standard_description: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
problem_activity: Narrative
The purpose of an Estimation Exploration is to practice the skill of estimating a reasonable answer based on experience and known information.
Launch
Groups of 2
Display the expression.
“What is an estimate that’s too high? Too low? About right?”
1 minute: quiet think time
Activity
“Discuss your thinking with your partner.”
1 minute: partner discussion
Record responses.
Student Facing
\(4 \times 18\)
Record an estimate that is:
|                    too low                     |                  about right                   |                    too high                    |
|------------------------------------------------|------------------------------------------------|------------------------------------------------|
| \(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\) | \(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\) | \(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\) |
Student Response
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Activity Synthesis
Consider asking:
“Is anyone’s estimate less than ___? Is anyone’s estimate greater than ___?”
“Based on this discussion does anyone want to revise their estimate?”


aligns: no