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### Teaching small group Algebra 2

Teaching small group algebra 2 was challenging and super rewarding. Now that I am out of the classroom, teaching algebra 2 is one of the things I miss most. So much growth happens in students between when they enter the course and leave it. There were always so many times when my students thought a topic would be way too hard and ended up mastering it not too much time later.

In this post I want to share some of the teaching ideas and materials that I used in my small group special education algebra 2 class. Every student had an IEP and most were in 11th grade. Some were seniors, but most seniors in small group math took consumer math. I'll also link towards the end some of the cheat sheets I made for our inclusion algebra 2 class that got a bit farther in the curriculum than we did in small group.

If you've taught 9th grade algebra, you will likely recognize some of the topics we cover in small group algebra 2. A lot of review was necessary to lay the groundwork for new topics:

These are the units we covered in small group algebra 2:

• Increasing and decreasing
• Domain and range
• Function/not a function
• Evaluating functions
• Graphing absolute value functions - vertex form
• Graphing quadratics - vertex form
• Graphing radicals - vertex form
• Function operations
• Factoring
• Complex numbers
• Graphing quadratics in all forms
• Polynomials
• Inverse functions

In our inclusion class, we also covered:

• Polynomial long division
• Synthetic division
• Exponential Functions
• Logarithms
• Graphing rational functions

## TEACHING SMALL GROUP ALGEBRA 2

If you've taught 9th grade algebra 1, you'll probably recognize some of the topics we cover in small group algebra 2. This is because a lot of review is necessary to lay the groundwork for the new topics.

Increasing and decreasing
Our year always started with an introduction to nonlinear functions and how their graphs compare to linear functions.

When is a graph increasing? When is it decreasing? We always started the year with an overview of towards and away motion graphs. As Lila and her friends raced to school, they got tired so they slowed down. The distance between the friends and home decreased as they ran from school to home, then increased as they raced back to school.

Teachers at my school also used motion sensors and a water lab to introduce motion graphs. There is also a virtual Desmos water lab.

Domain and range
We always spent extra time on domain and range since it comes up throughout the school year.

Students often had some trouble finding the domain and range of graphs. Dragging a pencil across the grid, then asking students to say, "stop!" when the pencil hits the graph, then again when the pencil left the graph, helped them identify the intervals' start and end points. Here are the practice cards we used and here is the reference sheet.

Warm-ups get pencils in hands and students working as soon as they enter class. We used this algebra 2 template throughout the year to graph functions.

Function vs. not a function
Identifying when a relation is a function always got a quick review.

We looked at relations represented in tables, graphs, mappings, equations and sets of coordinates to determine which were functions.

We can remain the same height year after year, but can we be two different heights at the same time? One is a function, one is not a function in that it doesn't make sense in real life. I drew these two graphs on the board and asked students which made sense. This brought us into the vertical line test for functions.

Evaluating functions
Leaving non-functions behind, we'd then get into evaluating functions given graphs, equations, word problems and tables.

We'd also learn to compose functions given different function forms.

Before teaching students how to graph functions in vertex form, I gave them a See, Think, Wonder sheet and put an absolute value graph (part of our algebra 2 word wall) and equation on the board. I asked students to take a minute to write down what they see, then what they think, then what they wonder.

My 11th grade algebra 2 students weren't totally familiar with this format, but I wanted to give them a few minutes to make the connection between the equation and vertex of a function in vertex form before we jumped into learning about them.

Graphing absolute value functions - vertex form
At this point in the year, my students started to need visual supports and reminders, which I provided through our algebra 2 word wall (with some algebra 1 references added in) and math cheat sheets

We graphed most functions throughout the year by completing tables. This provided extra practice evaluating functions, and the structure of always using a table seemed to work well.

After absolute value functions, we learned about graphing quadratics in vertex form

For a quadratic with a value = 1, the pattern from the vertex -- up 1, over 1; up 3, over 1; up 5, over 1, up 7 over 1 -- helps find additional coordinates once the vertex is found. We still completed tables, then used the pattern as a check. Students completed a set of vertex form task cards.

We graphed quadratics in vertex form by completing a table then plotting coordinates (video).

We analyzed the relationship between the graphs of quadratic functions and radical functions to set the stage for later when we learned about inverse functions, then review transforming vertex form functions before moving to our next unit.

Function operations
We then switched gears into function operations-- adding, subtracting and multiplying.

In small group, we focused on adding, subtracting and multiplying functions. We also reviewed evaluating functions with a fun dice activity.

Factoring
Next came factoring. One year I did decide to give students a multiplication chart, which helped those who did not know their multiplication tables. Students were generally thankful for the table, which I hadn't expected. I thought giving them a multiplication table to use during factoring would be an insult, but it didn't turn out that way.

Before jumping into trinomial factoring, we played a game of figuring out two numbers that multiply to a certain number and add to a certain number.

A lot of factoring was a review from algebra 1. It seems to be one of those topics that can be reviewed every year. We completed a lot of factoring activities. Finding GCFs of binomials and trinomials was more difficult for students than I had expected. The multiplication table helped as a support.

The Quadratic Formula was another algebra 1 review.

Even so, we practiced with the formula a lot.

Students used a Quadratic Formula template for their warm-up throughout the unit that helped organize the constants.

Complex numbers
We did a quick jump to learning about complex numbers, then went back to the Quadratic Formula so see how they show up there.

When students asked why there are imaginary numbers, I flicked the lights on and off and mentioned that we need the square root of -1 to explain the way electricity flows.

We then move to graphing quadratics in factored form.

We compare the axis of symmetry formula to finding the mean between 2 numbers. We also use the up 1, over 1; up 3, over 1... pattern when the quadratic's a value = 1.

I like point out the pattern that emerges when we graph quadratics. For a quadratic with an a value of 1, the pattern from the vertex -- up 1, over 1; up 3, over 1; up 5, over 1, up 7 over 1 -- helps find additional coordinates once the vertex is found.

This is one of my favorite units in algebra 2 because of how much students learn.

We start with a numberless quadratics activity that helps students with identifying the parts of the parabola they are being asked to find.

We had a quadratic keywords poster as part of our math word wall so that students could get a quick vocabulary refresher if needed.

Students practiced solving quadratic word problems, finding maximums, minimums, zeros and y-intercepts.

Next we moved on to solving radical equations.

We analyzed the "invisible" part of a radical graph that would be there if the radical was 1:1 with its quadratic inverse, and related it to the radical equation's extraneous solution

Polynomials
Sketching polynomials was another favorite unit because of all the learning that happened. At first, students think the equations are far too complicated-looking to ever be able to graph. But within a few days they are able to do it. We started with naming polynomials then moved on to sketching.

The polynomials section of our algebra 2 word wall helped students identify zeros, bounces, crosses, zeros and end behavior.

We used another template and cheat sheet for sketching polynomials. With all of the warm-up templates, students grabbed one on the way to their seat and completed it based on the information on the board.

Inverse functions
Usually the last unit we'd get to in small group was our inverse functions unit.

A hole punch can be used to investigate inverse functions in the coordinate plane (post and video).

By this time of the year, my juniors were the oldest students in the building because the seniors had already left, and were very excited for summer.

In algebra 2 inclusion:
To help support students in our inclusion algebra 2 class, I made a series of cheat sheets for student notebooks:

Polynomial long division

Synthetic Division

Exponential functions

Logarithms

Graphing rational functions

I hope this post has been helpful if you are a small group or inclusion algebra 2 teacher.