Activities to Encourage Collaboration #1: Surface Area and Volume of a Sand Castle!

In a time and society where students spend more time communication through text messages, Facebook, Twitter, Instagram and 14 other social media platforms that I cannot even begin to name, I find an ever increasing need to get my students talking to each other fact to face.  As a result I have been on a quest this year to implement as many collaborative activities as I can.   I have used many of them throughout this school year and have had some amazing results that include increased communication, retention of information, assessments grades and more positive attitudes (overall)!   Throughout the summer I will be sharing some of my favorites, some of my other favorite math teacher-authors and many others so that hopefully they can become your favorites too!

Today I am excited to share with you my Surface Area and Volume of a Sand Castle activity!  As we were finishing our three-dimensional figures unit in Geometry I was looking for a really good way to a) get the students talking and b) show them how the different figures can share dimensions to build the structures that we see on a daily basis.  Since I do not possess architectural skills and summer is upon us I decided to build a Sand Castle (as "Do You Want To Build A Snowman" is running through my head).  I started with a goal of including as
many of the main solids that I could and managed to include prisms, cylinders, cones, pyramids and even a hemisphere!  I worked to have the solids share bases, sides and dimensions whenever possible.  This is what I came up with!            
I also came up with a second version that has the figure divided into 11 smaller figures to help struggling students visualize a path to follow to solve it.  Additionally, this helps students to organize their work so that you and they can identify an error if they make one.  (I did not, however, hand this out to begin with as I wanted to see what they would do with it first!)


Before implementing this as partner/group collaboration piece I sat down and created a list of questions that I could ask as I walked around the room to point students in the right direction, get them thinking, communicating and solving without actually giving them the answer.  Some of the questions that I came up with:

1)  Are there any surfaces that aren't exposed?  Alternatively - are there any surfaces that shouldn't be used in surface area?

2)  Have you thought about breaking any of the larger figures into smaller ones?

3)  How are you arranging your work so that you can go back and check it later?

4)  Are there any dimensions that you don't have?  How can you find them?

5)  Do the unused surfaces from the surface area get used for volume?

FREE!!!! 

Finally the day arrived to implement this and I must say, it went AMAZINGLY!  After my students got over the expected moans and groans and sat down to start working on it, they had fun with it.  I heard great discussion, collaboration and genuinely helping each other understand instead of just giving each other the answer.  I set forth the "rule" that their final answers had to be within ten of mine (to account for rounding error) and that whoever was the closest won a prize (extra credit, candy, excusing of an assignment, ect.).  My students quickly turned it into a competition and worked hard to earn the prize.  I ended up with multiple students hitting my answer down to almost the decimal point - which is great! :)  Based on the feedback I can honestly say that they enjoyed it and felt that it really reinforced the concepts we have been learning in this unit!  

I have put the entire activity, including a multi-page answer key that highlights each piece and how to find their surface area and volume up in my teacherspayteachers store.  You can pick it for FREE here :)  I would LOVE to hear how you use it and implement it! Please comment below!

Why Collaborative Work Needs to Occur as Often as Possible

Looking back on my own schooling experiences I cannot clearly identify situations where we worked  together.  I cannot remember my teachers telling us to "turn to the person next to you and share your answer" or coming into the classroom and working in groups.  After talking to a few people who I went to school with I realized that I can't remember it because it rarely happened (except for labs in science class).  Knowing what I know now about the power of collaborative communication, this makes me incredibly sad.  I wonder how my own school struggles would have been diminished had I had the chance to work with others.  I know that for many of us, collaborative work and communication causes fear.  I addressed the ways that I handle this by setting up the classroom for collaboration from day one in a recent post (available here).  What I want to address today is not the HOW of collaboration but the WHY.

Reason one:  It helps to aid with classroom management.  I know, the first thought that goes through the mind is how in the world is it possible that getting them to talk will help with classroom management?  Hear me out, I promise it will make sense.  Teenagers have difficulty sitting still and listening for long periods of time, this is a proven fact.  Just watch your students for a few minutes and see what happens.  They start to shift in their seats, they doodle, they try to sneak a peek at their phone and/or they start talking to the people near them.  By taking collaboration breaks in a lesson such as "turn to your neighbor and work out this problem" or "collaborate with your elbow partners to restate ______________" you are giving them an outlet for that nervous energy.  It helps them to focus on what you are teaching and has the added benefit of identifying misconceptions about what you are teaching if they exist.

