Tag Archives: Algebra

Graph

Graph Example

Graph

This is an excellent free graphing software. I use this quite frequently in the office when I need to sketch a quick example for an item. In the classroom it can be used to create your own custom graphs for instruction and assessments. Students can also benefit from this resource. SHARE! It’s very intuitive and easy to navigate. Graphs can be snagged and/or saved to insert into just about any type of document, including websites. Click the “Graph” link above and get started. Have fun!

Negative Exponents

I get very upset when I hear students regurgitate rules for mathematical properties, but have no sense of why the rule exists. To be quite honest with you, it wasn’t until my second year of math education courses that I understood why a negative exponent essentially had the base and the positive version of the exponent end up in the denominator of a fraction. When I came across a negative exponent in the denominator of a fraction, I was quite befuddled. I essentially made up a new rule, when it’s negative in the “bottom”, I must take to the “top”. Yeah, that fixes everything, right? Not quite. Students are forever making up rules as they go along, adding to and modifying what they have been told in the past, creating bandaids of sorts to get them through to the next round.  How about we step back and give a logical reason for things, so students build upon and apply knowledge, instead of inventing their own.

Please take a look at this short piece that explains the effects of taking a base to a negative exponent. Every student needs to understand this reason.

NegativeExponents

Quadratic Equation Card Sort

I’m so happy I follow @Maths_Masters on Twitter! Such wonderful resources! I must share this one with my algebra teachers.

Quadratic Equations – The Main Ideas.

Better yet, give students the Group 1 through 5 titles from the card sort first and see if they can generate facts for each of them while working in groups of 3 or 4 first. After they have exhausted their knowledge, provide them with the card sort to work out. Finally, have the students, still within their small groups, compare what they came up with with this card sort. While students may not be able to generate all of the facts on their own, nor be able to word their facts as succinctly, the ownership students will experience when they connect what they wrote to the facts on the cards will be immeasurable.

Thank you William Emeny at http://www.greatmathsteachingideas.com/ !

GeoGebra Tutorials through Mathematics and Multimedia

GeoGebra Tutorials

This is such an amazing set of tutorials and lessons on how to use GeoGebra! I used this program for my graduate program and fell in love. Every school should have this installed on every computer for students to use to investigate, create, and verify geometric concepts. Please share with your teachers, parents and students. Thank you Mathematics and Multimedia!

Great On-Line Learning

I wanted to share with you Hippo Campus. This is a wonderful independent learning site for many courses, particularly algebra. Students are provided an opportunity to warm up to the lesson, reviewing and assess previous learned skills, and then move into video lessons that walk them through the mathematics unit. Instruction can be geared to the student’s pace. Opportunities to assess learning are provided throughout. The explanations are very clear and accurate.

If  I had one thing to change about the site it would be the font size. It seems a bit small and difficult to read, however, this is not in reference to the instructional window. This is regarding the scrolling lesson outlines to the left and the explanation boxes that appear to help students along. I find the key notes at the bottom of the instruction window very helpful. For instance, if the lesson, activity or problem involves a certain algebraic property or definition, this is provided below the window the lesson is being presented in.

If you teach algebra, this is certainly a site to have linked on your webpage or provided to students and parents for extra support for your class.

Amazing Math Software – FluidMath

I’m not sure how FluidMath found me on Twitter, but I’m so happy they did. Finally, someone has created a math software that WORKS for math teachers and the way they teach. I’ve used a Tablet PC since 2004, for both instruction and for personal use. My students absolutely loved the features a tablet provided me for instruction, but wow! If I had only had this software, I would have knocked their socks off!

FluidMath

These are only a few of the things I love so far:

  1. It reads math hand writing, including math symbols and formatting.
  2. It has graphing tools that are effortless, precise, readable and adjustable.
  3. It has just enough bells and whistles, such as color changing tools and styles, to capture students interest and allow for emphasis throughout instruction.
  4. The graphs act like Java applets that are completely responsive to changes made my hand.
  5. It can easily be used with Microsoft Word in creating assignments, assessments, and notes.
And, so many more.
What I would like to investigate with this software is how well it works with the functionality of Microsoft Office OneNote, particularly the recording feature. I would love to see a lessons recorded with the teacher/class speak using this software so that it can be uploaded and archived on the teacher’s blog or website. This way, if a student misses a lesson, they can simply cue it up later and not miss a beat!
I am very impressed with this software. I can’t wait to purchase a copy of my own! I’ll keep you posted!

Lesson Plan Map

Every July when I was a teacher, anticipation would begin to bubble up inside me with the start of the new school year just weeks away. This usually was invoked by the sights and sounds of back-to-school sales. Nothing got me more excited than the dollar deals at Target and Walmart, not to mention the penny deals at Staples. Oh how Staples misses my business.

In addition to my fetish for new school supplies each year, I was also addicted to meticulously planning out the next school year. This interest was usually sparked by summer workshops/trainings I was fortunate enough to attend. These activities always got my brain spinning on ideas of new activities, instructional techniques and the sequence of the curriculum. You would think not much would change from the year before; however, in all of my 10 years of teaching, I only once experienced back-to-back years where the courses I taught and the curriculum I used remained constant. All other years, I basically had to recalibrate my brain and my resources based around the grade and course I was going to teach. This included a curriculum map for the entire year. I would start with a blank printed copy of each month, and I would then pencil in the mathematics standard, objective, and even the chapters/sections in the textbook, along with all known activities I could use to teach that objective. This was not something I completed in a few days. This usually took me the better part of 2 weeks per course that I taught to complete, keeping a separate file per course.

