GCF Foldable – 4 Methods

The GCF foldable and videos below show four methods that you can use to find the G.C.F. (greatest common factor).  See the steps and examples that I chose for the GCF foldable below.


Method 1:  Make a List

Steps:

1.  List all factors for both numbers.

2.  Identify all common factors.

3.  Select the biggest factor that both numbers share.

Examples:

A.        12 and 36
GCF Foldable

B.        18 and 45

GCF Foldable


Method 2:  Prime Factorization

Steps:

1.  Find the prime factorization of both numbers.

2.  Compare the prime factorizations:  circle common prime factors.

3.  Multiply the common prime numbers.

Examples:

A.        30 and 16
GCF Foldable

B.        75 and 90

GCF Foldable


 

 

Method 3:  Venn Diagram

Steps:

1.  Find the prime factorization of both numbers.

2.  Fill out the Venn diagram.  Put the common prime numbers in the middle first.

3.  Multiply the common prime numbers from the middle of the Venn diagram.

Example:

GCF Foldable

 Video:


Method 4:  Ladder (Upside Down Division)

Steps:

1. Divide both numbers by the smallest prime number possible.

2. Continue the process until one or both numbers (on the inside) cannot be simplified any further.

3.  Multiply the prime numbers that you divided by.  (The numbers on the left.)

Examples:

A.        40 and 32

GCF Foldable

 

 

 

B.        12 and 18

GCF Foldable

Video:


GCF Foldable

I created this foldable using cardstock so that I could use my flair pens without them bleeding through the paper.

GCF Foldable Outside:

GCF Foldable

GCF Foldable Inside:

GCF Foldable

GCF Foldable – Two Flaps Open:

GCF Foldable

GCF Foldable – Two Flaps Open:

GCF Foldable

Do you know of any other methods that I should try?  Are there any of these methods that you have never tried before?

Coming Soon:  Would you prefer to buy the computer version?  Get it here (coming soon)!

GCF Foldable

Creating a Foldable on Any Topic

How do I create a foldable on any topic?


0101

SECTIONS:

First, I decide how many sections I will need based on the topic I plan to use.

For example, if I want to create a foldable on fraction operations, I will need four sections: adding fractions, subtracting fractions, multiplying fractions, and dividing fractions.  If I split each section approximately in half, I can separate the rules from the examples.

Once I know the number of sections needed,  I must decide which style of foldable I want to use.


0202

STYLE:

A few ideas come to mind right away:

Flaps/Windows

Benefits of Flaps/Windows:  

  • They help students focus on one topic at a time by giving them the ability to open just one section at a time.
  • The flaps are great for quizzing/memorization.

Disadvantages of Flaps/Windows:

  • Inevitably some students will accidentally rip off a flap.  Don’t worry, you can always tape it back on.
  • Some cutting is required to create the flaps/windows.

    Check Out Some Examples:

        4 flaps all facing the same direction

FractionsFoldable4FlapsAmyHarrisonOutsideFractionsFoldable4FlapsAmyHarrisonInside

If you chose to use this template, I suggest putting it in your math notebook so that the folds on the left hand side face the center binding.  The foldable goes on the right hand side page in your composition book to accomplish this.

Now, when the students open and close their books, they don’t have to worry about making sure that all of the flaps on the foldable are closed.  That is a great benefit of this foldable over the next option.  However, the flaps on this foldable are longer and can accidentally get torn off.

4 flaps with 2 on each side

FractionsFoldable4FlapsAmyHarrison2OnEachSideOutside

FractionsFoldable4FlapsAmyHarrison2OnEachSideInsideAmyHarrison

If you chose to use this template, it doesn’t matter if you put the foldable on the left hand side or the right hand side of your notebook.

If you put it on the right hand side of your notebook, the flaps on the right hand side of the foldable might misbehave when your students open/close their notebook.  Make sure that students close the flaps on the foldable before closing their notebook.  This will prevent the windows from getting smashed or torn off.

I enjoy the flap/window style because it allows for two sections for each topic:  one on the back of the cover, and the other inside the foldable.  When using this style, I like to keep it consistent:  all of the steps are on the back of the cover, and all of the examples are inside the foldable.

If you are having trouble deciding which flap/window template to use take a look at the shape of the sections and decide which one would be better for what you plan to write in it.

Both foldables have flaps/windows, and they take up the same amount of space.  However, I think the second option is better for writing the fraction operations steps, so I am leaning towards that one right now.


