standard_description: (+)Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.
problem_activity: Narrative
This Number Talk prompts students to use place value and properties of operations to multiply single-digit numbers by multiples of ten. The strategies elicited here help students develop fluency.
Launch
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.
\(4\times40\)
\(8\times40\)
\(7\times40\)
\(9\times40\)
Student Response
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Activity Synthesis
“How were you able to use
\(4\times40\)
to find the other products.” (I doubled
\(4\times40\)
to find
\(8\times40\)
. Once I knew
\(4\times 40\)
, I could count up or down by 40 to get the other products.)
Consider asking: “Why might it be helpful to first think of each expressions as multiplying a number and 4 instead of 40?” (We know many multiplication facts for 4, and that 40 is 4 tens. We can think of each problem as groups of 4 tens instead of groups of 40.)


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