## Tuesday, May 30, 2017

### Resources for Factoring Trinomials

Well this post was supposed to just be a quick post to link my factoring puzzles activity but it has turned into a longer blog to share all the resources I have used this semester (Spring 2017) for teaching factoring. So here are my activities that I feel really helped students with factoring this year. I am so happy with the way these activity turned out.

I learned all about the box method for factoring last summer while scrolling through twitter one night. It was life changing and I'll never go back!! If you haven't heard about this method you should check out this blog (Polynomials and Box Method) I did recently.

This semester I had two different preps Math 1 and Math 2, I started teaching quadratics early in Math 2 and hadn't made these resources at that point so it didn't go as smoothly. When I started quadratics in Math 1 I did these things that helped lead up to the factoring process. (We have previously covered Multiplying Polynomials & Factoring Polynomials by GCF)

2) Factoring Puzzles

4) Notes on Factoring Trinomials

5) Practice on Dry Erase Template Factoring Trinomials

Here are some student photos of the activities being used:

If you would like to download these files you can find them below:

## Monday, May 29, 2017

### Simplifying Radical Expressions Dry Erase Templates

Today I want to share another dry erase template with you that I tweeted about last week on simplifying square roots. This is probably the most retweets I've had yet so I know that you guys are looking forward to this file!!

I also created a different version for cube roots since we cover this in math 2 as well. Hope you guys enjoy. I haven't had the chance to use these yet since we are now finishing up our last week of classes and exams start next week but I'm super excited to use this template next year. I think having a printed copy of all the perfect square and cube numbers will help remind students which numbers need to be factors of the original number.

This idea was sparked first by seeing Sarah's version (pictured below) which is pretty cool too. She uses the birthday cake method of finding the prime factorization of a number. Check it out here.

If you notice in the tweet pictured I forgot to list my prime numbers like Sarah has in hers so I made another file with the primes. This will be more helpful to students when they are looking for their stop number in my method.

Now in my method the stop number will NOT always be a prime number like 30 for example. This number is a stop number bc the perfect squares below the number (4, 9, 16, 25) do not divide evenly into that number and the next perfect square (36) is too big. I tell my students when trying to find factors if the perfect square number they are trying is bigger than the number in their tree then it is a stop number and that it stays under the radical. This method may seem harder than taking the prime factorization of a number but with larger numbers it goes faster and has less work so I guess that is why I like it better.

Here are the two versions I have for Simplifying Square Roots

Squares - Version 1 (without primes):

Squares - Version 2 (with primes):

Here are the two versions I have for Simplifying Cube Roots

Cubes - Version 1 (without primes):

Cubes - Version 2 (with primes):

Student Work Examples:

If you would like to download these files you can find them below:

Simplifying Square Roots (without primes)
Simplifying Square Roots (with primes)

Simplifying Cube Roots (without primes)
Simplifying Cube Roots (with primes)

Do you want to see more of my dry erase templates???

Check out these other blog posts below:

Also in the future all of my resources will be uploaded in a google doc with links to each blog post so you can find things nice and easy. You can find these resources in the virtual filing cabinet tab on my blog page.

### Quadratic Formula Dry Erase Template

This idea came from Sarah when I saw her quadratic formula template. I teach this topic a little different so I modified it to fit the method I use in the classroom. Below you will notice with more time I have changed these templates again to hopefully make them more understandable to my students.

Sarah's Original:

Modified Version 1:

Modified Version 2:

Examples of Student Work:

If you would like to download the files you can find them below:

## Wednesday, May 17, 2017

### Hands On Number Lines

Last summer I found this post from Sarah about her printable number lines for her classroom. I fell in love and obviously printed them first thing when we started back to school this year. I have found them super resourceful when trying to explain adding and subtracting integers. Unfortunately many of my high school students still struggle with this along with multiplying and dividing integers.

Now fast forward to a few days ago when I was passing time scanning Pinterest for new ideas during commericals of one of my new favorite shows Famous in Love when I found this cool idea that sparked an even bigger idea.

I started thinking well I've been wanting to make individual number lines for each student desk but maybe a more hands on approach that could also be used to physically represent multiplication or division would be even better.

So I remember the random wooden blocks that I inherited from a previous teacher that had changed schools and I thought maybe I could make them into numbered beads that could create a number line for students to use in class.

