Sunday, December 28, 2014

Transformations Summative Assessment Project

My pre-algebra classes just finished their unit on transformations. They loved the graphing and finding something that 8th graders love to do right before winter break is worth its weight in gold! I found a mini-project that Pam at pperfectsquares shared on transformations. When I saw it, I knew I wanted to make it a summative assessment for my students. So I added a few things to Pam's mini-project and I think turned out to be a great assessment for my kids. Their homework the night before was to create the picture and write down the ordered pairs. I didn't tell them it was going to be part of their assessment so those that did their homework had a head start.

Picture Transformation Assessment

               Your summative assessment for transformations will be an in class project.

  • You will need to draw a pre-image of a picture that has 10 or more points. The pre-image should have detail to it and not just be a picture of a shape or letter like we did in class. 
  • Your pre-image should be completely inside one of the quadrants on the coordinate plane. It does not matter which quadrant you start in. It is your choice. Use your imagination when deciding on a picture and impress me!
  • Draw you pre-image and place points at all of the vertices. List the points and ordered pairs on the transformation summative activity chart.
  • Next you will accurately translate, reflect and rotate your image. You may do this in any order that you want. All points should be listed accurately with a title above it so I can determine if your transformations are correct.
  • Each image should have an arrow showing the direction that the image is moving,(remember we drew arrows), as well as color coding the image and ordered pairs.
  • You will have 2 days to complete this in class. (This actually took 3 1/2 days. We have 45 minute periods.) They will be left in class and passed back on day two. They may not leave the room. Remember to document all of the transformations and label the vertices correctly. Make sure to look at the rubric if you have questions.
   Here are some examples of their final products.
I love this one!

Very creative and neatly done.


This student worked so hard on her picture and getting her points exact. 
She wanted to give up and try an easier picture but I kept encouraging her. 
She did a great job and was so proud of herself!
As you can see, she went above and beyond the expected 10 points:D

Nicely done.

I like the color coding on this one.

   You know what this student was thinking about.

This is a great picture but this student did not list the transformation or show arrows to depict the movements. Still it is so pretty I had to show you.

I've included the documents for the lesson below. I'm not the greatest at writing rubrics so it isn't the best. Feel free to change it and send me a copy. If you do, that would be awesome.

Enjoy! This is the last post of this year. Where did 2014 go???
Til next year,

Sunday, December 07, 2014

Rotations interactive notebook page and a video link too.

          Right now my 8th grade pre-algebra classes are working through our unit on transformations. Rotations have proved to be a difficult concept for them to grasp so I started searching blogs looking for ideas. I was inspired by a table in a foldable that Nancy at geometry gems had on her site.  I knew I wanted to create that table for my students to place in their interactive notebooks as quick reference on how to graph rotations. We started with a pre-image in the first quadrant so they could easily discover the changes that occurred in the ordered pairs of the rotations. 

      Those of you who read my blog regularly know that the majority of my school is comprised of second language learners. I always try to give as many visuals as possible to help my students who struggle with vocabulary. We drew arrows to show the clockwise and counterclockwise movements. We also color coded the corresponding shapes and ordered pairs as well.

      We also wrote what it means to rotate 90, 180, 270 and 360 degrees. 

                                Click here for a copy of the rotations INB page tables.

     I was excited to find over 700 of these composition notebooks in a storage room that someone donated 3 years ago. My principal didn't know they were even there and I asked if the math department could have them and he said yes! We have brand new notebooks for all of our students. How cool is that!

     What is so nice about these notebooks is that the top is graph paper and the bottom is lined. Now I have to figure out how to use these. I am use to spirals and because I write large it is a challenge but I will work it out.

     I also wanted to share a video that my kids absolutely love. If you haven't seen Colin Dodd's videos you are in for a treat. I wish he was still teaching 8th grade. (Sigh) Here is a link to Colin Dodds on you tube to view his other videos too. Enjoy.

     I am excited about a project I am having the kids do next week. Can't wait to share it when they are finished. Pictures will be coming soon!

