## How I teach Factoring

Factoring is one of those skills that students must know how to do since they will use it in every high school math class. This skill is one of the most important skills and unfortunately some students never really get it. I hear calculus teachers complain about how their students can’t factor. Students should already know how to factor before entering calculus but why don’t they? Factoring will be in all the college entrance exams too because students need to know how factor for their college math classes. I know in Texas that students can know very little about factoring and still pass the Algebra EOC. Questions on the EOC can be figured out by working backwards from the answer choices. There usually is one question each year where students have to find one of the factors which does make it a tougher question. Students really do not learn how to really factor until Algebra 2.

When I was in high school the method that was taught was guess and check. We got pretty good at it but back then you knew your multiplication facts very well. When I first started teaching math, I honestly had no clue how to teach factoring. I’ve done every method or fad that came along but I have settled on a method after realizing that this is how it is taught in many college algebra classes. The method I use is GROUPING! I focus heavily on finding GCF’s and factoring by grouping and then when it’s time to factor the tough trinomial problems, we turn them into grouping problems.

I start the factoring unit by teaching the students how to factor out a GCF. To help them understand, I’ll sometimes call it “undistributing”. Once they understand how to factor out a GCF, then I give the students grouping problems. They are taught to group the first two terms and the last two terms and then factor out a GCF. I tell them that if they get the same answer in both parenthesis then they have worked the problem correctly. They factor out the common parenthesis and make another parenthesis with the leftovers. Once they get good at this then I talk about differences of squares and perfect square trinomials.

These are my notes from my Algebra 2 classes this year:

Next I teach them to spot easy trinomials and hard trinomials. I later explain that they are problems that either have an “a” equal to one or an “a” greater or less than one. I discuss how the signs work in trinomials:

• + + = ( + )( + )
• – + = ( – )( – )
• – – = ( – )( + ) the larger number gets the –
• + – = ( – )( + ) the larger number gets the +

When I teach the a = 1 problems, I tell the students to go to the last number and ask, “What multiplies to get the last number that will add or subtract to get the middle term.” Students can do this pretty well…especially if they know their multiplication facts.

When I teach the hard trinomials (a>1 or <1), I have the students draw a big X to the side of the problem. The students are directed to multiply the first term and the last term in the trinomial. They write that at the top of the X. The middle term goes at the bottom of the X. Next, they ask that same question about what multiplies to get the top number that adds or subtracts to get the bottom number. The students write it on the left and right side of the X. Now it’s time to turn the problem into a grouping problem. The students are told to write the first term of the original problem, then the two monomials they just found and the last term of the original problem goes on the end. Factor by grouping and they are done.

I know students should know this by the time they are in Algebra 2, but many of them don’t. I usually try to break these notes up into two days. I assign Games 1 – 6 of my Factoring Using Seek and Find. I love this activity because the students know if their answers are correct or not by finding the answers in the puzzle.

A quick tip on helping students that aren’t good with their multiplication facts. If they want to know for instance what multiplies to give you 300 that would subtract to get 44…Have students type 300/x into a graph of a graphing calculator, then go to the table. The table contains all the factors. I tell them to ignore all decimals. They will see a 50 and a 6 in the x and y columns. They can reason that if they subtract, they can get 44.

Factoring is a very important concept and students need this skill to survive in their upper level math courses. I finally feel confident that my students understand it since I now stick with a certain way of presenting it to them. I truly believe in the way I teach factoring and I hope that I have given you some ideas on how best to help your students successfully learn this concept!

For my Algebra I classes, I made some factoring matching cards you might be interested in: Factoring Matching Cards #1 and Factoring Matching Cards #2.

I also made 4 sets of Boom Cards. Boom Cards are awesome because you can have your students work through them as many times as they want until they understand. They are great for digital learning!

I finally have all of my factoring activities together in one bundle. You can never have too many factoring options. Factoring is a biggie and we all know how students tend to be weak in this area. The calculus teacher at my school is always telling me how students forget how to factor. This skill needs to constantly be recycled until it finally sticks!

