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:

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

Invisible Math

Math is invisible?  What does that mean?

Well, these parts of math aren’t really invisible, but we do have plenty of 1’s that like to hide and only pop out when needed.

For example:                        y = 1y                              or                        -m = -1m

Last week my student’s were combining like terms, so it was crucial that they recognized those invisible 1’s.

On Friday, I was looking through some old interactive notebooks, and came across a few pages titled, “Invisible Math” from the beginning of semester 1.  Here is what the handout looks like:

INVISIBLECOLLAGE

How can you use this handout?

  • Three-whole punch this handout and give to students for them to put in their binders.
  • For teachers using interactive math notebooks, you have a few options.
    • Option 1:  have students cut out the cards and paste into their interactive notebook
    • Option 2:  have students fold in have and paste into the notebook.

If you want to download the full size posters, you can do so here.

amyharrison

You teach ONLINE? AND What I have been up to this week!

You teach ONLINE?

When I tell others that I teach middle school math online, the first thing they say is, “How does that work?”, followed by an endless amount of other questions.

It seems like most people who I have come across do not know about online schools, so I will come back and update this if we change our plans throughout the year.  Maybe it will give a better picture of how some people teach online. To be honest, I didn’t know that there were online schools for middle school students until I looked into it and found a job, and I have taught for 6 going on 7 years!

Organized the Office

I spent tons of time organizing my office!  I needed to take a break from constantly being at my computer.

 

It is still a work in progress, but I am happy to have a place that I can work once school starts back up.  In the midst of my back to school fever, I went a little crazy decorating my office.  Early this week, I started putting up posters that I used to have in my classroom.  I got inspired by my fiance’s office that has pictures and posters.

The fun has only just begun… I am sure I will make plenty of changes as the year goes on.  After all, I will be spending a lot of time in there.  I will be teaching from 8:30-3:00 with a break for lunch and another break throughout the day. Technically, this will be more hours teaching than last year. However, I will not have as many videos and lessons to create (hopefully).  I will have trouble resisting the urge to make new videos and resources, so expect some new videos from me to show up on my vimeo profile.  Plus, I did promise to make a back to school video to send to my students, so I need to follow through on that.

Back to School!

Our first meeting is the 11th, so even before we have students, there is work to do.  Luckily, I got a lot done at the end of the school year to prepare for this year.  Of course I still have things to do, but it isn’t as overwhelming as it could have been.  I am the most concerned about our new structure of classes: how it will end up working out, and what it will be like when I am the main teacher for 7th grade.  I am happy that I will be teaching 7th grade Pre-Algebra, which is a class that I taught last year.

I am so excited to see everyone again and am looking forward to working with some new people this year!

A little about our class structure plan:

  • Classes will be Monday-Thursday
  • Friday will be open office
  • Each class period will last 1 hour and 30 minutes.
  • 45 minutes will be a large group
    • Led by me and assisted by the other 7th grade math teacher (there are two of them, but they will rotate) for the first class of the day only.  The rest of the day, they will be teaching their own class.  Ideally, we would like to have the students take a ticket out the door so that we can decide if they are free to go or if they need to stay for the remediation class.
  • 30 minutes will be a smaller group
    • The other 7th grade math teacher will be teaching a remediation class on the same topic that I taught that day during the 30 minutes directly after the 45 minute class.  They will take turns, so each of them will teach twice a week.  I will help them for the first 15 minutes, but for the second 15 minutes, I will have a break, tutor, or set up for the next class.
  • There will be up to 6 classes a day

Bought a Headset & Printed Products

I bought a printer and a headset.  I have yet to try the headset, but am looking forward to it! I did charge it.

IMG_1966

I printed some products (even though I can’t use the hard copy because I teach online) just to make sure everything was how I intended it.  I organized the products in two binders: one for stations, and one for other products.  I haven’t done all the products yet, but I am sure I will eventually.  Maybe I can use them someday in the classroom, or use them as a portfolio of my work.  I used my label maker to label the binders.  I can’t wait to start cutting out and laminating some station activities!

