options: Know that there are numbers that are not rational, and approximate them by rational numbers.

Compute fluently with multi-digit numbers and find common factors and multiples.

Use complex numbers in polynomial identities and equations.

Perform arithmetic operations with complex numbers.

Use properties of rational and irrational numbers.

Perform operations on vectors.

Represent and model with vector quantities.

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

Reason quantitatively and use units to solve problems.

Extend the properties of exponents to rational exponents.

Apply and extend previous understandings of numbers to the system of rational numbers.

Represent complex numbers and their operations on the complex plane.

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Perform operations on matrices and use matrices in applications.
problem_activity: Problem 1
Consider the set of numbers
$$6$$
,
$${4 \frac{1}{2}}$$
,
$$2$$
, and
$$5$$
, and answer the questions that follow.
a.   Graph the numbers on the number line and list the numbers in order from least to greatest.
[IMG]
b.   Write the opposites of each number and graph them on the number line.
c.   Order the opposites from least to greatest.
d.   Is −5 greater than −2? Explain using your number line.
Problem 2
Order the rational numbers below from least to greatest.
$${5, -4, -\frac{1}{3}, \frac{10}{3}, 3, 0, -4\frac{1}{4}, -4\frac{3}{4}}$$
What strategies did you use to determine the correct order?
Problem 3
A student orders three rational numbers from least to greatest as:
$${{{{{{{{{-5}}}}}}}}}$$
,
$${{{{{{{{{-5}}}}}}}}} \frac {1}{3}$$
,
$$6$$
Are the numbers ordered correctly? Choose the best statement below.


correct_option_index: 10