Graphs and Central Tendency

It has been a long time since my last post. We have been BUSY at school.  I have been covering for another teacher, so my evenings have been spent planning for another class.  It is a 7th grade class, so I was really having to regroup.

The kids were behind, so we were having to go in and hit all the concepts.  During this time of year (or any time of year for that matter), no one wants to be beat down with a bunch of notes.  Since I started doing an interactive journal in my 8th grade class, I thought I would go that route with these kids.  They responded so well!  They loved getting the information without feeling like they were copying down a bunch of "stuff".

During the fall, I reviewed over the different graphs and central tendency with my 8th graders.  I used turkeys and pumpkins.  I didn't think that theme would go well at this time of year, so I created baskets and bunnies.

Each basket represented a different graph.  The egg was glued on to each basket (in a slightly overlapping pattern), and it titled what the graph was.  The eggs serve as a tab for easy reference.  The graphs we reviewed were:

• line plot
• line graph
• stem and leaf plot
• bar graph
• circle graph
• venn diagram

Each bunny represented each measure of central tendency.  One ear was glued to each bunny (in a slightly overlapping pattern), and it detailed what the bunny covered.  When we finished we had a four-eared bunny!

Click here to get the template I used for the baskets/eggs and bunnies/ears.

The kids were able to go back and add some color to the foldable.  I loved seeing them pull them out and use them to help answer different questions.  The eggs and ears allowed for easy reference.  The kids were engaged and got the material I needed them to get.

The slowest part is the cutting!  I have found that when we do activities like this, it is best to go ahead and hand out the material when they come in, so they can start cutting as soon as they finish the bell ringer.  We also have to share scissors.  I plan on buying A LOT of scissors this summer!  Once you get past the cutting hurdle, it is smooth sailing!

Happy basket and bunny making!

Dilations & Scale Factor Journal entry

This year, I started an interactive journal in my math class.  I have LOVED it.  I can see such a difference in how the kids are understanding.  It allows for them to have a hands-on approach while learning how to take short notes that are to the point.  It is still a learning process, but I am loving the process!

A few years ago, I implemented, "Say NO to Oreos".  WHAT?????  Who could say NO to oreos?  We do this when we learn about scale factor.  The NO stands for New divided by Original.  We start this saying at the beginning of the year, and we use it all year.  In the past, I have always brought in three types of oreos:

• regular
• double stuft
• mini

We go through a lesson in which we start with the regular oreo and dilate it through an enlargement (the two types of dilations were discussed the day before); therefore, the double stuft is created. The students measure the oreos, and we calculate the scale factor used.

We then have the regular oreo and dilate it through a reduction; therefore, the oreo mini is created.  We do more measurements and get that scale factor.

The students have always responded very well to this.   Since I started journaling this year, I created a journal entry, so the kids could put down what they took away from it.

After each situation, we put the oreos down in the journal.  The characteristic of each type of dilation was included.

I created a little pop out which included our saying that we taped to the middle of the page.

The pop out opens up to reveal what the NO stands for.

I love how we were able to keep something from this activity that the kids can go back and look at.  The kids loved to eat the oreos!!

I am excited to see the finished journal!

Happy Dilating!!

The Amazing Math Race

I always have a six weeks project.  Four years ago, I was thinking of what project I could do for the fifth six weeks.  I had shown a few clips for CBS' Amazing Race during the year.  Of course these clips held mathematical content.  The class said it would be fun to do an Amazing Race, so the project was created.

The race has five questions with five events/obstacles.  It even has a detour and a roadblock.    The race features one question from the five categories:

Measurement
Probability/Statistics
Percent
Pythagorean Theorem
Proportions

We go outside during the class and they perform my race (in groups of 3-4).  They have a blast!  They are answering math questions, being outside, and performing tasks.  They don't even look at is as being work.

Only one member can use his/her legs to go to the question.

Blowing bubbles

Measuring diameter

Pythagorean Theorem

I allow each group to have:
dry erase board with a marker
formula chart
calculator

Once they solve the question, they bring me the answer on the board.  I must be able to see the work, and the label (if any) must be correct.  I have flags set up for each question.  They must go to that flag to work or rework the problem.  Once they are correct, they get to complete the event.  It always goes very smoothly, and the competitive nature comes out.

