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The exponent properties can be super confusing for students if they do not make sense of them.  For example, when looking at the expression: x5xno where in the expression is their an addition sign, but if you know the property, addition is used to simplify the expression. I want to share some tried and true tips for successfully teaching exponent properties. 

First off, I want to discuss what is NOT effective:  I highly suggest not just telling your students the rules.  Having them simply copy down the rules then practice them will be ineffective, especially for students who struggle with memorization.

What IS effective:  I want to present a four-step process for helping students discover and make sense of the exponent properties. This process includes: helping students make sense of the expression, modeling the expression, simplifying the expression from the model, and noticing the pattern.

Let's look at the expression: x5x
1. Make sense of the expression: 
I would start by asking my students, "What does this expression mean?"  Hopefully they could make sense that it is the product of x multiplied by itself 5 times and x multiplied by itself 3 times.

2. Modeling the expression: 
I would then have them write out the meaning of what they explained in the first step.  (x.x.x.x.x)(x.x.x).

3. Simplifying the expression:
We would then talk about how (x.x.x.x.x)(x.x.x) is the same as x8

4.Noticing patterns: 
After doing a couple of the same types of problems following this method I would then ask the students to look for a pattern.  Hopefully they would notice that the exponent in the simplified expression is the sum of the exponents with the same bases.

Lets look at another expression x5/x
1. Make sense of the expression: 
Ask your students the meaning of the expression

2.. Modeling the expression: 
Write out in symbols what they said in words from the first step.   (x.x.x.x.x)/(x.x.x). 

3. Simplifying the expression:  
You may need to review with your students that x/x=1, just as 2/2 = 1 or 5/5=1.  After canceling out, this will simplify to x.x = x2 

4. Noticing patterns:
Again, do the process a couple more times with similar problems.  Ask the students if they notice a pattern or a "shortcut"  They should notice that the power in the simplified expression is the difference of the exponents in the original expression. 

I follow this method with every exponent rule.  With the negative exponents, I create a table with the positive exponents, and have them notice a pattern and continue the pattern to discover negative exponents. 

By following this method your students will make sense of the exponent properties.    The best part about using this method is that if a student doesn't memorize this property they can always go through the process of modeling and simplifying. Memorization is not required.  If their is an expression such as x50x30, and your student cannot  remember the rule, they probably don't want to model the expression either...that would be a lot of x's.  Instead of telling them the rule, I often write a simpler expression, have them go through the process of simplifying, modeling, and noticing the pattern, then apply their pattern to the larger expression. 

If you are looking for some guided notes on exponent properties I have taken then time to create some.  Students will discover all the rules through this method and apply their learning on expressions.  You can Click Here to check out these exponent properties notes.

In the mean time,
Happy Teaching!

In my previous post I talked about ways to survive the last weeks of school, especially when state testing is over.  But now let's talk about how to survive the last day of class.  Before I share some ideas I want to share some ideas of what NOT to do.  These may or may not be from experience.

Don't just try to "wing it", meaning, trying to get through the class period without a plan.   I'll admit there were days during each school year that I had to "wing it" because my original plans fell through, and I actually got through the day pretty well.  However, doing this on the last day of school does not work.  Your students, especially if they are middle school students or beyond, will already be full of energy, and if the teacher doesn't have a plan, the students will take over. 😨

The other activity that I do NOT recommend is a bunch of work that you are going to have to grade.  Big tests and loads of worksheets may keep them busy and quiet, but what teacher wants to be stuck with a handful of papers to grade on the very last day of school?  I would recommend doing these items on the last week of school, but not on the last day.  Give yourself some time to grade the work before the last day.  That way you can still give feedback to your students and you are not left with a stack of work.  

Now I would like to share two activities that I started doing on the last day.  The students have loved these and they are low-stress for both students and teacher.  The first activity is a letter.  I have my students write a letter to my future students.  I have them write what they think the students should know so they can be successful in my class.  These are fun to read, and they are actually really helpful for my next year's students.  I always proofread them first, but at the beginning of the next school year I hand them out to students to read.  They love reading them, and they tend trust their peers more doing their teenage years, so it works out great.

