Triangle Inequality Theorem- CCSS 7.G.2

Chapter 10 of Carnegie Learning Course 2 (7th Grade) is Triangles.  The lesson sequence for the chapter is shown below.

• 10.1 "Triangle Sum, Exterior Angle, and Exterior Angle Inequality Theorem
• 10.2 "Constructing Triangles"
• 10.3 "Congruent Figures and Constructing Congruent Triangles"
• 10.4 "Triangle Inequality Theorem"

I won't even get into it with you that geometry constructions tend to be the bane of my existence and that students are now doing constructions that were previously done in HS geometry.  That post if for another day.

I will tell you that I love this lesson and my students enjoyed it too.  It involves giving every student a piece of pasta and then having them randomly break it into 3 pieces.  The students then measure the three broken pieces (I had them do it in cm).  

They put the three pieces together to see if they are able to form a triangle.  There is a table they fill out and then compare their results with their table group.

We have a triangle

Another triangle

Students diligently working

Busy mathematicians dressed up for a spirit day

I then had students come up to the SMARTBoard to record their data.  I made sure to call on students who had/had not been able to form a triangle.  Students recorded the same data on that was on the SMARTBoard, other than the first data set was from their own findings.

Sharing data with the whole class

This lesson does such a good job of building students conceptual understanding of the triangle inequality theorem.  They also are also able to figure out the triangle inequality theorem by looking at the data in the table.  They realize that the lengths of any two sides of a triangle must be greater than the third side.

The lessons ends with practice problems where students determine whether it's possible to form a triangle with a given set of side lengths and when given two side lengths, what can the conclude about the third length.

Prior to using Carnegie curriculum I used to model the triangle inequality theorem by cutting straws different lengths and then having student determine when they formed a triangle.

Slicing Three-Dimensional Figures- CC 7.G.3

CCSS 7.G.3 Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane section of right rectangular prisms and right rectangular pyramids.

I was really pleased with how the Carnegie Curriculum addressed this standard in the collaborative classroom text.  They devoted three lessons  to this standard:  slicing through a cube, slicing through right rectangular prisms, slicing through right rectangular pyramids.  My accelerated students really enjoyed these lessons and did a fabulous job working in their collaborative groups.

The lessons involved students making 3-d figures out of clay (although I used play doh).  Play doh worked very well and was easy to clean up and keep track of (each group got a different color play doh so there was no confusion).  I used the itty bitty containers that people give out for TOT sometimes.  This worked perfectly.  Each group had a container of play doh, a plastic knife, and dental floss.  Most groups preferred to use the plastic knife for slicing, but I did have a couple groups use the dental floss.  Students had to take turns shaping and slicing the figures.

This hand on lesson is something any teacher could easily put together.  I think it is helpful for students to see what those cross-sections look like because it can be difficult for students to sketch them.

My youngest son was not happy to see this play doh heading to school with me

Everything fit in a gallon ziplock

 Day 1 I forgot my camera so I have no photos.  Boo!  But really you can get the idea from the photos I took Days 2 and 3.  The students really enjoyed this hands on lesson and no matter how old they are, they still love play doh!

Slicing Day 2

More slicing Day 2

More slicing Day 2

 I only took one took two photos of them working the third day because I was so busy going around to each group and checking their answers with them.  Nice pyramid don't you think?

Day 3

Each lesson had a graphic organizer at the end where students had to cut out and match up the name of the cross-sectional shape with the appropriate diagram and verbal description of the way the figure was sliced.  I only took a photo of the graphic organizer the last day.  This one was done fairly neatly.  I tell you some of them lose those cutting skills they work so hard to develop in the primary grades by the time they hit 7th grade.  :)

Day 3 Graphic Organizer

I will admit that last year when I saw CCSS 7.G.3 I was kind of dreading it and thought it would be a pain and mess.  I am happy to say that the lessons were well developed and a perfect lead in to the lessons on surface area and volume (CCSS7.G.6)

Curriculum Planning

With our new math implementation we are fortunate enough to have some full planning days to put together our Carnegie units.  The planning days definitely help and are greatly appreciated, but we still spend hours upon hours putting everything together on top of what we are able to accomplish in an eight hour planning day and during our PLC meetings.

This coming Monday is a planning day where another 7th grade math teacher (who is absolutely awesome getting all our assessments and assignments together) will out as much as we can for our next five chapters (we need to get through two chapters for sure).  Our math interventionist will be working with us in the afternoon so I am excited to have her on board to help us create some interventions in advance, rather than after the fact, like we tend to do.

