Teaching Algebra 2? Then graphing polynomials is coming!
Coming up with ways to assess this can be a challenge.
Here’s a video of my mini assessments for this unit, along with tips for creating great test questions!
Here are the topics covered in the unit:
- General characteristics of the graph
- Degrees & leading coefficients
- Increasing & decreasing
- Zeros with multiplicity
- Domain & range
- Maximums & minimums
- X-intercepts & y-intercepts
- Writing possible equations
- Graphing in standard form
- Graphing in factored form
Tips for Creating Great Assessments:
Rewrite your questions.
Instead of just asking, “What’s the range?” (as in the first example), consider providing several choices and asking which is the domain and which is the range? In the second example, they could be the same or they could be two different answers.
Hint: If you click on the pictures of the assessment questions, it will automatically take you to that assessment where you can see even more examples.😁
Vary the depth of knowledge.
This can be as simple as telling students to select 3 answers or select “all that apply.”
Here, I’ve varied the questions within the x- and y-intercepts assessment.
In the first example, students know that there are 3 correct answers, but they also have to pay attention to the vocabulary (touch vs. cross).
Suddenly, you’re assessing whether students even realize that there is only one y-intercept, for example.
Here’s another problem. This time, it’s over zeros with multiplicity.
Don’t try to trick students.
I believe in challenging students for sure, but I don’t believe in trying to trick them into getting the wrong answer! I’m sure you don’t, either.
What I mean is that I always try to make sure I’m assessing the actual standard and not something else…
Here’s an example. In the problem below, seeing the actual coordinate point is not the “point” of the question! 🙄😂
Instead, I’m looking for student understanding of max and min.
If my multiple choice questions included answers like this
- (0.6, 0.4)
- (0.5, 0.3)
- (0.6, 0.3)
Well, I think you can see that I would then be frustrating students for no reason!
Instead, they are essentially choosing the correct quadrant from the answer choices and demonstrating their understanding of max and min.
Keep the questions broad.
Here, students are simply expected to pick the one answer that’s correct for increasing/decreasing.
When they look at the answer choices, they see that the answer could be about the increasing values or the decreasing values.
This requires students to look at different aspects of the graph and narrow down answer choices based on what they’re seeing.
Here’s another example from the characteristics of graphs assessment.
Think through the answer choices you provide.
Sometimes pre-made assessment questions have two obviously wrong answer choices and two reasonable choices.
This may be fine sometimes, but I think that lessens the value of the assessment overall.
Because if students can reason their way through the assessment, then you’re not assessing the standards of the content, you’re assessing reasoning!
And reasoning is important. Don’t think I’m saying it’s not!
I just think we should try to create assessments which require students to use their skill knowledge combined with their reasoning skills in order to do well.
Here’s an example that I think applies here. This is from the writing possible equations assessment.
Here’s another example from graphing in factored form.
Require students to show their work.
Occasionally, there’s nothing to show.
More often than not, though, in Algebra 2, students have a significant amount of work to show.
If you’re assessing electronically/online, Google Forms has got your back!
It’s simple to add the “upload your work” question.
Click here to see my Google Forms settings where I show you exactly how to create this type of question. You can read the post or watch it on the video!😊
Below is an example of what this question looks like in the Google Form.
This is the assessment for graphing in standard form.
Students have to do synthetic division twice, then quadratic formula to get all the zeros, and finally sketch the graph.
Quite a lot of work to show!
Also notice that I made the work shown to be 15 points (out of a 20 point assessment).
Match the type of question with the standard your trying to assess.
Mix it up. Don’t just make all multiple choice questions if the standard is better suited to something different.
Vary the types of questions by experimenting with dropdowns, radio buttons (multiple choice), grid answers, etc. Google forms has several options!
Here’s an example of a dropdown question covering leading coefficients and degrees.
I have to admit I usually use dropdowns when I want to have many answer choices (more than four!), so this picture only showing four answer choices isn’t my favorite.
Bonus tip: If you’re assessing problems in a different unit where students are doing lots of solving, dropdowns are great because x can equal a whole range of numbers such as -10 through 10. It makes it less obvious to the student what the right answer is likely to be, without doing the actual work!😁
Here’s an example of the checkbox grid from the increasing/decreasing assessment.
This one can be more of a challenge to set up.
ProTip! Be sure to look at the preview when you’re making questions of this type. Sometimes the margins affect the choices going across the top row, and it makes it hard to understand.
I hope this has helped you as you create assessments for your classroom!
If you have questions for me, I’ll most likely see them over at YouTube. Just leave a comment under this video.
Thank you! And remember…
You’ve got this!