options: 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.

Perform operations on matrices and use matrices in applications.

Reason quantitatively and use units to solve problems.

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

Represent and model with vector quantities.

Perform operations on vectors.

Extend the properties of exponents to rational exponents.

Use complex numbers in polynomial identities and equations.

Use properties of rational and irrational numbers.

Perform arithmetic operations with complex numbers.

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 multiplication and division to divide fractions by fractions.
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: 1