What's My Function?

The bottom x value is a 3.  It isn't very clear.

A few years I switched schools and in that move, lots of stuff ended up in my office area at home while it waited to go to it's new home in my new classroom.  Well, some of it never made it and after looking at it for the past 3 summers, I finally decided that it was time to dig through what was in the boxes and start organizing or throwing.

Here is a little gem that I came across in the files.  Writing the function rule from a table was a challenge for this particular class, so I had them make these cards.  Everyday, a new student posted their function table and the class worked to figure out the rule.  We then posted it for students to use for review on their own.  It was great practice, but it took a lot of time!  I think that is why is is still sitting in the file because it would impossible that I just forgot about   it! : )

I started thinking about this because I liked the premise of what I did.  So I came up with two alternatives to use instead.

1) Students would find a new partner each day and practice finding the function rule of their partner's card.  It would allow the opportunity for the students to practice coaching.  Also, it gives them an opportunity to explain their thinking and get clarification from a peer if needed.

2) Students could put the same information onto an index card.  They could do a mix 'n' match with them.  I could collect the cards and redistribute everyday and do a quick 5 minute review.  The index cards could also go into a station activity at a later time.

There are probably more ways to use this that my summer brain isn't coming up with yet.  Does anyone else have an idea of how to use this in the classroom?

A Bit of Humor at My Expense

Ok, so today was one of those days where my students had every right to tease me some for what I said.  It was completely unintentional, but I stepped in it a bit.

This was my prototype.  My pretty one I left at school.

We were making the modified shutter foldable that is pictured.  I wanted the students to shut the flaps and label the front of the foldable.  So, I am just in teacher mode, giving directions and I said, "Shut your flaps and label the first boxes Properties. . ."  My room became quieter and I had one of my kiddos look at me and say, "Did you just tell us to shut up?"  I said, "No, I want you to shut your flaps and label the front".  As I was modeling how the flaps opened and shut, I realized how I sounded and turned beet red.  I told the kiddos that I suppose that didn't sound right, even if it was really what I wanted them to do.  There was parroting of "Shut your flaps" in different voices and when the classroom became a little loud, someone would  call out, "Shut your flaps".  Then the class giggled and I shook my head and said, "You are never going to let me live this down!" to all the smiling faces saying, "Nope!"

Ahh...nothing better some days than to be completely teased by your 8th graders.  Considering that they will leave me for high school in a couple of very short months, I am privileged to have had this memory today to think about and smile.

Anyone else have a favorite memory about their 8th grade students?  Love to hear your story!

Update: Classifying Real Numbers Foldable

By far, my most popular post had been the classifying real numbers foldable.  Tomorrow I will be taking my Algebra students through the process to make it.  I did a couple of things to hopefully make the process smoother and I thought I would share them.

First of all, I changed the shape of the nesting number sets.  I did this just speed up the cutting process.  I then used the new shapes to make templates for each table group.  I've included the word document for anyone that wants it.  I would just print it out onto card stock and cut them out to make templates for the students to trace.



I also made a "how to" sheet for the students to follow.  This is more for my sanity.  Those who get lost or a step behind can look at the directions sheet and catch up.  This is only for the assembly of the nesting number sets.  If you would like it, it is below.  There are a lot of pictures, so it might take
some time to download.



I hope that these will help those of you thinking of using the foldable with your classes.  I am excited to try it with my kiddos tomorrow!

Update to the Update:
I tried this with my kiddos today.  The directions sheet with the pictures was amazingly helpful.  I explained what to do and then I saw several kids check the directions again.  I didn't have one goof up or have to give out another piece of paper! :)  I was very pleased.  The other thing that the kiddos latched onto was the smiley face stickers.  It really helped them to line up the template correctly and I wasn't asked at all if it was lined up right.  That is a trick I will definitely use again!

It did take time to assemble, so we filled in everything for the rational numbers and it's subsets.  Tomorrow we'll finish.  Next year, I am thinking of making the foldable a homework assignment to make it and then the next day we will fill it in and discuss.  We'll see...by next year I might change my mind altogether! :)

Comparing Real Numbers

I have noticed in the past that there are some students in algebra who can't set up the real number line correctly.  With that, I have noticed that placing numbers on a real number line is challenging for some students as well. 

For the lesson that reviews ordering and comparing real numbers, I was thinking that it would be a good idea to make a number line and do some ordering of real numbers.  I wanted something that would be compact and fit into the ISN. 

