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

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

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

Represent and model with vector quantities.

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

Perform operations on matrices and use matrices in applications.

Use properties of rational and irrational numbers.

Use complex numbers in polynomial identities and equations.

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

Perform arithmetic operations with complex numbers.

Reason quantitatively and use units to solve problems.

Extend the properties of exponents to rational exponents.

Represent complex numbers and their operations on the complex plane.

Perform operations on vectors.
problem_activity: Problem 1
Working together, it takes Sam, Jenna, and Francisco 2 hours to paint one room. When Sam is working alone, he can paint one room in 6 hours. When Jenna works alone, she can paint one room in 4 hours. Describe how long it would take Francisco to paint one room on his own.
Problem 2
Jamie and Ralph take a canoe trip up a river for 1 mile and then return. The current in the river is 1 mile per hour. The total trip time is 2 hours and 24 minutes. Assuming that they are paddling at a constant rate throughout the trip, find the speed that Jamie and Ralph are paddling. When Jamie and Ralph are paddling WITH the current (one way of their trip), their speed is
$${x+1}$$
. When Jamie and Ralph are paddling AGAINST the current (the other way of their trip), their speed is
$${x-1}$$
.


correct_option_index: 10