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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, YOU CAN CLICK HERE TO USE MINE.  I've included 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. 



     



Middle School is a time of transition for many students. As part of this transition, we as teachers expect them to start taking on more responsibility. Part of the problem, however, is that students change at different times and not all when we want them to.

My first year of teaching my idea was that every student would have a notebook and they would just listen to me and take down the notes from the board. My idea was to review their notebooks every so often to make sure they were getting down the notes. After reviewing their notebooks I saw that some students had great and fantastic notes just as I had wanted. However, others notebooks were empty, others had drawings, others had notes to friends, others were trying to take notes but they were very incomplete. I quickly learned that my idea was not very effective. Not because they didn't want to, but because they did not have the skills to do so. I didn't want to completely give up on my efforts to help them learn this life skill. However, I realized that having them take all the notes was not going to be effective and so I needed to find a balance between them taking notes and also them getting all the information.

 I decided to incorporate writing at the beginning of class through openers. Everyday I would have an opener on the board and they would have to write at least 3 complete sentences.  I felt like I was supporting language arts in my classroom. What I started doing, was having guided notes for them. I found some online that were good enough. They were not exactly what I wanted, but they would work, as I knew I didn't have time to make them as thorough  as I wanted them. I found this to be a very effective method; they were paying attention so they could complete their notes but it was they weren't so many notes that they were getting behind or lost.

After I took a break from the classroom and started making curriculum, I tried to  think of materials that I wish I had but didn’t. Of course, guided notes were at the top of my list. I knew this was something that I wanted to make. But I kept putting it off because I knew it was going to be a lot of work to get them as thorough as I thought that they should be. But I finally dove into creating them and I am so happy with the final product.

If you are interested in using some guided notes, check them out here. I currently have seventh grade completed, and will soon have eighth grade completed.

They are aligned to the common core. My goal is to have them as thorough and complete as possible. Feel free to email me at makesenseofmath@yahoo.com if you have comments or suggestions about them.
Middle School is a time of transition for many students. As part of this transition, we as teachers expect them to start taking on more responsibility. Part of the problem, however, is that students change at different times and not all when we want them to.

My first year of teaching my idea was that every student would have a notebook and they would just listen to me and take down the notes from the board. My idea was to review their notebooks every so often to make sure they were getting down the notes. After reviewing their notebooks I saw that some students had great and fantastic notes just as I had wanted. However, others notebooks were empty, others had drawings, others had notes to friends, others were trying to take notes but they were very incomplete. I quickly learned that my idea was not very effective. Not because they didn't want to, but because they did not have the skills to do so. I didn't want to completely give up on my efforts to help them learn this life skill. However, I realized that having them take all the notes was not going to be effective and so I needed to find a balance between them taking notes and also them getting all the information.

I decided to incorporate writing at the beginning of class through openers. Everyday I would have an opener on the board and they would have to write at least 3 complete sentences.  I felt like I was supporting language arts in my classroom. What I started doing, was having guided notes for them. I found some online that were good enough. They were not exactly what I wanted, but they would work, as I knew I didn't have time to make them as thorough  as I wanted them. I found this to be a very effective method; they were paying attention so they could complete their notes but it was they weren't so many notes that they were getting behind or lost.

After I took a break from the classroom and started making curriculum, I tried to  think of materials that I wish I had but didn’t. Of course, guided notes were at the top of my list. I knew this was something that I wanted to make. But I kept putting it off because I knew it was going to be a lot of work to get them as thorough as I thought that they should be. But I finally dove into creating them and I am so happy with the final product.

If you are interested in some guided notes for your classroom I have got you covered!

CLICK HERE FOR 7TH GRADE GUIDED NOTES
CLICK HERE FOR 8TH GRADE GUIDED NOTES


As always, I am committed to quality products.  Any questions or comments please feel free to email me at makesenseofmath@yahoo.com

Michelle

Great post on the benefits of using guided notes in your middle school math classroom.  Great for any 7th grade or 8th grade teacher who is looking for teaching ideas for math. #makesenseofmath



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.

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!


Great ideas to have a great start in your middle school math classroom. Things not to do on the first day so that your students are not stressed out.  Great read for all teachers. #makesenseofmath


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 in also using these in your classroom you can get your copy HERE
Great ideas to help your students develop a growth mindset in the classroom.  Perfect for middle school students to become better students! #makesenseofmath


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