I thought about using a piece of paper folded in half because I liked the idea that zero would be on the fold and in the middle of the line.  From there it was just a matter of putting positive and negative numbers on the number line.  I also added tick marks for every tenth.  I thought that this would help to place the numbers more accurately.

I then used some colored dot stickers cut in half to mark the position of two sets of numbers on the number line.  The stickers were a bit too big, but ultimately did the job.  I just made sure that the straight cut lined up with the numbers position on the number line. 

The lesson also deals with adding and subtracting real numbers.  I layered some sticky notes so that I could highlight two things:
1) The procedure the book uses for adding and subtracting real numbers with mixed signs, and
2) Reminders about fractions needing the same denominator and about lining up the decimal points.

I have been finding a lot of uses for sticky notes in the ISNs that I am trying to put together for the students.  (I hope I'm not alone in saying that I use sticky notes for everything and could probably join a 12 step program if one existed.)  I have been using them to highlight steps in procedures and to save space by layering ideas similar to the picture at the left.  Does anyone have other ways that they use sticky notes in their ISNs?

Addition and Subtraction Word Problems

This foldable is very specific to lesson 3 of Saxon, Course 3.  I wanted something this year that was more concrete and organized than what I did last year.  Classifying the problems comes up a lot it feels like during the beginning lessons of the book.  So I felt that it was important that the kiddos have something simple and straight forward to refer back to when needed.  I started with a square and folded the corners into the center.  I found it helpful to fold the square along it's vertical and horizontal lines of symmetry so that I could get the corners to match in the center better.  A little color and labeling and the outside was completed.

The inside is all organized the same.  I said if this classification was for addition or subtraction word problems, wrote the equations in words the same way the book did, and wrote the formula.  Then I made up an example similar to the book's example and solved it.  I also color coded the parts of the equation. 

I consistently used the same colors.  I am torn about that because the colors don't stand for the same thing each time.  It is just about position in the problem.  I don't want them just memorizing the position of the numbers in the problem and I am wondering if that will happen.  We'll see what happens when I teach it.
 

Sometimes Mistakes Aren't that Bad..

I made this simple little foldable to teach finding the value of an expression given the values of the variables.  My only problem after finishing it and looking at it for a second was that I made an equation not an expression!  After a big sigh I was back to the drawing board and did come up with something.  However, this got me thinking a lot.

I started thinking about what I liked about this.  I liked that it was a hands on manipulation of an equation.  It involved thought and planning to create.  It required an understanding of input and output to be able to create.  Students also had the freedom to customize the values on their foldable.  I likes how it laid out a mapping of a function.

There seemed like my "opps!" had a lot of good surrounding it, so I didn't want to let it go.  Then it hit me!  Linear equations are always tough.  Especially when they first start to learn about two variables.  When we make tables, there doesn't always seem to be a connection between how one variable changes and its affect on the other.  So, I went back to the drawing board again and here is what I created.

I really like it, especially for my 7th grade math kiddos.  The first introduction to equations with two variables will be this year.  Hopefully, this will help solidify the idea of what is happening in two variable equations.

Now, here is what I originally set out to create:

As students replace the "a" with a value, the value of the expression can be calculated and moved into position.  A couple of tips: 1) Think about how you want it to look in the INB, especially composition notebooks.  My first one was too big for the notebook and I had to downsize.  2) I found it was easier if I traced the yellow strips width onto the paper and then determined where to cut the openings.  It was also way easier to change the size of my strips than to try and open the openings more. 

Order of Operations

 I have been thinking about two lessons in my text that are three lessons apart from each other.  The first is a basic review of the order of operations and the other is about nested grouping symbols.

My thoughts have been very focused on how to make a quality graphic organizer or foldable that will help my kiddos think through the order of operations.  They tend to work from left to right which causes a problem in so many ways.

So the pictures are my graphic organizer for the review lesson.  I loved how Sarah at Math=Love (http://mathequalslove.blogspot.com) organized the letters to PEMDAS.  So I decided to use that as the left hand side of my table and then have 3 examples that come after it.  I wanted the kiddos to think about each letter of PEMDAS and decide if they had parentheses or exponents in the problem and not just start at the left and work right.

I am going to have them color code the letters of PEMDAS which are on their sheet already and add the  L –> R above multiplying/dividing and addition/subtraction.  Then, using their colors, I want them to color code the steps on the problem before we begin to solve anything.  Again, I am hoping to stop them from simply working left to right.