## 9 Exponential Functions Activities That Are A Must!

I could do exponential functions all year. I really enjoy them and think they are super fun. When I got my master’s degree, I did a study on exponential functions. I learned so much and I found that I was really interested in them. I created this first lesson more than 10 years ago and have been using it ever since! Creating that first activity sparked me into creating more and experimenting with some other ideas. I’m excited to share with you my list of 9 Must Do Exponential Function Activities!

(1) Exponential Function Poster Activity:

This is my very first exponential function activity that I ever created. It’s not the first lesson I teach when I’m starting this content, but it’s my favorite. This activity is the ultimate collaborative and differentiable activity. There are so many interesting exponential function situations! It’s been tried, tested and tweaked. Basically this lesson is a collaborative activity where the students are given an exponential scenario. The groups must create a multi-rep poster where they collect data, draw a graph, write an equation and answer a question.

The lesson opener is a bacteria problem. I want every student to get a feel of how they should work through one of these scenarios. The bacteria problem talks about what bacteria are and how they can multiply very quickly. I help the students go through the multi-representations to make sure they know what is expected of them when they start their poster.

Next, I show them their choices which are:

• A Chain Letter Problem
• A Zombie Situation
• A Tournament Bracket
• A College Football Situation
• Making Friendship Bread
• A Lovely Cockroach Scenario

Every situation usually gets chosen. You can entice students to create their own situation too. The college football situation was a student idea from years ago that I have improved upon to make it work better. Your students are amazing and creative, so don’t think that they wouldn’t be able to make up a situation of their own. The student of mine that created the football problem was not one of my top students, but because he was the one that thought of the scenario, he was interested and did a great job of completing the task.

After the bacteria problem, I turn the students loose and let them start their work. They are told to be creative and display the information in a way that is interesting and pleasing. I tell them to title the poster and make sure every person in the group writes on the poster. I supply the poster paper, the markers and the scenario sheets.

I’ve learned to watch out for misconceptions. Some students when creating graphs, will take the exact y-values and place those numbers on the y-axis. Here is an example below that I didn’t catch until it was too late. I cringe when I see this! (Not a very creative poster either…ugh!)

Once the posters have been created, it’s time for the Gallery Walk! I want the students to check out at least 4 posters. I’ve created a page that students fill in while looking at the posters. They have to write the title of the poster, determine the domain and range, decide if the situation is growth or decay and then write down one thing they may wonder about the situation. The conversations that I hear are amazing. They love getting to look at the other posters and they love to critique them as well.

I’ve had feedback from teachers that have taken my activity and changed it to fit their needs. One teacher used a speed dating strategy where the students worked through a problem on their own and became the expert. The possibilities are endless. Each teacher has their own unique way of teaching and their own unique classroom situation. If you have a group of rowdy kids that you don’t want up running around, then let them do their own problem on notebook paper or graph paper. You could even let them create the table and graph in excel and present the problem in a PowerPoint.

Check out this activity in my store: Exponential Functions Activity

(2) Exponential Function Activity in Google Slides Form

Out of necessity last year, I created a Google Sides version of the lesson above. I’m having a hard time deciding which one to use this year. Instead of making posters, the students create the table, graph and equation in Google Slides. This doesn’t sound very exciting except that my whole class was in the same Google Slides all working at the same time. I was 2000 miles away monitoring the activity. They asked me questions and I could see them working in real time. I loved it so much that I’m honestly going to have a hard time deciding what I should use. Maybe I’ll let one class do the posters and one class do the digital form and compare the two. If you are big into digital resources you will love this. I now have this version in my TpT store: Google Slides Exponential Functions Activity. Below is one of the slides that I graded. Looking at this now, I should have asked the students if this situation was discrete or continuous.

