standard_description: Interpret multiplication as scaling (resizing), by:
- Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.
- Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
problem_activity: Warm-up
The purpose of this Math Talk is to elicit strategies students have for solving equations in one variable, especially equations involving an expression in parentheses being multiplied by a coefficient. Developing fluency with these types of equations will be helpful in the associated Algebra 1 lesson when students substitute expressions in place of single variables and solve equations with expressions in parentheses.
In particular, students should see that to solve an equation like
\(100=10(x-5)\)
, a productive first step is to divide each side by 10.
Math Talks build fluency by encouraging students to think about expressions or equations and rely on what they know about properties of operations and equality to mentally solve a problem.
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
Solve each equation mentally.
\(100=10(x-5)\)
\(300=30(x-5)\)
\(15-971=x-4-971\)
\(\frac{10}{7}=\frac17 (x-19)\)
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?”


aligns: no