Fluency with Comparing Fractions

   I spend a lot of time in grades 3-5 working on developing strategies for comparing fractions.  I have written before about the 5 strategies my students use to compare fractions.  I also shared my favorite free computer game for kids who are working on fluency with comparing simple fractions.  Today I was working with an intervention group of fifth graders and had a few minutes at the end of our session.  I knew that I needed something quick and fun so I grabbed my regular old deck of playing cards.  

   We split the deck and each flipped two cards and made a fraction.  The first card flipped became the numerator and the second card the denominator.  This allowed us to make all kinds of fractions.   The person with the largest fraction won all of the cards.  Some of our fractions were less than one, some were equal to one and some were more than 1.  It was a great way for students to practice comparing fractions.  Out of the 5 strategies for comparing fractions, I saw students use comparing to a benchmark most frequently during this game.  It was a great way to reinforce the idea of one half, one whole and improper fractions.  I also saw students using common numerators to compare fractions and quite a bit of unit fraction reasoning.  My favorite use of unit fraction reasoning was when a student used the idea of unit fractions and the distance from one to compare 10/11 and 11/12.  "They are both missing one piece.  11/12 is missing 1/12 and 10/11 is missing 1/11.  Since 11/12 is missing a smaller piece, it is greater."         

     After a bit, we changed up the game and had each person flip 2 cards, use their smallest card as the numerator and their largest card as the denominator.  This made all our fractions less than or equal to one.  It made it so that the fractions were a bit closer together and required more critical thinking.  After a few minutes playing that way, we reversed it and had folks put their higher card as the numerator and the lower one as the denominator.  This was a great way to really reinforce the improper fraction, mixed number connection.  

This entire game took under 10 minutes and was a great way to reinforce some big fraction ideas!  I love how it requires no prep and is easy to differentiate!  By pulling out some of the cards in the deck, I could make this game based on friendlier fractions which would be great for third and fourth graders.

Book Study Launch

Looking for some motivation as the school year comes to a close?  Want to try a new structure for math class this spring and/or next school year?  Join us for a 5 part book study on Minds on Mathematics: Using Math Workshop to Develop Deep Understanding.  You can read all about it here!   

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Minds on Mathematics: Math Workshop Book Study

How is your professional reading coming?  Mine has taken a big hit over the past few months.  I find I am most inspired when I am reading a really good teaching book and have been putting it on the back burner for way to long.  I have been keeping up with my monthly issues of Teaching Children Mathematics and a few of my favorite teaching blogs but haven't had my nose in a really good math book in almost 3 months!  Last year, I read 14 professional books that I can remember and this year I am at 0.  With that in mind, I am putting my professional reading on the top of my priority list.  I think the end part of the school year is a great time to read a new book and try new things.  It is the time of year I sometime struggle with finding the joy in teaching and it is easy to get bogged down in testing and administrative tasks.  Reading a good book keeps me motivated!  Chatting with all of you about what I am reading really keeps me motivated and pushes me to try what I am reading in the classroom.

I am happy to announce that I will be hosting a new book study starting in 2 weeks!  I am going to be taking a look at Minds on Mathematics: Using Math Workshop to Develop Deep Understanding in Grades 4-8.  

You can read more about the big ideas in this book here or read the introduction and chapter 1 here.  

I will be posting on Saturday mornings.  

Here is the posting schedule:

April 2: Chapters 1&2

April 9: Chapters 3&4

April 16: Chapters 5&6

April 23: Chapters 7&8

April 30: Chapters 9&10

Hope you can join me on my journey to learn more about math workshop!  

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Jelly Bean Math

The countdown to Easter (and the spring testing season) has begun!  Today, I planned a quick little project with a group of 10 second graders that was super engaging and a great way to practice estimating, counting, comparing numbers and early division concepts.

It all started with little Dixie Cups of jelly beans (I used these ones).  I put the kids in 3 groups.  I gave each group a little cup of jelly beans and posted these directions on the SMART board.

Want to try this with your students? Grab these directions from Google Drive.

Two of my groups had 3 kids in them and one group had 4 kids.  I gave the groups with 3 kids 45 jelly beans and the group with 4 kids 60 jelly beans.  

I have really been working on independence with these kids and tried my best to step back and observe and not take over!  

I saw so many things that made my math heart happy!

Kids organizing and recording estimates

One group organized all their beans by color and then decided it would be much more efficient to put them in groups of 10.  The other groups went for groups of 10 from the get go. 

When each group had figured out how much they had, it was quite easy for them to figure out how much they were off by.  These kids are so flexible and fluent with double digit subtraction! 