Reason two:  Teenagers are social creatures who live in a world where information and communication is literally at their fingertips at all times.  As teachers who desire to meet our students in the ways that they best learn, retain and reference information we have to move outside of our comfort zones and meet our students how they learn best.  Today that means collaboration, communication, sharing of ideas and talking with classmates as often as possible.  Students need to work together to clarify information in their own minds.  I have even seen some "social media" templates that work perfectly to get at the information on the students' levels.

Reason three:  We need to teach our students how to work cohesively with all types of people.    We are preparing these students for the "real world" (I really dislike that term) beyond high school whether it is college, the military or the workforce.  Regardless of what path they take, there will be people that they have to be able to effectively communicate with.  As educators, it is our responsibility and privilege to give them the opportunities to practice and refine these skills.

Reason four:  Studies show that information is retained most effectively when it is shared with others. I saw this graphic online and it stuck itself in my brain.  This is why teachers need to to embrace collaboration.   We teach in a world of high stakes testing, constant competition, and we have to do what it takes to set our students up for success.  The majority of teachers get entrenched (and often trained) in the top part - passive teach methods.  In the past, it worked for the most part.  Looking, however, at the 5% (which yes, may be a little low) of information retained from lecture compared to the 50% for group discussion and the 90% (which yes, might be a little high) from teaching others I'm left with one thought - how can we not try???  If there is even a chance (and research shows there is) that group collaboration can help with retention, learning and connections between concepts we have to try.

Reason five:  If students don't communicate, you have no idea what they know and don't know.  I have had many students in my career who have difficulty showing their knowledge on paper but when you talk to them they can explain it fantastically!  Additionally, by talking to their classmates students will often clarify their own understanding.  In my experience, students can use the same words that you as a teacher use, but it sounds completely different to their classmates and can make a great deal of sense.  

Whatever the reason, I challenge you to try it.  Get your students talking and see what happens, you just might be surprised! :)

Super Spectacular Secondary Mathletes Giveaway!

A few months ago a group of teacher-authors from TeachersPayTeachers connected with each other and formed a collaborative group named the Secondary Mathletes. You all have been so supportive of all of us that it is time for us to give back to you! We are pleased to announce that we have come together to create a giveaway as a thank you for all of your support. Two lucky winners will receive a bundle of wonderful activities, games and resources that you can use in the first few weeks of school!  Each teacher-author has provided a short description of their resource and you can find links to their TpT stores as well as to the product itself!  Please enter the giveaway using the rafflecopter at the bottom!  The drawing will be open until July 18th!

1) From the SecondaryMathShop. I have included my Geometry Beginning Concepts Vocabulary Matching Activity. This activity is designed to serve a few purposes including reinforcing the foundational vocabulary from geometry, help students who are struggling with the vocabulary to visualize the terms and to help students review for an upcoming test. Included you will find four types of cards to match - - a term, a diagram, a name (label) and a definition - - as well as answer sheet! There are so many ways to use this activity!

2) From Hodges Herald. I have included my Multiplying and Dividing Fractions Bingo. Use this game to get your students back into mathematical thinking.  Students get to chose how to set up their Bingo boards which helps them to practice organization as well as how to write fractions.  A fun way to review previously learned concepts. This bingo game using Task Cards. Great for small groups or whole class. Self Correcting and loads of fun!

3) From Lindsay Perro. I have included my Back to School Math Activities for Middle School. We all know summer passes quickly! Some of your students will return to school eager and ready to learn, others will be hesitant to get back in the swing of things and will still be holding on to their summer! This packet includes 9 questionnaires, ice breakers and activities for back to school. 