We are lucky that we have Carnegie Learning a common core aligned math curriculum so we definitely have an overabundance of resources available.  As I am sure many of you will agree, teachers rarely are able to use the assignments and assessments as they are, that text companies provide.  This creates a lot of extra planning time to put everything together the way it works best for our students.  Again, I am quite lucky in that my colleague Bill, does almost all of that.  Our biggest task, is pulling together the best of what Carnegie has offered us for teaching the CCSS to our 7th graders.

I thought I would share with you the items that I list on our Google Doc as we do our Module Unit Planning so we can keep track of what everyone is responsible for and by what date they need to have it completed (well in a perfect world anyway).


Module Unit Planning:  A Module consists of two to three chapters

• Chapter Quiz Review/AK (Answer Key)
• Chapter Quiz/AK
• Chapter Quiz Retake/AK
• Chapter Quiz Correctives (students complete after the quiz)/AK
• Module Test Review/AK (This covers 2-3 Chapters)
• Module Test/AK
• Module Test Retake/AK
• Module Test Correctives (students complete after the test)/AK
• Assignments/AK
• Mathia Pacing/Assessment Guide
• Mathia Small Group Lesson
• Mathia Notes/Study Guides
• Warm-Ups/AK
• Exit Slips/AK
• Mini Lessons/Small Group Instruction from exit slip information
• Learning Goals/Assessment Correlation
• Cross-Referencing Assessment Questions to Lessons
• Lesson Plans
• Lessons on SMARTboard software
• Answers Keys to project on SMARTBoard
• Word Wall Vocabulary 
• Math Focus Wall Posters
• Foldables/Notesheets
• Anchor Charts
• Core Plus Activities
• Learning Stations Activities
• Tech Enrichment/Learning Support

Its easy to see why unit planning feels overwhelming when there are so many different items that need to be either created completely by a teacher or modified.  That does not even include having to work through the lessons ourselves and do all the problems.  That also takes quite a bit of time and we do not even spend any of our planning time doing that.  We all do that on our own time.

We also have two components to our curriculum: collaborative classrooms lessons out of the text and Mathia personalized learning software.  We are definitely focusing much more on planning for the collaborative classroom this first year.  

The items highlighted in green are the things we have been doing and planning all year.  Those are the things we always try to accomplish on our planning days.  The items listed in pink are things that we have done at least a few times throughout the year, but need to be more consistent with them.  The other 7th grade math teachers have their own versions of word walls and math focus walls so those two items I really put on the list to remind myself to keep up with planning them in advance.

I have found a few foldables online that I have used with my students and shared with my colleagues.  I would really like to increase my use of foldables and start using anchor charts in my classroom.  I know my students would benefit greatly from both.  I just always seem to run out of time to do this justice as I would like.

We have a 45 min class every other day called Core Plus and this quarter I have Enrichment on A Days and Intervention on B Days.  I would like to be more purposeful in creating lessons to use on my Intervention day so there will perhaps be less need for retakes, a girl can dream, right?!  I also would like to create some fun and engaging learning stations to use on both my CP Enrichment and Intervention days.  I have some great resources for that.  I just need to find the time to put the stations together.

I have a laptop cart always available to me because the students work on Mathia software 1-2 days a week (as well as during CP or Homebase at the end of the day).  I would like to start using the technology more on my non Mathia days.  Maybe doing some exit slips on a Google Form or trying out Socrative.  Please share your favorite ideas of how you would use laptops in your classroom, if you have unlimited access.  I would love to try some engaging technology because right not they really just do Mathia.

One thing that I feel is a non-negotiable going forward is using exit slips (or whatever formative assessment preferred) to get instant feedback on students that can be used for targeted small group remediation or instruction.  I did that last week and considered it a huge success.  I just have to make the time to create the exit slips and mini-lessons that go with them.

How do you go about planning your math units?  Isn't it crazy how much more is involved these days than just opening up the book and teaching a lesson and then giving homework and a quiz or test?  Next year our district is going to Standards Based Grading so that will again really change the way we do things.  I tend to think it will end up being easier in the long run as we focus more on Power Standards.  I feel right now we are trying to assess nearly everything we teach and it becomes overwhelming for both us and the students.  I would love to hear any ideas or suggestions you have for anything relating to unit planning (how you are able to do it all), luckily I am on a team so we are able to split up the work.

Math Focus Wall Photos-Updated

I wanted to share some recent photos I took of my Math Focus Wall.  I apologize for not posting these photos sooner as I feel I have been promising to post them since school started, but it really has been a busy year thus far.  Thank goodness for break and some time for me to blog!

The evolution of my Math Focus Wall has been a work in progress from my creative thought process and planning last school year to the background design seen in this post:  The First Sneak Peek  and the original design seen here: Take 1.