After we have done all of this, we are going to work the problem.  The students will fill in one box at a time as they work the problem following the order of operations.  My other goal of this graphic organizer is to have them see what showing their work looks like.  Sneaky, huh? :)  Also, if you like this graphic organizer, you can download it at the end of this post.

The next lesson on nested grouping symbols always seems difficult for the kiddos.  I think it is terminology.  They don't use "inner most" in their vocabulary often and "inner most" changes position in problems.  I wanted a foldable that would help them to see that they start at the inner most parentheses and work their way out.

To do this, I took a fairly simple problem and three different colored pieces of paper.  I folded them over about an inch and then glued them together at the fold.  I wrote the problem so that each part was on a different color.  I also number the order in which to do the parts.

Students will then lift the flap to reveal the value of the expression.  Then, they will work the second part. 

Lifting that flap reveals that the value of the green section's expression and the rest of the expression is solved using the order of operations.  The value of the entire expression is circled after all of the operations are preformed.

This last picture is how the page in the students INB will look.  After the initial foldable, I decided not to make another for the notebook.  However, if time, I would love to give them a problem in the next day or so and ask them to make the foldable for their problem.  It would be neat to display them in the classroom.

Anyway, I elected to have the students write two additional examples and highlight the step they are going to calculate before writing the next line.  The text also throws in the absolute value symbol as a grouping symbol, so I need to say something about it.  Thus, the note about absolute value at the end.

Variable, Factors, Terms, Oh My...

Lesson 2 in the Saxon algebra book focuses on the key vocabulary associated with expressions.  The text focuses on the words: constant, variable, coefficient, factor, and term.  So, to make the lesson not just a list of vocabulary words or a bunch of Frayer models, I opted for some simple foldables that define the key vocabulary.  The picture above is how I am setting up the INB page with the students.  The pictures below show an up close view of two of them.

The outside of the top foldable.

When students lift the flap, they will see the definition of the vocabulary word.

For the terms of an expression, I wanted the students to see it separated out more, so I made this accordion style foldable.

Inside each term is in it's own box and is labeled at the top as the first, second, third, etc. term of the expression.

What I really like about this lesson is the processing that I am going to have the kiddos do.  The Saxon teacher's edition has math background notes and in this lesson, they have a Venn diagram to show how the vocabulary words are related.  They also wrote some statements that were true based on the diagram.  I turned the statements into true/false questions and the kiddos need to use the diagram to determine if the statement is true or false.  I then ask the kiddos to write two true/false questions of their own based on the diagram.  I want to have them swap notebooks and see if a friend can answer their question correctly.  I think that it is a good tie in with the first lesson that also dealt with sets and Venn diagrams.  We'll see what happens in September!

Classifying Real Numbers Foldable

 The first foldable for next fall has been made!  The first lesson that I teach in my algebra text is on sets and real numbers.  When I think about classifying real numbers I always get the image of nesting cups that you used to be able to buy for toddlers.  I wanted to somehow bring that idea to the foldable that we made for this part of the lesson.

Now, I have seen the traditional Venn diagram of the sets.  My problem with it is that I have noticed that my kiddos have trouble picturing the sets of numbers and being within each other.  They often forget that 7 is an real number, rational number, integer, whole number, and natural number.  They will usually just say that it is a whole number.  I wanted them to see that whole numbers contain the set of natural numbers in a way that was different from the traditional diagram.  So I started by folding a piece of paper in half and putting real numbers on the outside of it.

When the students open the foldable they see that real numbers contain the set of rational and irrational numbers.

Now I realize that not all of the sets show up at once.  That is what I am going for.  Rational numbers have many subsets.  So to show that rational numbers hold the integers, the students have to lift the flap.

 Continue opening the flaps and you will see all of the subsets appear.  In each flap, I have the definition of the set, examples of what is included, and non-examples to try and help the classification process happen smoother.

Just through the assembly of this foldable there are so many opportunities to reinforce that a natural number is also a whole number or that a negative number is part of the integer, rational, and real numbers, but doesn't fit the definition of a whole or natural number.  I also like that it shows that the set of rational numbers holds integers, whole numbers, and natural numbers, but not irrational numbers.  Yet, at the same time, the kiddos see that real numbers hold rational and irrational.

