Fly on the Math Teacher's Wall: Buzz Worthy Back to School Blog Hop

     There is just something about back to school time that makes everything seem so fresh and new.  I love getting to know new students and seeing how much my old students have grown and changed.  We have been back in action for 3 days and I think I had forgotten how tired the first week of school makes me!  My classroom is ready, I am well on my way to establishing routines with my students and hopefully I will be back to blogging regularly!  Today I am linking up with my math blogger friends to bring you tips for getting your math class off to a great start!  I want to share with you some of the ways I set up my classroom and some of the routines I teach to help increase math talk in my classroom.  

Wait Time

One of the best things you can do to increase the math talk in your classroom is to be very aware of your wait time.  When you ask a question or listen to a student's response, how many seconds are you giving yourself and your students before you start talking again?  Some studies have shown wait time in the average classroom is about 1.5 seconds.  Not a lot of thinking can happen that fast!  Being aware of your wait time and practicing it from the first day of school will make you and your students much  more comfortable and you will notice an increase in the number of participants.  You might also notice that taking a few extra seconds to think about what a student says before responding or hearing from another student will increase your awareness of what students understand and are able to do.  I personally aim for a wait time of 10 seconds.  Don't be afraid to watch the clock or count to yourself when you are first starting out!

Re-voicing

When you re-voice a students' idea, it give your students a chance to hear the idea again and the student who shared it a chance to clarify their thinking.  When you have students re-voice each other's ideas, you give them the opportunity to take another person's perspective and hold them accountable for listening to each other.  Re-voicing can also slow the conversation down a bit so that kids can focus on the big ideas and those who require more think time a chance to clarify their thoughts.  

Room Set Up

When you are setting up your room for the back to school season or rearranging it for a fresh outlook as the school year continues, think about the spaces your students will be in for math talk.  If you really want kids to be talking to each other, make sure the way your room is set up reflects this.  I like having options for kids to talk at tables as well as space on the floor where we can do our number talks and other math discussions.   If you are seeing that kids will answer questions and engage with you but not with each other, I highly recommend sitting kids in a circle and removing yourself to the outside of the circle to get things going.  Once kids are more used to talking to each other and not just talking to you, I don't find this as necessary but it really helps when they are first starting out.  Also, remember to think about your wait time.  Kids will never have a chance to respond to other students if you are always jumping right in with a comment!

Pair Share 

If I had to pick a favorite strategy for getting kids talking about math, pair sharing would be my number one.  Giving kids a chance to talk to one or two other kids about how they solved a problem or what they were thinking gives them a chance to rehearse sharing their ideas and refine their plan for sharing their strategy.  Pair share can also help kids practice listening to another person's ideas and comparing them to their own.  I also like to hold kids accountable for listening to others so I often have them share their partner's strategy instead of their own when we come back to a whole group discussion.

Provide Focus Vocabulary

One of the reasons you want kids talking about math is to get them extra practice using math vocabulary.  I like using vocab cards to help kids focus on new words.  I will often use a magnet to attach focus words to the white board when we are discussing them.  If you are looking for vocabulary cards for grades K-8, check out this awesome (and free!) resource.  My vocabulary cards have the word and picture on the front and we write the definition on the back as a class.  That way it is in their words but it is there if they need it.  

I hope these ideas will help you get started setting up math talk in your classroom.  If you are looking for further reading on this subject, you should check out Talk Moves: a Teacher's Guide for Using Classroom Discussion in Math.  This book is full of ideas for getting kids talking across all kinds of math settings.  Great for grades K-6.  It also includes a DVD with video clips so you can see many of the ideas in action.  

Head over to The Research Based Classroom to check out more ideas for setting up your math class for back to school! 

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Monday Made It: Scrabble Math Bulletin Board Freebie

I have 3 more weeks of summer vacation but I have already been back in the classroom getting things ready!   When you have 3 small kids at home you have to take every second you can to stop by the classroom and get stuff done.  I have moved to a new and much larger room this year and have inherited a bunch of stuff because we are down a few classrooms this year as our enrollment has declined.  I spent a full day in the classroom last week and managed to pull together a few things. 

