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?


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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.


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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!


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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

 

 

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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:

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Download the .pdf here:  6thGradeCCSS_RP_Posters

or FREE from my TpT Store:  6thGradeCCSS_RP_Posters

Try Some Related Activities:

RatiosAndProportionalRelationships6thGradeAllStandardsPIN_AmyHarrison

amyharrison

First Week of School Ideas and Resources Part 1

IN A FEW SHORT WEEKS, WE GO BACK TO SCHOOL…

Are you looking for something to do on the first day or first week of school? This FREE questionnaire is great for that and for getting to know your students. Yes, you might not have enough time to read through all the responses, but they are nice to keep on hand. You will be surprised what students are willing to tell you when you just ask.

allaboutyou

All About You! (FREE questionnaire for first day of school)
• Two Pages (print front to back)

I just typed this up last night, but I have used something very similar every school year. I should have it saved on my computer somewhere… from before I organized my files.  I figured it would be much faster to re-create then to find it!  🙂  

I love to pass this worksheet out on the first day of school at the door.  With instructions on the screen to quietly complete the questionnaire, the students should get to work right away.  After all, it is the first day of school, so they aren’t sure what to expect and will be mostly obedient.  Obviously I don’t expect my students to sit there the entire class period filling out the survey, so an activity should be planned for after.  Maybe a pre-test?   Maybe an icebreaker? 

I don’t have a classroom anymore because I teach online, so if I want to use this activity I will have to change it greatly.  Here are a few ideas:

  1. I can k-mail (our form of e-mail with the students) all of my students the list of questions (or perhaps a modified list), and ask for their response.
  2. Create a Google Form for the students to fill out.  I can give the link to them at the end of class, and k-mail it to them as a back-up.
  3. As soon as I get the list of students, I can send them a k-mail with the questionnaire.
  4. I can decide not to use it.

How have I handled the first day in the past? I wrote a loose script one year, and completely winged it the next with my toolbox of activities and icebreakers.

How should you use this questionnaire?

Use on the first day or first week of school. You may or may not decide to read these, but it is a great way to get information from your students. I suggest handing it out to students as they walk in the room or having it on their desks. Then, they can get started on the questionnaire right away. Of course, make sure you have an activity for them to get started on once they finish.

What questions are included?

ALL ABOUT YOU!
• Your Full Name
• What name would you like to be called during class?

Note: If you don’t know the answer, or don’t feel comfortable answering, you can keep some questions blank.

ABOUT YOUR Family!
• Name(s) of parent(s) or guardian(s):
• Parent/Guardian’s Phone Number?
• Parent/Guardian’s E-mail?
• Do you have any brothers and/or sisters? How many?
• What are your brothers/sisters name(s)?
• Did any of your brothers/sisters attend this school?
• Do you have any pets? What kind? What are their names?

BACK TO YOU!
• What do you like to do after school?
• What is your favorite food?
• What is your favorite candy?
• Who is your favorite singer/band?
• What is your favorite TV show?
• Who is your favorite actor/actress?
• What is your favorite movie?
• What is your favorite sport?
• What is your favorite sports team?
• What hobbies you do enjoy?
• What is your dream job?
• Do you play any after school sports? Which ones?
• Do you participate in any after school activities or clubs?

ABOUT SCHOOL:
• What is your favorite subject? Why?
• What is your favorite math topic? Why?
• What math topics do you struggle with the most?
• What are you looking forward to learning in math this year? Why?
• Describe how you learn best.
• How do you plan to let me know if you need help with a topic?
• How much homework do you expect per night?
• How many pages of notes do you expect to take each day?
• What goal would you like to accomplish this school year?
• What time do you wake up for school in the morning?
• What time do you go to bed?
• Do you already know any other students in this class?

Finish the sentence
• I love teachers that…
• I dislike teachers that…

• Is there anything else that you want me to know?

The End.

Download the FREE printable version of this back to school questionnaire here.

Want to read about and download some more back to school resources?