I have each question printed on cardstock and laminated.  I have used the same questions since I started this four years ago!  I have enough questions for each group.  For my race, here are the items you will need in addition to the questions.

dowel rods, string and tape measure

hula hoops and measuring stick

Event flags (laminated and hot glued)

bubbles and bubble gum

After they complete my race, I give them the information sheet they need in order to create their own race.  They may work in groups of 3-4.  They must have five questions and five events.  It takes about two days to make it through all the groups. By the time we are done, the kids have answered 30-42 questions.  It is great, and we get to spend some time outside!

Here is the criteria:

The objectives of this project are to:
(1) help students better understand mathematical concepts and formulas by applying them in a fun and dramatic setting
(2) integrate math with competition and kinesthetics, providing students with the opportunity to utilize both their cognitive and creative abilities
(3) provide a motivational strategy that will encourage an appreciation for mathematics

The obstacle course must:

have 5 events and questions

feature the following mathematical concepts

• Measurement
• Probability/Statistics
• Percent
• Pythagorean Theorem
• Proportions

feature the following obstacles

• Road Block: A task in which only one team member can complete
• Detour: A choice between two tasks, relating to the same concept
• be contained to the “race area” and able to be performed

The questions must:

• Be written one per page (enough pages for each group)
• Have a solution provided to your teacher
• Feature the mathematical concepts listed above

Here are some pictures from student created races.

If you would like the complete race, you can get it at my store.

The kids will enjoy it, and they are learning!

Happy racing!

Math Sing-a-longs

For the last few years, I have done a sing-a-long project with my math class.

I give them the option of singing the song live in class, or pre-recording it and bringing in a video.  Most of the videos I receive are the kids standing and dancing to the song they made.  I love it when students go above and beyond the criteria.

This year, I had two really good videos.  They both had great original songs with a great video. The kids have voted in the classroom for the favorite video.  Since I created a class facebook this year, I have put the videos to a vote on there, as well.  I love seeing the parents promote and share the videos on their pages.  This has turned out to be a wholesome, family project with the voting.

Go to my facebook page and check them out:

Video 1:  Click here 
Video 2:  Click here 

Math in action

I am going to give both groups a prize, but the group with the most overall votes will get a special prize.  The next project is a commercial, and I have already heard different students say they were really going to work hard on it!  Cha-Ching!!!  Excited about math..... WooHoo!!!

The objectives of this project are:

(1) help students retain frequently used mathematical procedures by setting them to music/verse

(2) integrate math with music/verse/dance, providing students with the opportunity to utilize both their cognitive and creative abilities

(3) provide a motivational strategy that will encourage an appreciation for mathematics

Students will present an original song/rap and dance.

The song/rap must:

•  have a catchy title
• have a music accompaniment that will be played during the presentation 
• music of any kind can be used (preexisting or your own creation)
• preexisting songs can be used but the lyrics must be dubbed out
•      be less than 2 minutes but more than one minute in duration
•      consist of acceptable lyrics that cover any math topic (approved list)

Happy singing!

Let's ALL raise our expectations!

I tried something different this past week at school.  Wednesday - Friday, I had my desks set up for cooperative learning.  We were working on review concepts: area, perimeter, 2d and 3d figures.  I know all of these concepts have been taught to them, but I am once again faced with the question as to HOW our students are taught.  

From the first day of school, I make it clear to my students that I am here to help them, but I will not hold their hands.  When they ask me a question, I expect it to take place AFTER they have pondered the question.  I NEVER accept "I don't know" or "I can't".  The biggest hurdle is teaching the students HOW to ask a question.  

When a student raises his/her hand, I go to them and ask them what they need.  In the beginning, many of them tell me they don't understand the question.  I then proceed with, "Okay. What is YOUR question."  The student will then proceed to read the question to me.  I then ask again, "What is YOUR question."  I tell them that I can read the problem written, but I need to know what they are confused about.  Once we get through that, I continue asking them various questions about the concept.  By the time, I am finished, the student has usually answered the question they had.  I see the lightbulb.  