My big accomplishment for this week was creating and assembling a great bulletin board.  I have been thinking about different board games I love and how to use them in my classroom decor.  I have always loved scrabble but have never found a way to use it in a math classroom.  One night on TPT, I stumbled upon a Scrabble font and decided to create my own math vocab bulletin board out of scrabble looking tiles.  Here it is:

You can head to my TPT store and grab this set for FREE!  I would love if you leave feedback! 

I made the scrabble letters I needed with this great font from Darcy Baldwin Fonts.   Most of her fonts are free for personal use but you can also purchase commercial licences if you want to use them in a product like I did.  

The border for this bulletin board is part of an old Uno deck I found in at a yard sale this summer.  I love the way it incorporates numbers and is so colorful.  

I can't wait to show this bulletin board off to my students and have been brainstorming ways to make it interactive.  Here is what I have come up with so far:

What word has the greatest points value?

Which word is worth the least amount of points?

Find a word that you have never heard before and look it up in the math dictionary. 

Any other ideas?  

Head over to 4th Grade Frolics for more #MondayMadeIt ideas! 

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Beyond Invert and Multiply Book Study Part 4

We have made it to our fourth and final week of this book study!  It has been a great summer learning about fractions and I am excited to be back in the classroom putting what I have learned to good use.  If you have missed previous posts, you can check them out by clicking on the links below

July 8th Part 1: What is a Fraction?

July 15th Part 2: Addition and Subtraction with Fractions
July 22nd Part 3: Multiplication and Division with Fractions

July 29th Part 4: Discourse with Fractions  

Chapter 8 Developing Awareness: Six Strategies for Fostering Student Talk About Fractions

This section of the book steps away from the ideas about developing fraction reasoning and instead focuses on how to structure your class so that you can provide opportunities for kids to talk about fractions.  A lot of the strategies presented in this section are good teaching strategies that are also very beneficial classroom practices in general.  

Strategy 1: Using Strategic Tasks

If you want your students to build conceptual knowledge about fractions rather than just learning the steps of a formalized procedure, you need to make sure you are giving them tasks that have something worth talking about.  They might be open ended, able to be solved in multiple ways and will make your students think.  Selecting a task that they can use some prior knowledge to build up from is also a good idea.  I think the ability to pick strategic tasks comes with time and practice.  If the task you pick isn't working the way you want it to, try something else!

Strategy 2: Creating Records of Thinking

Having students record their thinking or ideas in some way is a great way to share their thinking with classmates and to help organize their thoughts.  I used to have kids copy down their thinking on an overhead transparency or on the board when it was time to share ideas.  Now that I have a document camera in every room, this has gotten so much easier to share what kids are thinking.  Some kids might need help recording their thinking when they are first starting out but it is a great strategy for building student talk.

Strategy 3: Building Visual Models

Get great math tools into your students hands!  Fraction manipulatives such as fraction strips, or Cuisenaire rods as well as number lines are a great way to build conceptual understanding and engage kids in a hands on way.  

Strategy 4: Reasoning with Benchmarks and the Number Line

I love how using benchmarks helps kids think about their calculations and the reasonableness of their answers.  Thinking about how close a number is to 1/2 or 1 can really help kids see if their answers make sense.  This is estimation at its finest.  

Strategy 5: Using Talk Moves

Out of all the talk moves described in this chapter, wait time was the one I needed to work on the most.  I was one of those teachers who would ask a question and expect an immediate response.  Since purposefully working on my wait time, I have noticed a huge difference in the number of kids who are ready to participate.  For a lot more about talk moves, check out this book.  

Strategy 6: Asking Students to Turn and Talk

This is one of my favorite strategies as a teacher and as a learner.  When I have a chance to talk to someone about my ideas, it helps me organize them, develop them and be better able to articulate my thinking.  I find the same is true for my students and I use turn and talk many times each day.  

How do you incorporate student talk in your fraction lessons?

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Monday Made It: Teacher Essentials Kit

Back to school fever seems to have gripped the nation!  I know some schools go back next week but I have 3 more blissful weeks left!  However, I am already headed into back to school mode and spent this morning shopping and creating.  I have many more made its to accomplish before back to school but today I want to share with you one I managed to get done today.  When you are done head over to 4th Grade Frolics for a lot of back to school inspiration.  

