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### Students love choice in Algebra 2

Who doesn't love choice? My Algebra 2 students love when choice is built into our activities. In my experience, when kids feel like they have a say in their learning, they take more ownership and work harder.

When a student can choose to complete 10 tasks for a 100% but has the option to complete 12 to get extra credit, there is real incentive there. When there is flexibility in accepted answers, the pressure is off and real learning can happen. Below are some of the topics we cover in Algebra 2 and ways I offer choice.

Function shifts:
The "blob activity" is one that the amazing math teachers at my school thought up. It's super easy to make and quickly assesses student understanding of vertex-form function shifts. Students are asked to shift the vertices of vertex-form functions (absolute value, radical, quadratic and cubic) into a blob that somewhere on the grid.

For instance in the picture above, students could record y = (x + 2.9)^2 + 3.5 and be correct. My students like that there are an infinite number of answers.

To make this activity...
Print a grid and draw an irregularly shaped blob somewhere on it. You can also draw the parent function on the grid or not - it's up to you. I like drawing it on there so that my students can better visualize the shifts.

Put the grid into a plastic sheet protector so that students can use a dry erase marker to shift their graphs. Then give each student an answer sheet with spaces for 5 equations for each function type.

Domain and Range:
We spend a lot of time on domain and range throughout the year. It's really rough at first, but by the end my students feel really good about it. I feel pretty darn good about it too. We do so many activities covering the topic, including a card matching activity and a scavenger hunt that summarizes learning.

Once students are confident in what they know, this domain and range math pennant is a great way to showcase student understanding. Students can choose which pennants they'd like to complete to show off what they have learned.

I love problems that give students a set of parameters and ask then to draw graphs. There are endless answer possibilities and these problems really get the kids thinking. In this Algebra 2 game there are 2 stacks of cards-- function types in 1 stack and function characteristics in the other stack. Each student in a group takes a turn choosing a card from each pile to make a "mix-match" of function and characteristic. Students then graph or write the equation, depending on which cards they chose, that satisfy the given characteristics.

Putting the graphing sheets in plastic page protectors lets students use dry erase markers and reuse the graph sheet throughout the activity. Each student gets his or her own equation recording sheet.

Polynomials:
As much as I hate to see my students struggle with word problems, literacy is pretty important across the board. Maybe most important of all is an ability to write. It takes a deep understanding of a topic to write about it, so writing in math helps students solidify their learning and really internalize it.

I recently made a set of 40 reflective Algebra 2 homework sheets that get kids analyzing, justifying and writing. This one above covers polynomials. Students are asked to find who - Pedro or Luci - wrote the correct equation and justify their answer. A term bank is given with directions to "use as many terms as you can". Every student response will be different. Some students will use all terms while others may only use a few. The next day, answers can be reviewed, leading to great conversation and a deep understanding of writing equations from given polynomial graphs. To make the term banks, I have found it easier to write an example student response then backtrack to make the bank.

It can take some of my students a long time to solve one quadratic equation, especially with the Quadratic Formula, so I like to add in a bit of choice. With this chain activity I let students choose any 10 problems to get a 100%. They can choose to do 8 for an 80%, etc. I check the links along the way so that they know exactly what their score will be. More often than not students aim for all 10 (and many aim for all 12!).

Activities in this post can be found in Algebra 2 Activities bundle.

And Number Talks:
I LOVE Number Talks. It took a really, really long time for me to finally jump in because I was confused about how they'd look in high school, how exactly I could apply them in class, and how my students would react. But now that I have tried them I will always include them as part of my year.

The very best thing about Number Talks is that they are all about student choice. Students are given a problem (like this percentage problem) and need to solve it without a calculator, pencil or paper. Each student can choose his or her own way to solve, which is so awesome to be a part of! You can read more about Number Talks in our classroom in this post Number Talks in High School Math.