2018 - Make Sense of Math
Teaching Percents in Middle School Math


How to Teach Percents in Middle School Math
Using bar models to teach percents of whole or to calculate the whole given the percent and part is a very effective way to teach percents conceptually. When introducing this way, I highly suggest starting off with percents that are divisible by 5.  You can eventually do any percent with combinations of 5% and 1% as a tenth of 10%, but start off simple.

Let's look at percents of a whole.


An entire bar will represent the whole.  Draw the bar and label the whole.


Then you need to divide up the bar based on the given percentage.  50% would be in half.  20% would be divided into fifths.  30% would be divided into tenths.  Use guiding questions to help your students think of how to divide the bar. If they are stuck, always dividing it up into tenths or fifths should work, as long as you are using percentages that are divisible by 5.  


Next you need to divide the whole up into that many sections.  Again, use guided questions to help your students figure out how to do this.  They should come to the conclusion that the whole divided by the number of parts is the amount per section.  Write that amount in each of the sections.


Lastly, determine how many sections you need for the given percentage.  The students should already know what percent is each section from the first step.  After the number of sections is determined, I like to color the sections in on my bar so students can visually see the percentage of the whole.  They can then determine the part by looking at the value of the total colored sections. 


Bar models can also be used with finding the whole given a part and a percent as well as finding the percent given the part and whole.  

Let me just put this disclaimer on this method:  Doing percents with bar models may take a lot of work at first.  Each problem will take longer than if you just gave your students an algorithm.  This is how it is with most conceptual teaching.  However, I know that as you teach conceptual at first, and take the time to have the math make sense to the students, they will retain the information, and in turn, you won't have to do all of the extra review at the end.

Get The Task Cards
If you are interested in the task cards used in the photos you can get them here. 
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Teaching Percents in Middle School Math




Using Writing to Make Sense of Math


Writing in Math?
My first two years of teaching middle school math went ok.  I was learning the ropes of running a classroom and honestly, just trying to survive.  I didn't have my students write too much, because "Hey, I teach Math."  The summer after my second year of teaching I took an intense master's class about math pedagogy...homework included.  I noticed something that the professor always had us do on our homework, and that was to explain our reasoning.  I suddenly had as much writing on my homework as I did actual math.  I quickly learned the value of writing in a math classroom. 

Yes, Writing in Math
To be able to actually explain in words how to do the math, takes the math to a deeper level.  Students have to actually think about the why instead of just passing through meaningless algorithms.  Also, as a teacher, have you ever tried grading a student's work, and you are just not quite sure if they understand the concept?  Having students write their thinking can take your math in your classroom to a deeper level, and seriously, grading papers becomes an easier task.  No more second guessing if the student really understands or not.  If they can accurately explain their reasoning you know that they really understand the concept.  

Strategies in Incorporate Writing in Math
There are a few ways you can have your students write in the math classroom.  One strategy is in a notebook.


You can give writing prompts on the board, a classroom screen, or on task cards and have the students write in their notebooks.  One suggestion that I enforced in my classroom was that they had to write in complete sentences.  I also put a minimum of three sentences.  Many students went beyond three sentences, but I learned I needed a minimum for some students in my classroom.  Also, another strategy I often incorporated was to have them include an example of what they were explaining.


You can also had out slips of paper and use them as exit slips. 

This is a great way to see how much your students understood the lesson.  Hand out the slips of paper with the writing prompt and have them complete the writing and hand it to you as you walk out the door.  Also, as a side note, if students know they have to complete these to leave class, they will be very engaged in the lesson ;). 

You can also use these slips of paper as openers.  Hand them to students as they walk in the classroom, and collect them when they are complete.  This also helps students not be tardy, because they have an assignment write when class begins.

Writing in my math classroom, seriously took my class to a new level.  If you have not yet tried writing, I highly suggest you do.  

