I. Number Sense and Numerical Operations

Because major areas of study at postsecondary institutions have different prerequisites, certain mathematics benchmarks are marked with an asterisk (*). These asterisked benchmarks represent content that is recommended for all students, but is required for those students who plan to take calculus in college, a requisite for mathematics and many mathematics-intensive majors. The high school graduate can:

I1. Compute fluently and accurately with rational numbers without a calculator:

I1.1. Add, subtract, multiply and divide integers, fractions and decimals.

(Associated Workplace Tasks: #1, 2, 3 and 6)

(Associated Postsecondary Assignments: #1 and 2 )

Example:

3 ÷ 1.2 = 15/4 ÷ 6/5 = 15/4 x 5/6 = 75/24 = 25/8 = 3 = 3.125

Example:

Estimate the total of a column of 10 to 15 numbers (typically, dollars and cents) and then add them manually (e.g., by grouping 10s).

I1.2. Calculate and apply ratios, proportions, rates and percentages to solve problems.

(Associated Workplace Tasks: #1, 2, 3 and 6)

(Associated Postsecondary Assignment: #2)

Example:

In the last four quarters, the returns reported for your mutual fund were, in succession, +2.33%, -1.75%, +3.02%, -2.54%. What was your return for the year?

I1.3. Use the correct order of operations to evaluate arithmetic expressions, including those containing parentheses.

I1.4. Explain and apply basic number theory concepts such as prime number, factor, divisibility, least common multiple and greatest common divisor.

I1.5. Multiply and divide numbers expressed in scientific notation.

(Associated Postsecondary Assignment: #2)

Example: Multiply by to obtain , adjust to conform first to the standard form for scientific notation to obtain , and round to the appropriate number of significant digits as determined by the original equation to obtain .

I2. Recognize and apply magnitude (absolute value) and ordering of real numbers:

I2.1. Locate the position of a number on the number line, know that its distance from the origin is its absolute value and know that the distance between two numbers on the number line is the absolute value of their difference.

I2.2. Determine the relative position on the number line of numbers and the relative magnitude of numbers expressed in fractional form, in decimal form, as roots or in scientific notation.

Example:

Determine which of the two fractions -3/5 and -4/7 is larger and which has greater magnitude without using a calculator.

Example:

Order the following numbers from least to greatest without using a calculator:

Example: Example: Approximate how much larger is than and check that approximation by dividing by to obtain ÷ = to see that is two billion times as large as .

I3. Understand that to solve certain problems and equations, number systems need to be extended from whole numbers to the set of all integers (positive, negative and zero), from integers to rational numbers, from rational numbers to real numbers (rational and irrational numbers) and from real numbers to complex numbers; define and give examples of each of these types of numbers.

(Associated Workplace Task: #3)

(Associated Postsecondary Assignments: #1 and 2)

Note: Negative integers are required to measure quantities such as temperatures below zero, rational numbers are required to measure quantities that are not integers such as the length of each piece of a 5-foot wire cut into two equal pieces, irrational numbers are required to measure quantities such as the length of the diagonal of a unit square, and complex numbers are required to solve equations such as .

I4. Understand the capabilities and the limitations of calculators and computers in solving problems:

I4.1. Use calculators appropriately and make estimations without a calculator regularly to detect potential errors.

(Associated Workplace Task: #2)

I4.2. Use graphing calculators and computer spreadsheets.

(Associated Workplace Tasks: #3 and 6)

(Associated Postsecondary Assignment: #2)