# Finding the GCF & LCM of 3 or More Numbers using the Cake Method

I wrote a blog post 2 years ago about using the cake method to find the GCF & LCM of 2 numbers.  (I absolutely LOVE this method and my students have had alot of success with it!)  I have been meaning to follow up on that post by sharing how to use this method for more than 2 numbers, and since I just got a question about this last week, I figured now is the time to write that post. 🙂

For this example, I will find the greatest common factor & least common multiple of 12, 15, & 18.

Start by writing the 3 numbers next to each other and drawing a “layer of cake” around them.  Take out any number that you can divide all three numbers by (in this case 3).  Then divide the numbers by 3 and write the quotients under the original numbers, drawing another layer of cake around them.  If there is something else you can divide all 3 numbers by, repeat this process.  In this case, though, there is nothing (besides 1) that I can divide 4, 5, & 6 by so at this point I like to CHANGE COLORS.  Now you need to find if there is any number you can divide some of the numbers by.  In this case, I can divide 4 and 6 by 2, so I write a 2 on the side (in a different color) and then divide the 4 and 6 by 2.  Since I am not dividing the 5 by anything, I just bring it down.  Repeat if you can divide some of the numbers by another factor.  In this case, I can’t, so I am done.

Find the GCF by multiplying all the numbers on the left that were in the ORIGINAL color ONLY!  (In this case, it is only “3”, so my GCF = 3).  Find the LCM by multiplying all of the numbers in the “big L” around the cake.  (That includes the numbers in both colors).  (For this example the LCM = 3 x 2 x 2 x 5 x 3 = 180).

In case my explanation makes no sense, I have included a second example showing this process.

As I said, I absolutely LOVE the cake method and have found that the students love it too and find it MUCH easier than other methods for finding the GCF & LCM.  I hope this post helped explain how to use it for more than 2 numbers!

Christina

You also may be interested in my GCF & LCM Halloween Riddle Sheet – available in my TpT store for \$1.

# Math Races – turning boring practice problems into fun activities

Yikes!  I’ve been back in school for 3 weeks now and this is the first time I am blogging!  I am going to do my best to be better about it going forward…but no promises 🙂

I have already completed my first units in all of my classes and am now working on my second units.  In my next few posts I am going to share some of the lessons I have done so far this year, but right now I am going to share what I did today in my 7th grade Pre-Algebra class because it went SOO well!!

I am working on rational number operations with my pre-algebra class this unit (positive & negative fractions and mixed numbers).  Yesterday I did adding & subtracting negative fractions without whole numbers and today I did adding & subtracting negative mixed numbers.  I have noticed over the years that students tend to struggle with this lesson since there are so many things they have to remember: integer rules, finding common denominators, borrowing with mixed numbers, converting improper answers to mixed numbers, and simplifying fractions.  Because I know that this lesson gives students trouble I wanted to give my class lots of practice without boring them to death.

We started by going over the steps as a class and writing them down in their notebooks.  I then had students complete some problems on mini whiteboards, step by step.  Having them show me each step really helped me catch and address any issues early on in the problems.  I then had the class split up into groups of 2-3.  (While I often choose groups for my students, I allowed them to make their own groups for this particular activity).

I had a set of self-checking task cards on rational number addition & subtraction that I made a couple of years ago, where the answer to each card leads students to the next card they need to complete.  If they answer all 20 cards correctly, the last card they do will lead them back to the card they started with, making them completely self-checking.  In the past I have had students simply work through them in small groups, which works well, but this year I had the bright idea to turn it into a race…and it was AWESOME!

Here’s how I ran the activity:

I printed two copies of the cards (so there wouldn’t be an issue of students not being able to get the card they needed) and spread all the cards out on a table in the front of my classroom.  I gave each group one card to start with.  Students had to work in their groups to get the answer to the card.  Once they had an answer they all agreed on, one person in the group had to run their card back up to the table and find the next card.

I could not be happier with how this activity went!  The students were sooo into it.  They were all working, engaged, and talking with each other to figure out where they went wrong.  They all wanted to win the race (despite the fact that the only “prize” was a sticker!)  They got lots of practice since there were 20 different cards in all.  Best of all, I heard multiple students say that it was the best math class ever as they walked out of my room today, so that is definitely a win in my book! 🙂

If you want to make a self-checking activity that you could turn into a race like this, you just need to write questions on index cards.  Put the answer to each card on the top of the next card to create a “loop” of questions.  If you don’t want to make your own, I have several sets of self-checking task cards available in my TpT store that you can check out, including a free mini set on the order of operations.

If you try a similar race activity with your class, I’d love to hear about it!

Christina

# Keeping Myself Organized Each Week

Just a quick post today to share a little organizational tool I am using this year…

I got the idea from Pinterest (not sure who it originated from) to assign myself different tasks for different days of the week.  I also can be a pretty forgetful person at times, especially after a long day of work, so I needed a way to help myself remember all the little things I need to do (like turn off the air conditioning at the end of the day).  I have combined those two ideas into one weekly to do list.  🙂

I broke up my days into 3 times that I have free time: before school, at recess, and after school.  (I didn’t include my prep periods because I like keeping them flexible and using them in the best way I see fit at the time.)

I started by listing all the things I need to do on a daily basis: listing my objectives on the board, posting homework online, saving & sharing my notes with my students through Google Drive, sending make-up homework assignments to students who fill out my homework accountability form, cleaning off my desk, and checking the air conditioner and windows to make sure they are off and closed.

Then I took the tasks that I do one or two times a week and assigned them to specific days:

• Update online gradebook: Mondays & Thursdays
• Write lesson plans for the following week: Mondays (then update them on Fridays if I am “off” my schedule)
• Make copies for the following week: Tuesdays (I’ll gather the papers on Mondays after writing my lesson plans so they are all ready to go)
• Write “do nows” on Socrative for the following week: Tuesdays
• Grade papers: Wednesdays & Thursdays (I am sure I will use my prep periods to grade other days, as well)

I assigned some of those tasks for mornings and some for afternoons.

The part I am most excited about is that I set up my weekly list to have room for sticky notes (1.5 x 2 inch size).  So, I will only print this list once for the year and any time something pops up that I need to take care of, I will stick a note on to remind me when to do it.  I often have students come in for help or to make up absent work during recess or before/after school, so I can just write it on a sticky note and attach it to this page so that I remember who is coming and when.

If you want to try something similar, you can download the editable PowerPoint (pptx) file by clicking the image below:

Christina

# Free Banner of the Standards of Mathematical Practice

After I shared a bunch of classroom décor ideas in this post, I ended up making another decoration for my classroom: a banner of the standards of mathematical practice.

It’s a simple black & white design that I printed on colored paper to make it pop and match the other bright colors in my room.  However, I was also thinking it could be cool to print it on white paper and have students work in groups to color the banners & add pictures to them to illustrate the meaning of each standard.  (I might do that next year – this year I’m just going to hang up the colorful version, after I reprint it – my printer is having issues right now causing everything to have streaks 🙁 )

You can download the banner FREE from my Teachers pay Teachers store!  While you’re there be sure to look around at some of the great deals today and tomorrow (August 1st & 2nd) during the big annual Back to School sale!  Everything in my store is 28% off with code BestYear.

Some of the resources from my store that I would recommend checking out this back to school season include:

Happy shopping!

Christina

# New Review Game: Try it Free and Win the Game of your Choice

I love playing games in my math classes! Here are just a few of the many benefits of good review games:

• they are a great way to practice any type of skill
• students love them
• students are engaged
• games encourage collaboration among students

I have found, though, that the key to keeping students engaged and enjoying games is to switch them up frequently.  No matter how fun a game may be the first few times you play it, the students will eventually get bored with it if it is the ONLY game you ever play with them.  Having a good variety of games to pull from really makes a difference in keeping up student enthusiasm and engagement levels.  Some of my go to games include Bingo, Jeopardy-style games, Attack, and standard whiteboard games, but I am always looking for new ones to add to the mix, which is why I teamed up with my husband again to create some new, fun interactive review games!

