Mathematics Through Play Book Study Part 1

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Welcome to week 1 of our Math Through Play Book Study!  I love seeing my students excited about learning math and engaged in doing mathematics.  I love seeing how young children work on big math ideas through play and am so excited to be reading this book.  After being just a few chapters into this book, I already have a few ideas for how I can incorporate more math into my own children's play as well as set things up at school to have more math play time.  

Here is the posting schedule for this book study:

Sunday March 29th: Chapters 1-3

Sunday April 5th: Chapters 4&5

Sunday April 12th: Chapters 6&7

Sunday April 19th: Chapters 8&9

If you are just joining us, head to this post for more details! 

Chapter 1: Play and Problem Solving

Kids need to play.  Some of my favorite activities in the classroom where I really feel like kids are engaged and learning math while solving problems have came from play based situations.  It is truly amazing how much STEM work can come out of play.  This chapter helped me think about how play connects with other areas of math learning to give kids a solid foundation.  "This connection making between images, words and symbols at an early stage will often help children avoid misconceptions at a later stage."  I love this idea about play laying a strong mathematical foundation.  Misconceptions and fragmented knowledge are two of the biggest thorns in my side when I work with older children and if some of this can be avoided by providing more play opportunities when they are younger than I am all for it.  This chapter helped me think about how I can ask more open ended questions, provide open ended resources, give kids more time to talk and embrace the opportunity when kids want to extend what they are working on.  These ideas are obviously great for play based math but I think they will also help me when working with older students.  

Chapter 2: Creating and Using a Mathematical Environment

More than anything this chapter makes me want to go out and create an outdoor classroom.  This would be a huge undertaking but I think it would be amazing!  I obviously can't do this all at once but it has really motivated me to look into some possibilities and think about how I can get kids outside more.  I need to do more research!  

As ambitious as creating an outdoor classroom sounds, there were many ideas from this chapter that I feel I could add easily and immediately.   There are several things I could do in many grades to create a more mathematically rich environment.  Many of these things I already have but I need to think about how to make some of them easily accessible to students.  

- Books about numbers

- Construction kits: block, Legos, Lincoln logs, etc. 

- Bead strings

- Measuring and weighing tools

- Number tracks

- Tactile number cards (looking for ideas for these!)

- A display area to display student graphics

- Blank booklets for students to make their own math books or to record their own thinking

- Washing line (loved these ideas!  Thinking about where this could fit!)

- Add some math components to the writing center: sheets of large numerals, sheets of math vocab, plastic shapes and rulers.

Creative Recording and Mathematical Graphics

I think this is an area where I need some improvement.  I have come a long way from being the worksheet queen and spend a lot less time coping papers for kids.  I have even had kids making their own record sheets for games and such the last few years.  However, I think there is still much for me to learn about helping kids record or capture their math thinking in their own way.  I love the idea of recording math being similar to mental math on paper.  I have found having the talk with kids about math class drawing being different from art class drawing to be important.  The suggestions in this chapter gave me some good ideas about how I can be more intentional in letting kids record their own ideas.  I definitely need to get working on a way to display children's math graphics!  

What were your thoughts on this week's reading?  Do you know of any great resources on creating an outdoor classroom?  What about ideas for tactile numbers or displays of children's math graphics!  Can't wait to read your thoughts!

Monday Math Literature: Fun with Balloons and Counting

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Every once in a while I will stumble upon a math literature book that my students and I can not get enough of.  Today I want to tell you about one of our new favorite books,  Zero, Zilch, Nada Counting to None

This book is about a young rabbit who gets a job in a balloon factory.  He is asked to blow up 100 balloons for a party.  He has a set of 10 racks with 10 slots in each rack to put the balloons in.  He blows up all 100 balloons and then tries counting to make sure there really are 100.  He gets ideas from other animals that are stopping by to drop things off.  He counts by 10's, 5's, 2's, and 1's.  The only problem is that he can't seem to keep track of which ones have already been counted.  He decides that the solution to this problem will be to pop each balloon as it as counted.  This leads to a hilarious conclusion and a great opportunity to talk with your students about how to organize and keep track when counting objects.  It is also a great chance to discuss and practice skip counting.  Even if I did nothing with the rich opportunities to discuss math in this book, I would still read it to students because it is an amazing story.  This book pairs well with counting and estimating routines and would be a great introduction or follow up to these ideas.  

If your students need more work on skip counting you might want to check out these other blog posts:

10 Ways to Work on Counting by 2

Count by 2 Math Literature

Teaching Math with You Tube Videos: Counting

Also our next book study starts this coming Sunday!  Head over to this post to read more about it!

