standard_description: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
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.


aligns: no