TpT Sale Spike

Next came the TpT sale.  I was in shock on the 4th (mainly because I had almost forgotten about the sale and had taken a few days away from technology), and especially the 5th… look at that crazy spike!  The crazy part is that most of those sales were late in the day on the 5th.  My spike motivated me to buy some clip art from a TpT seller to spread the love. Thank you TpT for hosting an amazing sale!Capture

Got Creative

I created some new products on Tuesday and Wednesday:

Then, I added an easy version to my product, Building Squares:  Icebreaker Puzzle (for the first week of school).

Was Inspired

I listened to most of Edmodocon on the 6th and was thoroughly entertained.  We are trying to decide if we will use edmodo next year.  We did not use it last year, but I used it the year before.

Today I realized that the TpT Math Back to School eBook for Grades 6-12 is out.

amyharrison

Back to School Ice Breaker Puzzle Activity

 Back to School Ice Breaker Puzzle Activity

Are you looking for an activity to use for back to school? You can’t lose with a fun icebreaker! This set of puzzles is challenging and guaranteed to make every student think whether they want to or not!

Slide1

Here are some pictures from my rough draft before creating this activity.  I created the entire activity on the computer, and was looking forward to print it out to have my fiancé try it to assess the difficulty level.  I went to my printer to print the activity, and was greeted by an angry printer that just kept eating my paper.  I was flabbergasted because I have only used my printer a couple times before, and it was brand new when I got it!  Also, it is telling me that I am almost out of ink… but I thought my ink was new too!  Either someone has been secretly using my printer, or it just decided to betray me.  Needless to say,I was super disappointed.  I just sat there with a frown on my face for what seemed like a few minutes.  Then, I realized, that I could just grab some paper, pencils, colored pencils, crayons, a ruler, and some fabulous folding and tracing skills to test this activity.  As I was recreating the activity that I made on the computer, I was constantly reminded that math is SO cool!  Equilateral triangles can form so many patters… so can right triangles!  Playing around with the shapes was a lot of fun.  I would love to come up with some new criteria and shapes and create some unique puzzles.

Note:  These puzzle pieces do not “go together”, but here are all the pieces sorted by number.

Slide3

Once I finished creating the puzzles, I took pictures of them before cutting them out so that I would have something to refer to if I got confused later.  Then, I cut out the pieces.  I tried putting the puzzle together, but it was taking too long, so I decided to make some adjustments to change the difficulty of the puzzle set.  In the process, I discovered two great ways to lower the difficulty level:

1.  Make sure that all the numbers are facing the same direction.  (See the example above)  By having all the numbers face the direction, the puzzle could have quickly became too easy (especially if this fact is given out as a clue), so I decided to write the numbers facing all directions to start.  Later, I decided to change it to increase the ease of making the product, and to make the puzzle easier (once the clue is given out).

2.  Color code to change difficulty levels instantly!  This activity has 6 puzzles with 4 pieces in each puzzle.  I chose these numbers on purpose because they offered flexibility when determining the difficulty level.  On top of that, having a nice number like 6 allows you to easily discard 2-4 puzzles without affecting the results.

Here is how I created the difficulty levels:

  1. Easy (1 blue, 1 purple, 1 red, 1 yellow, 1 green, and 1 orange):  6 puzzles, all different colors, 4 pieces in each puzzle
  2. Average (2 blue, 2 purple, 2 red):  6 puzzles, 2 of each color, 4 pieces in each puzzle
  3. Difficult (3 yellow, 3 green):  6 puzzles, 3 of each color, 4 pieces in each puzzle
  4. Mega Challenge (6 orange):  6 puzzles, all the same color, 4 pieces in each puzzle

Other ways to change the difficulty:  take out and entire puzzle or set of puzzles.

An Example of a Completed Puzzle (1 of 6):

Slide4

Puzzles Sorted by Color: 8 Pieces (2 Puzzles) per Color

Slide5

As you can see from the picture above, a simple paperclip (yes, that is a mini-gel pen… but same concept as a paper clip) will suffice.  You can store the pieces in a plastic bag, in pencil pouches, or pencil boxes.

Walmart    Pinterest

Read more about the icebreaker puzzles here.

Purchase a printable version that is ready to use here.

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