If you want some great prompts for your 6th grade, 7th grade or 8th grade math classrooms, or the products in the photos above you can click on the links below.
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Using Writing to Make Sense of Middle School Math





Teaching the distributive property


Teaching the Distributive Property

1) Make Sense of Multiplication
Students need to make sense of the meaning of multiplication in terms of groups.  Students may have previously learned multiplication as repeated addition, though this is accurate, extend their understanding to multiplication as meaning groups of.  For example, 2(x + 3)  means 2 groups of x plus 3.  Another example, 3(y - 1) means 3 groups of y minus 1.

2) Model the Expression with Manipulatives
Algebra tiles are great for modeling expressions, however, if you do not have Algebra tiles you can either make them with paper, or use objects to represent the variables and constants.  Have your students model the expression.  For example, they know that 2(x + 3) means  2 groups of x plus 3.  So now model the expression with manipulatives.  See photo for example.



Model with manipulatives for 3(y - 1)


After students model the expression have them write down what they see with combining like terms.

If your students see the connection between the initial expression and the simplified expression at this point, that is great.  If they don't, that is ok.  Your goal for this step is that they conceptually understand multiplying expressions. 

3) Model the Expression with Symbols
Now, instead of using manipulatives have your students write out the variables and the constants.  In the photo the expression 2(x+3) is modeled by writing out the groups. 


Here is the model for 3(y -1)

Again, have your students write the simplified version after modeling.  At this point, if your students have not already noticed the "shortcut" guide them through questioning. Ideally you want your students to make the connection so they retain the information.  

4) Multiply using the Distributive Property
Once your students have a strong conceptual understanding of the distributive property move on to actually using the property when multiplying.  Students should understand that every term from one expression needs to be multiplied by every term of the other expression.  Understanding this concept will greatly help them when multiplying binomials.  One strategy I use with my students are circling the terms including the signs. This helps students not miss the negative signs.  

Another strategy is drawing lines.  Lines become extremely helpful when multiplying binomials and beyond.  


If you don't have time to make your own notes about the distributive property, I've got you covered. I created two pages of notes to guide students in discovering the distributive property as well as FUN and ENGAGING stations so they can practice what they have learned. 
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Middle school math guided notes


Guided Notes in Middle School Math are Essential
It was my first year of teaching and I was drowning, like all first year teachers. I was teaching 6th grade, 7th grade, and 8th grade math, and I was the ONLY teacher teaching those subjects. My mentor was teaching 9th grade math. One day she introduced me to some guided notes that she had made for her students. She continues to tell me how great they are.
  • Easy for students to follow along
  • Doesn't do all the work for them
  • Great to refer back to when needed
  • Keeps students organized
  • Promotes inclusion
  • Promote equal access to material

"Those are so great!" I thought. Except no where in my day did I have time to make guided notes for my students, although I wanted to SO badly. 

So...I went searching online hoping that someone else had made them and I could purchase them.  I searched, and searched, and searched, and I could not find any guided notes that were as thorough and engaging as I would have liked. 

I settled with some that I had found, they were ok, but definitely not as in-depth as I would have liked. The concept worked great for my students, but I wish they were more detailed. 

Fast-forward 7 years later, and I decided to take a break in teaching to stay home with my little family.  I dove into designing middle school math curriculum.

One of the first product lines I made were the middle school math guided notes that I never had but so desperately wanted while teaching.  I worked so hard on them, making sure to never cut any corners, and I love how they turned out. 

Create your own guided notes for math
If you haven't incorporated guided notes into your math classroom, I highly suggest doing so. You can create your own guided notes by first outlining how you plan on teaching a certain topic. 

Don't forget to think about important vocabulary, and any review of topics you will need to do before diving into the new content. 

Create a variety of math problems to use in your notes. Make sure to leave out words that you would like your students to fill in. 

Most importantly, keep the notes clean and organized.  