The second activity I do is a fun review game.  I have always done this in groups of 3-4 students, thought it certainly could be doing in pairs or individually.  I hand out the following paper. 
I then give the students 5 minutes to fill in each box with a term or concept that they have learned this year.  Each word must start with the letter in the box.  After 5 minutes, the students take turns sharing their answers and scoring their grid.  They receive one point for each box they filled if and only if nobody else had their same word.  The students have really enjoyed this activity, and it's a great way for them to review concepts that we have learned throughout the year. I have attached a link to the pdf document so you can download and use in your classroom.

Congratulations on another successful year of teaching!

You did it...almost.😖. You taught everything outlined in the curriculum for the end of year test...and your students nailed it.  Problem is, however, there are three weeks of school left, now what?  I stressed about this every single year. I tried different things every single year.  Here are some strategies and ideas to keep you sane. 

1)  Routines.  This is probably the most important.  The last thing you want to do is make the class feel different to the students.  Not sticking to the routines you have established will result in students not knowing what to do, therefore they start acting out.  Treat every day like another day at school. 

2)  Expectations.  This goes along with number one.  Don't let your expectations slide, students will pick up on it and take advantage.  Expect that they continue to try their best.  Expect them to complete their work. Expect quality work from them every single time. 

3) Keep your students thinking.  I know you're tired, and I know your students are tired...but it's not over yet.  Do not assign busy work to your students.  Busy work is work that doesn't require much thought.  Your students will get bored and may perceive the work as unimportant.  Once the kids do not see the work as important...you're toast. 😲

1) Just keep on teaching.  Some years I created my own end of year test that was given not three weeks before school was out, but with only a few days left.  I continued teaching, connecting, and reviewing their math up until MY end of year test, not the state test.  Giving it just a few days before school was out was just enough time to correct it, and review it with the students.  

2)  Cumulative project. A cumulative project in math would be a large project that ties in many concepts that your students learned during the year.  The great thing about cumulative projects is that students will be able to see how many of the math concepts intertwine and are used in the real-world.  May I suggest, however, that the project is planned out very well.  Know what your students will be doing every single day for the project.  When I did this, I feel like that is where I failed.  I had a cumulative project planned, and I gave specific dates for when they needed to have certain parts of the project completed, however, it was not planned daily.  The problem I encountered is that students were "enjoying" the end of the year, and then procrastinated the work time. So it was like a handful of days where they weren't working much, and a few days where it was like chaos, because they were all trying to get done on time.  So if you go this route, just make sure that every day has a specific task that needs to be complete.

3)  Smaller real-life tasks.  This is where I have felt the most successful with the end of year.  Real-life tasks also combine concepts that students have learned throughout the year.  However, they are not as large as the cumulative project.  They are real-life tasks that can be completed in one or two class periods.  Tasks such as budgeting, planning a trip, designing a scale model, etc...  They are engaging, yet not overwhelming. If you need help coming up with some end of year tasks  Click Here for some that I have created, and my students have loved.

You've made it this far....just keep swimming! 💜

After my second year of teaching my state switched to using the Common Core State Standards.  While the standards weren't too different from the standards we were already using, how they wanted us to teach math switched drastically.  No more feeding students algorithms, they wanted students to discover, apply and connect.  I was totally on board with this switch, but the problem was ALL of our textbooks were now considered old. I suddenly had no resources for my students to use.  However, that summer before school started I went to various classes that taught about how we would now be teaching math.  They also addressed the issue of our lack of resources.  They taught us how we could actually use our old resources but we just needed to reverse the questions.  This idea was brilliant!  Let me give an example,  a math question may have said something like, "Find the volume of this rectangular prism with a height of 3 inches, a width of 2 inches and a length of 10 inches."  Instead, reverse the question, "Create a rectangular prism that has a volume of 60 cubic inches. Justify your answer."  So much more reasoning goes into the second question.  

I used this idea of reverse questioning and created an activity called "What's the Question?"  Essentially, I give students the answer to the question, and they have to come up with the question.  Many times there is more than one answer, but as long as students can justify their reasoning it works for me.  

I am giving away a sample page so you can get an idea of this activity, and use it with your students.  You will see deep-thinking increase in your classroom!

CLICK HERE for "What's the Question?" sample page

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