Are your Algebra 2 students struggling with polynomials and polynomial long division? There is a free PDF cheat sheet in this post that can be downloaded, printed and given to students for their notebooks. The sheet can also be enlarged for a math word wall.
Complex numbers are amazingly fun to teach in Algebra 2 because it is the first time students have ever seen them. It turns many of their previous “no solutions” into answers, how exc…
If anyone knows what algebra even is, lmk.
Are your students struggling to graph polynomial functions? In this post is a free cheat sheet for the steps of graphing polynomials, as well as links to other helpful resources for teaching polynomials.
This handy guide includes the algebraic equations for multiplying binomials, dealing with radicals, finding the sum of sequences, and more.
Do your students struggle to graph logarithmic functions? This free pdf printable cheat sheet walks Algebra 2 students through the steps of graphing a log. It's a great sheet to hand out during a logarithms unit for students notebooks or to enlarge for a bulletin board.
Logarithms help you add instead of multiply. The algebra formulas here make it easy to find equivalence, the logarithm of a product, quotient, power, reciprocal
Need to know how to do synthetic division? Could you use a free math cheat sheet for the algorithm and a video to go along with it? Well you're in the right place!
My Algebra 1 students have just started their unit on sequences. This is my first time teaching sequences in Algebra 1 because it used to be in the old Algebra 2 standards. For the past four years,
I've never really known what to do about teaching radicals in Algebra 1. Oklahoma's Algebra 1 standards currently have students simplify expressions involving radicals in Algebra 1. This is not the
[UPDATED – Sept. 25 2015] We have just spent a week working with quadratics in MPM2D and today I had students create their own angry birds level. The only real requirement was for them to create at least two flight paths and model them with quadratic equations. I was hoping to see how they relate the […]
Last week we were studying matching Verbal Descriptions to a graph. Some students are naturally good at this, and others really struggle. Despite my best efforts to teach this topic, when looking at a Speed v. Time graph that increases and then decreases, many students will invariably choose the answer choice that indicates someone is walking up a hill and then down a hill. I decided to try an interactive approach this year and selected twelve graphs and 18 verbal descriptions. I had the students cut out the verbal descriptions and then work together in groups to match the descriptions to the graphs. This activity turned out to be quite difficult for many of the students and looking back, I decided that having six incorrect answers was just too much and made the activity unnecessarily difficult. I reworked the activity to include only three incorrect answers in an effort to make it a little less time consuming. You can download the activity here.
Twenty-two engaging problems for matching phrases to algebraic expressions. Students like this activity. You could enlarge the worksheet and cut out the phrases and expressions ahead of time - or have students do the cutting - then have them paste the matching pairs on a large colored sheet.The prev...
There are many different versions of the Angry Birds Parabola Project. We compiled the best methods to use with your class. Transforming Parabolas.
Increasing and Decreasing Functions Activity
Algebra is all about graphing relationships, and the curve is one of the most basic shapes used. Here's a look at eight of the most frequently used graphs.
Defines functions and includes examples of tables, graphs, mappings, and lists of odered pairs.
Basic Parent Functions Writing Transformed Equations from Graphs Generic Transformations of Functions Rotational Transformations Vertical Transformations Transformations of Inverse Functions Horizontal Transformations Applications of Parent Function Transformations Mixed Transformations More Practice Transformations Using Functional Notation For Absolute Value Transformations, see the Absolute Value Transformations section. Here are links to Parent Function Transformations in other sections: Transformations of Quadratic Functions (quick and … Parent Functions and Transformations Read More »
"Be kind whenever possible. It is always possible." ― Dalai Lama
Introducing Quadratic Factoring with Conspiracy Theory in Special Ed Algebra 2
This lesson helps my algebra students learn to factor polynomial and quadratic expressions. The notes and activity make teaching this topic so much easier.
