options: Use complex numbers in polynomial identities and equations.

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

Represent complex numbers and their operations on the complex plane.

Perform operations on vectors.

Perform operations on matrices and use matrices in applications.

Reason quantitatively and use units to solve problems.

Use properties of rational and irrational numbers.

Represent and model with vector quantities.

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

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

Perform arithmetic operations with complex numbers.

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

Extend the properties of exponents to rational exponents.

Apply and extend previous understandings of numbers to the system of rational numbers.
problem_activity: Warm-up
This warm-up prompts students to compare four expressions. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the items in comparison to one another.
Launch
Arrange students in groups of 2–4. Display the expressions for all to see. Give students 1 minute of quiet think time and then time to share their thinking with their small group. In their small groups, ask each student to share their reasoning why a particular item does not belong, and together find at least one reason each item doesn't belong.
Student Facing
Which one doesn’t belong?
A.
\(i^2\)
B.
\((1 + i) + (1 - i)\)
C.
\((1 + i)^2\)
D.
\((1 + i)(1 - i)\)
Student Response
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Activity Synthesis
Ask each group to share one reason why a particular item does not belong. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which one does not belong, attend to students’ explanations and ensure the reasons given are correct. During the discussion, ask students to explain the meaning of any terminology they use, such as real part or imaginary part. Also, press students on unsubstantiated claims.


correct_option_index: 10