Monday Math Literature: Fun with Math at Home

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Welcome to this week's edition of Monday Math Literature!  I have been having so much fun the last few weeks playing with the recipes and math ideas in this great book.  

Eat Your Math Homework

This book includes 7 different recipes that kids and adults can make together.  There are ideas for incorporating math before, during and after cooking.  As part of my quest to get kids playing more I have found a lot of great ideas in this book.

The lesson I want to share with you is called Milk and Tangram Cookies.  It was done with a few upper elementary students who are a bit behind and then some younger students joined us at the end.  Check it out!

These students have had some experience with fractions.  I was concerned about some of their conceptual understanding of fractions and wanted to take this opportunity to review a few big ideas.  Many of the ingredients in the recipe called for half a cup.  I decided to only put out the quarter and eighth cup measuring cups and the half teaspoon and half tablespoon.  This contrives it a bit and helps students review and think about what they know about fraction equivalencies.   

The students read the directions and started thinking about how they were going to use the measuring tools I gave them and still follow the recipe.  

Practicing with measuring, fractions and more. 

It takes two quarter cups to make a half cup. 

We were supposed to bake these in a square pan.  I didn't have a square pan but have several circular and rectangular ones.  The kids problem solved and decided to go with a circular pan.  The directions include a traceable template to help you create tangrams but we just eyeballed it.  Notice how we had to make a square first.  This led to a great discussion about polygons versus non polygons.  

We pre-cut the cookies before putting them in the oven. I highly recommend this because if you make a mistake on the dough, it is easy to fix.  Much of the lines disappear as they bake, but you can still see where they were and it is an easy step to re-cut along the old lines.   

As the cookies were baking, I took a suggestion from the book and gave the kids a paper set of tangrams.  They were highly interested in them knowing that their cookies were going to be like this momentarily.  They spent some time creating different designs as well as composing and decomposing shapes.  

One of several designs.  This one sparked a great discussion about the different angles in the shapes and led to us sorting the shapes by the types of angles they have.  The kids were so impressed that all the triangles had equivalent angles despite being different in size.  Also the parallelogram sparked a great debate about angle size and obtuse versus acute angles.  

We had so much fun exploring more with the cookies that I didn't get to take a lot of pictures.  We repeated some of the ideas we found on the paper tangrams and extended some ideas about angles.  Then we had two primary students join us and the older kids did a little lesson with them on the number of sizes and angles the names of the shapes.  

I love this book and can't wait to try out the last few recipes.  I had the BEST TIME doing the lesson on fraction chips and I think it is an excellent match for any kids who need some more practice or motivation with fractions.  I love having fun with my students and giving them a memorable experience to anchor their math understanding.  This book has been an excellent addition and I am excited about using it in other ways.  It can easily be adapted for older and younger students but I would say the best grade range is 2-5.

If you teach other subjects besides math, there are other books in this series that look just as engaging.

In other Math Maniac news, you can now find me on Instagram.  I will be doing a giveaway over there over the next few days and would love for you to check it out!  My best selling QR code scavenger hunts will be up for grabs so head over to enter!

Also, my newest book study will be starting soon.  We will be looking more at math play.  Head to this blog post to check out all the details.  

New Book Study Announcement

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The countdown to spring is on!  This is the time of year that I can't wait to get outside and dig in the dirt.  I also like to re-commit myself to professional reading because it motivates me to be my best as the school year comes to a close.  I have not done much professional reading since finishing up the Number Talks books study and I can't wait to dig into a few more good books.  With the emphasis this time of year on standardized testing, I wanted to pick something to keep teachers minds off of testing.  I have done some exploring with math play and am interested in reading more about play based learning.  So I have decided for my next book study, I will be digging into Mathematics Through Play in the Early Years.  

Each Sunday, I will be posting my thoughts about a few of the chapters and I would love to have you join me.  You can participate by leaving a comment here or writing your own blog post and linking it in the comments section.  

Here is the posting schedule

Sunday March 29th: Chapters 1-3

Sunday April 5th: Chapters 4&5

Sunday April 12th: Chapters 6&7

Sunday April 19th: Chapters 8&9

Grab a copy of the book and finish your school year strong!  

Fly on the Math Teacher's Wall Squashing Fraction Misconceptions

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I love fractions!  Today I am linking up with some of the best math bloggers out there to bring you the Fly on the Math Teacher's Wall Blog hop.  Last time, we talked about place value and this time we are talking about squashing fraction misconceptions.  One of the biggest misconceptions I had when I first started teaching is that finding a common denominator is the only way to compare fractions.  Boy was I wrong.  After reading a great teaching book and listening to my students share their invented strategies, my misconception has been cleared up.  Today I am going to share with you 5 different strategies for comparing fractions.  

