standard_description: Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, Ö3) lies on the circle centered at the origin and containing the point (0, 2).
problem_activity: Warm-up
The purpose of this warm-up is to encourage students to reason about properties of operations in equivalent expressions. While students may evaluate each expression to determine if the statement is true or false, encourage students to think about the properties of arithmetic operations in their reasoning.
Launch
Display one problem at a time. Tell students to give a signal when they have decided if the equation is true or false. Give students 1 minute of quiet think time followed by a whole-class discussion.
Representation: Internalize Comprehension.
To support working memory, provide students with sticky notes or mini whiteboards.
Supports accessibility for: Memory; Organization
Student Facing
Is each statement true or false? Be prepared to explain your reasoning.
25% of 512 is equal to
\(\frac14 \boldcdot 500\)
.
90% of 133 is equal to
\((0.9) \boldcdot 133\)
.
30% of 44 is equal to 3% of 440.
The percentage 21 is of 28 is equal to the percentage 30 is of 40.
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:
Do you agree or disagree? Why?
Who can restate ___’s reasoning in a different way?
Does anyone want to add on to _____’s reasoning?
After each true equation, ask students if they could rely on the same reasoning to determine if other similar problems are equivalent. After each false equation, ask students how the problem could be changed to make the equation true.


aligns: no