Dividing the jelly beans equally between each group member was fun to watch.  Each group started by giving everyone 10.  Two of the groups were convinced that there would be a leftover bean that would have to be cut up.  The rationale was that because 15 is odd, there will be a leftover.  They were surprised to find that there was none left!  The main strategy for sharing out the beans was to give each person 10 and then share them out 1 by 1 until they were gone.

This part took a total of 14 minutes (including a few minutes of eating the beans!)

Then I pulled the group together and had each group share out how many beans their group got and how many each person ended up with.  There was some outcry over one group getting 60, but it provoked an interesting discussion about how each kid ended up with 15.

I then presented them with this problem."There are 10 second graders in this room and I gave you each 15 jelly beans.  How many jelly beans did I give out?"  I gave kids a minute to think at the circle then sent them off to grab a white board and show me what they knew.  I chose this problem because last winter when I was reading Children's Mathematics I became very intentional about making sure kids have the chance to solve Base 10 Story Problems.  Since 10 kids were in this group, I thought it would be interesting to see who used base 10 knowledge to solve this problem.  I gave out 10 groups of 15 but some kids used the idea of that being the same as 15 groups of 10.  

This student used base 10 knowledge to solve the problem (and the distributive property!)

Another student who used base 10 knowledge

This student added 45+45+60.  They used the number of jelly beans each group had.

Total time for this was 25 minutes.  We had a lot of fun, the kids got some good practice and I got to learn some new things about what strategies my students have.  How are you working on estimating and counting in your classroom?  Want to try this out?  Grab the directions from Google Drive! 

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100th Day Fun!

Today was our 100th day of school!  It was a busy day and I am exhausted!  Here are few of the things we did:

100th Day Bulletin Board

I saw this idea in my son's school and instantly loved it!  Our 100th day is always around Valentines day so having kids think of 100 reasons we love our school was perfect.  I cut 100 hearts out of pink paper and glued them to a piece of chart paper.  We passed it around the school and had kids and adults write reasons they love our school.  I will definitely be doing this again next year but I will be using heart shaped post-it notes because I won't have to cut anything out and they will be a bit bigger.  The hearts were a bit on the smaller size for something I wanted to make a bulletin board out of and kids could really only fit one word.   Here were a few of my favorites math, feeling of community, caring teachers, amazing students, respect, safety, creativity and honesty.

 100th Day Swag

The primary teachers in my building are great about making 100th day hats and glasses and such with their students but I find kids of all ages love 100th day swag.  I made these fun 100th day ties and bracelets with my older students.  I myself supported a 100th day tie, several bracelets, my 100th day pin a 100th day crown and a pair of 100th day glasses that my son made with his class and let me borrow.  There is nothing like a bit of swag to make it feel like a holiday. 

100 Equations

Over the years with my grade 3-6 students we have celebrated the 100th day by writing 100 equations in whatever area we have been working on.  This year I made it more official and dressed it up with some cute clip art.  My grade 4 kids just learned the traditional algorithm for subtraction so they rolled dice to create 100 three and four digit subtraction problems.  The fifth graders just finished a unit on adding and subtracting fractions so they did some dice rolling to generate and solve 100 fraction addition and subtraction problems.  We took all 100 problems and organized them on chart paper to make a display to share in the gym. I love this idea because you can do it with any grade and with any topic.  A great way to celelbrate the 100th day and still work on your current unit.  You can grab my printables from Google drive here. 

100th Day of School Workout

I found this little routine on You Tube when I was looking for a 100th day book.  We have been working on adding more movement breaks into our day and it was fun to have a special one for the 100th day.  If you want to jump right into the workout, skip to the 2:10 mark.  We watched the whole thing through once and then did it a few more times throughout the day starting from 2:10.

Literature

I pulled out a lot of my favorite 100th day books to read to various grades today.  Here are a few of the books that were being read around our building today.

What a fun day!  What is your favorite way to celebrate the 100th day?  

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Hands on Fraction Fun

Coming into this school year, I knew that the thing my fourth graders struggled with most last year was fractions.  I remember chatting with the teacher they had for third grade math about their strengths and needs and fractions came up over and over again.  After reading Beyond Pizzas & Pies and Beyond Invert and Multiply this past summer I had plenty of new ideas and lessons to try out but I still hadn't quite figured how I wanted to kick off this unit.  This class in particular has a huge span of ability levels and experiences and I wanted everyone to be able to access this first lesson without it being to easy for half the class.  I also wanted to provide them with a hands on experience using fractions in their world.

I decided to have them in mixed ability groups exploring some fraction manipulatives.  I put a manipulative at each table along with a large piece of chart paper and a variety of markers.  Their task was to explore the materials and write down anything they noticed.  I had 4 stations each with different manipulatives.  We used fraction bars, fraction circles, cuisinare rods and measuring cups and spoons.  

