Answer:
This warm-up encourages students to use the meaning of fractions and properties of operations to reason about equations. While students may evaluate each side of the equation to determine if it is true or false, encourage students to think about the following ideas in each:
The first question: Dividing is the same as multiplying by the reciprocal of the divisor.
The second question: Adjusting the factors adjusts the products. If both factors increase, the resulting product will be greater than the original.
The third question: The commutative property of multiplication.
The fourth question: Decomposing a dividend into two numbers and dividing each by the divisor is a way to find the quotient of the original dividend.
Launch
Display one problem at a time. Tell students to give a signal when they have an answer and a strategy. After each problem, give students 1 minute of quiet think time and follow with a whole-class discussion.
Student Facing
True or false?
Student Response
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Activity Synthesis
Ask students to share their strategies for each problem. Record and display their explanations for all to see. Ask students if or how the factors in the problem impacted the strategy choice. To involve more students in the conversation, consider asking:
“Who can restate ___’s reasoning in a different way?”
“Does anyone want to add on to _____’s strategy?”
“Do you agree or disagree? Why?”
After each true equation, ask students if they could rely on the reasoning used on the given problem to think about or solve other problems that are similar in type. After each false equation, ask students how we could make the equation true.
Step-by-step explanation:
