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).

Notebook Divider Tabs: math-in-the-middle.com

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.

Notebook Divider math-in-the-middle.com

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!

imag0610_1.jpg  imag0615.jpg

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.

imag0619_1.jpg

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!

Thanks for reading,

Christina

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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.

divisibility rules half sheets

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).

divisibility demo

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

divisibility pic1

 

Thanks for reading,

Christina

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Breaking Down 2 Step Equations

Today I’m writing about a simple idea that makes 2-step equations easy for kids – a box “trick”.

2 step equations box trick

Students obviously have already learned how to solve one-step equations before being introduced to two-step equations, so I introduce 2-step equations by giving students a simple one-step equation.  The only difference is that I use an index card instead of a variable in my equation.

box trick pic1

Put an equation like the one pictured above on the board and tell students to solve it for the index card, which they should be able to do easily since it is a simple one-step subtraction equation.

Once they solve the equation for the index card, lift up the original card to reveal what is underneath it (in this case 8x).  It also works if you write 8x on the backs of the index cards and just flip them over.

box trick pic2

So, since the index card = 8x they now need to solve the equation 8x = 56, which is another simple one-step equation that they should already know how to solve.

box trick pic3

Do another example or two with the class and then discuss how to decide which part of the equation goes under the index card (whichever part comes first using the order of operations).  Have students replicate the process in their notebooks by giving them a 2-step equation.  They need to draw a box around the part that would be under the index card.  First solve the equation for the box and then solve the new equation for the variable.

box trick pic4

I have found that this method really helps students make sense of solving 2-step equations by turning them into two 1-step equations.  How do you introduce 2-step equations in your class?  Do you do something similar?  Please share in the comments!

If you are in need of resources to supplement your lessons on one and two step equations you may be interested in the following activities in my TpT strore:

one-step equations integers pic1  2 step equations bingo pic1  2 step equations partner matching pic1

Thanks for reading,

Christina

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Hands-On Integer Operations (Part 3: Multiplication & Division)

Multiplying and dividing integers are, in my opinion, the hardest operations to teach to students and it took me a few years before I found a good way to have these operations make sense to students.  After I am confident that my students are comfortable adding and subtracting integers, I move on to the final two operations.  (Click here for my post on teaching integer addition.  Click here for my post on integer subtraction.)

I begin with a class discussion of what multiplication means.  Once the students are able to tell me that multiplying means “grouping,” I pull out the two-color counters again…

I start with a positive x positive:  2 x 3.  We discuss how this means “make 2 groups of 3”.  The students show me this with their counters and get 6 as an answer.

pos x pos

I move onto a positive x negative problem: 2 x (-3).  This means “make 2 groups of -3”. The students are able to do this easily with the two-color counters, as well, by making 2 groups of 3 red counters to get an answer of -6.

pos x neg

Now we get to harder questions:  negative x positive and negative x negative.  I ask the class “if a positive times a number means to make groups, what do you think a negative times a number means?”  Then we come up with the idea that a negative times a number must mean to take away groups.

So we do a negative x positive problem: -2 x 3, which means “take away 2 groups of 3”.  Obviously the students can’t take away groups when there are no groups to begin with, so I ask the students what to do.  Because they are familiar with having to add zero pairs to take away numbers from our lesson on subtraction, the students are able to tell me that I will need to first make 6 zero pairs and then take away 2 groups of 3 yellow counters, leaving them with 6 red counters, or -6.

neg x pos

Finally, we move onto a negative x negative problem: -2 x (-3), meaning “take away 2 groups of -3”.  The students are able to figure this one out on their own based on the last example, so they again add 6 zero pairs, but this time take away 2 groups of 3 red counters, leaving them with 6 yellow counters (positive 6) as their answer.

neg x neg

I give the students problems to try on their own and then we come up with our formal rules for our notebooks:

Same signs:  multiply the absolute values of the numbers and make answer positive

Different signs:  multiply the absolute values of the numbers and make answer negative

Coming up with “real-world” examples for adding and subtracting integers is easy – you can use elevators moving up and down, temperatures rising and falling, and gains and losses in football.  It was much harder for me to come up with a “real-world” example for multiplication to give my students, but I finally have one that I am happy with that makes sense to the students and that I can use to show all 4 types of multiplication problems!