We thought it would be fun to bring some arcade-style fun into the classroom so we created a Claw Machine Review Game.  It can be played in teams or non-competitively.  (I tend to teach competitive students so I plan to use the team-mode with my classes).

There are 5 different categories in a game, which are listed on little cards along the bottom of the claw machine.  The claw (crane?) moves back and forth in the machine.  Have a student either toss a koosh ball at the interactive whiteboard if you have one that supports touch or simply click with a mouse to stop the crane and pick up a card.  It will pull up a random card from the category it is in front of.  Have each group come up with an answer and then reveal the actual answer.  Award points to teams with correct answers and either subtract points or do nothing to teams with incorrect answers.  Once all questions from a category have been asked, the category card will disappear from the machine.

You can also adjust scores at any time by clicking the little +/- button on the bottom right-hand corner.  (One idea that could add to the competition/excitement would be to subtract points from a team that doesn’t successfully pull up a card when they toss the ball at the screen).

At the end of the game, the final team scores and standings are displayed.

You can play a full game for FREE to try it out to see if you like the idea & set-up of the game!  Just click on the picture below to play the free Demo Game.  (It should open in a new tab right in your browser).

If you try out the free Demo and think that you would like to play a claw machine game with your class this year, simply leave a comment telling me which of the 4 games listed below you would like to win.  On Monday, August 1st a random winner will be selected from everyone who leaves a comment and I will email the winner the game of their choice!  The choices of Claw Machine Games to win are:

• Algebra Back to School Review (Includes: integer operations, evaluating expressions, simplifying algebraic expressions, properties, and writing expressions)
• Decimal Operations (Includes: addition, subtraction, multiplication, & division of POSITIVE decimals, along with decimal word problems)
• Solving Equations (Includes: one-step equations, two-step equations, equations with variables on both sides, multi-step equations, and writing & solving equations)
• Operations with Negative Fractions (Includes: addition, subtraction, multiplication, & division of positive and negative fractions & mixed numbers, and comparing/ordering negative fractions)

(Click the pictures below for a closer look at each game.)

Here is a video preview of the Algebra Back to School Claw Machine Game:

UPDATE 8/1:  This giveaway has ended.  Since there were 9 entries I used a random number generator to select a number between 1 and 9 to choose a winner.  5 came up, so Lisa (the 5th person to comment) is the winner!

Thank you so much to everyone who entered and for all the kind comments about the game.  If you’d like to purchase a claw machine game, they are on sale (along with all my other resources) today and tomorrow for 28% off with code BestYear.

Christina

# Idea for a New Classroom Management Plan

Ever since I made my Homework Accountability Form, I have been thinking of a way to use Google Drive for behavior management.   I am still not 100% sure about my new classroom management plan but figured I’d post it here to hopefully get some good feedback on it and then decide from there if I want to use it, tweak it, or go a completely different direction….

So here it is:

I am thinking of setting up a google sheet for each student I teach before school starts.  It will take a bit of time since I teach over 100 students, but once I set them up, any additional time on this will be minimal.  The sheet will list the most common behavior infractions I encounter and also an “other” category.  (Right now I am thinking of using “off task”, “disruptive”, “out of seat”, and “calling out” in addition to “other”.)  I plan to share the sheet with the student (set to “can view” so that they can see it but can’t edit it 🙂 ) and also share the link with their parents (probably include it in my introductory email).

