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

Calculator
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.

Note
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.

PERFORMANCE INDICATORS	INCLUDES	EXAMPLES
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 arguments.	• Truth value of compound sentences.	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
ideas.

PERFORMANCE INDICATORS	INCLUDES	EXAMPLES
2A. Understand and use rational and irrational numbers.	• 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 numbers.	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
Operations

Students use mathematical operations and relationships among them to understand
mathematics.

PERFORMANCE INDICATORS	INCLUDES	EXAMPLES
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 procedures.	• Distributive and associative field properties as related to the solution of quadratic equations . • Distributive field property as related to factoring.	See Classroom Idea 3D.