4) From Live, Love, Math. I have included my Integer Operations Seating Cards. This file includes a set of 30 seating cards (4 to a page). Each card has an order of operations problem involving integers which the student will solve in order to find his/her seat in the classroom. I have my desks numbered 1-30 and this is how I set up my seating chart at the beginning of the year or anytime I want to change seats. Each problem has a unique solution, so it is a good discussion starter when you see two students trying to sit in the same seat or in this case, trying to find a negative seat! All answers are positive.These problems do include negative numbers as well as exponents and all four operations. Some are harder than others, so you can give some of the easier ones to kiddos who haven't mastered the skill yet in order to give them a confidence boost. There are also two blank cards in case you have a class larger than 30.

5) From Scaffolded Math and Science. I have included my Interactive Notebook: Solving Algebra Equations. This download includes 8 pocket flippables showing the solving process of 8 different equations. Once put together, each pocket holds a series of different-sized cards that align to show the steps of solving. On the bottoms of each card (out of sight when the cards are all in place) are explanations for each step. Students can add each card to its pocket while reading why each step was taken to solve the equation. 

6) From Teaching High School Math. I have included my Algebra - Line Them Up - Solving Two Step Equations. In this activity, students are each given a task card with a solving two step equations problem and a QR Code. Students are given a couple of minutes to solve their problem. Then they are invited to get up and
arrange themselves in order of their solutions from smallest to largest. After they think they have themselves in order, the teacher walks by and scans their QR Codes. The teacher announces the solution on each card. If students are lined up correctly, they win! This is a great activity for the beginning of school because it gives students a chance to interact in a non-threatening way. It gives you the opportunity to see who your leaders will be. This activity would probably best be used in a Geometry class where all students have already learned to solve equations.

7)  From All Things Algebra.  I have included my Order of Operations, Evaluating Expressions, One-Step Equations Review.  Rolling review activities are perfect way to have students work together, yet work on their own problems. Students love to roll the dice to choose the problems, and are amazed that two different problems can have the exact same answer. The matching answers also provide a means of self checking. This particular rolling review activity contains order of operations, evaluating expressions, and one-step equations. This would make a terrific back to school review to brush up on some basic skills!

8) From MissMathDork. I have included my How to be a Good Mathematician - 14 colorful posters for your classroom! So many students don't know what it means to be a Good Mathematicians These 14 bright and colorful posters serve as a constant reminder! Included in this product:

*14 bright and colorful posters
*14 colorful, but more printer friendly posters - these also print beautifully in black and white without losing the details
*A handout for your students to keep close at hand to remind them of the qualities of a Good Mathematician. (The handout is available in 4 colors, and one printer friendly version)



9) From To the Square Inch - Kate Bing Coners. I have included my Scientific Notation Guided notes and Task Cards CCS: 8.EE.A.4. This product is designed to help students learn, apply and practice the concept of Scientific Notation. I have included in this product:
*Scientific Notation Notes
*Scientific Notation to Standard Form Notes
*Products and Quotients in Scientific Notation Notes
*20 Scientific Notation Task Cards
*Recording Sheet
*Science Connection Worksheet

10) From Lessons withe Coffee. I have included my Print and Go Interactive Math Bulletin Board {Boggle}. This edition of the P&G Bulletin Boards is Boggle. Students are given instructions and a worksheet to write down answers on. Once this wall is set up, not only do you have a beautiful wall, but you also have a conversation starter. For this particular game students are to pick two numbers and simply add or subtract them. YOU CHOOSE what numbers to use. I have decimals on mine, but I will change to fractions after one week. The idea is that you change the numbers each week. This could be money, whole numbers, integers, absolute values, square roots, or exponents. HECK! Throw in some expressions with variables to add! This set includes:
**BOGGLE header – KG Wake Me Up**
**Directions Letters – KG Cold Coffee (My Current favorite font!)
**Student Direction Bubbles
**16 Star bursts with white box for writing numbers
**“Boggle Work Sheet” File folder sign
**Boggle Work Sheet

We are giving away a bundle to two  lucky winners so enter below!!! :)

a Rafflecopter giveaway

Follower Celebration Giveaway!

I logged onto my TeachersPayTeachers seller page this morning to find that I have hit 400 followers!  I am so excited that I've decided to go a quick giveaway of my 8 Standards for Mathematical Practice Posters!  If you win you'll be able to choose from one of the three designs!

