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 Math Talk is to elicit strategies and understandings students have for expressing total lengths and areas, given some dimensions. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to combine like terms to express a total length and express an area of a rectangle in different ways using the distributive property. In this activity, students have an opportunity to notice and make use of structure (MP7) because there are opportunities to invoke the distributive property and to replace expressions with equivalent expressions.
Launch
Display one problem at a time. Give students quiet think time for each problem and ask them to give a signal when they have an answer and a strategy. Keep all problems displayed throughout the talk. Follow with a whole-class discussion.
Student Facing
A rectangle is partitioned into smaller rectangles. Explain why each of these expressions represents the area of the entire rectangle.
[IMG]
\(7(7+7+4+4)\)
\(7(2 \boldcdot 7 + 2 \boldcdot 4)\)
\(7^2+7^2+4 \boldcdot 7+4 \boldcdot 7\)
\(2(7^2) + 2 (4 \boldcdot 7)\)
Student Response
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Activity Synthesis
Ask students to share their strategies for each problem. Record and display their responses for all to see. To involve more students in the conversation, consider asking:
“Who can restate
\(\underline{\hspace{.5in}}\)
’s reasoning in a different way?”
“Did anyone have the same strategy but would explain it differently?”
“Did anyone solve the problem in a different way?”
“Does anyone want to add on to
\(\underline{\hspace{.5in}}\)
’s strategy?”
“Do you agree or disagree? Why?”


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