I was cruising around the dollar store this morning getting my back to school organizational essentials.  I was thinking about all the things I needed to get done at home and in my classroom before I have even less time.  One thing I had been thinking about was creating an emergency box of essentials to keep in my classroom.  I have had various supplies stuffed into my filing cabinet for years but I really wanted to do this in a more organized fashion.  Because I have already dropped a lot of my own cash on classroom essentials, I wanted to keep this low budget.  I picked all of this stuff up at the Dollar Tree and the grand total was $10 and about 10 minutes of time.

Here is the list of essentials I included:

- Plastic box to hold it all

- Mini sewing kit

- Tylenol

- Tums

- Cough drops

- Travel toothbrush & toothpaste

- Mini hairbrush & hair ties

- Sugar free gum

- 2 kinds of hair clips

- Mini deodorant 

This covers the essentials for me!  I will be set when I leave the house without brushing my hair or when I finish my coffee on the way to work and really need to brush my teeth.  It will also be great to have a sewing kit because I have been known to rip off buttons or seams while at work.  I also but in the essentials for when I am not feeling well.  I am feeling much more prepared for back to school!  This would also make an excellent gift for a teacher friend.  I made one for a friend who is starting her first teaching job.  It includes the same things I put in mine, and I just tied a little bow around it for presentation.  

What are you working on this week?  

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Beyond Invert and Multiply Book Study Part 3

Welcome to week 3 of our Beyond Invert and Multiply book study!  Last week, we looked at decomposing numbers to help with fraction addition and examined the 6 mistakes kids often make when subtracting fractions and mixed numbers.  That post got lost in cyber space for a few days but is back in action now so if you missed it, be sure to check it out! 

Here is the posting schedule. 

July 8th Part 1: What is a Fraction?

July 15th Part 2: Addition and Subtraction with Fractions
July 22nd Part 3: Multiplication and Division with Fractions
July 29th Part 4: Discourse with Fractions

Chapter 5 Developing Awareness: Multiplication and Division Problem Types

Several years ago when reading the Common Core standards, I stumbled upon a few tables in the glossary that I found so interesting.  One was the table about the different problem types for addition and subtraction word problems that we talked about 2 weeks ago and the other was the table for the problem types for multiplication and division that is featured in this week's reading.  Here is the table they are referring to: 

If you need to see a larger or easy to print version of this table, check it out here! 

I printed this table and tacked it to my planning bulletin board and began making over my math class.  I started at the fact level before moving up to multi digit multiplication and division and finally fractions and decimals.  Now my students get to experience all 9 problem types at each level.  Some problem types are harder than others especially if your students have never been exposed to that type of problem.  You can read more about how I address these problem types here. I encourage all teachers to take a good look at their curriculum and see what problem types are not being represented.  Make sure your fraction multiplication and division units contain a diverse group of problems!

Chapter 6 Making Sense: Multiplication with Fractions 

This chapter got me excited for teaching fractions this fall!  I know I will be working with an intervention group of sixth graders right off this fall and there were so many ideas in here that made me think about this group.  I still have 31 days before I am due back at school but this book is really making me think about heading back!

I loved the term "constructive struggling" used at the beginning of the chapter.  Apparently this term is used in the book Faster Isn't Smarter which looks like a book I will definitely have to check out!  I have seen some of students' best ideas come from constructive struggling yet it can be so hard for teachers to let kids struggle.  I used to be that teacher who couldn't stand to see kids struggle and would jump in way to soon.  This is something I worked on with peer conferencing a few years back and I still like to check in with colleagues when we are co-teaching about when we should jump in and when we should leave kids with a little disequilibrium.  