(3) Tower of Hanoi

Find a Tower of Hanoi game on the internet or have the students download an app on their phone. The object of the game is to move the discs from one stack to another stack in the least amount of moves. You can never put a larger disc on top of a smaller one. The number of discs and the least number of moves is an exponential function. It’s fun to let the students play a while and get them to create a table of the number of discs and the least number of moves and then see if they can figure out the exponential function.

(4) Twizzler Decay Activity

Tasty and fun. This is a freebie I’d like to share with you! I love using this as a quick lesson opener. Students measure a Twizzler and jot down the data in a chart. The student folds the Twizzler in 1/2, cuts it and measures it. Each time the student continues this step until there is not enough Twizzler left to work with. They plot the table and then lots of discussions can take place about decay or even the concept of half-life. Click Here for the Freebie: Exponential Function Twizzler Freebie

(5) Exponential Function Unit

This is the first thing I start with when I introduce Exponential Functions in Algebra 2. I refuse to stand up and lecture over this topic so I let the students work through this unit at their own pace. I copy the pages as a booklet. Students can use a calculator and even partner up if they want to work with someone. I let them work through the unit and figure out most of the information by graphing and using the information that they have already learned earlier in the year about transformations and domain and range. I do have to talk about asymptotes because we have not discussed this concept much up to this point. I teach on a block schedule and it takes most students a good 2 class periods to get this packet done. Topics covered are transformations, e, compound interest, 1/2 life, growth, decay, domain, range, y-intercepts, asymptotes, an inverse problem, writing equations from tables, growth and decay model scenarios, a paper folding activity, assessments and bell ringers and lesson closers. There’s a ton of information. I usually get the students to trade and grade after all is said and done. I feel like they learn a lot by working through this on their own. Students need to see that they can work on their own and figure things out. If you are interested, click the link: Exponential Functions Unit.

(6) Exponential Function Task Cards

I have a set of 20 Exponential Functions Task Cards. For some reasons, students do very well with task cards. If you put these same 20 questions on a worksheet, some students will be bored or are overwhelmed with thinking about doing a 20 question worksheet and they will give up. Take the same 20 questions and put one on a card, now they will sit there and work through them. It’s amazing! This set of task cards would be a great review right before an assessment. The task cards cover recognizing growth and decay from an equation, transformations, key features of graphs, the growth and decay model and compound interest.

(7) Sierpenski’s Triangle

How do you get all of these activities done? Part of my strategy is to do them in stations. Really math labs or centers would be more accurate. It would be hard to time these stations and expect students to be completely finished with each task. The Sierpenski Triangle activity, the Tower of Hanoi and several more exponential phenomena are discovered and tinkered with during my Exponential Stations Resource.

I love the Sierpinski Triangle activity because not only do the students create beautiful art work, they have to collect data on the number of shaded or unshaded triangles. We then put all of the triangles together to make a giant Sierpinski Triangle!

(8) Compound Interest Study

Students are told that they have inherited some money but to receive it, they must follow some rules. Every student in the class will probably end up with a different situation. Each student gets 4 cards that tell them how much money they inherited, how long they have to invest it and 2 different compounding options to compare. They work through their problem and then share their information. This study sparks lots of good conversations and helps the students realize that compounding doesn’t make much difference but time invested does make a difference! Get the Compound Interest Study Here!

(9) Marble Slides Exponential Function Desmos Activity

If you aren’t using the Desmos Graphing Resources, you need to start. I love the Marble Slides Activities and so do the students. There are several Marble Slides Activities for various functions. The object is to change the equations so that when the marbles are dropped, they travel the correct route and hit all of the stars which means success. Students learn how to manipulate the equations so that the marbles do just what they want. Very fun and engaging!

So there you have it! If you can get most of these activities and lessons done, then your students will know tons of awesome math content. I have all of these activities bundled (except for the google slides activity) into one package for 20% off. If you are intersted, then click on the pic below. If there is something that you can’t find, please let me know. I’d love to add things that teachers are looking for. Thanks for visiting this article.

Happy Teaching…