Til next time,


Sunday, November 16, 2014

A function foldable I like

     I was introduced to foldables about ten years ago when I taught out of the Glencoe math series. Our Pre-Algebra and Algebra books had directions for a foldable at the beginning of each chapter that were created by Dinah Zike. Back then we used loose leaf paper and the lines were guides for the folds the kids made. There weren't pre-printed foldables or flipables or graphic organizers for students. The students made these foldables and took notes for each section in the chapter. They loved them and would not forget to bring them to class everyday. 
    There are a few of those original foldable templates that I use today. This is one of my favorites that I have adapted to use when I am introducing my 8th graders to functions. Instead of loose leaf paper, I use graph paper. I love making foldables from graph paper because it is so much easier to read. At our school, we ask each of the students to bring in a package of graph paper to their math teacher at the beginning of the year. We keep in the back of the room and if students need it for any other class they can just take what they need. Then we pass out the paper as needed and there is always more than enough for the entire year. That way there are no worries about students not having paper.
    The first step to make this foldable is to take a piece of graph paper and fold it in half. I call this folding the paper the hamburger way. If we fold it the other way it is the hot dog way.

    Then open it up and cut off four squares on the top left section of the graph. 

If you are using a composition notebook you should measure the width and cut the right side of the graph paper so it fits into your notebook.

   I use 5 sheets of paper, one for linear functions, absolute value functions, quadratic functions, cubic functions and rational functions. I could probably use less paper if I combined some of the functions together.

    Then you staple the pages together to make a booklet like so. It will open like a book and then also have flaps.

                         Just lift up the flap to add the function tables and graphs.

     When I teach functions, I prefer to use the large function tables that have four columns. This way the students see exactly where the numbers in the function table come from. This is beneficial for my students who struggle to follow the math involved to find the y value.

      I have an entire page empty on the left. I haven't figured out what I am going to place there. Maybe have students do a summary or state something in their own words???? Ideas are welcome.

                  Then I do the same for quadratic, rational and cubic functions.

     The students will be using a graphing calculator later but I like to initially start out with them making the tables and graphs to help their understanding. Since I write large I like this foldable because there is so much space because of the flap at the top. I have to admit it, I'm addicted to foldables. They just make me happy.
Til next time,

Wednesday, November 05, 2014

Our Halloween Contest

     This is the third year that the math department at my school has had a Halloween contest for our students. The students guessed how many candies were in a container that we had in a display case in our hall. The first year we did this, we had a large container filled with candy corn and last year the container was filled with small candy pumpkins. The containers looked very nice and the winners received all the candy. However that candy is just so sweet!  Ugh, it sends shivers down my spine thinking about how sweet it is. The winner received the container with the candy and had their picture taken. The picture was posted in the display case and it was placed in the yearbook as well. This year instead of candy I found pumpkin containers filled with cheese balls. We placed two containers in the display case and students gave their guesses to the math teachers. I actually found the actual number of cheeseballs in BOTH of the containers. Don't worry, I used plastic gloves. When the teachers were giving me their guesses to determine the two winners, we were all shocked at some of the guesses the kids made. 29 cheeseballs, 109 cheeseballs, 14  and 72 were numbers that kids actually thought were the total number of cheeseballs. WHAT!!!! How is it even possible? This just confirmed that our students need help improving their number sense.

These two young ladies both guessed there was a total of 2000 cheeseballs in both containers.
They were the closest to the 2012 actual total.

     So we have decided to do a couple of things to help our kids improve their estimating abilities. First of all, we decided that we are going to have bimonthly contest so the students have an opportunity to make an estimate more often than just once a year. For our winter theme, we are going to get a tall thin container, probably from IKEA, and put red and green peppermint candies in it. Valentines Day is going to be candy hearts. I would be fun to find something in the shape of a heart to be the container for that season. Spring will be something in spring colors and we still need to figure out May. ( Suggestions anyone?) I will also put a cup next to the containers and show how many items are in one cup to help them get a start on a good estimate.
     The next step, and I am sure some of you are yelling this at the computer screen right now, is to start using Andrew Stadel's, Estimation 180 site daily.  I showed this site to my department and everyone loved it. (Thank you Andrew for this awesome site.) So we are starting all together next week. I am going to run off the sheets that accompany the site for students estimates. It is going to be interesting to see how their estimates improve throughout the year.
     We are going to start with these two ideas along with everything we are already doing in class and see what happens. I'll keep you posted.
    Oh, one more thing. One of my students whispered this to me:
Student: "Mrs. Lichtenberger, Ms. Arman told me a secret."
Me: "What did she tell you?"
Student: "Length times width times height."
Me thinking: "Gee, who knew that was a secret?"

