Clear Fractions and Decimals from Equations Early!

I've moved this topic to the beginning of the school year and I will always teach it at this time from now on!  I feel like it has helped my algebra students tremendously.  

By learning to clear decimals and fractions at the beginning of the algebra course, students are able to absorb the concept quickly, feel like they are learning something new as they "brush up" their equation-solving, and are able to apply it throughout the entire year.  It has become a strategy my students use often.

The textbook my school used didn't introduce clearing fractions and decimals until the systems of equations unit midyear.  This meant that students were trying to learn how to solve systems of equations and how to clear fractions and decimals at the same time.  Many of them struggled with this.  No such worries now!

If you need materials to assist you in teaching this topic, check out "Clearing Decimals & Fractions Foldable" and "Clearing Decimals & Fractions Practice". 

MATHO!

I think MATHO is my favorite review game. 

It is easy to play and kids love it!  

As a teacher, it is easy for me to set up, and I know my students are getting great practice, so it is easy to justify "game day".  It's a win for everyone!

I have made some MATHO games in which I cut questions apart, draw them from a container, and read them to students.  Others involve a student handout that is much like a study guide.  For these games, I roll a 30-sided die to randomly select problems.  You could also put slips of paper with problem numbers on them into a container and select problems that way. 

I keep track of the questions I have selected and the answers to them on the sticky note.

Yes!  An effective review ...

Students mark answers with highlighters, switching colors each round.  There are no beans all over my floor.  😜

You can find MATHO games here on a variety of middle and high school topics.  Instructions are included with the materials.  If you have an idea for one you don't see, please let me know.  I'd love to create one for you!

Here is a MATHO game about using the Pythagorean Theorem.

Multi-Step Equations with No Solution and Infinite Solutions

I’ll bet if we took a survey of the topics math teachers enjoy teaching most, solving equations would top the list. 

Actually, let’s find out how YOU feel about this.  Participate in the survey here: Create your survey with SurveyMonkey  

When I introduce equations with no solution and infinite solutions, I use these notes.  I’ve found them to be a quick way for students to compare these equations to those with one solution.  The interactive nature of the foldable notes helps to keep students focused.  Incorporating the checking of answers into the notes helps to make the rather abstract concept more concrete.  Students especially need to test multiple solutions to the infinite solution equation to help them grasp the idea, so I've included an area for that.

What next? ... Students need practice! 

Many textbooks and worksheets include very few problems with no solution or infinite solutions.  My belief is that students need a problem set that makes them think carefully about each problem.  If there is a good mix of equations having one solution, no solution, and infinite solutions, they must analyze each problem carefully.  I’ve found that textbook materials may contain only two or three special case equations in a problem set of 20-30 questions.  I want my students to have a problem set in which there are frequent examples of no solution and infinite solution.  That way, they must pause often to carefully analyze their solutions.  This increases the chances that they will actually remember what I am teaching them!  To provide more targeted practice, I created my own materials to use to teach this topic.  If you are interested, you can find them here along with the notes.

Typically, it doesn’t take very long for students to catch on to solving these sorts of equations.  However, it is very important that your students continue to see examples of no solution and infinite solution equations regularly throughout the year.  Bell work is an easy way to provide that review.

Motivate the Easy (Button) Way

It is amazing how motivating an Easy Button can be!

I've had mine ever since my husband tucked this one into my Christmas stocking several years ago.  I took it to school and it sat on my desk for a while, but was often covered by papers.  (I'm sure this never happens to anyone else, right?)  Because of this it rarely got used.  Eventually, it ended up in my desk drawer and I forgot all about it.

Last year, as I was cleaning that desk drawer, I noticed it.  Now, it is hard to look at an Easy Button and not test it out ... so, I did ... and the batteries were dead.

After replacing the batteries, I proudly set it out on my desk.  Before it got covered up with papers again, a student noticed it.  Of course, the student asked to push it.  My response was, "Get a 100% on your assignment and I'll let you do it."

Just like that, the Easy Button became a wonderful motivational tool.  Middle school kids put extra effort into their work just so they could push the Easy button!

Now, the Staples Easy Button is a staple in my classroom!  

Back to School: This is Me Presentations

Over the years I've tried an endless number of get-to-know you activities with my students.  Some were good... some not so good.

This year, I tried something a bit different and loved how it turned out!  I really need to stick with this as a Back to School activity.

I simply called it "This is Me".  It is not a particularly unique idea, but the execution worked great for me.

First, I created a short Prezi to introduce myself to my students.  (FYI: This is the first Prezi I've ever created, I narrated as I was presenting which is why some information may not seem complete, and I only showed a short part of the video that is included.)  You could use any format to tell the kids about yourself.  At the end, I gave them the challenge "This is me.  Now, tell me about you!"  

The only additional instructions were to keep it short (2-5 minutes) and that any format, paper or digital, could be used.

I gave students a few days to create, and then spent a few minutes at the beginning of the class period for presentations.  With about thirty students per class, this took 20-30 minutes per day for three days to complete.

