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I chose this problem on page 99 because I initially had trouble creating a word problem that made sense. After working through ideas of different scenarios, I finally decided on water leaking from a cup to represent the function.

Once I graphed the problem and created the table, the word problem made sense and seemed to represent what was happening in the problem. Seeing all the different ways to represent the problem allowed me to make more sense of the function.

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The questions asked by the teacher in this video helped facilitate the students' understanding by allowing students to explain their thinking and invite other students to build on their ideas. The questions also allowed students to take their peers' ideas and put those ideas in their own words, which helped clarify what others were saying.

The teacher then asked students the advantage of each type of representation and why seeing all three helps students better understand functions.

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Chapter 4 connects to the Five Equity-Based Practices in Mathematics Classrooms in many ways. The first connection is Going Deep With Mathematics. The chapter does this by allowing the reader to create their own problems to make sense of functions instead of just giving examples of word problems.

The next connection is Leveraging Multiple Mathematical Competencies. The chapter shows this in the Connecting Representations of Functions video and the Interpreting graphs to Create Context video. Students in these videos have different abilities and use these differing abilities to work together to solve function problems.

The third connection is Affirming Mathematics Learners' Identities. An example of this is shown in the videos by allowing students to share their knowledge with one another to understand the problems. The teacher even lets students know that common misconceptions are part of the process and allow students to work through the misconceptions to better understand what is going on.

Challenging Spaces of Marginality is seen in the chapter videos by showing all students as equal members in each group with a variety of ideas that are valuable for working through the complex problems.

The final connection is Drawing on Multiple Resources of Knowledge. In the Interpreting Graphs to Create Context video the students use their prior knowledge of slope and rate of change to evaluate the function and make sense of what is happening at each point of the graphs in the problem.

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Chapter 4 from our textbook allowed me to see all the different ways a function can be represented. Connecting the equations, graphs, and tables allowed me to better understand functions and make sense of them in the context of a word problem. This information not only helps me gain a better understanding, but will help me teach functions in the future. I learned that it is important to use all representations of functions when developing understanding and clearing misconceptions.