Accordion

Benefits of Accordion:  

  • If you are starting with copy paper, there is ABSOLUTELY NO CUTTING necessary. However, if you start with a template from the computer, you may want to cut off the excess margin.
  • The foldable takes up less space than the flap/window style, so there is more room to write on the notebook page next to the foldable.
  • It is less likely that a student will rip off part of the foldable because it is all one piece of paper with no cuts.

Disadvantages of Accordion:

  • It is harder to only show one section at a time.
    • In this example, adding and subtracting are shown at the same time, and multiplying and dividing are shown at the same time.
    • If students need to “block out” the other sections, consider having them use a piece of cardstock (so they can’t see through the paper) that is cut in thirds to cover the other section.
    • Another option:  have them put a folder over the section they need to cover.

SEE AN EXAMPLE HERE:

I chose this option because it is similar to some other foldables that I made recently, so I was determined to make something with this template.

Another reason I picked this one?  The other flap/window options are the FIRST that came to mind, so I thought that this one might be more unique.

Need more reasons?  I decided that it might be helpful to have both addition/subtraction showing at the same time since they have nearly all of the same steps.  Then, I realized that multiplication/division can benefit from being next to each other as well.  After all, division becomes multiplication after flipping the second fraction!


0303

CREATE YOUR TEACHER FOLDABLE

  • Fill out your cover/titles depending on which style you chose.
  • Decide the steps/rules you want to use.  Write them out on your foldable.  Make sure there is enough space for students to write everything comfortably.
  • Determine how many examples you have room for.  Write them out.
  • Solve all of your examples.  Make sure that you have enough room to fit all of the necessary work.  If you need more room, consider taking out one or more examples.

Here is what my accordion style fraction operations foldable looked like after I typed up my steps and wrote in some examples.

After I took these photos, I decided to add some lines to separate each of the problems.

I started with my student version that had numbers for the steps and all of the questions typed.   Then, I wrote out the steps and solved all of the problems.  I put a box around my answers.

Later I typed up all of the steps and answers to get a completed “Answer Key” foldable.

MultiplyingDividingFractionsSideComplete_AmyHarrisonAddingSubtractingFractionsSideCompleteAmyHarrison

 

 

0404

CONSIDER MAKING MULTIPLE VERSIONS

Now that you have completed your teacher foldable, YOU ARE FINISHED!  Make sure that you have your complete version (a.k.a. answer key) for your reference and partially completed versions for each class.  All of these can be made by hand, but you may want to consider making versions on the computer for easy printing and copying.

Check out my typed student versions and answer key:

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If you are going to go to the computer, make one version that is the same as what the students will fill out.  Then, you can print it and make two-sided copies.

You just saved your class some time since they won’t have to write every single problem. PLUS, there is something to be said about having a typed worksheet-like paper with all of the questions already on it.  It is impossible for students to write down the problems incorrectly and they are easily distinguished from the work and answers that the students will write in.

Typed Student Version 1:

MultiplyingDividingFractionsSideStudentVersion1_AmyHarrisonAddingSubtractingSideStudentVersion1_AmyHarrison

 

INCLUDED IN FIRST PRINTABLE STUDENT VERSION:

  • All Titles (Adding Fractions, Subtracting Fractions, Multiplying Fractions and Dividing Fractions)
  • Text on the Cover (FRACTION OPERATIONS) and Operation Symbols
  • All Questions

Students will start with the printed foldable above, write out the steps, work out the problems, and write the answers to get the completed version to glue in their math notebook.

Completed Student Version:

MultiplyingDividingSideStudentVersion1COMPLETE_AmyHarrisonAddingSubtractingSideStudentVersion1_COMPLETE_AmyHarrison

Creating even more versions can be helpful if you want to show only one part at a time. However, this can be accomplished by covering most of the foldable with paper.

I created a second student version that has all of the steps already typed out.  This will be great for accommodations or if I am looking to save some time.

Typed Student Version 2:

MultiplyingDividingFractionsSideStudentVersion2_AmyHarrisonAddingSubtractingSideStudentVersion2_AmyHarrison

INCLUDED IN SECOND PRINTABLE STUDENT VERSION:

  • All Titles (Adding Fractions, Subtracting Fractions, Multiplying Fractions and Dividing Fractions)
  • Text on the Cover (FRACTION OPERATIONS) and Operation Symbols
  • All Questions
  • Steps Typed

NOT INCLUDED IN EITHER PRINTABLE VERSION

  • Steps
  • Worked out problems

REMEMBER:

By taking the time to type up the questions, you will save your students and yourself some time.  Simply make copies instead of having to create everything by hand.  Now you can use the same foldable template next year, unless you are teaching a new grade 😦

WOULD YOU PREFER TO PURCHASE THE COMPLETED FRACTIONS FOLDABLE AND TEMPLATE INSTEAD OF MAKING YOUR OWN?  GET IT HERE!

