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

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

Represent and model with vector quantities.

Use properties of rational and irrational numbers.

Reason quantitatively and use units to solve problems.

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.

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

Perform operations on vectors.

Extend the properties of exponents to rational exponents.

Perform operations on matrices and use matrices in applications.

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

Represent complex numbers and their operations on the complex plane.
problem_activity: Warm-up
The purpose of this warm-up is for students to review plotting and labeling points that include negative coordinates and use repeated reasoning to generalize patterns in the coordinates of points in each quadrant (MP8).
Digital
Launch
Arrange students in groups of 4. Assign each person in a group a different quadrant. Tell students you will give them 2 minutes to plot and label at least three points in their assigned quadrant, and up to six if they have time. Give students 2 minute of quiet work time. Give students 4 minutes to share their points and their coordinates with their small group and look for patterns in the coordinates of points in each quadrant. Follow with whole-class discussion.
Though the paper and pencil version may be preferred, a digital applet is available for this activity.
Student Facing
Plot points in your assigned quadrant and label them with their coordinates.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Print
Launch
Arrange students in groups of 4. Assign each person in a group a different quadrant. Tell students you will give them 2 minutes to plot and label at least three points in their assigned quadrant, and up to six if they have time. Give students 2 minute of quiet work time. Give students 4 minutes to share their points and their coordinates with their small group and look for patterns in the coordinates of points in each quadrant. Follow with whole-class discussion.
Though the paper and pencil version may be preferred, a digital applet is available for this activity.
Student Facing
Plot points in your assigned quadrant and label them with their coordinates.
[IMG]
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
The focus of the discussion is for students to explain why the following patterns emerge:
In quadrants I and IV, the x-coordinate of a point (or the first number in an ordered pair) is positive.
In quadrants II and III, the x-coordinate of a point is negative.
In quadrants I and II, the y-coordinate of a point (or the second number in an ordered pair) is positive.
In quadrants III and IV, the y-coordinate of a point in is negative.
Ask the students to share any patterns they noticed among the coordinates of the points in each quadrant. After each student shares, ask the rest of the class if they noticed the same pattern within their small group. Record and display these patterns for all to see. If possible, plot and label a few example points in each quadrant based on students' observations.


correct_option_index: 0