Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

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ConnectionsSession 06 OverviewTab atab btab ctab dtab eReference
Part A

Observing Student Connections
  Introduction | Investigating Functions | Problem Reflection #1 | Connecting to Logarithms | Problem Reflection #2 | Classroom Practice | Observe a Classroom | Your Journal


Think about the student work you just observed and reflect on the following questions. Once you've formulated an answer to each question, select "Show Answer" to see our response.

Question: How does this problem provide an opportunity to assess students' understanding of functions that are graphed using technology?

Show Answer
Sample Answer:
The students encounter the limitations of technology in terms of the number of significant digits that can be displayed. They become more aware of the importance of window size, since the graph behaves differently in various portions of the coordinate plane. Such considerations help students develop a more careful examination of the connections between various forms of representation.

Question: How does this problem entice students to informally consider limits?

Show Answer
Sample Answer:
The specific discussion about the x value when x = -100 leads students to consider the value of 2x and to engage in mathematical reasoning. Also, the rapid growth of y with positive x values encourages consideration of an expression that approaches a value of positive infinity as x takes on larger values.

Question: How does this problem encourage the exploration of mathematical connections?

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Sample Answer:
Connections are made to simpler concepts, such as significant digits, the effects of rounding, and scientific notation, and to real-world examples. Students are introduced to future topics, such as limits and the rate of growth in an exponential function. Students connect graphical and algebraic solutions for y when given x = -100. They also discuss the meaning of linear function and use reasoning to establish that the portion of the graph that looks linear is not. Finally, they make connections to doubling functions.

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