Floral

Polka Dot

Gray

Please enter below!  :)

a Rafflecopter giveaway

"Noise" In A Classroom - It's Not Always A Bad Thing!

When I first starting teaching (oh so many years ago!), I wanted a quiet classroom.  Almost to the level of hearing a pin drop.  Why?  Simple.  A quiet classroom, in my mind, was a sign of great classroom management.  It meant that my students were engaged, working and I was in control of the room.  I dreaded the question "can we work together" because working together leads to noise, noise leads to chaos and chaos lead to bad classroom management.  While I was right about chaos equaling bad management, I have learned that I was very wrong about the rest.  Noise and chaos are not the same thing.

A few years ago, as I got more comfortable as a teacher, as a part of the staff and with my subject matter I started relaxing a little and exploring other classroom structures.  I found that when a teacher structures it correctly and with strong expectations in place from the beginning, student collaboration can be one of the most powerful tools a teacher can use!  The key, I have found, is to start small at the beginning of a year or a term, before jumping into stations or collaborations that require a great deal of movement around the classroom.  I would describe the progression like this:

Step one:  Establish clear communication with your students about what your expectations are when they are talking to each other, participating in a classroom discussion or engaging in a group activity.  The clearer you are about what you expect, the easier it is to control the classroom and the students without requiring silence.  

Step two:  Start with small discussion pieces that are short and structured.  I will ask students to turn to their neighbor and complete an example problem together and then pick a random pair to come to the board to do it for the class.  This serves several purposes:

      ** It sets a time limit and destination (solving the problem), 
      ** It gives them clear direction for their talking
      ** It allows me to rotate and hear what they are talking about
      ** It gives me insight into whether they understand what we are doing (and I can correct it with questioning immediately)
      ** It involves all students since they don't know who will be called to go to the front board.

Partner Worksheet

Fold It Up

A great resource that I have found that helps to transition from this step to the next is made by Teaching High School Math called "Algebra Solving Equations Partner Worksheets".  In this activity students are paired up.  Each student works their problems individually, then they compare answers (which are the same even though they did different equations!) and talk through them if their answers don't match!  

I also really like a resource that I found by Live Love Math called "Fold It Up - Multistep Equations Practice"  It has students create a foldable and solve problems at the same time!  This is great for getting students talking and to break out of the mold of stand and deliver for note-taking.  

Step three:  Do an activity that requires small movement and group collaboration.  Task cards or investigation activities are fantastic for this!  I like using task cards because they can be used so many ways.  You can have the students pass the task cards from pair to pair or between small groups.  Additionally, you can set-up the task cards at stations and have groups of students rotate from station to station.  I also like investigation activities at this point because they require interaction, collaboration and hands-on learning but don't have to require students to be up and moving if your students aren't ready.

Congruent Triangles

Left, Right, Answer

I feature a few investigation activities in my TpT Store including Cut and Paste Activities.  One of my favorites is on Proving Triangles Congruent.  In it, students work in small groups to identify the method or methods being used to prove the triangles congruent and then cut them out and paste them under headings.  The discussion and collaboration that comes out of this is amazing.  I have included it in a money saving bundle that includes proof practice as well.

Task cards are fantastic!  I cannot say enough how much I love them!  They break concepts down into small tasks, help students to focus in on specific topics and encourage great collaboration.  One of my favorite ways to take task cards to the next level is made by 4mulafun called "Left, Right, Answer".  It turns using task cards into a game and more!  (You can check out a blog post about how to use them here.)

Step four:  This is usually the final step.  At this point your students are used to talking to each other and know what your expectations are when they do so.  They are (usually)  pretty good at keeping the noise level at a reasonable level and staying focused.  At this point you can really start having fun.  You can do activities that require large movement such as relay races, gallery walks where instead of tasks being at centers, they are posted on the walls and students are in almost constant movement. Getting to this point really is my favorite place.  I LOVE to see my students up, moving, interacting, collaborating and just generally getting to experience how much fun math can be.

Relay Race

I have seen so many products on TeachersPayTeachers that work here so well.   All Things Algebra has a fantastic relay race on Solving Systems of Equations.  This activity has students checking each others work and racing to get it done. I love it because the students have to not only be able to complete their part but also have to be able to look over the work of others to make sure it is correct!   Prizes could definitely be involved.  