Til next time,

Sunday, October 19, 2014

Veteran's Day

     We don't have Veteran's Day off any more. Some people complain about that but not at my school. We have  Veterans come to our school and we honor them. Each department decides how they want to participate and last year almost every department did something. The math department decided to make picture graphs and completely decorate the math and science hallways with them. We had about 700 pictures and it looked awesome! Below is a picture of two of our former students who visited and talked to classes about their experiences. We had at least a dozen Veteran's come and speak to our History/Social Studies classes and Reading/World Language classes. Each of our students met two Veterans during the day. Three of the veterans were from our staff.

Former Students.

     Our day started with an assembly. The whole school said the pledge of allegiance and then 2 students sang the National Anthem. We watched a video on the history of Taps. Then one of our students played Taps for everyone. Our fabulous chorus sang, God Bless America. Then all of our veterans were introduced and gave a short introduction to the students. The students learned more about them throughout the day. We all brought in food and we ate breakfast and lunch and several snacks all day. It was quite a spread! Our celebration started several years ago with just one veteran speaking and each year it just gets better and better. I can't wait for this year!!!     The graphs that the kids made were from Anthony and Linda Iorlano at teachers pay teachers. We did make changes and making some 4 quadrant graphs. I can't post the changes because of copyright. These were definitely worth buying! We had a total of four different pictures but I only have pictures of two of them.

Nice USA graph

This is a graph of the Iwo Jima statue. We had a discussion in class about that battle.
We did not change this one to 4 quadrants.

Not sure which department did these but they turned out nice.

     I would love to see and hear what you do for Veteran's Day at your school. All math ideas are welcome because I need something different or different graphs for our 8th graders to do.

Til next time,

Squares, Cubes, and Fractional Exponents

     I have decided that this year I am not going to be able to get a full blog post done! It seems like this is one of the busiest, craziest years I have had in a very long time. Everyone I talk to in my district feels the same way so I am not alone, thank goodness. How about all of you? Are you feeling the same stress that I am? Or is it just my district? Just letting you know that the foreseeable future is going to be short posts with a few pictures. At least that way I will still be able to do some reflection and sharing with all of you.
      The other day, I was browsing the teacherspayteachers site, one of my favorites, and I found a great interactive notebook page from RoxyGirl on Fractional Exponents. I like the way she laid out the problems so I bought it and used it with my 8th grade Pre-Algebra class. I really like to have a practice page to go on the left so I created a sheet for the kiddos to do.  I also had them write the answers on the bottom half of the sheet as well. This was a great extension of the lesson but a bit difficult for my lower level students. 

I cannot show the right hand page because of copyright but go to  RoxyGirl at teacherspayteachers to see or buy it. One of my goals in my never ending quest to help my students with their number sense is to show the different forms of numbers. These notes fit into that category perfectly.

Click here to download Square and Cube roots and Fractional
Exponents practice page. 

     I am absolutely loving my Interactive Notebook this year. There are so many pages and topics I have to share and hopefully I can do these short posts until everything calms down a bit.

Til next time,

Sunday, October 05, 2014

Distributive Property - another take on the combo meal idea

     Who doesn't love the combo meal that Sarah at math = love posted a while back to show the distributive property? If you haven't seen this go look at it now. It is fun. There are so many versions of this lesson on blogs and Pinterest and I love them all. Imagine how excited I was when I saw Jessie's worksheet on this at Mrs. Hester's classroom. Perfect! Exactly what I was looking for. The only changes I made to Jessie's sheet was to make an Smartnotebook file. I am fortunate enough to have a SmartBoard in my room and thought it would be fun to make a lesson with pictures of the hamburger, fries and soda so the kids could move the items to display what the meals contained and then write down the expression with the distributive property. Here is a picture of how it looks but the actual file is so much better.

You can have them use the distributive property on this slide or else you could use this for showing how to add like terms.