Update:

 I added this post to the Interactive Linky Party at 4mulaFun.com (http://www.4mulafun.com/).  Go and check it out for some other great ideas related to INB!

(8-10-14) I was going through Pinterest and I came across this slideshare at http://www.slideshare.net/ProfessaX06/real-number-system-foldable-5151675.  In it, there is a foldable very similar to the one that I created.  I must have seen this at some point and have forgotten when I made my version of it above.  My apologies to the authors below for using their idea and not giving them proper credit. 
 

Linear Inequalities

This week is my last full week with my 8th grade algebra students.  One of the topics for the week was linear inequalities.  In the past, I have found that the kiddos have had a lot of trouble understanding why we shade one half plane or the other.  I saw on either a blog or Pinterest (sorry I can't find either one) of a teacher that plotted points that were solutions to the linear inequality.

So, here is my take on the idea.  I made this worksheet to guide the kiddos while they worked.  I asked the student to pick points and determine if they were solutions to the inequality or not.  If the point chosen was a solution, they were to graph it on their graph at the top of the page.  I also gave the kiddos a bank coordinate plan and asked them to plot all of the solutions their group found.

What I found was that the kids immediately noticed linear patterns for the solutions.  They were saying all of the double numbers seem to work, like (2,2).  Others found complete chaos and couldn't figure out how others were finding so many solutions so quickly.  We had to go to a band concert, so I had to cut the exploration time short.  But, I was loving what I was hearing as they tried to find solutions.  When some kids got a line parallel to the boundary line they thought they had found all of the solutions, so there was a great authentic math discussion.  I was so happy with how the activity went.

Next time, I would give each group a different color marker and ask then to plot all of their solutions onto one class graph.  That way we will have a larger number of solutions to observe and draw conclusion.  I would also not do this activity on the day we have a shorten class. 

The graphic organizer is what I used to wrap up the basics of graphing linear inequalities.  It is based on lesson 97 from the Saxon Algebra textbook.

Absolute Value Inequalities

I opened up my teacher edition last night to review the lesson and make some notes.  I got to the rules of the absolute value inequalities and froze for a second.  The definition was terribly technical.  It took me two readings to make sure that I got it and my heart sank a little.  I started trying to figure out how I was going to get the kiddos to understand that definition.  I started looking through other resources that I had and found an explanation using two cases.  After reading that, I created the the following chart:

I got my examples from the McGraw-Hill Algebra 1 (2012 edition) textbook.

I left the case 1 and case 2 parts blank and worked them in class along with drawing the graph of the solution.  I like the idea of what I did, but I would like to redo it a bit.  I would take out the "and" and "or" part by the inequality symbols.  I don't think the kiddos got it right away.  Next time, I will have them write it by the solutions graph.  I am also not happy with the special cases part of the notes.  Oh well!  Summer is almost here and I am sure I'll find inspiration during it. 

Pythagorean Theorem

Tomorrow, I will be teaching a lesson on the Pythagorean Theorem.  I wanted to let the students actually see why it worked.  However, with the school year so close to ending and the end of the year events canceling more math classes than I can spare, I was stumped how to do it.

As you can see, I was able to put together a graphic organizer for them.  The best part of this organizer was taken from Jennie's idea at mathfoldables.blogspot.com.  She had this nifty way of showing students that the sum of the square of the legs is equal to the square of the hypotenuse.  That proof makes up the upper left hand corner.

The formula and the transposed formulas to find the length of the legs are in the upper right hand corner.  The bottom left is example problems and the bottom right is an explanation of Pythagorean Triples and two examples.

The template for Pythagorean Theorem proof can be found at http://www.teacherspayteachers.com/Product/Pythagorean-Thereom-Proof-Foldable-Template-496569.  It is a free download.  The students color each sides a different color.

Then under the hypotenuse side, the students color 16 squares the same color they did for side b and 9 squares in the same color they did for side a.  What they will see is that their are enough squares to hold all of side a and side b.

Another Foldable

I am starting to feel very good about how well my kiddos are understanding now that I have been using foldables.  I see them being used and referred to much more than their notes ever where.  It takes some thinking to put together a foldable for the lessons, but I have been doing it so far and I am pleased with the results, so it is keeping me motivated to continue with them.

I am also pleased with the data that I am getting back from the practice problems I am making them do before they start their homework.  I am thinking about mixing it up next year and putting some of the questions onto index cards and having them do a "scoot" activity in their table pods.  I have to think a little bit more about it, but I like the concept of it.  I just want to do things that are more active than filling out a worksheet.  It is my goal for this summer to find more ways to do that.