temp

  • Positive x Positive: It is 0 degrees outside.  The temperature is rising 2 degrees every hour.  What will the temperature be in 5 hours?  [The students know to do 2 x 5 = 10 degrees, so they are multiplying the rate the temperature is changing, which in this case is positive since the temperature is rising, by the time, which is also positive since I am talking about the future]
  • Negative x Positive: It is 0 degrees outside.  The temperature is dropping 2 degrees every hour.  What will the temperature be in 5 hours?  [-2 x 5 = -10 degrees – the rate is negative since the temperature is dropping, and the time is positive]
  •  Positive x Negative: It is 0 degrees outside.  The temperature rises 2 degrees every hour.  What was the temperature 5 hours ago?   [2 x (-5) = -10 degrees – the rate is positive, since the temperature is rising, but the time is negative since I am talking about going backwards in time]
  • Negative x Negative: It is 0 degrees outside.  The temperature drops 2 degrees every hour.  What was the temperature 5 hours ago?  [-2 x (-5) = 10 degrees – both the rate and the time are negative]

 

I teach dividing integers just by using the inverse of multiplication.  For example, I give the problem -24 ÷ 4.   Since they already know multiplication of integers rules they simply ask themselves 4 x ? = -24, so the answer must be -6 since a positive x negative = negative.

Students then come to the conclusion that multiplication and division use the same rules since they are inverses.

Once the students understand the rules, they have no problem solving multiplication and division problems, as they find multiplying & dividing integers to be easier than adding and subtracting.  I have them complete worksheets and/or play review games with them for practice and then I move on to practicing all 4 operations together the next day.

Click the image below to download a FREE page students can add to their notebooks  for a quick reference on integer operations.

int ops rules

If you are looking for more resources on integer operations, check out my Integer Bundle, which includes 21 (differentiated) worksheets, 4 games, and 3 sets of task cards.

integer bundle pic1

I would love to hear how other teachers teach integer operations, especially real-world examples for multiplication and/or division.  Please leave a comment if you would like to share!

 

Thanks for reading,

Christina

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Hands-On Integer Operations (Part 2: Subtracting Integers)

After I spend 2-3 days teaching integer addition (click here to read my post on adding integers) and am confident my students are comfortable with it, I move onto subtraction.

I start by giving students two color counters again and put an easy question on the board for them to solve independently:

-5 – (-2)

Since students are familiar with subtraction meaning “take away”, they are able to solve this problem without any assistance.  They start with 5 red 2-color counters and take 2 away, so they are left with 3 red counters (or -3).

sub int pic1

I always hear “this is easy!” at this point, but that sentiment goes away quickly when I give them the next problem:

-5 – 3

This one is not so easy for them.  They start with 5 red counters again but this time they need to take away 3 yellow ones, which is obviously impossible since they don’t have any yellow ones to begin with.  When I ask the class how I am going to take away 3 yellow if I don’t have any yellow to begin with I usually hear the following two responses:

  1. “Just flip 3 of the counters over to the yellow side and then take them away”.  I ask the class why I can’t just flip 3 of the counters over and someone is always able to tell me that if I flip 3 of them over, I have now changed the -5 to a +1, so it’s a completely different problem now.  (Sometimes I have to actually demonstrate this for them to see it).
  2. “Just add 3 yellow ones to the -5 and then take them away”. Again I ask the class if this makes sense and someone is able to tell me that  I have now changed the -5 to a -2 if I add 3 yellows to it, so once again it is a completely different problem.

After seeing those two suggestions fail one of my students is able to figure out what to do…instead of just adding 3 yellow ones to it, I should add 3 yellow and 3 red to it because that is essentially just adding zero to the -5 three times, which isn’t changing it at all.  (This is why it is really important to drive home the concept of zero pairs when teaching integer addition!)   Once I add those counters to the -5, I am able to take away 3 yellow ones to finish solving the problem, and am left with 8 red counters (or -8).

sub int pic2

I usually do one more problem with the class to make sure they get the concept of adding zero pairs so that they can take away what they need to take away.  Then I have them practice several problems on their own:

-8 – (-6)

-4 – 2

3 – (-7)

10 – 12

-5 – 4

-9 – (-7)

1 – 5

2 – (-3)

Once they are done using the counters to solve the problems, we check the answers as a class, and I ask the class to come up with a rule that they can use to solve the problems without 2-color counters.  It sometimes takes a little guidance from me, but eventually we come up with the rule that subtracting integers is really the same as adding the opposite.  I have them write our “official” rule in their notebooks along with some examples.

subtracting integers notes

We shorten the rule to “keep, change, change”, since they are keeping the first integer the same, changing the subtraction to addition, and changing the second integer to its opposite.  The students love this rule because after they do “keep, change, change” they are just solving an integer addition problem, which they already know how to do!