I borrowed the sand table from Kindergarten and threw in a variety of measuring cups and spoons. Most of these I found this past summer at the Dollar Tree.  The dark orange cups are a set of ancient Tupperware cups which I LOVE because they have a 2/3 and a 3/4 cup.  These were so great for kids to use to explore non-unit fractions.  Kids spent lots of time filling and ordering cups.  They also liked filling and organizing the spoons.  Because the sets included 1/2 cup, 1/2 tsp and 1/2 Tbsp kids were also able to explore the idea that the size of 1/2 can change based on the whole changing.  

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As students made discoveries, I had them jot them down on chart paper.  This was a great way to record what they had discovered to share with the other students at the end of class.  We also went back to this chart paper part way through the unit to review some ideas.   

Each group had about 12 minutes at each station.  We spent the last 15 minutes of class having each student share something they learned.  We posted all the chart papers and refereed back to them as our unit progressed.  I was able to keep the sand table for the first 2 weeks of the unit and several times I had kids (especially those in my intervention group) go back to the sand table to explore something specific around the ideas we were learning.  

If you have the chance, I highly recommend starting off your fraction unit with this kind of hands on exploration.  Even if you don't have access to a sand table, putting some measuring cups and spoons in a bucket of rice or a bowl of water would also give kids a similar experience.

Looking for more ideas for teaching fractions? Check out the Fly on the Math Teacher's Wall Blog Hop to get lots of great tips!

I posted a new Valentine product today!  It is a great way to give your kiddos extra practice with double digit subtraction.

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Announcing Movin' It Math!

About 6 years ago, I came up with a game to get my students up and moving around during math class. I called it Movin' It Math and made many versions on index cards. As the years have passed and beautiful clip art and desktop publishing has gotten easier, my cards have migrated to computer generated. Over the last 11 months, I have been working on getting them in a shareable format. This weekend after many hours of putting final touches on, I have released my first 4 sets. Each set includes 40 cards, directions for Movin' It Math and 10 other activities you can use these cards for. These cards are the ones I find myself using over and over again.  We have been using them everyday in K and many days at the beginning of grade 1! 

I have many more versions of Movin' It Math that are sitting as files on my computer waiting for finishing touches.  This game as spanned my classes K-6.  I have cards for addition, subtraction, multiplication, division, finding fractors, fractions, classifying 2-D and 3-D shapes, classifying angles, geometry terms and more.  I am excited to share these with you in the coming weeks.  

Here is a peek at the rules of the game and how I have been using these cards with K&1 students over the past 2 months.  My first grade students are pretty fluent with these numbers now but I see many more months of great activities for K kids as they transition from learning numbers 1-10 to learning numbers 11-20

Movin' It Math!

The Caller

This game is a fun way to practice math for a whole class.  Before playing this game, you will want to make sure your students are familiar with these cards.  There are 40 cards in each set.  Use the representations your students are most familiar with.  You will  need one less card than the number of kids who are playing this game.  Poly spots are VERY handy for playing this game  but not required.  If you have poly spots, have kids stand with their toes on the edge of the spot but not covering the card.  If you do not have poly spots, have kids stand with one foot on either side of the card.  You will need the small numeral cards for this game.  Cut the numeral cards apart and put them in a container that your students can put their hands into. 

Toes on Spot

To play the game, choose one kid to be the caller.  This kid stands by the bucket with the small cards in it.  The rest of the kids go find a spot and put their toes on it.  When kids get to a spot, have them figure out what their card is (and keep it to themselves).  The caller reaches into the bucket, pulls out a card and says the number loudly.  If a kid is on a spot with the number that was called, they are SAFE and don’t move.  Everyone else has to move to a new spot.  The caller also goes and takes any spot.  One kid will be left without a spot.  This kid is the caller for the next round.  They go to the bucket, pull out another of the small numeral cards and say that number loudly.  Anyone who has that number on their card is SAFE and doesn’t move.  The rest of the kids need to move to a new spot and figure out what number is on their new spot.  The caller also takes a spot.   The caller is continuously changing with each round.   You can keep playing rounds in this way until your students have had enough.  There is no winner or end to this game. 

If you don't have spots....

There are many ways to adapt this game to fit the size of your class.  I have also used it with a small group but find it most successful when there are at least 5 kids.  When kids are new to this game, especially if they are young or have a hard time listening to directions, I will teach them the game in a group of 5 or so kids and we will play as a whole group after kids have had some experience on a smaller scale. 

If you find your kids are not moving around trying to find another spot because they all want to be the caller, you can adapt this game by having all kids have a spot and being the caller yourself.  This works really well for some groups of kids.  You can also use call sticks to pick a caller for each round.

Take it outside!