I also made a weekly class behavior tracker form that I am going to print out each week for each class.  On it, I have codes for each of the behaviors that are included on the sheet.   I will keep the class behavior tracker handy on a clipboard along with some extra paper in case I need to write additional notes/reminders to myself.  My plan is to give students a warning the first time they commit an infraction.  When I warn them, I will make a diagonal mark on my clipboard tracker to indicate that they were warned.  (The warning might be in the form of a “look” or a simple reminder to get back on task).  If they commit the same infraction in the class period, I will then make a diagonal mark in the opposite direction to turn it into an “x”.  (If you would like to use a similar form, you can download it as an editable PowerPoint file here.)  I am planning to transfer the forms to a binder after each week so that I can refer back to them at a later date if necessary.

At the end of the day I will look back on my class behavior trackers for each class to see which students got an “x” (meaning that they did not heed the warning they were given).  I will then go into that student’s Google Sheet and write the date (and a description if it is in the “other” category).  That counts as one mark on their tracker sheet.  When they get to 5 marks or more on their sheet, they will need to serve a detention.

I will start over with a new sheet each marking period to give students the chance to start with a blank slate.

Like I said, I am still not 100% sold on this idea but here are my thoughts (positive and negative) about it:

• It’s a really easy way to keep parents informed.  Once I give them the link (and explain the process to them), they have the ability to check up on their children’s behavior anytime and get instant feedback on whether or not their child is doing what they are supposed to be doing in class
• After the initial setup it should be really easy to maintain.  It’s a matter of making a mark or 2 in class and then writing the date at the end of the day if anyone got an “x”.  Shouldn’t take more than 2 minutes.
• It would be really easy to use with a team, as well.  You can share it will all of the teachers in your team so that they can all edit it, and then just assign each teacher a different color or have them write their name in addition to the date any time they make a mark on a student’s tracker.
• I like that I first give students a warning, before their tracker gets a mark, to give them a chance to change their behavior.  I also like that they get multiple chances before getting a detention – although I don’t know if 5 is too many chances, not enough, or just right…
• I don’t know how I feel about the fact that technically this system would allow a student to be warned 5 times for 5 different behavior infractions without getting a mark on their sheet….is that fair?
• I also don’t currently have a plan for what to do if a student gets an “x” and then does the same thing again (a 3rd time) that class period.

Bottom line is: I am torn about this idea…in some ways I feel like it could be very effective and at the same time I still have some doubts and questions.  I would definitely welcome any thoughts or suggestions in the comments!

Christina

# Decorating the Secondary Math Classroom

I won’t actually be able to get into my classroom for a few more weeks but I figured I’d share my plans for classroom decorations now…

Every year I do the same “theme” if you can even call it that – black bulletin boards with bright pops of color.  I’m a creature of habit so this year’s “theme” will be no different :-).  I do, however, have some new decorations to add to my room this year that I’m pretty excited about…and I have spent only around \$15 on it all!

•  I made a “Mathematicians” acrostic poster that lists some of the mathematical process standards as well as other traits/skills students use in math.  I didn’t want to spend alot on printing, so I looked around and found shortrunposters.com.  I got it printed in 18×24 with 1.5 MIL Glossy Lamination for just \$6 plus around \$4 for shipping!  It took about a week to get the poster after ordering and it came out awesome – I couldn’t be happier with the quality (or price)!!  If you are interested in purchasing the poster to print yourself or have printed professionally you can buy it from my TpT store for \$1.25.  (The download includes the black background version I printed and a white background version of the poster).  Click the picture below to buy the poster.
•  Comics: Most years I hang up some corny math “funnies” in my room.  They are a great source of FREE decorations for the classroom.  This year I am tying them in with my black & brights by printing them out in black & white, mounting them on different brightly colored papers, and putting black construction paper “shadows” behind each one.  I think that will really help tie them into the room decor better this year.  (If you need a good source of math jokes, comics, and puns, you may want to check out my Math/School Humor Pinterest Board – I have well over 100 pins to choose from!)