The research around how kids learn fraction multiplication always interests me and it seems each time I read a new fraction book, I get a new take on how to teach it better.  I really liked the ideas presented about teaching fraction multiplication (and multiplication in general) from a measurement standpoint.  I always struggle to help kids understand how finding a fraction of a fraction translates to multiplication because I have never been able to connect it to whole number multiplication.  On page 9, this paragraph made me stop in my tracks: "Given the problem 4 X 3, if one considers a multi-unit length of 4, iterated three times or a multi-unit length of 3 iterated four times, one arrives at 12.  This could be thought of as "four iterations of length 3" or "three iterations of length 4" or the shorter "four of 3" or "three of 4."" There is my example of how the word of can be used in whole number multiplication.  Right there!  I can't wait to see how this will help me this year!

Next week we will be wrapping up this book study and I will be getting busy preparing for back to school!  Look for a lot more blog posts again in August as I tackle the beginning of the year things and get back to teaching! 

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Beyond Invert and Multiply Book Study Part 2

Welcome to week 2 of our Beyond Invert and Multiply book study!  Last week, we looked at some research around fractions and dove into the 12 different problem types for addition and subtraction word problems.  This week we will be taking a closer look at fraction addition and subtraction.  

Here is the posting schedule. 

July 8th Part 1: What is a Fraction?

July 15th Part 2: Addition and Subtraction with Fractions
July 22nd Part 3: Multiplication and Division with Fractions
July 29th Part 4: Discourse with Fractions

Chapter 3: Making Sense: Addition with Fractions

Fraction addition used to be my enemy.  I remember struggling with fraction addition more than I struggled with any other topic in elementary school math.  I learned it in such a rote and procedural way and it didn't make a lot of sense to me.  Now when I think back to that experience and I read some of the research on fraction addition, I see myself in the classic cases of how not to teach fractions.  I was that kid who really didn't know what estimating was or how to do it and I had no sense of the magnitude of fractions.  In elementary school I would have really struggled with the problem they presented on page 42; "Estimate the answer to 12/13 + 7/8.  You will not have time to solve the problem using pencil and paper."   This is presented in a multiple choice format with the choices being 1, 2, 19, 21 and I don't know.  I would have been in the 76% of kids who could not answer this question correctly.

So how do I keep my students from following in my footsteps?  First I make sure they have a strong foundation in part to whole reasoning, equivalence and magnitude.  If they are not there yet with these foundational ideas about fractions, I give pull them for booster groups, do additional whole class lessons or meet with them during Guided Math time.  If you are looking for ideas for helping kids develop these foundational understandings, check out Beyond Pizzas and Pies or A Focus on Fractions.

It struck me when reading this chapter how similar fraction addition is to whole number addition.  We often treat it as a brand new topic but I think we miss out on connecting it to what kids already know about whole number addition.  The properties all still hold true and some of the strategies kids developed when learning basic addition can also help them when learning fraction addition.  I feel like the idea of decomposing numbers to make friendly tens and hundreds is something we are doing very well at my school.  However, I don't think that we are using this skill quite as well with fractions.  The video clips from lesson 3.4 really opened my mind to some new ideas to try this year.


My other big take away from this chapter was activity 3.6.  As someone who was terrible at estimating and didn't really get it, this activity would have really helped me out.  I also like that it could be used for any operation with any number.  This is definitely a routine that is getting added to my math classes.  This is the activity where you give students a problem and have them tell you all they can about the answer.  I particularly liked the sentence starters for those students who are stuck:

• The answer will be more than ______ because _________
• The answer will be less than ______  because _________
• The answer will be between _______ and ________ because ________

Chapter 4 Making Sense: Subtraction with Fractions

This chapter really got me thinking about the mistakes kids make when subtracting fractions.  It seems like it as the inverse of addition, subtraction should be very similar but it always seems to trip up a lot more kids.  Here are examples of some of the most common mistakes for fraction subtraction. 

• Seeing the numerators and denominators as separate whole numbers and subtracting across both of them.  
  

• Finding a common denominator but not making the corresponding change to the numerator.
  

• When presented with mixed number subtraction, ignoring the fractional part and just subtracting the whole numbers or vice versa. 
  

• For a problem where the minuend is a whole number and the subtrahend is a fraction, thinking the whole number has the same denominator as the fraction.

• The borrowing issues! On the left the student does 4 - 2 but then ignores the fact that is should be 2/4 - 3/4 and switches them around.  On the right, the student borrows a whole and turns it into 10/4. 
  