Common Denominators

Yes, you can compare fractions with common denominators.  However, this isn't always the most efficient way of doing things and it involves a lot of steps and a lot of calculation which means there is a lot of places where you can make mistakes.  The good news is, it works every single time and sometimes you just can't figure out which fraction is larger without it.  

Common Numerators

The long lost twin of common denominators, finding a common numerator is just like finding a common denominator.  However, sometimes the numerators already are the same and sometimes it can be more efficient to calculate a common numerator than a common denominator depending on the numbers in the problem. 

The numerators already match!  Use this to help you compare the fractions instead of finding a common denominator.  

Comparing these two fractions is tricky because they are very close together! Finding a common denominator would work but look how much easier it is to find a common numerator for this problem because the numerators are much friendlier numbers to work with then the denominators.  Most kids will instantly know the LCM of 3 and 5 but I bet they won't know the LCM of 17 and 27! 

Comparing to a Benchmark

This is a great strategy that can be very efficient on the right numbers.  If your fractions are close to a benchmark number like 0. 1/2 or 1, this can be so quick and easy!  

These two fractions are great to compare using a benchmark because one of them is a bit less than 1 and the other is a bit more.  

One of these fractions is a little more than one half and the other is a little less than one half.  This makes them easy to compare using a benchmark!

Draw a Model

Model drawing is so important in the development of fraction understanding.  I certainly don't want to leave my fifth graders in a place where they need to draw a model every single time they need to compare fractions but it is an excellent stepping stone and one that should not be skipped.  When students draw models, they develop some big ideas about fractions and help make a visual model in their head that they can refer to later if needed.  I spend a lot of time teaching good model drawing in second and third grade.  There are many ways to draw models, but I like to focus on using rectangles because they are easy to partition and if you partition them all in one direction, it is a quick jump from a rectangle model to using a number line.  

The farther apart two fractions are, the more reliable model drawing can be.  When the fractions get very close together, small model drawing inefficiencies can lead to students getting the wrong answer or concluding that the fractions are equal when they are now.  The student who can use a rectangular model like this one is just one step away from really understanding number lines.  

This student used a number line to compare these fractions.  Notice that if the fractions were really close together, this model drawing might not work.  It also takes some time to set up and draw accurately.  Partitioning into equal pieces is definitely a conversation to have with students as you work on model drawing.  I introduce the number line model in grade 3.  

Unit Fraction Reasoning 

Unit fraction reasoning is often one of the first strategies to develop.  It starts in first grade when you are partitioning rectangles into halves and quarters and a student notices that one half is bigger than one quarter.  It develops from there and as kids get more comfortable with using unit fractions it can lead to some great ideas when comparing fractions.  

This student used the fact that each of these fractions is missing a pieces that is a unit fraction to help him figure out which fraction was bigger.  Don't let the writing fool you about the amount of time the student took to figure this out.  He just looked at them and knew each was missing one piece and the one missing the smaller pieces would be the bigger fraction.  The writing was done during the sharing of strategies and is an attempt to capture his thinking for the other kids to see.  

If you want to see what strategies your students have for comparing fractions, here is a quick little worksheet that will give you an idea of some of the strategies your students have.  The numbers were chosen strategically to illicit a range of strategies.  

Ready to learn more about squashing misconceptions?  Head on over to Beyond Traditional Math to read more about the importance of the whole! 

Great Teaching Books: Fluency Through Flexibility

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I like to read.  Yes, I have spent the last 9 years teaching just math but I still love reading.  I may not like teaching reading as much as I like teaching math but to the shock of my students, I do know how to read.  They seriously look at me like I have 2 heads when I make a comment about helping them with a reading assignment.  I read whatever I can get my hands on.  To the shock of many of my colleagues, I read a lot of teaching books.  I read at least 1 teaching book per month and often will be in the middle of 2 or 3 at a time.  I love hearing what other teachers are doing in their classrooms and how they are applying educational research to improve their teaching practices.  I have so enjoyed doing book studies on my blog (like Children's Math and Number Talks) and love how they get me to slow down and interact with other teachers about what I am reading.  However, there is just no way I can keep up with my own reading doing book studies, so I will also be sharing with you some of my favorite teaching books as I read them and a few of my past favorites. (Like A Focus on Fractions) 

Today, I want to share with you a book I read a few weeks ago.  I have been working on a blog post about fluency with addition and subtraction facts since October.  Now, usually I just write a blog post and hit publish, but this one has been bothering me.  I feel like talking about fluency can be a loaded conversation.  In my post, I am trying to convey the importance of fluency and kids thinking flexibility while not making it all about speed.  Yes, figuring out facts quickly is important but focusing on developing thinking strategies is so much more important than pushing speed so much that your students just become fast counters.  We need to move them beyond counting strategies.  I have been struggling with these words for months but this book has essentially said what I was trying to say in my blog post and really conveyed that being fluent requires number sense.  If you are a primary teacher or a teacher who has always wondered why some kids seem to develop addition and subtraction fact fluency while others can't seem to get there than this book is for you. 