I assign subtraction problems for homework that use small numbers so that they can use counters if they want.

The next class period, I have the students practice integer subtraction with partner worksheets and/or self-checking worksheets and I assign problems with large numbers for homework the second night so that they are forced to use the “rule” instead of 2-color counters.

The following day I have the students practice both integer addition and subtraction.  I never used to take an extra day to review both operations but I found that some students are good when they are just adding or just subtracting, but get mixed up when they have a combination of the two operations.

To review both operations, I break the class up into 3 groups and do centers.  I have one group working with me on mini whiteboards solving integer addition and subtraction problems.  I have another group working on integer addition & subtraction self-checking task cards.  (I love, love, love self-checking activities because they allow the students to see for themselves if they know what they are doing!)  I have the third group playing a Bingo game on adding & subtracting integers.  I have found this stations day to be very valuable in giving students the practice they need with adding and subtracting integers and the kids always enjoy it!

I move onto integer multiplication & division the next day (which I will write about in my next post).

If you are interested in checking out the self-checking task cards or bingo game I use on adding & subtracting integers, click the images below.

add and sub integers self check task cards pic1     int add sub bingo pic1

Thanks for reading,

Christina

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Hands-On Integer Operations (Part 1: Adding Integers)

Integer operations are truly a make or break middle school math concept.  Students who “get” integers will be much better off than students who don’t, in terms of their future math success.  That’s why I really take my time when teaching integers each year.  I’m breaking up my blog post on teaching integer operations into 3 separate posts so that it’s not too ridiculously long. 🙂

There are a variety of ways to teach integer operations, but my absolute favorite strategy is using two-color counters.  I have found that some students struggle with using number lines and rules for integer addition, but if I give them two-color counters, every student is able to successfully add two integers.

I always start my lesson on integer addition with a discussion of zero pairs.  I usually do this by asking students what happens if I take one step forward (+1) and then take one step backwards (-1).  They tell me that I haven’t moved at all (or that I have moved zero spaces), so that’s how we form a conceptual understanding that 1 + (-1) = 0.

Once they get this, I pull out the two-color counters and tell them red is negative and yellow is positive.  I hold up one red and one yellow and ask what that equals, and they (usually) answer zero, which tells me they actually do get zero pairs (hooray!)   I then show them a handful of counters (some red and some yellow) and ask the class how many I have.  We discuss how all the zero pairs cancel each other out and whatever isn’t part of a zero pair is the answer. I like using virtual 2-color counters on my Board instead of trying to hold up actual counters since it’s easier for the class to see.  This free website is perfect for that purpose.

counters

Once we’re done with the introduction, I have the students work on some addition problems individually.  I put a bunch of problems on the board for the students to solve independently using the two color counters:

  1. -4 + 3
  2. -2 + (-6)
  3. 8 + (-12)
  4. -7 + (-2)
  5. 4 + (-1)
  6. -6 + 9
  7. -8 + (-1)
  8. 5 + -4
  9. -7 + 3

After the students finish showing each problem with the counters and writing down their answers, we go over the answers as a class.  I then ask the class to come up with integer addition rules based on the answers we got.  I start by having them come up with 3 rules (one for negative + negative, one for positive + negative, and one for negative + positive).

The students are typically able to come up with the rules using the examples from the board (which are color-coded):

  • Negative + Negative:  add the numbers & the answer is negative
  • Positive + Negative:  subtract the numbers & the answer is the sign of whichever number is bigger
  • Negative + Positive:  subtract the numbers & the answer is the sign of whichever number is bigger

We then have a discussion about why the 2nd and 3rd rules are the same. It usually takes awhile to get the answer I’m looking for… students tell me that it’s because it doesn’t matter what order you add numbers in and I ask them how they know that.  Eventually someone is able to come up with the answer of the commutative property of addition. 🙂

Then the students write down the two “official” rules in their notebooks:
adding integers notes

That takes me to the end of the class.  I give the students homework on adding integers (all with small numbers so that they can use 2-color counters if they want/need to).