• Context problems!  When writing word problems, there is a thin line between a fraction subtraction a fraction multiplication problem.  I like to give my students this little printable pictured below, have them cut the stories apart on the thin black lines and have them sort them according to which operation they could use to solve them.  Many students think they are the same at first glance.  Look closely!  A few words changed make for a big difference in the operation and approach for solving the problem.  If you want to try these with your students, you can grab them from Google Drive.  

  

  Grab this freebie here!  

  What mistakes do you see students making with fraction subtraction?  Leave your response in the comments section below or head over to my Facebook page and let us know what you think!

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Beyond Invert and Multiply Book Study Part 1

Welcome to the first installment of our Beyond Invert and Multiply book study.  You can order this book at Math Solutions or on Amazon.  There is a great video introduction to this book here if you want to learn more about it.  

This book is written about fraction operations and is a follow up to Beyond Pizza and Pies.  I have received several emails and Facebook messages from folks asking which book they should get if they have to pick just one.  My answer to that is that if you teach grades 2-3, go with Beyond Pizzas and Pies.  If you teach grades 4 and up you REALLY should have both.  If your students lack the foundation knowledge covered in Beyond Pizzas and Pies, many of the activities suggested in Beyond Invert and Multiply will be a struggle for your students.  

Chapter 1: Fractions As Numbers

I love the way this chapter starts off with the classroom scenario of the human number line.  This is a great way to introduce kids to big ideas about number lines and doing it in a big way like this makes it very memorable.  I feel like kids really get the idea of equal spacing when doing a human number line and I think this is a great way to review what number lines are before moving into working with fractions on a number line.

The chapter lays out these 5 foundational understandings about fractions that kids need in order to compute with understanding.  These are the things that you will find your students tripping up on when learning fraction operations.  These are the things that are worth devoting some class time to before jumping into fraction operations.  They are all big conceptual ideas and together form the foundation for fraction understanding. 

• Fractions are numbers and follow the same rules and properties as other rational numbers. 
• The unit fraction is the building block of fractions.
• Fractions can be decomposed and recomposed in infinite ways.
• Equivalent fractions represent different ways of naming the same value.
• All rational numbers can be expressed as fractions in the form a/b, where b does not equal 0. 

The other thing that really struck me in this chapter was how important number lines are.  Over and over again you see how they can help kids see fractions as numbers.  The activities and DVD clips in this section do such a great job capturing the power of the number line.  It is hard to believe that less than 10 years ago, I had never used a number line for fractions in my own mathematics or with my students.  

Chapter 2: Addition and Subtraction with Fractions

This chapter dives headfirst into the research on problem types for addition and subtraction word problems.  These problem types are used with whole numbers and should also be used with fractions. If you use the Common Core for your standards, these problem types are detailed in the glossary.  I wish this table was right in the standards themselves because many people miss it.  I have included a snapshot below!  If it is out of focus or hard for you to read, you can click here to see a better copy.  

If your students have never experienced these problems with whole numbers, I would be hesitant to introduce them with fractions.  I think it is worth the time to go back and do some of these problem types with whole numbers before expecting kids to do them with fractions.  When my school first started paying attention to all the different problem types, we started with the primary students on single digits, moved up to double digit computation and then finally used the different problem types with fractions.

Which problem type is this?  Feel free to peek at the table above! Grab these cards here:) 

How would your students do on this one?  Would they use subtraction or a missing addend? Which problem type is this? 

I think there is a lot of value in sitting down and writing some of each of the problem types for your students to use.  It can be challenging at first, but gets much easier with time.  If you want to explore some problems that have already been written, you can check these out!
Addition and Subtraction Facts
Double Digit Addition and Subtraction
Fraction Addition and Subtraction

There was also a chapter on the different problem types in Children's Mathematics.  You can read my thoughts on that here!

Your turn!  Please tell us how you are doing with fractions in the comments below and what you thought about this week's reading.  Has your school addressed the different problem types for addition and subtraction?  How are your students doing at developing the 5 foundational understandings for fractions?  

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