FractionOperationsAccordionStyleFoldable_COVER.png

CHECK OUT ANOTHER FOLDABLE I MADE WITH THIS TEMPLATE FOR CONVERTING BETWEEN FRACTIONS, DECICMALS, AND PERCENTAGES:

FractionsDecimalsPercentsFoldable_PIN [Autosaved] [Autosaved]

 

 

AmyHarrisonBWSquare

FREE 6th Grade Ratios and Proportional Relationships Common Core Math Posters

Are you looking for common core math posters for the 6th grade ratios and proportional relationships standards?

Try these FREE posters:

This slideshow requires JavaScript.

Download the .pdf here:  6thGradeCCSS_RP_Posters

or FREE from my TpT Store:  6thGradeCCSS_RP_Posters

Try Some Related Activities:

RatiosAndProportionalRelationships6thGradeAllStandardsPIN_AmyHarrison

amyharrison

Inevitable Excitement from the TPT Conference Has Cost Me Last Night’s Sleep

Inevitable Excitement from the TPT Conference Has Cost Me Last Night’s Sleep.

My Positive Experience at the TPT Conference on July 11th, 2014.  

When I first got an e-mail about the conference, I started out by thinking it would be weird to go because I was only a seller for less than a year… to feeling energized and motivated after the conference… a complete 180.  #TPT2014 #TPT14

Some people might think I am crazy due to my willingness to hang out with strangers for the day, but it makes me feel right at home…

Since I was in middle school, I have been very willing to socialize with others, especially if I don’t know them very well. In fact, I would say that I was most comfortable with friends first, then people I didn’t know at all, and finally was the least comfortable with acquaintances.  I thought I was so wise in middle school… oh boy!  I will never trade my best friends for anything, but do agree that sometimes the “acquaintance stage” has a history of being incredibly awkward. Then again, I tend to over think everything!  (Thanks Mom…)  Sure, I do get uncomfortable easily, but I can still talk to anyone if I have to or want to.  I can thank my dad for the social gene.

Even though I am super new (less than a year) to Teachers Pay Teachers, it was great to see the teacher that got me started on TPT, Lindsay Perro.  I didn’t even know how to pronounce her last name until she stated her name at the TPT Conference Session.  Nevertheless, a colleague showed me a sample of her coloring pages, which enticed me to try this TPT thing for myself.  I noticed the teacherspayteachers.com/Store/Lindsay-Perro along the bottom of the page, so I investigated when I got home.  I realized that she specialized in middle school mathematics, which really excited me.  After all,  I had been teaching middle school math for 5 going on 6 years. Let me be clear:  I created worksheets, quizzes, and tests for my department regularly, but I had never tried to sell and market my products.  I completed my TPT investigation over the summer, signed up, and the rest is history!

paulandamy

Paul & Amy

During the cocktail hour, I inadvertently got a photo taken with Paul.  I was taking a picture for someone else that I had just met. What seemed like a few minutes later, I was still standing there next to Paul and his arm was still around me… oops!  Clearly he was thinking that I was waiting for someone to take a picture, so I got my phone out of my purse and had someone take a picture. However, I am not proud of how I look because I did not give myself enough time to get ready in the morning.  My “excuse” is that I was too lazy to get up because I live in Vegas so didn’t have very far to go for the conference.  In all reality my excuse would have been that I couldn’t handle being out-of-town if the conference were across the country. Sometimes I am hopeless when it comes to getting ready to go somewhere… Especially now that I spend most of my time at home now that I teach online.