So far one down and seven more to go. Hopefully I'll buy some more blocks and make more so I can do pairs instead of groups of 3-4. I was really hoping they would have been smaller so they worked well on top of the desks but I did -30 to +30 so that was too many blocks to lay out across a desk.

Here are some examples of how I'll be using them:

Multiplication

Division

This is how I want to implement them into my class next year.

I want to use the first couple of weeks as days to include number talks to help build a deeper knowledge of mental math. During those days I plan to break out the number lines and do some mental math with addition, subtract, multiplication, and division. I really hope that they will then understand how useful the numberline can be in doing basic calculations. I'll try to keep calculator use to a very minimum and used only for major tasks like graphing and exploring functions.

After the first coupe of weeks I'll have some sort of laminated card thing for their desk tops I think. Haven't created that yet but it's in the works. Check back for that post later.

To introduce the number lines I'll probably first do a few simple examples on the board of addition and subtraction using a number line and then give them a few examples to model using their number lines. Then we can repeat those same steps with multiplication and division.

If you would also like to make these handy dandy number lines yourself here are some resources I have found on amazon that can help you begin your process.

Wooden Blocks
(I used 3/4in block - large but easy to write my numbers on)

String Stuff
(For now I have just basic yarn but it is picking really bad so I think I want
to try some of the elastic jewelry cording next time)

Drill Bit for Small Holes
(I did not do this - so very thankful for an awesome AG teacher at my school who made my first set and next couple sets might be done by my dad unless he teaches me to use it)

If I did my calculations right use a 1/16" drill bit because I think that is a little bigger than 2mm since the string stuff above I gave you are all 2mm. Hopefully I can update this part soon.

## Saturday, May 13, 2017

Today I want to share with you how I do standards based grading. I'm sure it is different from what other people do as everyone decides what works best for them. When I first started reading blogs and getting connected on twitter I realized pretty quickly that standards based grading was the new way of grading.

What really hooked me was the idea of being able to see in detail what my students understand. Before SBG I knew they had a grade but I couldn't tell you one bit what they really understood because their grades reflected a mixture of topics at that time along with effort and participation grades. In my opinion the traditional grading style to me has way too much fluff type grades. For example, giving grades for completing an interactive notebook. Now don't get me wrong because I used to do this myself. But does a student's organizational skills or dedication to note taking really show what they have mastered in your class??? I hope you would say no. Now that doesn't mean these things won't help increase their grade; because we all know that having the appropriate materials for studying will result in better preparation for a test and thus give students better test scores.

That does not mean I don't care about my student notebooks because I do so much that I almost force my students to take notes. I stand near them, hand them a pencil, and give them that glare like you better do exactly what I ask or else... but I have had those who just sit there quietly and stare at you. That is annoying but what else can you really do. You can lead the horse to the water but you can't make them drink.

So if I don't give effort and participation grades then what do I grade???

Tests and Standards

Yes that is it!!

In my state (NC) we have a resource called SchoolNet that I use to create tests online for my students to take at the end of each unit. This resource I'm told was created by the same people that make our end of course exams so they are supposed to be the most reliable resources available to us at this time. These tests are very hard for the average to lower level student because they are mostly word problems and often take more than one skill to complete.

I do handpick the exact problems I want for them to answer because I want to make sure there are at least two problems in each standard on their test. I do this because it is multiple choice and I am trying to avoid them just guessing correctly and then counting that as mastery of a standard. I made this mistake once and realized that a few students who got NO other standards correct managed to get the hardest standard correct because I had only selected one problem for that specific standard and they randomly got it right.

For this reason my grading style is not a 100% guarentee because of the multiple choice and the possibility that they may have guessed on a question. What I keep telling myself is this is how they are evaluated in the end so I need to overlook it for the larger picture. I have deteremined for me that choosing assessments that are self grading is best because then I can focus my time on the data instead of the time it takes to hand grade all the papers.

So here is my SBG process from beginning to end:

1) Create units for each class that has specific standards "skills" that students must master to understand that unit completely.

2) Create test for each unit and select at least two questions for each standard

3) Evaluate unit tests to determine mastery of standards for all students individually.

I create a google doc after each test that looks similar to the model above. I type in the standards for each unit and leave a row below them to add in the questions from their test that correspond to that standard. Then I pull up each test and mark which questions they got wrong.

If you are from NC then I highly suggest you use schoolnet for testing as it is supposed to be the best resource for end of course testing that we have to use.