Add caption

         There are more pages as well as extras to add more combinations of meals. Hope you enjoy using this in your classrooms.
Download a copy of the files here:
You will need Smart Notebook 11 to view this file 
                  Combo meals distributive property SmartBoard notebook file
I've also included a power point for those of you who don't have SmartBoards.
                            Combo meals distributive property power point
       I can't wait to use this next week with my Pre-Algebra 2 classes. Thanks to Sarah and Jessie for your great ideas!
 Til next time,

Sunday, September 21, 2014

A few more exponent Interactive Notebook pages

          Here is another quick post with an Interactive Notebook page on exponents. My students need lots of practice comparing and ordering numbers so I made this page for their INB's. I am stressing looking for patterns right now and I love problems 17-19 and 22-25. It took lots of wait time and allowing them to struggle but they discovered the pattern for how to find a two-digit perfect square without a calculator or just multiplying it out. What was great is that they then asked, " Does this rule work with 3 digit numbers?" I started to do the happy dance when they began to wonder and want to see if this was true or not. So they worked through the problem to find the answer to their question.

     This exponent unit is going to be long but worth the time. To have the students understand the magnitude of numbers, how they compare and how they show the same value in different ways is also part of my goal this year to improve the number sense of the students. See my post on Teaching number sense to my students.

       I originally made the page below an exit slip but then wanted to have them write an explanation of the steps so I just added it to the INB instead.

By the way this rule does not work for 3 digit numbers. Just thought I would put that down here in case some of you wanted to see if it worked on your own first. LOL.

Til next time,

Thursday, September 11, 2014

Student Planner Plan and Having a Paper Trail

     For several years I was fortunate to work on a team with 4 other teachers, English, Science, US History and Science. The "Purple Team", Kathy, Erin, Kendra and Judi, were an amazing group of teachers. Everything just clicked which made it a joy to work with them. We created several great strategies to work with students who were struggling for a variety of reasons but one of my favorite is the Student Planner Plan. We developed this plan for students who are not completing their homework or projects. They are not being truthful with their parents, telling them there is no homework or that they completed it at school. (Ever have this happen?) This plan becomes a communication tool between school and home as many of our families do not have internet service to check posting online. 
      Our students have planners that they carry with them all day long and I am sure most of your students have them as well. There is a copy below of the form that we have the parents, students and the teacher sign during a conference where work completion is an issue. The contract states the responsibilities of each of the parties so there is no confusion. We also talk to the parents about immediate daily consequences. If the student does not have the planner signed or if work was not turned in, the student does not have privileges for that day. They are able to earn their privileges the following day if they have the planner signed by the teachers, have turned in the work for the day, and if they bring home any work that needs to be worked on for that evening. The parents/guardians have to look at the planner and sign it as well. For the parents that follow this plan we have had wonderful results.  

This is a page that we email home to parents/guardians.
This is the copy we use during parent/student/teacher conferences.
    Click here to download a copy of the Student Planner Plan pg 1 and Student planner plan pg 2.

      One of the most important things I learned early in my teaching career was to keep a paper trail of contacts and meetings with students and parents/ guardians. This may have changed over the years with the technology that we have now, but I still keep a paper trail.  I have never regretted taking the time to do this because when you need proof of contact, you need something in writing. At the conference I sign the contract along with the student and parents. I then make a copy for the parents so they can hang it on the refrigerator for reference. I put my copy into my discipline binder. For the parents that follow this plan the results have been amazing. For those that do not follow through, we have a signed reference that this is a strategy that was agreed to by all parties. 

     It is wonderful when this works for the student. Everyone is happy, the student learns to become organized and manage their time, the parents have the communication they need from the teacher and I am thrilled to have a tool to use in these situations to help the families. 
Til next time,

Monday, September 01, 2014

Exponents Interactive Notebook Page

     I have a quick Interactive Notebook post today on exponents. After all, it is Labor Day and I am looking forward to just relaxing. I don't know why short weeks at school always seem longer than regular weeks. Why is that?

     The top section of the right page is from math = love. I love the exponent and how you can pull it out to see the expanded form.

     I have decided this year to show the reasons behind many of our rules. We are also stressing the problem solving strategy, looking for a pattern. This page show why any number to the zero power is equal to one. Click here for Zero power graphic organizerI didn't want to hide this behind a door of a foldable, I want the students see it every time they open their notebooks to this section. So many of my kids still think it should be zero. UGH!