Here is another foldable that I did with my students.  I focused on making them tell me what they thought the process was after seeing the examples.  That is why the inside of the foldable is incomplete.  I just gave myself enough to get the ball rolling with the kiddos.  What I learned from this is that I haven't stepped back enough this year to listen to them and their thinking.  They weren't sure what to say and afraid of saying the wrong thing.  Talking in partners and small groups helped to open them up.  I will be working more of this in next year where I consciously make myself stop and listen.  I just learned a lot from this lesson and have found an area to improve and that is good.  It is a new direction to push myself and hopefully become a better teacher for whatever is left this year and definitely next year.

On the front of the foldable, we wrote reminders of perfect squares, prime numbers, powers of 10, and some patterns for variables.  We also wrote the answer to what a radical expression was and the product property of square roots off to the side.

The inside had 3 examples and then the steps to take to for each strategy to simplify radicals.  As I said in the post, part of the steps are missing because I only wrote enough to get the ball rolling with the students.

Cutting and Pasting 101...

Well, over the last two weeks I've learned that my 8th graders have forgotten how to cut and paste from kindergarten.  We made an accordion foldable for using substitution to solve a system of equations.  I anticipated that it would take 15 minutes to assemble and then 15 minutes to go through.  Hmm...that was really good in theory.  The assembly took 30 minutes.  So, I'm revamping this one for next year.

It helped the kids to understand substitution and it was nice that they could view two steps at a time.  The kids seemed to like that about the accordion style.  You can take a look at what it looked like below.  It takes two pieces of paper to get all of the steps down.  Next year, I think I will turn it into a chart.  Most likely will be faster to complete.  However, if kids are making them all year, then it might be a lot faster.  I only started doing this with 8th grade this past trimester.

The cover says "Steps for Solving Systems of Equations by Substitution"

The steps are down the left hand side and then an example is down the right hand side.  Next year, I will have 2 examples.  One will be like y= 2x-3 and y=5x+9 and the other will be like 3x+2y=10 and 4x-5y=13.

   A few days later, we made foldables for elimination by addition and subtraction and by multiplication.  We waited a few days because my school uses Saxon.  So they had other lessons on other topics in between the substitution and elimination lessons.  These foldables went a little faster, but I had the charts cut out and and booklets put together.  I only have 30 kids, so it wasn't so bad to do.  This format seemed a lot better for the kiddos.  So I am keeping that in mind for the future.

Here is what that foldable looked like.

The two columns are labeled "Addition Example" and "Subtraction Example".  The steps on the left I made using Creately.

The two columns on the chart are labeled " Multiply 1 Equation" and "Multiply 2 Equations".  Again, the steps were made using Creately.

Here are the files for the different foldables that are pictured here.

 

Friday Success

So, this week I was trying to use foldables for notes instead of just letting my 8th grade Algebra students write their own notes like I have been.  On Friday, we finished our second foldable of the week (crazy week with field trips canceling a few our classes).  After making the foldable, I have been having the students work on a skills sheet that I am calling "math workshop" for lack of a better title right now.  While students were working on the skill sheets and using their foldables (rarely saw them referring to their notes before without encouragement), I started hearing, "Oh! I get it.  It's like the example under the third flap." or "Hey, I actually get it!".  I had more than one student say that this lesson was easy.  I was getting more and more excited with each positive that they gave.

This year has been a struggle for me to teach math in a way that it hasn't been before.  I really felt like I lost my math groove.  What I realized on Friday was that I had been holding myself to a program too strictly.  When I followed the prescribed lesson, but put my twist on it, things started to click and I was so happy and sad that I didn't figure it out earlier.  Now that we are on a roll, I want to keep the momentum going and finish strong at the end of the year.

Here are some photos of the foldables we made this week.  I am sorry about the picture quality on some of them.  It was the best photo I could get.

This is what I wanted the students page to look like in their notebook.  The two vocabulary words are Frayer Models folded in half so we could fir more than one on a page

This is the simple foldable that we did for the first day.  The students filled in the example part of the foldable the rest was typed in for them.

 

 

 

 

 

 

These two pictures are our foldable for direct variation.  There were five examples in the textbook and I made each one a flap of the foldable.  I also had the paper not folded exactly in half so we could write the definition and direct variation equations at the top and it would be visible for the students.