I finished up my unit on Systems of Equations before the Thanksgiving break and was left with a two-week window before the district said I had to give a Mid-Year Exam. The pacing guide had us starting polynomials and quadratics, but that was not a unit I wanted to break up over the Christmas break, so I decided to spend these two weeks on Radicals. In the past two years, I have crammed in Radicals right before we start reviewing for the EOC, so I liked having the unit at this time instead because I didn't feel so rushed. Coming off Systems of Equations, this was also a chance for students to catch their breath with an easier concept -- before we head into quadratics and really blow their minds ;) We started with a quick review of the Laws of Exponents and this free foldable. I added some notes for students to fill in summarizing the rule for each step before I sent it to the copier. I showed them how to expand each problem and then asked them to come up with the rule, which helps them to visualize what's going on, and gives them a strategy to go back to when they forget the rule. Negative and Zero exponents always throw students for a loop, so they needed their own sheet of notes. I loved this post from Scaffolded Math and Science about Negative Exponents. We did these three problems and then I asked students to find the rule. We continued the pattern to see that what happens when you have negative exponents. Again, the students summarized the rule and had a pretty good understanding. So I put them to the test with this puzzle. I love listening to students talk about these problems and watching their understanding grow. We finished up with a word problem about exponential growth. I love how this problem has students interpret what the negative exponents mean in the context of this word problem - I was proud that students in each class came to the conclusion that negative exponents would indicate time before the experiment started. It also helps them solidify the idea that a zero exponent doesn't equal zero, because it represents the starting point. Day 2, it was time for radicals! Like last year, I was determined not to teach a trick. I showed them both how to simplify with prime numbers and perfect squares. I write out a lot of steps, and often students find ways to simplify and shorten once they understand what they are doing. I also made a point of explaining every step. "The square root of 2 squared is 2, so I can simplify it as a whole number outside the radical. But the square root of 5 is an irrational number, so I leave that inside the radical." By repeating this step (what seemed like a million times), I didn't have students trying to bring the number with its exponent outside the radical. I did, however, still have some students tricked by this check all that apply. That last problem always leads to a debate, but I had far less students thinking it was correct that in years past. We practiced simplifying radicals with this coloring activity. I love that the answer bank allows students to self-check as they go. There is nothing worse than practicing a skill incorrectly, so I like when they have to stop and find their mistake when their answer doesn't match one of the choices. Plus the coloring provides a nice brain break! For Day 3, I put a problem up on the board with variables inside the radical and asked students to decide what to do. I've been focusing a lot on hooking everything to their prior knowledge. Someone suggested expanding x^3, and then students could see variables were really no different than dealing with factors. I love these Check All That Apply question types for this topic. After a few examples, they practiced with a puzzle. Students had to be careful to "attend to precision" because several of the problems and answer choices were similar. This forced students to really focus on their exponents and see the difference between having x^3 inside a radical and x^4. It also meant that students didn't have to keep re-creating a factor tree for each problem. I heard great discussions about what happens when the radical has a coefficient in front of it too. Next we moved on to Operations on Radicals - adding, subtracting and multiplying them, which I introduced with these fun {FREE} Interactive Notes. Students practice applying the operations on radicals to find the area and perimeter of shapes - and the shapes are super fun to color! We also did some regular practice problems on the neighboring page. Students practiced with a Versatiles activity and then completed an exit ticket/ mini quiz. Here is a link to the exit tickets if you want to use them. That left us with one day left for review/wrap up. I love having an extra catch-up day like this at the end of the unit. The exit ticket provided me with some great data for who needed remediation (students who had been absent for a few days were super confused) and who was ready for some enrichment. I reminded students that so far we had been dealing with square roots, which have an index of 2, and then I presented a problem with an index of 3 and asked students how they thought it would be different. Then I did one with an index of 4 - they knew right away what to do. Next students completed a variety of assignments - those who needed help completed this maze. I love how they receive instant feedback by finding their answer in one of the arrows. This maze was perfect for those students still struggling with the overall concept or students who had missed a couple classes over the two -week period. Some students wrapped up the Simplify Radicals Coloring Activity from earlier in the week. Those who were up for a challenge took on the Operations on Radicals Coloring Activity. Again with the answer bank, this time in the flower petals. Students with extra time answered some pennant problems - these are my go-to when I have a few minutes left at the end of class that needs to be filled. Plus students love decorating them and seeing their work on display on the walls and halls. I also gave students the option to retake the Exit Ticket/ Mini Assessment if they were unhappy with their grade or thought they could do better. I love giving students the opportunity to challenge themselves to get a better score, and to see improvement. Sometimes just one class period makes all the difference in their understanding - like this student who went from a 50% to a 100% :) Totally RADICAL!
We are finishing up our Quadratics unit in Algebra 1 and I wanted to share some of my favorite foldables and activities. Below is a cut and paste activity that we did as soon as we finished going over the basic key terms of quadratics. For the ROXS column, I tell my students that the acronym stands for Roots, Zeros, X-Intercepts, and Solutions to help them with the vocabulary. Students did extremely well on this activity and in hindsight, I did not know how much I would appreciate adding the factors columns. Here are some Transformations of Quadratics interactive notebook pages that I used. I really liked these pages because students were able to visually see the transformation and explain what was "happening." After the foldable, students worked on their first partner activity of the new year. I forgot how much collaboration and communication occurs when students work together on partner activities. Students really enjoy checking their answers with a partner! We spent two days covering transformations of quadratics and on the second day, students completed the following Desmos Challenge that was created by MathyCathy and Michael Fenton: I absolutely LOVED this Desmos Challenge and so did students. If there are any more Desmos challenges similar to this one, please send them my way! This is all we were able to cover before Spring Break so I knew I had to create a review game when students came back. I ended up making a PPT review game where class periods ended up competing for the most point. The class period that received the most points received a jolly rancher and free homework pass. I don't know about your students, but my students LOVE companions! The following day, we went over the vertex form in their notebook and completed a Google Slides activity in Schoology. Below is a Google Slides activity that I assigned to students where they had to copy and paste the triangle to the correct location. Thank you so much for taking the time to read this post. If you end up trying some of these activities and foldables, I would love to know! If you would like to use the activities and foldables, click on the links below: Quadratic Key Terms Quadratic Key Words Graphic Organizer Transformations of Quadratics Foldable Transformations Partner Activity Google Slides Vertex Form Activity (FILE - MAKE A COPY)
Review of Polynomials Factor and Remainder Theorems Polynomial Graphs and Roots DesCartes’ Rule of Signs End Behavior of Polynomials and Leading Coefficient Test Putting it All Together: Finding all Factors and Roots of a Polynomial Function Zeros (Roots) and Multiplicity Finding Polynomial Characteristics Using a Graphing Calculator Writing Equations for Polynomials Solving Polynomial Inequalities Conjugate … Graphing and Finding Roots of Polynomial Functions Read More »
Introducing Quadratic Factoring with Conspiracy Theory in Special Ed Algebra 2