Keep in mind, this regimen was largely due to my OCD tendencies, but in the end, it sure did make for an easy year. With that said, I won’t lie. I was never able to stick to it exactly, but it served as a road map for the year and kept me focus on what needed to be accomplished. After about year 7, I began to construct this file using Word, strictly for the purpose of sharing with fellow teachers. When I taught in South Carolina, it was a requirement to submit typed lesson plans each week, and post these to our website each week for parents and students to access. Looking back now, and after becoming an avid user of google docs, I really wish I had created a “one-stop-shop” for anything dealing with my lessons. This would include notes, activities, and assignments. Of course, it’s not until I stop teaching that I thought of this and have the time to create an excel file, in conjunction with google docs, to accomplish this task. Funny how things happen.

The file Excel Lesson Link is a template to use to map out your curriculum for the year. This file is actually accessed via my google docs page, as a shared file, hyperlinked within this file. In the Excel Lesson Link file are two other files that are linked to my google docs page that illustrate the capabilities of the file. One is a lesson plan and the other is an activity I used with my algebra students, already link to this blog. When you create your weekly lesson plans, all you have to do is upload them to your google docs page, as a shared document (anyone who has the link can view), and copy the link into the excel file as a hyperlink. In the excel file, clicking on “Insert” and then “Hyperlink” will allow for you to choose the text that displays in the file for the link you are sharing. You can attach all the files you need for each week, or per day, in the colored portion of each day on the calendar. The white section for each day can be used as the descriptors and content information, like the standard and objective and the textbook information. This document can be used in any capacity you so desire. Keep in mind, the goal of this file is to have it act as your one-stop-shop file. You could access it from any computer and pull up the files you need for your lesson. In addition, files and information is so much easier to share with fellow teachers, parents and students.

A few notes about goggle documents:

Google documents is a tool within gmail. If you do not have gmail, you would need to create an account. There may be another functionality out there similar to google docs that I’m not aware of. I will only speak of what I know for this post’s purpose.

I would create a structure of file categories and names per your class structure before uploading any files. This may consist of a main file of let’s say, “8th Grade Math”. Then I might break it up into chapters or content areas, class periods, or maybe even semesters or 9 weeks categories. The number of files uploaded may be very high, so creating subcategories will be very helpful for when you need to find a file. Creating the shell of an outline will prove to be very helpful in the end. Be sure that you “share” each file, requiring the link in order for a person to access the file. I would not make any of your files public. Lastly, it is in your best interest to pdf you’re the file before you post it. Otherwise, your files may be altered without your permission. That’s just not a situation you want to find yourself in.

I hope this resource helps you get organized for the year, if not for anyone but for yourself. If you’re unfamiliar with google documents, please play around with this before trying to utilize the excel file. It IS a great resource and DOES make your life easier. Like always, please feel free to contact me if you have any questions shannon.m.richards@gmail.com .I truly want to help make your teaching-life easier.

It’s always my pleasure!

Files for this post:

Lesson Plan Map Word File

Lesson_Plan_Map Pdf

Excel Lesson Link Excel 2007

Lesson Plan Map 97-2003  Excel 97-2003

Solving Quadratic Equations

Here I go again…talking equations. Must be the Libra in me!

As a follow-up to my last post, Simplifying Radical Expressions, this instructional piece transitions to quadratic equations in which simplifying radicals is necessary. Solving quadratic equations is the precursor to graphing quadratic equations and studying the nature of parabolas. This unit hinges on students bringing all of their knowledge of solving equations and factoring, while also acting as a springboard to understanding everything there is to know about parabolas.

The instructional piece below is intended to help you teach your students to solve quadratic equations. Inside the Word document are links to previously posted material that you may find helpful. The pdf version is there in case you’re unable to open the Word file. As always, I look forward to your comments, questions and suggestions. I also encourage you to post instructional strategies you have found successful in your classroom.

Solving Quadratic Equations Word File

Solving Quadratic Equations Pdf

Simplifying Radical Expressions Presentation

I posted a while back an instructional piece to help teach students how to simplifying radical expressions. Well, since then I have composed a Powerpoint presentation that you can use as an instructional resource. This is a lengthy presentation; however, it is quite comprehensive. Limited animations have been incorporated in order for you to be able to customize it for your instructional/learning needs. As always, please let me know if you feel an important concept/example has been omitted. I’d be happy to include it and repost. Feedback welcomed! 🙂

Simplifying Radical Expressions

Ketchup Time!

So, it’s three months out from the end of the school year. This is the last nine week period or quarter students have to show you what knowledge they have of mathematics. Have you already left for Spring Break?

It’s unfortunate that students wait until the last-minute to pull up their grades, but don’t check out just yet! Now is a good time to make those phone calls to parents of students who grades are a D or F. As uncomfortable as it may be to make these calls, keep in mind that you, the teacher, are just trying to be proactive. When making these calls, keep in mind, parents are going to want options for their students. This may involve asking for morning/afternoon tutoring, test/quiz retakes, turning in late assignments and/or extra credit/extra assignment work. Before making that first call, outline what options you are willing to live with so that you are ready to work with the parents. Being put on the spot by a parent who is asking for the moon and stars to be moved so their child can pass math is never a good thing.

In addition, be ready with all marking period grades for each student, including current missing work. This puts you in the driver seat with the parent and you come out looking like the true professional you are. Keep the conference call focused on the student’s grades and performance in  your class, and any behavior issues that may come into play with the student not meeting his/her personal best in your class. Do not talk about issues that are occurring in other classes the student has.  That’s for the teachers of those classes to handle. You are only responsible for the learning of the students in your classroom during their period in which you have them. Keep in mind, it’s not to late to call for that face-to-face parent conference! I highly recommend not waiting until May/June to tell a parent their child failed your class. There are things you can do now to help students be successful. Ketch’em up!

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