Now, this concept is not well liked by many of my students. Most of my kids tell me that they have heard how hard I am.  I always take that as a compliment.  This past week, my kids conducted a survey in which they created a question and then had to do different things with the data.  One group asked who the favorite teacher was.  He thought it would hurt my feelings that I had only received a few votes.  I told him that I was not here to be the favorite teacher.  Most students do not like how hard I am and that I have high expectations.  I told him my feelings would be hurt if they said I was the easiest teacher.  I know that when students walk out of my classroom, I have done the best job I can to not only teach them math but provide them with tools they can use anywhere. 

We are NEVER finished in my class.  We have numerous projects going on in and out of the classroom.  The kids are given many opportunities to express and use math in many different ways.  I always see such a difference by the end of the year.  My kids learn many skills, and that is what they should learn in all classes.

As they were working in groups this week, I was shocked as to how many of them had no concept as to what perimeter and area really meant.  Most could tell me what the formula meant, but they had no idea what the concept meant. It just made me realize that not all teachers push the students like they could be pushed.  Self-discovery is a wonderful teaching tool.  I am always there to let the student know if what they discovered is correct, but they figured it out on their own.  That is powerful.  As teachers, we must realize that we need to let the students take control of their learning.  Let them find out the answers on their own, and we are there to offer support and help keep them on the path to learning.  Through life, we will make mistakes, and there are many times in which students arrive at a thought that is not correct.  Through effective questioning, we can easily get them back on the right track.   

Although it has been disheartening to see how unprepared some of these students are in the self-discovery path, it has also been wonderful to see what happens when they finally get it!  I am not saying that every student did not understand these concepts, but many of the students did not. I teach my students as if they were my own child.  I can only hope that my son's teachers push him to his highest potential.  

Imagine how wonderful our schools would be if we all set and kept our high expectations!  It is easy to just go over and tell a student how to find something out, but tomorrow that same student will have the same question.  Many students won't be happy about it at the time, but in a few years, the students will look back and appreciate what was done for them.  Let's give them the best we have, so they can be the best they can be!

Happy High Expectation Setting! 

All About Circles

I created this activity my first year teaching.  It has been one that I have shelved for the last few years, but I am dusting it off and bringing it back.  I even made a few changes.

In class this week, I am really hitting the cooperative learning aspect.  I have arranged my desks in groups of 4, so the entire class period will be spent with a group.  I hope they will be able to take away that group work is not about one person doing the work.  It is about being there to help someone else out.

With 8th grade, we do a quick review over 2d figures.  With this, I include a review over circles. With each group of desks, I have placed these items in a storage box:

• scissors
• bottle of glue
• roll of tape
• crayons or map colors
• ruler

Each group will have an information sheet (one for the group), that details the parts of a circle.  They will each use a paper plate to create the same circle.  Each person will be responsible for his/her own circle.  Here are the materials:

• paper plate
• plastic straws
• yarn 
• glitter

I will manage these supplies and distribute as needed.  I don't like to waste, so these kids will learn how to recyle the left over glitter!

The students will follow these steps:

• Outline the smaller circle within the plate
• Use glitter to illustrate each radius (there are three)
• Use a straw to illustrate the diameter
• Use yarn to illustrate the chords
• Shade each central angle one color
• Shade the inscribed angle one color
• Label the points

Of course, the diameter will have a straw, glitter and yarn.  In my example, I have them placed on top of each other to show each one.  On the back of the plate, they will create a key.  We will hang a few of them from the ceiling.  On Thursday, they will create a 3d mobile, as well, so my ceiling is about to leak geometry!

Go to my Store for the FREE downloadable activity.

I think the kids will enjoy the hands on activity, and I believe the parts of a circle will sink in a little more than if they just wrote it on paper.

They will also be modeling solids with blocks and beginning the 2d/3d book (I will post this tomorrow).  They are going to be busy little cubs tomorrow, but I find many of them work much better knowing they have a lot to do.

Happy circling!!

Cootie Catchers AKA fortune Tellers

How many of you remember making cootie catchers or fortune tellers as a kid?  I remember making a ton of them!  I decided to bring the concept into my classroom.

