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
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Top Four Passionate Math Teacher Blogs
What an amazing set of blogs! Which activities are your favorite?
There are so many ideas here that can be replicated throughout the algebra curriculum. Just because your students are essentially teenagers, they still want to get up out of their seat and learn in a fun interactive way. Don’t deprive them! Let’s get creative!!!!
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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/ !
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In doing some reading on current technologies in mathematics classes, I came across Mathtrain.TV, wonderful resource created by students for students. These are short 5 minutes or less videos that students created to instruct on particular math content such as solving multistep equations or graphing linear equations. Teachers can also create short tutorials and post them to their school website to share with students and their parents.
To get started simply download the free software Jing at TechSmith.com. A stylus and tablet would be best for mathematics content, but not necessary. The videos are saved to your personal webpage on Screencast.com . Each video can be saved in folders and can be secured individually depending on the intended audience. If students have access to a particular folder, they can see any video saved within the folder. I see this working very well with a folder for each course you teach, i.e. 7th grade math, 8th grade math, Algebra I, or a folder for each class period. There’s so many opportunities to explore!
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With finals around the corner, how do you review the year’s curriculum with your algebra students?
I posted a while back “Algebra Alien” which is a fun way for students to represent their algebraic understanding using their notes and assignments. Another such cumulative review could be created by 46 teams of students, with each team focusing on a particular content area, writing a range of potential test questions. Once the set of questions are finalized, a cumulative practice exam can be created and administered to the whole class. Each team could then instruct/explain the correct responses for their sections and field questions as necessary. This type of review reinforces student’s understanding of their assigned content area, while creating student “buyin” to the review process. One word of caution…if students are allowed to pick their teams based on the content they like best or know better than the others, you’re hindering them from fully reviewing the content areas they in which they need the most help. Assigning students a particular content, based on their formative assessment performances throughout the year, will provide them one last opportunity to learn the material from a peer base. This can be done very inconspicuously, by prearranging the teams. With that said, its best not create a team of students that consists of students who have a poor or incomplete understanding of the same content. This type of review will take a great deal of planning and student mapping to the best team configuration, but when done properly it can have an amazing effect. What students may not have learned through your instruction, may finally comprehend through the instruction of their peers.
Please share your method(s) of facilitating a cumulative review for algebra.
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Here I go again…talking equations. Must be the Libra in me!
As a followup 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
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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
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By shannonrichards

Also posted in Current Discussion, Simplifying Radical Expressions

Tagged Absolute Value, Algebra, Monomials, NonPerfect Squared, Perfect Squares, Properties of Monomials, Properties of Radicals, Radical Expressions, Rationalizing the Denominator, Simplifying Radical Expressions, Simplifying Variable Expressions, Square Roots

Recently a student needed assistance on simplifying radical expression for his algebra class. He sent me several examples that he needed help understanding. After explaining how to simplify this wide variety of examples, I was motivated to write a formal segment on this topic to include here for fellow teachers and students to use. Feel free to send me other examples you’d think would make a nice addition to this piece. I look forward to hearing your comments and suggestions, and as always I look forward to hearing from my editors for any needed corrections.
🙂
Simplifying Radical Expressions
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This is the hardest time of the school year! The time between Thanksgiving and the winter break/holidays are so stressful. If you’re like most, you’re behind in your curriculum pacing and you need to start preparing your students for semester exams. This coupled with all of the interruptions this time of year brings, like plays, performances and celebrations, albeit as nice as they are, you’re struggling to keep the focus on learning. I’ve been there!
This is just a small list of ideas to help keep the pace on track and help you make it to the end of the semester. Please feel free to add any ideas and suggestions that may have worked for you in the past.
 This is that time of year where working in groups may not feel like it’s a good idea, but you might want to incorporate some into you lessons/activities. Students are social beings. They have a ton of built up energy and they need to release it. Forcing students to work independently, because their behavior has not warranted otherwise, may be a recipe for disaster and may increase the number of classroom interruptions. Allowing students to work in 2’s, or 3’s if necessary, may help students release some social energy while working on an assignment/project. Be sure the activity students are working on is relevant and meaningful; otherwise, students may become a major disruption.
 Think handson! Allow students to participate in kinesthetic activities that involve color and different textures. Allow them to be creative in displaying their understanding of the topic being learned. This is not to say let students “color” their assignment, but if students can have some creative license in doing their work, they will appreciate the freedom. Most of all, display student work! Showing off their successes will motivate them more than you know.
 Allow your stronger students act as facilitators in small group activities while you work with students who may need some remediation prior to the semester exam. This should be an activity that takes minimal instruction and revolves around review material. The students in the class should be able to work independently on an activity while you work with individual students, but you have assigned students to use as instructors when students in class have questions. Be careful how you advertise this. I have picked students based on grade and attitude, but announced to the class that these are the “goto” people for their section. Of course, clear classroom rules and procedures MUST be in place prior to this type of activity.
 Open up time for tutoring sessions, either in the morning, during a “free period”, or in the afternoon. While providing incentives for attending tutoring sessions is inappropriate, because getting to tutoring may not be feasible for all students, students will feel rewarded getting help in a smaller setting. This may not feel like it would impact the classroom instruction and help with pacing, but it does in a huge way. If you can get those 25 students caught up during tutoring, they will be able to follow you during the remaining instructional periods. They will appreciate understanding what they did not know before, and be motivated to keep up with you in class. Draw them in during class to answer questions or to summarize a concept if you feel their ready. This is the time to reel them back into the class!
I hope this sparks some ideas of things you can do in your classroom. Please share!
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There was an error on the second page. The value of x on both of the equations should have been 4. This has been corrected and the new file has been attached.
Being Strategic in Solving Equations PartII
I want to thank my new online editor and dear friend for finding this. : )
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