This game can work in the classroom if you have some open space but works really well in a gymnasium or a large open space.  This game is also great to play outside!  If you are playing it outside, having the poly spots makes it much easier.  It keeps the cards from getting muddy/dirty and a little piece of tape between the card and the spot and the wind isn’t a problem.  If you are doing it outside without poly spots, make sure there isn’t any wind!

Once kids are familiar with this game, you can switch out the cards for more challenging ones as the year goes on.  To see all the Movin’ it Math cards available, click here. (At this time, I am just getting started posting these so more will become available each week!)

The Cards That Keep Going

When I first started out, I had one way to use these cards.  I quickly learned that if only used each set of cards I made one way, I would be spending a lot of time making cards.  Because of this, these cards have evolved into something I use over and over again. In the following pictures, I will share with you some of the other ways I use these cards. 

Flash

A great way to work on subitizing!

Go Fish

A game that is easy to teach and valuable to know!  Any 2 cards that represent the same number can be a pair!

Compare

A fun way to introduce and practice using the <, > and = symbols.  We like to play with the rule that whoever has less gets to keep both cards!

Pyramid

I spent hours when I was in sixth grade playing the solitaire card game pyramid 13.  In this version of pyramid, we find pairs of cards that represent the same number.  

Flip and Tally

This years' first grade group is crazy for tallying and keeping track.  I made up this little workstation as a great way to incorporate that.  I tried it out with some K kids this week and it was a bit challenging for some but we are working on it!

Sorting Cards

This is simple but kids seem to really like it.  We pull out the numeral cards, work together to put them in order across the top of a table or in the first row of a pocket chart.  Then we pass out all the cards and kids put them where they belong.  Then we take a few minutes to look at the cards as a group and fix any that are wrong.  If you take some of the cards out of the deck, this activity can lead to a nice introduction to ideas about graphing. 

Find a ____

This is my adapted version of Movin' It Math that I like to play with my intervention groups.  I put out some dots and some cards and ask kids to find a number.  After each kid is on a representation of that number, I ask them to find another one.  It is a great way to get a small group moving! When it is pick up time, I have each kid pick up all the representations of a given number. 

Each Movin' It Math resource includes more ways we use these cards in the classroom and much more detail about how to play each of the games above.

Here are the 4 sets released so far!

Want all 4 sets?  Click on the picture below to check out the money saving bundle!

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Conference Time!

We are 7 weeks into the school year and gearing up for parent teacher conferences later this week.  In our school, we try to schedule all conferences on a Thursday evening or Friday morning.  This way if multiple folks need to be involved in the conference, we are all in the building at the same time. The evening hours also work much better for parents.  

As the math specialist I get invited to attend the difficult conferences.  If a student is behind or in some cases very ahead of their peers, I will often be asked to join the conference.  Classroom teachers also invite me when they know parents have specific concerns or when it is a student I have a lot of contact with.  Sometimes I am asked to sit in on a conference because the parents are very difficult or have expressed opinions about their students math learning that do not show understanding of how or why we are teaching math as we do.  Depending on the reason for the conference and what the concerns are, I have many approaches but here are a few things I always do in conference situations.

- I like to start on a positive note by sharing a recent piece of student work that illustrates something they can do well or something that shows how far they have come.  Because I do so much formative assessment, I have a lot of student work samples available to choose from and can always find something positive.

- I then like to have parents share how they think their child is doing and any concerns they have.

- I am all about data driven decision making so then I will share any assessments.  For primary students this often includes individual interviews, especially if a student is behind.  I go over the current assessment results and show their progress over time if applicable. 

- I show other student work and point out specifically how the work illustrates them progressing or not progressing toward meeting the standard.  I also like to explain what the next steps are in terms of what we are working on next.

- I prepare myself to answer the hard questions.  Why are you teaching it this way instead of that way?  These big questions parents have when they are new to my school or my way of thinking about math used to really challenge me.  As I have become more experienced and read more research on math education  I have been better prepared to answer these questions.  I like to show parents that it isn't MY way of teaching that I am going for but rather what the research says works.  

- I focus on the big mathematical ideas for that grade.  For each grade level I can think of 3-5 things that are the most important things kids have and understand in order for them to be successful in the next grade.  If a student is behind, I focus the conference on the most important skills and make sure my discussion focuses on how to move a student forward with these big ideas.

This year, in addition to my role as a math specialist (part interventionist and part coach), I have 2 groups of students that I am doing the primary math instruction for.  This means that I will hopefully get to meet with the parents of kids in these groups because their classroom teachers don't see them for math.  To help out with ones I might miss and to keep the classroom teachers up to speed on what their students are doing in math, I have been gathering data and putting together some things that can be shared with parents.  One of the things I created for my fourth grade group was this quick reflection on their learning.  I loved seeing their responses and it gave me great information about how they are feeling about math!

Want to use this with your students?  Click on the picture to get it from Google Drive. 

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