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Hello Group 2, Here is the wiki space I created for working on probe 2. We can have all of our discussions and make all of our suggestions here. When we feel the probe is ready to be "published" I will create another Google Doc and send you the link.

The topic of probe 2 was giving the students a verbal representation of a linear function, for example:

Alyssa’s dad started a bank account for you with $10.00 and required you to place your allowance each week of $5.00.into the account. Which of the choices are correct representations of the function described above?

The answer choices will be different representations of the verbal representation, for example:

a) y = 5x + 10 b) graphical representation c) ???

Please use the following color code so we can identify who is commenting:

Gina - Red Luis - Blue Steve - Black Cole - Green _____ Based on research about conceptual knowledge, multiple representations can used as an indicator of conceptual understanding. Research also indicates that being able to provide a "non-example" demonstrates conceptual knowledge. Therefore, the following probe is being suggested.

Proposed probe

Alyssa had $105 in her bank account. She got a part-time job, earning $8.15 per hour, and deposited all the money she earned into her bank account. Which of the following does __**NOT**__ represent the amount of money in Alyssa's bank account if she works 20 hours per week?

a. //d// = 163//w//+ 105 (distractor) I can't say that this answer is incorrect. In fact, this is correct for the amount of money in her bank on a weekly basis...this is why I am proposing to change a little bit the wording on the problem statement. Now this is a distractor since this do not represent the formula to calculate the daily rate of change. Please let me know if you agree so I can expand the distractor explanation.

b. (distractor) This also will be a distractor since represents the ernead money in a weekly basis instead of a daily basis as stated in the problem statement.
 * ~ x ||~ y ||
 * = 0 ||= 105 ||
 * = 1 ||= 268 ||
 * = 2 ||= 431 ||
 * = 3 ||= 594 ||
 * = 4 ||= 757 ||
 * = 5 ||= 920 ||
 * = 6 ||= 1083 ||

c. (distractor)

Same with this distractor, but we need to be careful with this one as students can argue that both the correct answewr and this graph have the same slope, of course if we always compare days with days and weeks with weeks.

d. //b// = 8.15//h// + 105 (answer)

I am proposing b = 32.6//d// + 105....Also on this one please let me know so I can expand....

What do you think? Great!, How about switching distractor (a) to d = 105w + 8.15....or did you have a specific reason for using 163 as the slope?


 * The probe is asking the student to identify the ****// __incorrect__ // representation. Answer choices a, b, and c are correct representations of the word problem and therefore distractors. Each distractor is based on the amount of money deposited into the account weekly. **


 * Answer choice d is incorrect and therefore the answer for the probe. This representation is based on the hourly wage not the weekly income. **

**Teachers’ Notes: Graph Variations and Interpretations **

Grade level for “Graph Identification to Another Graph Interpretation” Probe
 * Grades K -2 || 3-5 |||| 6-8 || 9-12 ||
 * ||  ||   || * || * ||

__Q __uestioning for Student Understanding


 * What d o students understand conceptually about slope as a rate of change through graphical, tabular, and algebraic representation when presented with real life application problem?**

__U __ncovering Understandings


 * Slope Interpretation (rate of change) Content Standard: Algebra and Measurement Variation: Slope **


 * Part II (using different representations to find slope (rate of change) through word problem / graphs / slope y-intercept form) **

__E __<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">xamining __S__tudent Work **