standard_description: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
problem_activity: Narrative
This warm-up prompts students to carefully analyze and compare equations. In addition to calculating the value of each expression, students also think about the structure of each expression, including both the operations and the numbers (MP7). In the synthesis, students compare an equation with addition and an equation with subtraction to focus student attention on comparing operations and reasoning about the relationship between addition and subtraction.
Launch
Groups of 2
Display image.
“Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
1 minute: quiet think time
Activity
“Discuss your thinking with your partner.”
2-3 minutes: partner discussion
Share and record responses.
Student Facing
Which one doesn’t belong?
\(10 = 6 + 4\)
\(16 - 5 = 11\)
\(11 = 6 + 4 + 1\)
\(3 + 8 = 11\)
Student Response
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Activity Synthesis
Display equations B and C.
“How are the equations the same? How are they different?” (They both have the value 11. The first equation uses subtraction while the second one uses addition. The 11 is on the right hand side in the first equation and on the left hand side in the second equation. In the second equation 11 is written using three numbers and there are only two in the first equation.)


aligns: no