Here are some things I included in my middle school math guided notes
✔️ In-depth
✔️ Quality problems throughout the notes
✔️ Additional practice problems at the end of each section
✔️ Room for extra notes
✔️ Page numbers and topics on edges for easy reference
✔️ Included all number lines and coordinate planes for graphing
✔️ Focus on discovery over algorithms
✔️ Focus on making sense of math

Get These Notes for Your Classroom
I imagine if you are an educator in the classroom or a parent homeschooling your children, you do not have time to make guided notes.  

That's why I have made my middle school math guided notes available to ALL educators and parents who are looking for some relief. 

Whether you are teaching virtually or in the classroom, these math notes are for you. 

✔️ In the classroom: Print packets and teach

✔️ Distance Learning: Print packets (or have students print packets) and teach online following them.

✔️ Easy to follow along because they are very thorough! Students can easily go back and review a topic if needed.


See what other educators are saying about Guided Notes from Make Sense of Math

  • I love these notes! I have the 6th, 7th, and 8th grade year long guided notes bundle and my year is so much smoother because of them. For a school that does not have a textbook for math this is an absolute life saver. - Allison M.
  • "I wish I would have bought sooner!" - Eleni L. 7th Grade Math Notes

  • "This bundle is saving me a ton of time and energy while I lesson plan for next year." Nicole M. 7th Grade Math Notes

  • "These are amazing guided notes. They are thorough and move through the material in a way that makes sense to the students." Allison L. 7th Grade Math Notes

  • This helps a ton with planning and making notes for the students to follow!" Zach M. 8th Grade Math Notes

  • Awesome resource. I love the ease of use and how quickly I can use in the Diverse Learner Setting. Thank you so much" Patience S. 8th Grade Math Notes


If you need these in your classroom click on your grade level below to get them now.


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Middle school math guided notes


First Day of Middle School Math

Stress out Your Students on the First Day of Middle School Math Class
1) Give your students a test
You want to know what your students know and what they don't know.  What better way to assess their understanding than a test.  Better yet, you can hand them a test right when they walk in the door.  Tell them where to sit, and tell them to work on the test the entire period.  This way you can look at the tests later and better plan what you need to review with your students.

2) Be super strict and NEVER crack a smile
You want your students to respect you, right?  Well, you better let them know that you are in charge.  If your students see any weakness in you, especially the first day, they will take advantage of you the rest of the year.  Be stern, be strict, lay down the law, and most importantly NEVER crack a smile. 

3) Make your students feel like failures
Give your students some really hard math problems the first day.  Tell them that their understanding of these problems will go on their grade. Better yet, put them into groups and let them talk about these math problems.  Those students who are afraid of math will feel so stressed out, they will feel like they failed on the very first day. 

These are great tips to make sure your math students feel super stressed out on the first day.

Have a Great First Day of Middle School Math
I hope you caught my sarcasm in this post.  Many students are afraid of their new math class before they even walk in the door.  Love them, respect them, make them feel like winners and that they can be successful.  Be careful with giving  pre-tests the first day....or even the first week.  Once the relationship between your students and you is more solid, and routines are in place, pre-tests can be given.

Thank you for having courage to teach math.  May you have a great year!


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First Day of Middle School Math


Growth Mindset in the Math Classroom


5 Keys to a Growth Mindset
A growth mindset is a powerful tool in a math classroom.  Students need to learn that they are capable people who have control over their own learning.  I created a mindset questionnaire to give to my students at the beginning to of the year to understand their mindset.  You can download a FREE copy of the questionnaire HERE.  Here are 5 keys to a growth mindset that are very effective, especially in a math classroom.

1. When I Struggle My Brain Grows

Growth comes through challenges.  Often time students think that if a concept it not "easy" for them then they have a problem. Struggle should be important, encouraged, promoted and celebrated in your math classroom.  Teach your students that when they are struggling that their brain is growing. This will help them view struggle as a positive rather than a negative. 

