options: Perform operations on vectors.

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

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

Reason quantitatively and use units to solve problems.

Represent complex numbers and their operations on the complex plane.

Represent and model with vector quantities.

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

Perform arithmetic operations with complex numbers.

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

Extend the properties of exponents to rational exponents.

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

Perform operations on matrices and use matrices in applications.

Use properties of rational and irrational numbers.

Use complex numbers in polynomial identities and equations.
problem_activity: Warm-up
The purpose of this warm-up is for students to reason about numeric expressions using what they know about operations with negative and positive numbers without actually computing anything.
Launch
Explain to students that we sometimes leave out the small dot that tells us that two numbers are being multiplied. So when a number, or a number and a variable, are next to each other without a symbol between them, that means we are finding their product. For example,
\((\text-5)\boldcdot (\text-10)\)
can be written
\((\text-5) (\text-10)\)
and
\(\text-5 \boldcdot x\)
can be written
\(\text-5x\)
.
Display one problem at a time. Give students 1 minute of quiet think time per problem and ask them to give a signal when they have an answer. Follow with a whole-class discussion.
Student Facing
Decide if each statement is true or false. Be prepared to explain your reasoning.
\((\text-38.76)(\text-15.6)\)
is negative
\(10,000 - 99,999 < 0\)
\(\left( \frac34 \right)\left( \text- \frac43 \right) = 0\)
\((30)(\text- 80) - 50 = 50 - (30)(\text- 80)\)
Student Response
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Activity Synthesis
Ask students to share their reasoning.


correct_option_index: 6