     The student practice page has students going back and forth between the different forms of the numbers. I am stressing that these are all different forms of the same value. See my post on teaching number sense to my students. Click here for a copy of the exponent practice sheet.  I am already having my students memorize their square numbers. so I have several on the work page. Sorry about the quality of the picture. I will try to replace it later.
     Good luck to all of you who are just starting school tomorrow. Hoping everyone has a wonderful year.
Til next time,

Sunday, August 24, 2014

Kagan Structures

     I am so excited! Two weeks ago, my school finished its first all day training on how to use Kagan Structures in our classrooms. The entire school is participating in three training sessions throughout year. I have been teaching for a long time and didn't ever think there would be any training I could receive that would improve my students behavior during group work. Well, I was so wrong. When Kagan instructors say, "It's all about engagement," they are so right. In the past when my classes have worked in groups there were always those students who just did nothing, while others would just hide from me. Some students would work hard and others would be talking and off task. It was hard to keep them all engaged. So here are a few things that I learned and started using with my classes this week.
    The first thing I needed to change was how to get my classes to be quiet and listen. I have always used the 3-2-1 countdown, given them the stare or said, "Shhh, shhh, shhh." I became very frustrated that I had to waste so much time on this. Our trainer said that simply saying, "Signal Please,"  then raise your hand and have all the students raise there hand and look at you. You say nothing else, just sit and wait. When everyone is quiet and looking at you say, "thank you," and then continue with what you want to say. Now this seemed very elementary to me but I saw it work with the 50 middle school teachers in my building during our training. Now if you can get middle school teachers to stop talking that is quite a feat! I started using the quiet signal this week with my students from day one. These were actually the first words out of my mouth in all of my classes. I am here to tell you that I am shocked that it is taking less than 5 seconds to get everyone looking at me and quiet. We also had our first assembly Friday and the teacher leading the assembly used this quiet signal and over 700 students became quiet and attentive. All of our teachers are using this quiet signal so the kiddos know exactly what to do. So simple, how come I didn't know to do this years ago?
     The next thing I changed was how my classroom was arranged. All of the tables or desks are now in groups of four and at an angle so that everyone can see the teacher without turning around. In the center of each of the tables are Kagan mats.Click here to see Kagan Mats from the Kagan catalog. I am still in the process of placing the finishing touches on my room. Pictures of my classroom will be posted later this week. (Our open house is Thursday so you know it will be finished by then!) A teacher at my school made mats that are similar and I cut them into four parts placing one on each desk. Unfortunately, my desks do not make a flat surface so the mat won't stay put. Cutting the sections apart and securing them with packing tape should work for awhile.
     The next step was to keep the kids engaged and accountable for their learning. Every ten minutes you need to change your engagement to keep their attention. The first day consisted of getting to know you activities. The next day the problems were math based. I wanted the kids to understand that there are many ways to solve a problem and that some problems can have multiple answers. I guess the easiest way to explain this is to give you an example of some of the problems we did in class last week. 

     Warm up #1

Which number does not belong and why:
36     81     9     25     72

Teacher: I am going to give you 1 minute of quiet think time to find the number in the list that does not belong. Write the number you found with an explanation of why it does not belong with the other 4 numbers.

     I put on my timer, click here for an Online stopwatch, and let them work. After the timer went off I said this:

     Teacher: You will be working with your shoulder partner and explaining what number you chose and why that number does not belong with the others. If your partner has a different number than you write down their number they along with their reason. You will have one minute  to share. Partner A will start and Partner B will listen. Ready, go.

   It is important to give the instructions first and save who is going to begin til last. That way everyone is listening to the directions. I put the timer on and walked around the room while students shared. Then we did the same thing with partner B explaining the number they wrote down. Next, we shared as a group with the student 1 (look at the mats) explaining what their partner had and going around the table. The group created a group list that we shared as a class when they were finished. I gave them 3 minutes to do this.
    As you can see, everything is timed, and anywhere from 25% to 50% of the students are talking and explaining during the activity. Instead of me explaining everything, the students are explaining and learning from each other. There are no more students hiding and not participating. The activities we started with this week have no right or wrong answers so I am creating an environment where they feel safe sharing with each other. ( I of course thought that 72 didn't belong because it was not a square number. Other possibilities, 9 is the only single digit number, 25 is not divisible by 3 or 9, and 25 because the sum is not = to 9.) Any other answers that you see?

                                                   Warm up #2

                                         How many squares do you see?

     This was a puzzle I found on Facebook a couple of years ago. The kids love this one and there is a short video that shows the best answer for this problem. Again, I stressed that the question is, "how many squares so YOU see?" There are many different answers, none are wrong, but one answer that is the highest number of squares. Click here for a video that shows the best answer for How many squares?

