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

Perform arithmetic operations with complex 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.

Use properties of rational and irrational numbers.

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

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

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

Perform operations on vectors.

Use complex numbers in polynomial identities and equations.

Represent and model with vector quantities.

Extend the properties of exponents to rational exponents.

Perform operations on matrices and use matrices in applications.

Reason quantitatively and use units to solve problems.
problem_activity: Warm-up
The purpose of this activity is to remind students of a few details to keep in mind when doing arithmetic with signed numbers, particularly that subtracting a number has the same result as adding its opposite, and the sign of the product when multiplying two negative numbers, or a positive by a negative number.
Student Facing
Sort these into two groups, so that the expressions in each group all have the same value.
\(3-5\)
\(5+3\)
\(4 \boldcdot 2\)
\(\text- \frac13 \boldcdot 6\)
\(5 - \text-3\)
\(\text-4 \boldcdot \text-2\)
\(3 + \text-5\)
\(\frac13 \boldcdot \text-6\)
Student Response
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Activity Synthesis
Use students’ explanations for why expressions are equal to draw attention to things to keep in mind when doing arithmetic on signed numbers. For example:
Subtracting a number has the same result as adding its opposite.
\(3-5=3+\text-5\)
Multiplying a negative number by a negative number results in a positive product.
\(\text-4  \boldcdot \text-2\)
and
\(4 \boldcdot 2\)
are both equal to 8.
Multiplying a negative number by a positive number results in a negative product
\(\text- \frac13 \boldcdot 6\)
and
\(\frac13  \boldcdot \text-6\)
are both equal to -2.


correct_option_index: 5