• Target Dollar Spot finds:  I LOVE the dollar spot in Target!!  This year I found some fun bright colorful decorations that will go perfectly in my room!  I got a pack of punch out signs/pictures for \$1 that included a welcome sign and some motivational quotes that I will put up.  I also found cute packs of colorful pennants.  (24 per pack, \$1 each – I bought 2 so that I’d definitely have enough).  I am writing the names of all of my homeroom students on them and will then punch holes in them, string them, and hang around the room.  The best part is they are dry erase so I can use them year after year! (Not bad for \$2!)

• I also found cute bulletin borders at the target dollar spot that match the little pennants.  They were packs of 15 for \$1, which is great…but I made it an even better deal by cutting them in half lengthwise to make 30 skinny border strips per pack!
•  I wrote about my ABCs of Algebra Math Alphabet last year… It was a big hit so I made a couple of new versions of the math alphabet this year – the ABCs of Middle School Math and the ABCs of Geometry.  Each one has the same fun, bright design and features a vocabulary word for each letter of the alphabet.  I am planning to hang the middle school version this year in my room.  I will be hanging it above my chalkboard on black paper.  I am using the skinny borders I made as the border around the alphabet.

You can buy my math alphabet sets in my TpT store for \$4 each and print them at home for free – I kept the backgrounds white to make them printer friendly.  Click the pictures below to purchase!

I will have a better idea of what, if anything, else I need for my classroom once I get in to look at what I have.  I hope this gave you some budget-friendly ideas for your room! 🙂

Christina

# Organizing Student Notebooks with Dividers

Today I’m sharing my newest step towards improved organization in the classroom: notebook divider tabs.  (I got the idea from a blog post by Sarah Carter and knew that I wanted to modify them to work for me in the upcoming year).

I decided that this year I am going to make notes worth 2 points per day.  Students need to include a summary/explanation and completed worked-out examples for each lesson (which is where the 2 points are coming from).  In the past I made notes worth 20 points per unit, but in reflecting on it, it doesn’t really make sense because some units are 10 lessons long while others are only 6.  I collect and grade notebooks on days that students are taking the unit test.

So, here’s where the divider tabs come in…before each unit I will give students a divider to glue in their notebooks.  A little tab sticks out the side with the name of the unit on it.  On the divider I listed all of the lessons that are included in the unit.  I figure that will be an easy way for students to make sure that they aren’t missing the notes to any lessons (which will be especially useful for students who were absent).  It will also serve as a checklist for me while I’m grading.  Next to each lesson I can write 0, 1, or 2 for however many points students earned for that day’s notes and record their final grade for the unit on the bottom where I left a space for it.

The beauty of the tabs is that I can flip right to the correct unit without wasting time trying to find their notes.  I also think they will be useful to students, as if I ask them to refer back to an earlier topic, they should be able to find the lesson pretty quickly.

I made the dividers small enough that they won’t waste a page of the students’ notebooks.  I think I will have students write the vocabulary for the chapter on the first page (next to the divider) and then start with the first lesson’s notes on the back of that page.  The divider doesn’t cut into any of the useable space on the back of the page at all, which I am really happy about since I hate wasting paper!

I made my dividers print 3 per page, so I just print them, cut on the two dotted lines, and hand them out to the students.  They fold on the solid line and then put glue on each side and make sure to leave the tab sticking out the side of the notebook when they glue it in, and that’s it!

If you’d like to try out similar dividers for your class, I set up a 3 per page divider template in PowerPoint that you can use.  Just click the image below to download the editable pptx file.

Other school-related things I have been thinking about/working on recently:

Have you used dividers before with your class?  Are you thinking about trying them out this year?  Please share in the comments below – especially if you have any tips for using them since this will be my first attempt!

Christina

# Holding Students Accountable for Homework

Today I thought I’d share my new homework policy for next year which I’m pretty excited about!