Fluency Through Flexibility: How to Build Number Sense

This book really follows the idea of Cognitively Guided Instruction.  The activities in each section are based on children sharing and comparing ideas and strategies about how they got they answers.  Many of these activities are also easy to adapt to a Number Talk.  All of the activities are designed with best practices in mind and all blacklines are included.  Busy teachers will love having a set of blacklines that can be made once and used over and over again in a variety of games and activities. 

I think the most powerful part of this book is that it is such a good mix of theory and practice.  The beginning pages outline the why of teaching this way and the rest of the pages tell you how.  Unlike other books that are all theory with a few examples thrown in, this is a book that you can but in a busy teacher's hands and have them going with new and engaging activities in a matter of days.  I also think this would be an excellent book for special educators and para professionals that work with kids in math.  

As a math leader in my district, I am often asked to provide professional development in math teaching to other teachers and para educators.  This book would make an excellent resource to use in conjunction with this kind of professional development around early numeracy and additive reasoning.  It would be a great resource for everyone who works with K-2 teachers to have access to both for its theory and easy to implement classroom ideas.  

Want to grab a copy of this book?  You can head here to pick up your own.   You can also read more written by this author over on her blog, The Recovering Traditionalist.  

Number Talks Book Study: Part 6

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Welcome to the conclusion of our Number Talks book study!  After learning about number talks several years ago and implementing them in my classroom, it is great to finally read the book and have some time to reflect on how number talks have changed the way I teach math.  If you missed some of the previous posts, you can catch up on them below.  

Posting Schedule
Part 1: January 11th Chapters 1 & 2
Part 2: January 18th Chapter 3
Part 3: January 25th Chapter 4
Part 4: February 1st: Chapters 5 & 6
Part 5: February 8th: Chapters 7 & 8
Part 6: February 15th: Chapter 9





Today we will be looking at chapter 9 which wraps up some of the big ideas of number talks.

Getting Parents Involved

When I started making the transition from a teaching by telling model to a inquiry based constructivist approach, I had many parents balk and struggle to understand this "new math" their kids were learning.  I did a few things to help alleviate their fears but their is certainly more I could have done to help ease this transition for them.  If I were to do it all over again, I would do many of the things suggested in chapter 9.

- Host a school wide Family Math Night.  We have done this at my school since the very beginning and families love it.  We host it in the middle of winter when there is less going on and families are looking for something to do.  We have excellent attendance and it is such a fun night for families.  You can read more about our Family Math Night here.
- Host grade level math nights.  At our school this started with the Kindergarten teacher wanting to reach out to parents and grew up from there.  The way do it is to offer child care in the gym and bring the parents down to the classroom.  There we can take them through a number talk or let them experience some other aspect of what they might see in their students' math class.  We finish the night by bringing kids and parents back together to play some of the math games or center activities they have been working on in class.  These grade level math nights are certainly a huge commitment of time but they don't need to be done every year and offer huge rewards for the time invested.
- Get parents into the classroom!  The best way to get parents to see what their children are doing in math is to have them in the classroom for math time.  We have had parents make a weekly commitment in the past but are currently very short on classroom volunteers for math time.  This is definitely an area where my school could use some work.  If you have a good system for getting classroom volunteers in your school, I would love to hear more about it!

School Wide Number Talks

Watching the DVD let me see how powerful it is to have students in fourth or fifth grade who have had years of number talks under their belts.  The idea of number talks began in my school as a K-2 initiative and has since spread to grades 3 and 4.  Since we have had quite a bit of staff turn over in the 4-6 grade classrooms over the past 2 years, we still have more work to do incorporating number talks into upper elementary classrooms.  I really want my older students to have the same deep understanding of multiplication, division and fraction operations that they do of addition and subtraction.  I am planning on making number talk professional development a big part of the coaching part of my role in grades 4-6 next year once I know which teachers will be teaching math at those grade levels for the foreseeable future.  I am excited to have this DVD and the excellent number talks happening at the lower grade levels in my building to serve as models for good number talks.

Your Practice: A Closer Look

If you haven't had a chance to look at the reflection questions on page 333, make sure you make the time.  These 8 questions really helped me think about how number talks are going and what I need to do next.  I am going to wrap up this book study by asking you to think about reflection question #8: "Remember to start small in making shifts in your classroom practice related to number talks.  Write down one change you will make."