It was so worth the time!  Presentations took the form of posters with photos and drawings, Prezis, Keynotes, iMovies, and creations using various apps.

I definitely learned more about my students than I normally do in a whole school year! For example:

• I can tell you who my artists, music lovers, digital experts, and athletes are.
• One student showed a "Three Stooges" video clip because he loves to watch the old black and white movies.  How else would I ever have learned that?  Also, the other students loved it!
• I have students who have spent years living in other countries and some who spend summers in other countries.
• I learned about foster families, adoptions, mission trips, family ancestry, baptisms, family members, pets, 4-H, scouts, athletic accomplishments and more.
• A number of my students moved to the United States from other countries and/or have relatives who live in other countries.
• One student produced a unique iMovie using a puppet.  Is she a budding actress or movie producer?

Passions and interests of all sorts were shared.  This was so eye-opening for me!  As a math teacher, class does not often lend itself to having of discussions that reveal this sort of information. 

One more thought to consider ...  I had a student last year who had just moved to my very large school and did not know anyone.  She came to me one day after class and asked me if I knew anyone who was interested in (fill in the blank).  She said that she was "looking around" to find other students with similar interests and hadn't noticed anyone.  Could I help?  

Now, students may not usually approach a teacher in this way and ask for assistance in identifying potential friends.  However, as students were giving their "This is Me" presentations, I wondered if classmates were listening and watching for opportunities to make connections.  I hope it helped someone out there in my classes who was feeling lonely to connect with someone.

Memorizing Perfect Squares

There are times when memorizing information in math class can be so helpful!

In elementary school, students are frequently given timed tests over multiplication tables and other basic facts.  Sometimes, timed tests are appropriate for secondary students, too.  

I have my middle school students memorize the perfect squares from 1 to 400.  Quick recall of perfect squares is especially beneficial when using the Pythagorean Theorem and when simplifying radicals.

Perfect Square and Square Root Flashcards

Good old-fashioned flashcards are a great tool for memorization of facts!  I have created these FREE flashcards.  

I like copying them on colored card stock, which I've found lasts better over time than laminated cards.  Here they are in use: 

 

It has been my experience that one minute fifteen seconds or a minute and a half is an appropriate amount of time to allow for a timed quiz over perfect squares.  It is long enough for students who know the information to answer all of the questions, yet not so much time that they can just multiply to get the answers rather than recall them from memory.

If you don't want to make your own quizzes, mine are available here.  Six versions of the quiz and four practice quizzes are included.  

I upload the practice quizzes to my school's learning management system for students to use to prepare.  They import them into Notability which makes it easy for them to duplicate for LOTS of practice! 

The actual quizzes I give are on paper.  I tend to give them to my entire class three or four times and then record the best score each student has achieved.  You can certainly continue giving the quizzes until mastery is achieved if that is your goal.

Does anyone else still give memory quizzes to secondary students?  If so, what do you have them memorize?

Word Problems: Rational Number Calculations

Do you have that one standard you always feel you could teach more effectively?  

For me, it is this one:
Indiana Academic Standards
8.C.1: Solve real-world problems with rational numbers by using multiple operations.

Here is the related Common Core standard:
CCSS.MATH.CONTENT.7.NS.A.3
Solve real-world and mathematical problems involving the four operations with rational numbers.

Part of my issue with this standard is simply that I can't find enough word problems.  If you are like me, it is a difficult task to gather enough word problems to provide an adequate amount of practice using all of the various forms of rational numbers.  I'll need to incorporate both positive and negative numbers in the form of integers, fractions, and decimals. Also, if my students are to truly master this standard, they will need to do a fair amount of problems including these types of rational numbers.

After lots of fruitless digging around searching for the type of multistep problems I need, I decided to write them myself.  I've created a set of twenty task cards with word problems that focus on rational number calculations.  Most of the task cards include multiple questions.

I have created these word problems to resemble those that may appear on standardized tests requiring students to apply skills. This is a challenging set of task cards that will make your students think!

Rational Number Calculations Word Problems

I'm planning to dive right in with these this year!  (I'll let you know how it goes.)  Students entering my pre-algebra and algebra classes should be able to calculate with rational numbers.  I am beginning the year by encouraging them to show me what they already know ... no reviewing!  

I do plan to allow students to use resources such as the skills review materials that go along with their textbook, or an online tutorial or video lesson.  Then, they can ask me for help if they still have questions.  I will reteach material to individuals or in small groups as needed.  I expect to learn a lot about my new students through this activity!

Sometimes, I think we don't require students to be responsible for what they have previously learned.  Instead, we assume they haven't mastered concepts.  I believe this is why teachers often begin each year by reviewing.  The problem is ... doing this communicates to students that they really don't have to learn the content because we'll reteach it anyway.  They become "lazy learners".  I want my students to know that learning what I am teaching is expected.  Yes, each student will learn at a different pace, but everyone should be actively involved in the learning process.  After all, this engagement is what I hope will result in retention of the material and that is the goal!