2. I CAN Learn Math

A common misconception in society is that there are two types of people "Math People" and "Not Math People." If a student has labeled them self as as "Not a Math Person" or even worse, if a parent has labeled their child (which I have seen way too many times) as "Not a Math Person" then this student believes that they are not able to learn math.  Teach your students that ALL people can learn math.  Believe in them as a teacher, remind them often that they can learn math, and they will believe this too. 

3. I Don't Understand YET!

Many students get down on themselves because they don't understand concepts quickly.  This is especially a problem if their is that one student that constantly yells out that everything is "EASY!" In fact, the word "EASY" was banned in my classroom for the problems that it caused.  Teach your students that it is OK if they don't understanding everything right now, but that they will eventually understand if they keep working on the concept.  YET is a powerful word.  Use it constantly in your classroom!

4. Mistakes Allow Me To Learn

Mistakes are often viewed as negative.  Who wants to make mistakes?  This needs to change, mistakes need to be viewed as something positive, especially in a math classroom. Just think about your own life, how many times have we made a mistake, and learned to never do that again.  Encourage students, especially on assessments, to analyze their mistakes.  Rather than just having them do test corrections, consider having them analyze their errors and specifically writing about what mistake they made.  Spend time talking about mistakes, don't ignore them and just talk about the right answer.  Constantly talk about the power of learning from your mistakes.   

5. My Effort and Attitude Determine My Success

This one goes along with #2.  Many students believe that they cannot be successful in mathematics because they simply do not have the ability.  They think of it as something you either have or do not have.  Students need to be taught that they can control their success!  They can control their effort and their attitude and this directly affects their level of success.  Some students will need a constant reminder of this fact throughout the year.  

To help my students remember these 5 keys, I made posters for my classroom.  I also made coloring pages with these 5 keys on them so they can put them in their binders or lockers as a constant reminder.  If you are interested you can check them out in our store or on Teachers Pay Teachers.

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Growth Mindset in the Math Classroom






Keep Math Alive During Summer
Doing math worksheets is likely not on the list of activities your students or child wants to do this summer.  In fact, I read about a recent study from the Harvard Graduate School of Education that math worksheets during the summer do not actually improve a child's math performance. Instead, the Harvard Graduate School of Education suggests that by helping your child see and use math in every day life you can help prevent summer math loss.   You can read more about this study Here

Here are some great suggestions to keep math alive for your student during the summer. 

1. Real-World Integers - Take a picture of three examples of people or companies using integers in the real-world.   

2. Grocery Store Rates -  Go to the grocery store and take three pictures of unit rates on the labels.  Explain how you can use this information to save money. 

3. Interviews - Interview an adult who is a stay-at-home parent and how they use math in their life.  Write a short report about what you learned.  

4. Budgets - Learn how to make a budget through research and/or by talking to an adult who uses a budget. Create a fake budget for a salary of $2,500/month. 

5. Architecture -  Draw a scale drawing of your bedroom.  Include a scale, and at least three items in your room. Use the scale drawing to discover different ways to re-arrange the furniture in your room.

6. Real-World Fractions - Take a picture of three examples of people or companies using fractions in the real-world.   

7. Interior Design - Calculate the surface area of your bedroom walls.  How much paint will you need if you want to repaint the walls?

8. More Interviews - Interview a professional who uses math in their career.  Write a short report on what you learned.

9. Advertising - Search a grocery add and cut out three adds that advertise products as multiples/$, such as 2/$5. Figure out the unit cost of each product.

10. Math In Nature -  Learn about the Golden Ratio, and find examples of this ratio in nature. (I had my students do this once, and they loved it!  The Golden Ratio is so fascinating!)

Talk with Your Kids about Math
Adults often over look how often they use math in their lives: calculating distances, budgeting, area for gardens or decorating, cooking, etc... Talk with your child or students about how you use math every day and help them open their eyes to the math that lies at their fingertips.

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Keep Math Alive During Summer






How to teach exponent properties


How to Teach the Exponent Properties
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. 

Exponent Properties Guided Notes for YOU

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.  

In the mean time,
Happy Teaching!

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How to teach exponent properties


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