotation, and dilation.
• Line and point symmetry.
See Assessment Example 3C.
3D. Use field properties to justify mathematical
• Distributive and associative field
properties as related to the solution
of quadratic equations .
• Distributive field property as related
to factoring.
See Classroom Idea 3D.
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