My homework assignments are worth 2 points each and I grade them only for completion.  While students work on their do now problems on Socrative I walk around and record grades for each student.  In the past I’ve given out 2’s, 1’s, and 0’s.  Next year I decided to get rid of 1’s, so students will get a 2 if they attempted every problem AND showed their work.  If they didn’t do the homework, only did half of it, or didn’t show their work they get a 0.  After students finish their do nows we go over homework answers as a class and then I answer any questions about the homework.  Most of the time I don’t spend more than 10 minutes on this entire process, including the do nows, so that I have 30 minutes for my new lesson.  (You can read about & download my homework grade recording sheet here).

In the past I haven’t accepted late homework because we go over the answers in class so it seemed too easy for a student to ‘borrow’ a classmate’s assignment for their late work.  Next year I decided that I will accept late homework, but it will be a separate (but similar) assignment to the original homework assignment.

So…here’s the part I’m excited about.  I created a ‘Homework Accountability” Google form to hold students more accountable for their work.  While I’m walking around checking for completion, students who get a 0 need to fill out the form, which I will keep a link to in my Google Classroom for easy access.  The form is pretty simple: they will fill out their name, their reason for getting a 0, and either check off that they want to complete a make-up assignment or that they are accepting the 0.  Since all students are on their chromebooks at that time working on their do nows it will not be disruptive to have them fill out the form, nor will it be embarrassing for the student.

At the end of the day I will check responses to the form and email/share make-up assignments with the students who requested them.  All make-up work must be handed in by the unit test day.  I will not accept make-up work after that point since the idea is that completing the homework should help prepare students for the test.

I will give students full credit on the first 2 make-up assignments they complete in a marking period, but they can only earn 1/2 on any additional make-up work they complete, to hopefully discourage students from taking advantage of the system.  While it will require a little bit more work for me to come up with make-up assignments it isn’t a huge deal.  When I write my lesson plans each week I will simply come up with a 2nd homework assignment each night so that I’m prepared.

I am excited to try this out because it gives students a chance to explain their reason for missing an assignment (without wasting class time on excuses), gives them a chance to make up for it, and gives them responsibility as they will not have the opportunity to make up an assignment unless they fill out the form and ask for one.  I also have documentation from the student that can be shared with parents, should a pattern form that needs to be addressed.  (I still plan to record student grades each day on my own record sheets, as well, so I am not relying solely on students filling out the form, but they won’t be able to make it up unless they fill out the form).

What are your thoughts on this homework policy?

Christina

# Improving Number Sense with the Divisibility Rules

I decided to make divisibility my first lesson of the year for 7th grade next year for a couple of different reasons: it is a skill used in many different concepts throughout the year and it really helps promote overall number sense in students.

The divisibility rules (hopefully) help students be less dependent on their calculators, which is an area I am hoping to improve on this year.  So even though it isn’t the most exciting lesson of the year, it is an important one, and I think it’s a good way to begin the year.

I go over the rules for 1 – 10 with my students.  (I used to skip over 7 but every year students ask me if there is a rule for 7….so now I give them the rule along with an example for which the rule could be useful (i.e. 231) but then explain that 9 times out of 10 it is easier to just do the division than it is to use the rule).

In addition to the rules I give students tips, like if a number isn’t divisible by 2 then it isn’t divisible by any other even number.  Tips like that help with divisibility by 8, since that isn’t the most useful rule.  I tell students to only check for divisibility by 8 if (1) the number is divisible by 2 and then (2) if it is divisible by 4.

I made half-sheets the students can stick in their notebook with the divisibility rules.  You can download it free by clicking the picture below.

To make the lesson more exciting I enlisted the help of my programmer husband.  He was able to build an interactive divisibility rules game that my students can play on their chromebooks, which I am super excited about!  In the “Divisibility Challenge” game, you can choose which rules you want to practice and then either play for mastery, speed, or just for practice.  I think I am going to originally have students play for mastery, where they need to play until they get 10 questions correct.  I plan to begin class the next day with a speed competition to see who can get the most questions correct in 3 minutes.  Competition always seems to get middle school students involved and engaged!  Click below to try a round free.  (It should open right in your browser).

If you are interested in getting the full game for your class it can be purchased in my tpt store for \$6.