Correlations to the Secondary Mathematics Benchmarks

KEY:

Number

N.A.1 Rational numbers.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Identify rational numbers, represent them in various ways, and translate among these representations. A.1 PK.A.1 I1, MR2
b. Understand and use inequalities to compare rational numbers; apply basic rules of inequalities to transform expressions involving rational numbers. A.1 PK.A.1 I2.2
c. Locate rational numbers on the number line and explain the significance of these locations. A.1 PK.A.1 I2.1, I2.2
d. Know and apply effective methods of calculation with rational numbers. A.2 PK.A.2 I1, I1.1 2, 16, 28
e. Recognize, describe, extend, and create well-defined numerical patterns A.3 PK.A.3
f. Solve practical problems involving rational numbers. A.2 PK.A.2 I1.2 2, 16, 28

N.A.2 Absolute values.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Know and apply the definition of absolute value. A.1 PK.A.7 I2.1
b. Interpret absolute value as distance from zero. A.1 PK.A.7 I2.1
c. Interpret absolute value of a difference as "distance between." A.1 PK.A.7 I2.1

N.A.3 Prime decomposition, factors, and multiples.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Know and apply the Fundamental Theorem of Arithmetic, that every positive integer is either prime itself or can be written as a unique product of primes (ignoring order). A.4 PK.A.4 I1.4
b. Explain the meaning of the greatest common divisor (greatest common factor) and the least common multiple and use them in operations with fractions. A.4 PK.A.4 I1.4
c. Write equivalent fractions by multiplying both numerator and denominator by the same non-zero whole number or dividing by common factors in the numerator and denominator. A.4 PK.A.4

N.A.4 Ratios, rates, and derived quantities.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Interpret and apply measures of change such as percent change and rates of growth. B.1 G.1 A.1 I1.2
b. Calculate with quantities that are derived as ratios and products. B.1 G.1 A.1 I1.2
c. Solve data problems using ratios, rates, and product quantities. B.1 G.1 A.1 I1.2 2, 25
d. Create and interpret scale drawings as a tool for solving problems. B.1 G.1 A.1 A.1 K7
e. Use unit analysis to clarify appropriate units in calculations. A.1 A.1 K8.1
f. Identify and apply derived measures. A.1 A.1 K8.2 16
g. Use and identify potential misuses of weighted averages. A.1 A.1 S.1.b L2.2 2

N.B.1 Estimation and approximation.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Use simple estimates to predict results and verify the reasonableness of calculated answers. A.5 PK.A.5 MR5, MR8
b. Develop, apply, and explain different estimation strategies for a variety of common arithmetic problems. A.5 PK.A.5 MR5 2, 16
c. Explain the phenomenon of rounding error, identify examples, and, where possible, compensate for inaccuracies it introduces. A.5 PK.A.5 MR5 24
d. Determine a reasonable degree of precision in a given situation. A.4 A.2 MR5 7, 24
e. Interpret and compare extreme numbers (e.g., lottery odds, national debt, astronomical distances). A.4 A.2 I2.2
f. Apply significant figures, orders of magnitude, and scientific notation when making calculations or estimations. A.4 A.2 I1.5, MR5
g. In a problem situation, use judgment to determine when an estimate is appropriate and when an exact answer is needed. A.5 PK.A.5 MR5

N.B.2 Exponents and roots.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Use the definition of a root of a number to explain the relationship of powers and roots. A.2 A.1 O3.b J1.1
b. Estimate square and cube roots and use calculators to find good approximations. A.2 A.1 I2.2, I4.1, M5
c. Evaluate expressions involving positive integer exponents and interpret such exponents in terms of repeated multiplication. A.6 PK.A.6 J1.1
d. Convert between forms of numerical expressions involving roots and perform operations on numbers expressed in radical form. B.1, B.5 C.1 O1.a, O1.b J1.1, J1.2 19
e. Interpret rational and negative exponents and use them to rewrite expressions in alternative forms. B.1 C.1 O1.b, O1.c

N.B.3 Real numbers.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Categorize real numbers as either rational or irrational and know that, by definition, these are the only two possibilities. A.3 A.2
b. Establish simple facts about rational and irrational numbers using logical arguments and examples. A.3 C.2
c. Show that a given interval on the real number line, no matter how small, contains both rational and irrational numbers. A.3 part, A.4 part C.2 part, C.3 part
d. Extend the properties of computation with rational numbers to real number computation. A.3 A.2

N.C.1 Number bases.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Identify key characteristics of the base-10 number system and adapt them to other common number bases (binary, octal, and hexadecimal). B.1 opt J.1 opt
b. Convert binary to decimal and vice versa. B.1 opt J.1 opt
c. Encode data and record measurements of information capacity using various number base systems. B.1 opt J.1 opt

N.D.1 Complex numbers.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Know that if a and b are real numbers, expressions of the form a + bi are called complex numbers, and explain why every real number is a complex number. D.1 B.1 O2.a I3
b. Identify complex conjugates. D.1 B.1 O2.b
c. Determine complex number solutions of the form a + bi for certain quadratic equations. D.2 C.1 E2.a, E2.b J3, J3.5

N.E.1 Computation with complex numbers.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Compute with complex numbers. B.2 opt O2.b

N.E.2 Argand diagrams.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Interpret complex numbers graphically using an Argand diagram.
b. Represent the complex number z = x + iy in the polar form z = r (cosθ + i sinθ) and interpret this form graphically, identifying r and θ.
c. Explain the effect of multiplication and division of complex numbers using an Argand diagram and its relationship to the polar form of a complex number.