                                                  Warm up #3
        Find a word worth $0.60 when A=$0.01, B=$0.02, C=$0.03,etc.

     The last problem that the kids work on last week was the = 0.60 cents problem. It was so much fun watching the groups work to try to find a word that would = a sum of 0.60 cents. Watching the kids, I realized that I need to work on problem solving strategies with them. I thought the very first thing the groups would do was to make a list of the alphabet with the corresponding numerical value next to each letter. They didn't! Most of them were counting through the alphabet for every single letter. Using the guess and check strategy most groups did come up with a word. They loved this problem and my Algebra classes wanted more time to work on it the next day.
     One of my students was excited because he found that the word, yes, added to make 60 cents. However, he had the letter s as being worth 20 points when it should have been 19. When I looked at his list of the alphabet the letters were in this order; m, n, o, p, q, U, r, s, t .... At first I laughed to myself and explained to the student that q is followed by u in words but not in the alphabet. I was also sad because it reminded me of how much background knowledge I think my second language students have but may be missing.
     The structures I have used so far are the rally robin, round robin and stand up-touch down. I am also using random grouping until I have some test scores for my classes. I will explain how to create groups and what these structures look like in a later post. I need to go through it on my own first. 

Til next time,

 Disclaimer: I am not a certified Kagan instructor. All of the information given are my thoughts and reflections of the training I attended, as well as activities that I decided to implement.

Saturday, August 16, 2014

Free Foldable Templates

     It's the beginning of the new school year and I am trying to improve my Interactive Notebook from last year. Most of the time I create foldable templates myself which is very time consuming. Sometimes I have students make their foldables freehand without a template to cut, but that takes more time. I needed to save some time so I went to one of my favorite sites,, to see what templates I could find for free. ( I spend way too much money on my classroom so I always look for free items first.) Having a blog, I wanted to have templates that allowed for electronic downloads.   Most of the free templates did not allow that. Bummer! After searching for awhile, I found a few I that would allow this. The first five in the list can be used to share electronically. Of course, if I use these I will give credit to the person who created them. I thought that some of you would like to have a list of all the free templates I found as well so here they are! Have fun!

Free 6 door flap book foldable available from Miss Mathematics HS at

Free 8 door flap book foldable available from Miss Mathematics HS at

Free Magic foldable template from Coach Academics at This is the foldable that I used for my Unit 1 8th grade Pre-Algebra vocabulary. It is awesome!  You really have to incorporate this one somewhere in you Interactive Notebooks.
Free pentagon foldable from Amy Hendricks at

Free Mini books and foldable templates by  Luanne Angelo at

Blank template for various subjects by Inspiring teaching design at 

Here are some templates and examples in Spanish but these templates can be used for any language. There is a cool word wheel that I may use for vocabulary by Cuevas' corner at

A large variety of templates that are not just for vocabulary as stated in the title from English 10 Mother Hen at

     I hope you can use these for your interactive notebooks and that it saves you some time. Everyone have a great new school year!

Til next time,


Tuesday, August 12, 2014

Like terms/ unlike terms foldable

     Well I am in overdrive right now. My first day of school with students is Monday and I am scrambling to get things organized. The posts you are going to see in the next few days will be all over the place. The one below is an improvement on what I had the kids do last year on like and unlike terms. Sorry about the poor quality of the pictures, my battery was almost dead.

     Go here to see what I did last year with like terms.  The kids wanted to make their own shapes for the like terms and unlike terms and they turned out great. I wanted to add the section on combining like terms to the same page and then have a few practice questions for the students to do. I'm happy with how it turned out.

     Those of you who have read my blog for awhile know that I have students place their leftover colored paper in a basket. These foldables are made out of those scraps which makes me happy:) 

     The combining like terms foldable is from Sarah at everyone is a genius. I like the way that she has the students color code the different  like terms. It just gives an added visual for the students who need it. Sarah has so many good ideas on how to start your interactive notebook. If you haven't gone to her site go there now! You will be happy you did.

  Click here to get a copy of the like terms practice sheet.  I may decide to put this on white paper and have students color code the like terms. I do think some of them will still need the color coded visual.

     Well I'm off to try to do another foldable. I need to spruce up my square roots and cube root pages. 

Til next time,
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