4) Post standards for students to mark off on their unit sheet (First Picture Above) and spiral review to help students relearn missed standards.

I have created workbooks for each of my classes that have practice problems and tons of schoolnet (word problems) to continue practicing skills throughout the school year. I do not give homework so the workbook is how I spiral in my review. At the beginning of each period I give 5-10 review problems from this book for review. I walk around to see which questions students are struggling with and then I review those questions as a group on the board.

Another resource I have found extremely helpful is Delta Math. I will be blogging about this soon but if you can't wait check out the link. I love this program because their are detailed explanations for each question that a student completes. I find this very helpful for students who are great self learners. When we use this website I am able to help with more complex questions or questions from students who struggle severely verses just simple mistake issues.

5) Students retake standards to prove mastery. In my opinion proving mastery level is understanding how to identify, calculate, and solve the basics of a standard. So while the original test is more advanced mastery of a standard and shows they can apply what they have learned the retakes are more basic to determine can they answer a simple problem from that standard. Others may feel different but when many of my students are below grade level I am trying my best to just get them to meet the basic requirements of each standard in my course.

Here is what a standards retest looks like:

***They are allowed to retest as many times throughout the semester
as they need to in order to show mastery of a standard***

I would like to say I have these pre-designed before students are ready for retakes but I am not that organized yet. Maybe this will be a summer goal. It is important to remember to change the problems for each retake. A piece of advice is have students keep all their old retests and have them bring them to you when they need to retry so you do not give them the same retest. Or use this retest check list I created so you can mark off which version of the retakes you have already given them. I almost but the version cody on the standards retest paper that the students get to write on but then I thought about how easy that will be for the students to cheat with if they know what the answers are from students who got their questions correct.

6) When students get retests correct I update the google doc with C for correct verses if they get it right on the test I put a 1 for correct on the first time. I then update their grade and change it in the system. Here is an image of a unit that finally shows 100% mastery of all standards in a unit. YAAAYYYY!!! This very rarely happens as students give up way too easily. That is why I changed this year to allow them to continue to retake all units even into our second 9 weeks after report card one. This shows them I am willing to give them the whole semester to keep trying.

If you look really close at the grades you will see there is only one student who met mastery for all six standards on the first try (on the test). They are the only students who recieve a 100. Students that get all the standards correct after retesting they can recieve as high as a 95. I do this just to show a slight difference in the grade book for students who understood material at the time of the test and those who needed more time to show mastery.

7) Determine how you want to do your grade percentages for the unit tests and the standards.

I feel as though standards are way more important long term but I also think the tests are important because students need to feel some responsibility in being prepared for the test in the beginning. So I originally choose 10% classwork, 20% test, and 70% standards but I found students would bomb test and not care because percentage wasn't high enough to really effect their grade. Then I tried 25% classwork, 30% test, and 45% standards. This is currently my percentages but if you remember I mentioned I only grade tests and standards well because I never have enough grades for what administration wants I include a few classwork assignments to have more grades in the computer.

Next year I am thinking 1st 9 weeks do 10% classwork, 35% test, 55% standards. Then 2nd 9 weeks 40% test and 60% standards. I will eliminate classwork because they will continue to get credit for their standard units even if they were in the 1st 9 weeks. Remember I said I wanted to allow them to continue to retest until the end of semester. Well the only way I can do this in a semester with two different reporting terms is to carry over any standards grades that were in the 1st 9 weeks into the 2nd 9 weeks. This does not include tests from 1st 9 weeks because those are no longer allowed to be retaken. I do allow students to retest on a unit if they ask me (but this has only happened once or twice). Here are a few screen shots of what my gradesheets look like from 1st and 2nd 9 weeks so you understand what I mean.

These are grades from my math 2 honors class so they are actually really good. Unfortuantely my standard classes do not show this much progress. You might notice some of the test grades are really low but you have to remember these are not just simple tests they are from school net and alot of the questions are word problems and more complex. Also one thing I started doing this year and love is all my tests are cumulative which helps again with spiraling the material and hopefully keeping my students from forgetting the standards at the beginning of the semester.

Hopefully this post will help inspire someone who is considering standards based grading. Remember there is no right or wrong way to step up your SBG just test it out and see what works best for you. I'm sure you will decide what works best for you as time goes on.

If you would like to download any of the resources mentioned in this blog you can find them below:

Unit Standards List for student notebooks