TA DA!  I think I am finally happy with it

After a few months of school and actually using the wall with my students I realized that I needed to have two separate sides to reflect the two different courses I teach.  On the left is the board for my accelerated math 7 class and the right side is for the three sections of math 7 I teach.  

Accelerated Math 7

Math 7

I also changed up some things to make the board work for our class needs.  It specifies the CC 

standards, lesson, topic, and student objectives for each day, as well as, the Mathia pacing expectation for that week (that is what unit students should be on in our computer program).  The poster on the top left of the board is the Mathematical Practice Standards and as you can see I still need to get my Problem Solving Strategies Posters on the top right.

You can see Math Vocabulary to the left of the Focus Wall

Creating a Math Focus Wall was a major goal of mine for the 2012-2013 school year and I am very happy with and proud of how it turned out.  It was a lot of working putting the wall up this summer.  I am also finding it very time consuming to have to create all the posters that go up and can change daily.  I use sentence strips for the goals and lesson topics, but it is easier to print out the common core standards and lesson information.  

Of course this will all be done for next year, but this year it is a ton of work.  I try to create everything in advance for the chapter so it is all ready to go.  I like to make sure the focus wall is done for the next day so I don't have to worry about it in the morning when I get to school.  I did not realize how labor intensive this all would be because we can do three to five different lessons per week and when the lesson changes so does the focus wall.  I do feel it is worth the effort to have this information prominently displayed for students around the SMARTBoard which we use daily.

What it looked like on a different day

I would be happy to answer any questions you may have about the math focus wall.  #made4math

#Made4Math A few random things

This will be a quick post to share a few things I made today.  I realized that I have had a to do list of things I have been wanting to make on the computer since school started.  As is always the case, once school starts the things I want to do/make get replaced by the day to day minutiae of keeping a classroom running:  the planning, teaching, grading, reteaching, retaking, lather, rinse, repeat.

Seating charts/class lists binder

Vocabulary for word wall and CCSS posters

Math Focus Wall Labels

I finally was able to print out some new labels for my math focus wall.  I will be posting photos of the new and improved focus wall soon.  I have changed up what it looks like from what I had at the beginning of the year as I have seen what works and what could be improved.

After school I finished up my CC standards posters for The Number System domain (we are currently working on).  I also finished writing up the vocabulary words and will laminate them and the posters tomorrow.

Goals for 2012-2013

I really need to stop this late night blogging pattern of the past couple nights.  The past two days have been jam packed with school related projects, back to school outlet mall shopping, fall baseball games, and a wonderful dinner with my parents.  Tomorrow I am heading into school to spend the day working on my classroom, as my boys are with my parents.  I am hoping to finish up my Math Focus Wall I have been busy working on and get some other things set up in my room.

This coming year is going to be a wild and crazy ride for me with implementing a new curriculum, Carnegie Learning, and a new personalized learning delivery model.  Can you say overwhelming and beyond exciting and innovative?  I am so energized for this coming school year, but will feel better once I feel I have a handle on how this will all work.

This year my classroom goals will really be driven by the initiatives that my district has chosen to undertake, including Personalized Learning Model with Carnegie Learning Curriculum, Standards Based Grading District Committee and Lesson Study Facilitation.

Stop:

• Spending so many late evenings at school.  Last year I felt that I was NEVER home to help my two younger sons with their homework  due to all the after school meetings I had and trying to keep up with everything in my classroom.   I really need to change this year.  My goal is to pick one night a week to stay late at school, two max.  I need to make sure I remember that my own kids need to come first and they need guidance on their own homework.  Trying to keep working mommy guilt at bay as many of you know all too well.
• Wasting time an energy on things I cannot control.  I must repeat the Serenity Prayer to myself on a daily basis and really remember why it is I chose to be a teacher.  I also need to keep in mind that everything I do needs to be for and about my students.
• Spending time on things that do not directly impact my goal achievement.  It is so easy to get sidetracked on the day to day classroom minutiae and lose sight of what is really important.

Continue:

• Co-teaching.  Last year the sped teacher and I really became more effective working together after taking a co-teaching class together, but due to my having a student teacher 4th quarter things we weren't really co-teaching at the end of the year.  I am really excited because we will be co-teaching both afternoon math classes this year.  Looking forward to taking our co-teaching to the next level!
• Using learning stations for review and differentiation in the classroom.  Also using them more in my Core Plus class.
• Working with my 7th grade math team during PLC time to implement our new program to fidelity and working together on compacting and assessment.