Identifying which equation could be used to solve a problem is a weak area.  In today's lesson, I had the kids answer 10 multiple choice problems out of Motivation Math.  All of the problems I selected asked them to find which equation could be used to solve the problem.  Here is what I had them do:

• Read the problem
• Analyze the problem (find the facts)
• Solve the problem
• Write the equation (the solution to the problem) 
• If necessary, use a calculator and determine if the equation selected is reasonable.
• Create another problem in which the same equations would need to be used.

The last part created a lot of discussion with many of the kids.  We went through this example as a class.
I can make $8 per hour babysitting.  If I work15 hours, which equation could be used to find t, the total amount of money earned?
a.  t = 15/8
b.  t = 8(15)
c.  t = 8/15
d.  t = 8+15
We agreed that equation b is what we would need.  I told them that they needed to create a brand new problem in which the equation, t = 8(15) would be used.  We came up with this.
There are 8 students in the class.  Each student has 15 pencils.  How many pencils are there in all?  Once we did this, a lightbulb went off for many of them.

Okay, now here is where the cootie catchers come into play.  I gave all the kids a white piece of paper in which I trimmed off the excess to make it a square (a big paper cutter is a time saver for this).
Here are the steps to make it:

• Fold the paper and create a diagonal.
• Unfold
• Fold the paper again and create the other diagonal.
• Unfold
• Take each corner and fold it where the end meets the center of the paper.  Do this for all four corners.
• Turn the paper over.
• Take each corner and fold it where the end meets the center of the paper.  Do this for all four corners.
• On the side with the squares, we put colors.  Some of the kids got creative and used highlighters, etc.
• On each of the 8 triangles, we wrote the page number and problem to one of the problems I had assigned.  I assigned 10, so they chose 8.
• Under the problem number flap, the kids wrote the equation they believe can be used to solve the problem.

We will finish this assignment up tomorrow.  I will have the kids go around the room with the cootie catcher they created, and they will play the game.  They will get to see if the equation they selected is the same as the other person.  If it is not, they will have a discussion as to why they selected the equation.

Outside part of the cootie catcher

Page number and problems listed on each triangle

Equation that can be used to solve the problem

The kids were really excited about making these.  Many of them had made them before and could not believe we were doing this in the math class.  They are anxious to go around the room tomorrow and actually play.

I am in the process of making some that can be used for measurement, formulas, etc.  That will be another post!

Happy Cootie Catching!

FACEing Math

At a math conference two years ago, I came upon the booth FACEing Math.  The concept is to use problems and create a particular face.  Problems are designed for various topics and grade levels.  You give the students a paper with the intial outline of the head and a sheet with the problems.  If the answer is a, then they draw this.  If the answer is b, then they draw that.  There is even a book without problems, so you could design your own.

The kids really enjoy doing these.  I use these in math stations, and I also leave them when a substitute will be there.  A picture of what the finished product should look like, is also included in the book.  The kids are able to look at the correct picture and see where the mistakes (if any) were made.  Although, all of the faces should somewhat resemble the same thing, they are all still different.

We lost our art class this year, so I have tried to incorporate as much drawing, coloring, etc as I can.  Even though I teach 8th grade, the majority of them love to color!  It is fun to watch them try and sketch out some of the aspects.  I show them what my sketches look like, so they don't feel so bad!  An artist I am NOT!!!

Here is an example of what the sheet with the problems looks like.

This student highlighted the choice of the answer she selected.

When I left this for the sub, I only printed the first page.  There should have been two.  I am not really sure what happened there.  If I had printed the other page, all the colors would have been the same.  Since, I left it off, the kids chose what color they wanted to use.

Here are a few of the ones that are hanging up in the hall.

As you can tell, this one was an Egyptian face.

You can find more information about using FACEing math at her website:  http://www.faceingmath.com/facingmath/Main.html

I hope you are able to incorporate this into your classroom.  The kids really do enjoy it!

Happy FACEing!

Math Creations with Chick Peas

Here is a fun activity I do with my kids when we review over 3d figures.  I like to do this before we get into surface area and volume.  Let's face it!  If they don't know which figure they are dealing with then the surface area and volume will more than likely be wrong!