Miss Math Dork has relay races where students do problems and draw a part of a figure.  One of my favorites covers the topic of Circumference and Area of Circles around a circus theme!  Which even team gets the circus scene drawn first, wins!  And as we all know, middle and high school students love competition and prizes! :)  She also has templates so that you can make your own!  

No matter what pace you take it at, collaboration and communication between not only teacher and student, but student to student as well is of critical importance.  I look back at those first few years and wonder why I thought I had to have a silent class to have control of it!  What do you do to encourage collaboration and communication?  What are some of your favorite activities?

Get Out The Scissors and Glue - It's Cut and Paste Time!

There are so many skills that we strive to master as children from writing, coloring and of course using scissors. As we move through school cut and paste activities are highlighted and incorporated often because they achieve so many goals and can be used so many ways. Some of these uses can be to match two related things (i.e. the number one with the word one) or to combine various parts of things to make a whole (i.e. the parts of a snowman or a turkey). Doing such things really help students to "see" the connections.

As we move up through the school years, however, this method of teaching and enrichment really starts to fall by the wayside. We get so busy trying to prepare students for the next grade, the next test or for college that we forget that we can use other techniques besides just "stand and deliver", homework, tests and quizzes. Additionally, at the secondary level these methods are not usually highlighted, taught or to be honest, encouraged. As my years as a teacher have gone on and my students have changed so much, however, I have started to seek out new methods to make connections and help students to see how the math topics we discuss interact with each other.

Congruent Triangles

The first time I did a cut-and-paste activity I was sure that it was doomed to failure. I mean, these are high school students after all, and cutting and pasting is
an elementary task. But everything else I had tried to get my students to see the methods of proving triangles congruent were not working so I needed to try something else. I laid in bed that night brainstorming (that is, after all, where teachers do their best thinking!) and racking my brain about what I could do. I came up with a task where my students were given a set of triangles that were marked with one (or more) method(s) of proving triangles congruent and they had to sort them. I decided to go beyond sorting on a piece of paper, however, and made them actually cut them out and paste them into their categories. The students LOVED it and more FINALLY got the methods and what they look like! I was floored that something so "elementary" worked so well! 

Algebraic Proofs

Similar Triangles

I went on the create similar activities on proving triangles similar that not only had students cutting, pasting and identifying the similarity methods but also had them practicing the angle sum theorem and setting-up and solving proportions.  As we started a unit on logic and proof I devised a way to make algebraic proofs a little more interesting and again help to engage them As need arises, I'll create them on other topics as well - which is currently segment and angle addition proofs!

Domain and Range

It was with little surprise to myself then, that when my Algebra students started struggling with domain and range that I turned to my favorite website to find some resources to help them and I found the best cut-and-paste activity on domain and range. It gives students graphs, mappings and tables and asks them cut out the domain-and-range cards and paste them on to the corresponding graph/table/mapping cards!  The activity came as a part of bundle made by ScaffoldedMathandScience. It was amazing how many students not only finally "got it" but the great conversations and collaboration that occurred.


I have since picked up cut-and-paste activities by the fantastic Lindsay Perro including some on Writing Equations and Point-Slope/Slope-Intercept forms. I have also picked some up by the amazing activities from All Things Algebra on Linear Inequalities and 4 The Love Of Math on Order of Operations.  I shopped at MissMathDork  for help on Translating and Matching One - Step Equations and Factoring when a > 1.

 I love cut-and-paste activities and have many more on my wish list for future visits. I encourage you to reconsider using some traditionally elementary techniques in your secondary math classroom. You might just be surprised at the results! What are your favorite "elementary techniques" that you adapted to the secondary level?

Dear Santa...Nerd Libs Link-up with Mel and Gerdy

Mel and Gerdy

Some spectacular people named Mel and Gerdy have started a Saturday Linky Party called "Saturday Nerd Libs".  I am new to all of this but when I saw that this week's is a letter to Santa, well I just had to join in the fun! :)

Jump over to their blog (Mel and Gerdy) and join in on the fun!