IMG_1746

temporary tatoo

Even though I still feel new, I have started to feel much more comfortable after attending the conference.  Before I felt like I was on my island; A familiar feeling for me, as I was the only person teaching my topic for several years.  Distancing me further, I never bought any other teacher’s products, and didn’t have anyone to collaborate with. Luckily, I found a perfect counterpart to bounce ideas off of last year!  Yay 🙂

Now back to the conference… Ok I’ll be honest, I did still feel a bit like an outsider at the conference at times.  It seems like everyone has business cards, use graphics on their products (typically purchased from other TPT sellers), blogs regularly, have a Facebook page, pins a few times a week, etc… whew…  When I spoke with sellers that have been going at it a little longer than me they told me that I need to get on the TPT Seller’s Forums and on Facebook. Recently, I have read a few of the posts on the sellers forum, but there is so much… I will go back again soon and try to find something to comment on.  I am looking forward to meeting some new friends in other sellers.

amyharrison

 

Blank Coordinate Planes – Reproducible

 Free Blank Coordinate Planes (Reproducible):  6 to a page  Great for use in the math classroom!

Description:  Blank coordinate planes.  6 to a page.  Each coordinate plane includes -5 to 5 (5 spaces on each side of the x-axis and y-axis).  The graphs are not numbered.  The graph is dark, so it will print and copy nicely.

coordinateplanereproducibletitlepage

 Here are what the graphs look like:

cp1

                                                                              cp2

If you download the free pdf, you will get the two reproducible pages below:

blankcoordinateplane6light

blankcoordinateplane6dark

 

Free Blank Coordinate Planes (Reproducible):  6 to a page and 12 to a page.  (Each graph goes from -8 to 8)

Description:  Blank graphs to use when graphing coordinates and equations on the coordinate plane.  Each graph goes from -8 to 8 on both the x-axis and y-axis.  There are two options for copying:  12 to a page or 6 to a page.  Reproducing will be a breeze with the dark lines, sure to show up using any copy machine.

blankwhitecoordinate

Here is the .png image of coordinate plane:

cp3

If you download the free pdf, you will get the two reproducible pages below:

Notice:  These pictures are edited slightly.  For example, the copyright at the bottom is much smaller, but the number of graphs on a page remains the same.

cp62ap

coordinateplanes12toapage

How did I create the coordinate planes?  

I made them in MS Word by creating a table.  I added the number of rows and columns I needed, made sure that all of the cells were square, darkened the lines for the x-axis and y-axis, and I was finished!

Note:  I have all of the images grouped with a white background so that they will show up with the dark blog theme.  Lately, I have been making my backgrounds transparent on images because I think it looks nicer.  Thank goodness for the preview button, otherwise a few of the images would have blended right in with the dark background.

How do I use the coordinate planes now?  

I use these coordinate planes (usually just one image at a time, not the full page) in the online classroom while helping students.

In the past, I printed the full page for students to do graphing homework sometimes.  However, almost always, I would take the single .png image and insert it in to a word document that I made.  Here are a few thumbnails of examples:  

preview slope graph 2      the corrdinate plane quiz

This was completely necessary as the clip art in blackboard collaborate has not been working for most of the school year.  It does work now, and has an option for a coordinate plane that can be grouped as the background.  The coordinate plane takes up the whole page, so it isn’t always the best option if you have other things on the page that you need to see.  Here is a thumbnail of the coordinate plane that takes up the whole page:

largecoordinateplanebbc

The blackboard collaborate clip art coordinate plane works very well online, but I would imagine that the light colored lines wouldn’t copy well.  This is the dilemma I was constantly faced with when reproducing coordinate planes in the past.  In fact, it is why I decided to create some dark coordinate planes.

Wow… I still have so much more to say about coordinate planes, but this is all I can handle for now 🙂

aharri5on

Order of Operations Quiz

OrderOfOperationsQuiz via pdf

Order of Operations Quiz

OrderOfOperationsQuizAnswerKey

This quiz can be used for middle school math.  I used it in 7th grade math last year.  I love the way the quiz is set up.  There is room for the student to show their work and it is VERY easy to grade!

OrderOfOperationsQuiz via pdf

If you need a quiz with a similar format, let me know!

aharri5on

 

Resigning with the hope of great change.

I officially accepted employment at an online school today!  Sadly, I also resigned from my “normal” teaching position today.  I have heard many very negative comments about online schools, but I am willing to take the risk because I genuinely believe that online teaching/learning is the way of the future.  I know that most teachers do not agree with me. Hopefully teaching at an online school will be a positive experience that can help me sway some of those teachers.

NO MORE... CLASSROOM

NO MORE… CLASSROOM

 

Topics for Consideration:

1.  What will I do with all of the items from my classroom?  Should I sell them?  Will I need them again someday?

2.  What will I do to keep myself “socialized”?

 

More Later.

-aharri5on