Start:

• Researching and figuring out the best way to do conferencing with my students.  This will be an integral part of our personalized learning model.
• Consistently doing some form of daily review with my students.  I started off strong with warm-ups last year, but then kind of fizzled out at the end of the year.
• Really focusing on some of the things I learned during my Guided Math Book Study this summer.  I am really excited about my Math Focus Wall and really making my classroom a numeracy rich environment for my students this year.
• Implementing Carnegie with fidelity and really focusing on the Common Core and Standards for Mathematical Practice.  I am so lucky to have a great curriculum to help me implement common core the way it is meant to be.

#myfavfriday My favorite Math Teaching Resource Books

I am jumping in to the twitter verse with today's post.  I am not sure if my hashtag worked so if you are here from twitter be kind.  I am a twitter infant.  :)  Today I would like to share with you some of my favorite math teacher resource books.  For some reason in the past few years, maybe it's due to my mental maturity (not old age I tell you) or the fact that the older I get the more of a math nerd I become, but whatever the reason, I have spent some serious change lately on buying math related resource books.  This hopefully redeems me for reading the Shades of Grey Trilogy in a matter of days.

1)  Challenge Math by Ed Zaccaro.  I purchased this book six years ago, after I was lucky enough to hear Ed speak at the National Gifted and Talented Conference in Chicago.  If you ever have the chance to hear Ed speak I highly recommend it.  The book's chapters are arranged by math topics, so there is a chapter on fractions, one on ratio and proportions, and so on.  One of the things I love the most about his book is that each topic has three levels of problems: one, two, and Einstein.  This makes it easy to differentiate in your classroom.  It would be an excellent resource for your problem solving repertoire.

Source: Amazon.com

2)  Becoming a Problem Solving Genius by Ed Zaccaro.  I am a super fan of Ed Zaccaro and purchased some of his other books a few years ago.  I love this book because it actually teaches different problem solving techniques you can use.  For example there is a chapter on venn diagrams and how to use them as a problem solving strategy.  This would be another great addition to your problem solving toolbox.

Source: Amazon.com

3)  Accessible Mathematics, 10 Instructional Shifts That Raise Student Achievement by Steven Leinwald.  This book was required reading last summer as part of our District K-12 Math Review Committee.  I would recommend this book to anyone who teaches math!

Source: Amazon.com

4) Mathematics Station Activities for Common Core State Standards published by Walch Education.  I previously posted how I used this book for Ratio and Proportional Reasoning Learning Stations.  This book is divided by common core domains.  This book is a great resource if you do stations.

Source: Amazon.com

5)  Elementary and Middle School Mathematics, Teaching Developmentally by John A. Van de Walle, Karen S. Karp, and Jennifer M. Bay-Williams.  This is the most expensive book I have ever purchased.  I read so much about this on blogs last summer.  I believe this is sometimes used as a college textbook for future math teachers.  I have perused this book and know it will be an excellent resources for me as I delve more into the common core standards.  This book was written before common core, but it does reference it in the 8th Edition I purchased.  This will be my go to resource as I work to build conceptual understanding and procedural fluency in my math students.

Source: Amazon.com

6)  Guided Math by Laney Sammons.  I participated in an online  Guided Math Book Study with several other teachers this summer.  I really want to implement some of the facets of guided math into my classroom this year.  I loved the book study and have a to do list a mile long of things I need to do to get ready for guided math this school year.

Source: Amazon.com

I would love to hear from all of you what your favorite math resource books are!  We are leaving Door County today and heading to Green Bay for the Packers Family Night and swimming at the Tundra Lodge Waterpark.  Happy Friday to you!

Ratio and Proportional Reasoning

I cannot believe how hard it is to keep up with blogging.  We have been in a curriculum review process this school year and it has made my school life busier than I could have ever imagined.  The good news is that we are meeting today to choose a curriculum and then we can finally move forward in the planning phase.

About a month ago I was home for a day with a sick boy.  I ended up spending the day doing laundry and working on planning some activities on Ratio and Proportional Reasoning aligned to the common core.

Great resource book!

I have been reading the book Ratios, Proportions, & Proportional Reasoning Grades 6-8 for a few weeks in order to better understand the depth of what is expected with the new CCSS in math.  I have also been spending time going through the Progressions for the CCSS in math, draft for 6-7 Ratios and Proportional Relationships. I have found this document to be a wealth of information for this particular CC Domain.

My binder for Ratios and Proportional Reasoning

You can check out my previous post on Learning Stations for Ratios and Proportional Reasoning.  I highly recommend the book featured in that post for some great CC aligned learning station activities.  For those of you who follow me on Pinterest I think I will be adding a board on Ratio and Proportional Reasoning so I can pin specific activities for this CC domain.  In this previous post I shared a Ratio and Proportional Reasoning Foldabe I did with students.