standard_description: Extend polynomial identities to the complex numbers. For example, rewrite x^(2) + 4 as (x + 2i)(x – 2i).
problem_activity: Narrative
The purpose of this warm-up is to elicit the idea that tape diagrams are similar to bar graphs and can be used to represent the same data, which will be useful as students make sense of the tape diagram throughout this section. While students may notice and wonder many things about these images, recognizing that tape diagrams can show comparisons like a bar graph is the important discussion point.
When students make connections between the different ways the representations represent the same categories and quantities, they reason abstractly and quantitatively and look for and make use of structure (MP2, MP7).
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]
[IMG]
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
“The 2 images at the bottom are called diagrams.”
“What do you think the 15 and 8 represent in the diagrams at the bottom?” (Its how many students that picked apple juice and how many students picked grape juice.)
“What does the question mark in the diagram represent?” (The difference between the number of students that picked apple juice and grape juice, how many more students picked apple juice than grape juice, how many fewer students picked grape juice than apple juice.)


aligns: no