standard_description: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
problem_activity: Narrative
The purpose of this warm-up is to elicit student ideas for how a tape diagram could be used to represent a Take From problem involving lengths. This will be useful when students solve story problems in the context of length in a later activity. While students may notice and wonder many things about these images, the connections students make between the image, the tape diagram, and the equation are the important discussion points.
Launch
Groups of 2
Display the image.
“What do you notice? What do you wonder?”
1 minute: quiet think time
Activity
“Discuss your thinking with your partner.”
1 minute: partner discussion
Share and record responses.
Student Facing
What do you notice? What do you wonder?
[IMG]
[IMG]
\(54 - 16 = {?}\)
Student Response
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Activity Synthesis
“What do you think the diagram and the ribbon could have in common?” (Maybe the 54 is cm or in, so 16 is how much of the ribbon is being cut off.)
“What could the question mark represent?” (The longer part of the ribbon after it is cut. It represents the value of
\(54-16\)
.)


aligns: no