Chick Pea Activity

Materials Needed:  Chick Peas, toothpicks, baggies or cups

Preparation:  You can purchase the peas in a can or dry in a bag like black eye peas.

The ones in the bag are much easier!  Just let them soak in water overnight.  The ones in a can stink!  Drain the water out, and they are ready to use.  Before each class, put about 1/3 cup of peas in a cup or baggie with some toothpicks.  Keep extras at the front for the kids to come up and replenish if necessary.

Objective:  Create 3d figures using chick peas and toothpicks.  The peas are used for the vertices of the figure, and the toothpicks are connected through the pea.  The students are able to create the figure, using a hands-on activity.  They are also able to make connections between the prism and pyramid. 

Create: 

Square Pyramid

Rectangular prism (remember a cube is still a prism)

Triangular Pyramid

Triangular Prism

After creating the four figures, have the students:

List the similarities and differences (at least two) between:

Triangular Pyramid and Square Pyramid

            Triangular Pyramid and Triangular Prism

Triangular Prism and Square Pyramid

Triangular Prism and \Rectangular Prism

Rectangular Prism and Square Pyramid

Rectangular Prism and Triangular Pyramid

Identify the shapes of the faces for each

Identify the shapes of the base(s) for each

Calculate the number of edges for each

Calculate the number of vertices for each

Extension:  If time allows, have the students create a different pyramid and prism.  Tell them they must be able to correctly name the figure.

Conclusion:  Discuss some of the similarities and differences as a class.  Make sure you go over the shapes of the faces for the pyramids and prisms.  Remind them how each figure is named for the shape of the base.  Also, the base is not necessarily what the figure is sitting on. 

Clean up:  For less mess, have the students dismantle the figures.  Place the toothpicks and unused peas back in the cup, and the used chick peas can be thrown away.  Keep a couple to use for examples.  Some kids will want to take at least one of the creations with them!

Arrays can do so much

Do you use Arrays in the math class?  We do!  With arrays, you are able to accomplish so much:

• Identify dimensions
• label fractional parts
• Calculate Perimeter
• Calculate Area
• Create Equivalent fractions with scale factor
• Model the fractional parts
• Compute the four basic operations

By the time I get the kids in 8th grade, we review over the arrays, but they are already familiar with them. I do not make the kids model every time they do a fraction computation, but it is a tool in their toolbelt.  Some of the kids do model each time because they see it that way.  Fractions are tough!  Modeling with arrays offer so much.

You can model with arrays with graph paper or you could use the color tiles.  In 8th grade, I focus on graph paper. 

The most difficult fraction computation is division!  We do not teach the short cut of "keep it, change it, flip it!"  We teach them how to divide the fractions.  The arrays do allow for a model to be created in which the kids get a better understanding as to what division of fractions means.  When you teach the shortcut, the understanding is lost!

Arrays are a great tool to arm the kids with. 

Happy Modeling!

Project Based Learning

I think projects are a great way to learn and understand a concept.  Projects usually take a little time, and they allow the students to take ownership. 

This week, I am at the CAMT math conference in Houston, TX.  On Thursday, a colleague and I will be presenting a session on Projects in the classroom.  Throughout the years, we have come across some fun and interesting projects.  Under my "Goodies" tab, I have the links to my wikis which goes into detail for the projects I use.  Some projects have been borrowed and tweaked, and I have created some projects. 

This past year, I brought BizMovie into my classroom.  This is a great project that includes business, finance, and technology.  The kids create a movie production company.  They applied for the various positions in the company.  They must keep up with all the financial aspects that go along with running a business.  They use kerpoof to design an animated commercial and movie.  At the end of the project, I had my kids present their marketing campaign to other students.  We opened the box office, and the kids were able to "purchase" tickets to the movies they wanted to see.  We then showed the movies, and the kids were able to see if they made a good purchase.  It was GREAT!  The kids learned so much.  It is also great for team work.  A few groups wanted to fire a member for them not doing their job.  How much closer to real life can you get?  I will definitely be doing this project again!  Here are couple of links to the commercial and movie.

