Communicate 4.2.1

In the course I teach, Advanced Algebra, I have quite a few assignments that students complete.

This is one of the assignment students complete: Rational Graphs and Radical Equations Handout

The standards it covers are:

Understand solving equations as a process of reasoning and explain the reasoning
MGSE9-12.A.REI.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Represent and solve equations and inequalities graphically 
MGSE9-12.A.REI.11 Using graphs, tables, or successive approximations, show that the solution to the equation f(x) = g(x) is the x-value where the y-values of f(x) and g(x) are the same.

Interpret functions that arise in applications in terms of the context
MGSE9-12.F.IF.4 Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function which models the relationship between two quantities. Sketch a graph showing key features including: intercepts; interval where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

MGSE9-12.F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.

Analyze functions using different representations
MGSE9-12.F.IF.7d Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.


Here is an example of student work: https://drive.google.com/file/d/0B60QLjf8TJQ9TTgxTXptUWpkN0E/view?usp=sharing

Finally, here is the feedback I left for the student. A few things I include:

• how many points they earned on a question they got wrong.  Instead of just saying you got 4/5 correct I try to give partial credit.
• an explanation of the correct answer or how to get to the correct answer.
• positive encouragemenyt