First Week of School Ideas and Resources Part 2

First Week of School Ideas and Resources Part 3

First Week of School Ideas and Resources Part 4

amyharrison

Do You Need FREE Printable Coordinate Planes?

blank 5.1 3

Example of blank coordinate plane worksheet. The circles are for problem numbers. Note: 5 spaces on each side of the x-axis and y-axis

When I started teaching, reproducible coordinate planes were like gold.  If a colleague had a unique page, I was all over it!  I especially loved pages with bigger graphs (more spaces on each side of the x-axis and y-axis).  I had some coordinate planes that looked like a complete mess, but I loved them anyways.  Who wants to make students draw coordinate planes repeatedly?  Not me!  I will dig around and see if I can find a sample of this wonderfully awful graph paper to post.  

 

When I tried to print coordinate planes that I found online, they were often too light to copy.  They printed beautifully and I thought all was good… then they betrayed me.  As soon as I tried to copy the coordinate planes, I was frantically pushing STOP on the copy machine because they weren’t coming out AT ALL.  Some of the lines were showing… some weren’t… it was a mess! If you are a math teacher, I’m sure you have been there.

After a while, I found my favorite sheets of reproducible coordinate planes to keep tucked away in my file cabinet for safe keeping.  I NEEDED them, and couldn’t risk loosing them.

Then, one day a colleague shared a file with me that had the most beautiful little coordinate plane I had ever seen.  It was SO DARK!  Without even trying to copy it, I knew it would be flawless!  The best part was that it was on the computer!  I saved it as an image and used it for every coordinate plane related worksheet I made for the next few years.  Later, I decided to make my own coordinate planes, and have developed a collection!

printablecoordinateplanespurple

About my free coordinate planes:  Maybe I got a little carried away with the darkness of some of the graphs, but I thought it was necessary due to my past coordinate plane reproducing nightmares.  When I update this file again, I will probably include even more darkness options.  Who knows, maybe I will get crazy and put numbers on the x-axis and y-axis.  I have never been a fan of that though… I think the numbers just get in the way.

Example of blank coordinate plane worksheet. The circles are for problem numbers.  Note:  7 spaces on each side of the x-axis and y-axis

Example of blank coordinate plane worksheet. The circles are for problem numbers. Note: 7 spaces on each side of the x-axis and y-axis

So, Do You NEED Some FREE Printable Coordinate Planes?  Of course you do!  Here are a few options:

Option 1:

I updated my blank coordinate plane resource.  It has grids with 5 or 7 spaces on each side of the x-axis and y-axis.  There are a variety of displays:  1, 2, 6, or 12 to a page. Some of the pages have circles for question numbers.  This setup is perfect for math homework, especially if problems are assigned out of the book.  printablecoordinateplanespurple1

Option 2:

Here is a -8 by 8 Blank Coordinate Plane that comes 12 to a page or 6 to a page.

I do have some other coordinate planes that are not posted online.  I will consider getting those added sometime soon.  Some of them are bigger.  For example: 10 spaces on each side of the x-axis and y-axis, full-page, 1 quadrant (for distance/time), etc.

printablecoordinateplanespurple2

My original intention was to put all the coordinate planes that I have together in one document. However, I quickly realized that the document was over the 10 page suggestion for free products, so I made myself stop.  Sometimes when I am making products, it seems like the pages multiply before my eyes before I know what happened.

Does this post sound familiar?  I originally blogged about free coordinate planes here.  Click to find pictures of some of the coordinate planes.

amyharrison

What can you do with the extra time after a lesson?

Try the Guess a Mystery Number game.  It is great for a warm-up or for when you have extra time after the lesson.  Download the free game.

Guess a Number

Here is a sample of a completed game:Guess a Mystery Number Game

How to get started…

• Pick a 3 Digit Number
• All digits have to be unique (they can’t repeat).

The class will guess until they get the right answer.

As you go, encourage the students to cross off digits that cannot be the correct answer based on proof.

Ways to involve students…

• One student can come up with the secret number.
• Another student can come up and write on the Smart Board.
• A third student can call on the students to guess.
• The rest of the students can make guesses.

It becomes easier as numbers are crossed off, so all students feel comfortable participating.

This activity is good for a quick warm-up or extra time at the end of class.

Be sure to print out multiple game tables because they will get used up fast!

Download a free copy of the game (.pdf):  Guess A Number Game

amyharrison

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