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
This Number Talk encourages students to look for and make use of the structure of numbers in base-ten to mentally solve division problems. The reasoning elicited here will be helpful later in the lesson when students divide large numbers using increasingly more abstract strategies.
Launch
Groups of 2
Display one expression.
“Give me a signal when you have an answer and can explain how you got it.”
1 minute: quiet think time
Activity
Record answers and strategy.
Keep expressions and work displayed.
Repeat with each expression.
Student Facing
Find the value of each expression mentally.
\(90 \div 3\)
\(96 \div 3\)
\(960 \div 3\)
\(954 \div 3\)
Student Response
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Activity Synthesis
“How did each expression help you find the next one?”
Consider asking:
“Who can restate _______ 's reasoning in a different way?”
“Did anyone have the same strategy but would explain it differently?”
“Did anyone approach the expression in a different way?”
“Does anyone want to add on to____’s strategy?”


aligns: no