The next day I don’t teach a new lesson.  I just have the students practice adding integers using the rules.  We do a few problems together after the do now and checking homework.  I then break them into pairs based on how well they seem to be doing with the lesson.  I have them do partner matching worksheets where one person does the 20 problems in the left column and their partner does the 20 problems in the right column and they have to find the matching answers.  If some of their answers don’t match, I have them redo those problems and work together to identify their mistakes.  I made 3 different levels of the worksheets so that each pair is challenged appropriately.  I love partner matching activities because they keep the kids engaged and the students are able to check their own work and help each other out, freeing me up to focus my attention on struggling students.

(For students who really struggle without the two-color counters,  I tell them to draw little + and – signs to illustrate the problem the same way they would have with the counters.  This helps remind them whether they should add or subtract and what sign their answer will be.)

For homework on day 2 of integer addition, I tell the students to study for a quiz tomorrow and I assign self-checking worksheets for written homework.  Then the next day I can ask if anyone has any questions before the quiz because with the self-checking sheets, they already know if they were successful with the homework or if they need help, without me having to check each answer with them.

For the integer addition quiz I give the class 10 problems on Socrative so that I can see the results instantly.  If the majority of the class did well, I move on to subtraction (I will write about how I teach integer subtraction in my next post).  If they struggled with the quiz I spend the rest of the period reviewing addition again.

While I usually teach a lesson a day in my math classes, I really drag out integers because they are so crucial to future lessons.  There is absolutely no point in moving on to subtraction until students have mastered addition.  Most of my classes have been good with it after just the two days, but I have taken the third day (after the quiz) with some classes who needed more practice.  I then requiz them the following day.

(If you are interested in purchasing the integer addition partner matching or self-checking worksheets I use, click the images below.  Each set of 3 differentiated worksheets is $1.75.)

integer addition partner matching pic1Integer addition self checking sheets pic1

Thanks for reading,
Christina

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Ideas for Setting Up Math Notebooks

With all the buzz on interactive notebooks lately, I thought I’d share how I do notebooks in my math classes for people who are looking for an alternative to cutting and pasting foldables into a notebook.

ideas for setting up math notebooks

I have gone back and forth a few times between having my students use binders or notebooks, but for the past few years I have gone with 3-subject spiral notebooks.  They are a good size and I like that they have built-in dividers with pockets and the fact that pages can be neatly torn out when needed thanks to the perforation.

The front section of the 3-subject notebook is used for notes.  The middle section is for classwork and homework.  The back section is used for scrap paper or looseleaf if I want something torn out and handed in.  I like to set it up this way so that the front section is a nice, organized resource they can use to refresh their memory on how to do something without having to root through pages of work.  (It also makes checking their notes easier when they are all in one place)!   I also like the fact that the students are not staring at their notes when they go to do their classwork or homework, so they can try the problems on their own, but they can easily flip back if they need to reference the notes.

Taking notes in my class is mandatory.  Each day (in the “notes” section of the notebook), students are required to (1) title the notes with the day’s topic, (2) write the date, (3) write a summary/explanation of how to do the day’s lesson, and (4) give an example, solved correctly and showing all work. Here is a sample of what I expect in a day’s notes for a lesson on subtracting decimals:

math notes example

I collect notebooks on chapter test days and grade the “notes” section while my students are taking the test.  I collect on test days so that students make sure they have all their notes in order (and hopefully look them over) before taking the test and because they obviously don’t need their notebooks while they are taking the test.  Notes are worth 20 points per chapter and I grade them using the following rubric:

pic of rubric

Click here for the pdf version of my notebook rubric

Click here for the editable version.

Most of my students are pretty good about taking good notes since it is a big part of their grade.  They know that simply taking good notes each day in class is an easy way to get a 20/20 averaged into their grade each chapter, which is a good motivator for most students!

For classified students with special note-taking requirements in their IEP’s, I provide guided notes on which they basically just need to fill in the blanks, but the guided notes I give are in the same general format with both explanations and examples each day.  I also save the notes I write on my interactive whiteboard each day and share them with my classified students on Google Drive.  That way if they weren’t able to finish filling in their note sheets in class, they can fill them in at a later time.

I am in the process of typing up my guided notes and making them a little nicer.  (As I complete sets, I am putting them in my TpT store along with practice sheets and application sheets that correspond to the lessons).  You can grab my set of notes, practice sheets, and application sheets on simplifying algebraic expressions free for the next few days!  Click  the image below to get this set while it’s free!

simplifying expressions pack pic1

How do you handle note-taking in your math class?  I would love to hear ideas from other teachers!

Thanks for reading,

Christina

 

(Also, all paid items in my TpT store are on sale today, August 19th for 28% off with code MORE15)!!

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