commercial:  http://www.kerpoof.com/#/view?s=2gs11buIrgo5cjs45M00-d-429ce4-x2

movie:  http://www.kerpoof.com/#/view?s=2gs11buIrgo5cjo44w00-d-b625ef-x2

I really need another project that deals with 3d measurement.  Currently, I have the kids create a commercial that deals with a 3d figrure.  The commercial can either be selling their product (whatever they turn the figure into), or a movie promo like "Attack of the killer cubes".  They must discuss how to calculate volume and surface area of the figure.  I like this project, but I also need one in which the kids are actually using a 3d figure.  I am thinking about this:

• the kids are assigned a 3d figure (the figures we discuss will all be assigned)
• the object will be to create the figure using the materials I provide
• Each material will have a different $ amount, and they will be allowed to be spend x amount of money
• they will be assessed on durability, creativity, and the object must meet the criteria for the 3d figure
• to add technology, they will do a write up on the class wiki that details the volume and surface area of the figure.  They will then create a qr code that will link to the wiki, and the qr code will be displayed with the figure. 

I am still working it out, and I haven't typed up the project info yet.  Hopefully, I will work the kinks out.

I think a project over similar figures would also be good.  Proportions are a difficult concept to grasp. 

For this, we could use life-size models of different objects, and the kids could scale it down or up and then create the object.  I am trying this out in my Percent Baseball digital menu board under "build it". 

Last year, I came across an activity using CSI math (this activity can be found at my middle school math wiki).  The kids created a perpetrator.  They had to draw it to scale.  This worked out pretty good, but I think an additional project would be good to help with similar figures. 

I think projects are great, and I am constantly adding to my project list.  Not all projects need to take a long time to complete.  I incorporate individual and partner projects in my class.  Hopefully, I will pick up some more projects at CAMT.  Maybe some of you did, as well!

Middle School Centers???

I am thinking about doing centers in my math room this coming year.  I am not sure how this is going to work out with middle school kids, but I am anxious to see.  I am going to design my centers around the big topic we are discussing.  Last year, I was able to have a laptop cart in my room, so we had some laptops for the kids to use.  They were used every single day.  I have a class wiki, and they are responsible for doing different things on the wiki.  I am hoping that I get laptops again!  Oops....I got off track a little bit.  Back to the centers!

I am wanting to get away from regular book work.  Now, I have always incorporated projects and activities, but there are some good problems in certain books/workbooks.  I have never believed that kids need to do 100 problems over a certain topic.  If they cannot do 10, then 100 is not beneficial, and if they can do 10, then they can probably do 100. Anyways, I have always chosen certain problems from the book.  I have learned that I must give my kids a time limit.  I set a timer, and at the end of the allotted time, we go over the problems (so they get instant feedback).

Now that I have set up the background, here is what I was thinking for the criteria for my centers.

• I want to have 5-10 different stations (depending on how many laptops are set up).  
• They will rotate through the stations in groups of three (I am big on partner work).
• They will get 15-20  minutes per station (different topics may require more time).
• This could take two-three days to complete the Centers.
• The kids will have a log sheet for all the centers.  Since we are just practicing skill, I am not really concerned with a certain grade for each activity.  Many of the centers will really be focused on practice and a daily grade for participating and completing.

Here are the centers I want.  Again, this will be focused on a particular topic.

• Smartboard activity over the topic
• One-two laptops used for a wiki discussion over the topic.  This may in the form of a discussion post or a project on the wiki in which students will build upon what the other students have already written.
• Word problems (5-10) on cards.  This center will involve a hot dot pen in which the student will use the pen to select the answer.  The pen will tell them if the answer is correct or incorrect.  
• Skill/word problems (10-20) on cards.  One student will read the question and be in charge of the answer.  The other two will have buzzers.  They will buzz in when they know the answer.
• Two-three laptops set up for online practice from qtopia and similar sites.
• Book work (I firmly believe paper and pencil is still crucial).  5-10 problems from a book or workbook.

All of the centers will provide instant feedback.  At the end of the Centers, I will give a short quiz to assess and see if any reteaching needs to occur.  These are my thoughts so far.  The first big topic we go through is Proportions.  This includes: scale factor, similar figures, and proportional relationships.  Hopefully it will come together.  It all sounds great in my head!