## Saturday, January 31, 2015

### Number Talks Book Study: Part 4

Welcome to week 4 of our book study on Number Talks.  This is a great book for K-5 classroom teachers, special educators and math specialists.  It is also a great book for administrators and other educational professionals to read to learn more about what good math teaching looks like.

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
This week we dive right into the grades 3-5 section, looking at strategies and ideas for number talks around addition and subtraction.  Next week we will be taking a look at the chapters around multiplication and division ideas for grades 3-5 then will be wrapping up this book study the following week.  Four weeks down and only three to go!  Hope you are keeping up!

#### Chapter 5: How Do I Develop Specific Addition and Subtraction Strategies in the 3-5 Classroom?

If you think or have ever thought the traditional algorithm was the only or the best way to solve multi-digit addition and subtraction problems, than this chapter is going to open your eyes to an entire new possibility.  Instead of teaching kids how to do arithmetic problems, this chapter focuses on how to elicit invented strategies from students.  You will be amazed at what students will come up with given the right environment.  These are efficient and elegant strategies based on place value and the properties of addition and subtraction.  The best part is the teacher's role is to facilitate thinking, not to tell kids how to do it!

I can't say enough about the power of students learning math this way.  My school has gone from teaching kids how to do an algorithm and making them practice it a million times to a number talks model where kids are constructing their own knowledge and building on the ideas of their classmates.  Now we have kids who truly understand math and operations as opposed to kids who have memorized a procedure.  The biggest change of all has come from teachers of older students who never have to say, "this kid forgot how to subtract!"  What they used to mean when they said that is that the kid forgot the steps to the procedure and didn't have any other method to fall back on.  Now we know kids really do know how to subtract and if they haven't done a subtraction problem in a few weeks or months, the knowledge they have about subtraction is so interconnected with other things they know and have constructed for themselves, that this knowledge does not fade.

#### Chapter 6: How Do I Design Purposeful Addition and Subtraction Number Talks in the 3-5 Classroom?

This chapter made me really wish I had read this book before starting Number Talks in my classroom.  There are so many ideas for problem strings to do with students to get at the strategies you want them to have.  I learned a lot of what this chapter presents through trial and error.  Here are a few things that struck me from this chapter:
- The subtle difference in how kids make friendly numbers is the essence of the different strategies.
- We want students to have a toolbox of strategies based on reasoning.
- Giving kids problem strings allows them to apply strategies they just heard used to the next problem.
- The idea of compensation is HUGE!
- In subtraction, the distance the numbers are from each other will effect what strategies are efficient.
- Remember the benefits of putting problems in context.
- Embrace the power of negative numbers.

### Fun and Free Computer Games: Fraction Flags

Anyone working on fractions with kids in grades 1-3?  I recently found a fun and free computer game that is great for students who are working on exploring part whole relationships.  It is called Fraction Flags and it a lot of fun.  Check it out!
 A peek at the home screen.  By using the arrows near the bottom of the page, you can select a few options for students.  They can design flags using different combinations of halves and quarters.
 Students can be as creative as they want.  While enjoying the creative process they are also being exposed to some of the bigger ideas around fractions like part whole relationships and equivalency.

 By giving kids multiple designs to make and allowing them so share their designs with others, students can see many ways to make fractions such as one half.

 I love having students build this one with all fourths because it is a great way to expose kids to the idea that the pieces do not have to be congruent to be equal fractions.
If you are doing basic fraction work with students, this is a game you might want to bookmark for later!

Looking for more fraction fun?
 Grab this free game to play with your students before or after trying this computer game. It makes a great math center or scoot game!
You might also be interested in:

Do you have a favorite fraction game?  Tell us more in the comments below!

## Monday, January 26, 2015

### "Snow" Much Fun Blog Hop

Happy Monday!  Today I am joining up with some new blogging friends to bring you the Snow Much Fun blog hop.  This blog hop is a way to share with you some new ideas to keep you kids engaged and learning during those long winter months.  We have kept this a short hop so it is a great way to get some new ideas and check out some new blogs without being overwhelmed.  If you are new to my blog, welcome.  I am The Math Maniac and I love teaching math.  I am a K-6 math specialist and believe in the power of conceptual understanding.  I have a lot to say about math teaching and post frequently on this blog about all kinds of math subjects.  You can also find me on Facebook, Pinterest and TPT.
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Today I want to share with you how I try to bring winter fun into the classroom with math story problems.  No matter what grade I am working with and what type of computation my students can do, it is always more fun to use a context.  Using a winter context is a great way to have fun with the season and get kids solving problems they are really interested in.  Here are some of the ways I get kids engaged!

#### Picture Problems

There is nothing like a fun winter scene to pull my youngest learners into a problem a really get them thinking about math.  A visual images goes a long way toward helping these little learners contextualize a situation and solve a problem.  I like to start picture problems by making a few of my own for students to solve.  Then I let them make their own picture problems.  It is easy to create a background out of construction paper and then kids can draw, use stickers or use stamps to create the rest of the scene.  My favorite winter theme for picture problems is penguins!
 One example of a picture problem.  Click here to grab this one and another penguin freebie!  After solving a few of these as a class, let your students make up their own.

#### Winter Literature

Have some winter literature you use every year in your classroom?  It is amazing what kinds of math word problems can be made based on kids' books.  It might be the words in the story or it might be the pictures in the book, but something in almost every book can inspire a word problem.  I have been really focusing on this over the past 2 months and with practice it has gotten easier and easier to come up with good math problems based on popular non-math picture books.   I like to make these problems into little task cards and stick them in the book where I will be sure to remember to ask them.  Here are a few sets I have made for popular winter picture books.  Please feel free to use these with your students and I hope they inspire you to keep going!
 Here are some problems that go along with The Mitten
 These problems I used with Snowman at Night

 Problems for Tacky the Penguin

For my older students, I like to write winter themed problems on task cards.  Then I take the task cards and we go to our gymnasium and spread the cards out.  Then kids move around the gym solving problems and recording answers.  When we have had a long week cooped up in the classroom it is great to give kids this chance to have a bit of extra movement.  On days when we can't get into the gym we use them in the classroom and play a version of scoot or some game where we can move from desk to desk at the very least.  If we get a sunny and warmish day, we might even venture outside and solve a few problems outside.  Our winter task cards are a mix of ones I have written for the students along with ones we have written as a class and kids have written independently.  Here are a few to get you started!

 If you are working on double digit addition and subtraction you can grab this freebie from my TPT store

 If your students need to work on multiplication and division facts, this freebie will get you started!

How do you keep kids engaged during the winter?

Head over to Keep 'Em Thinking to learn about how to make Snowflake Crystals with your students!

## Saturday, January 24, 2015

### Number Talks Book Study: Part 3

Welcome to week 3 of our book study on Number Talks.  This is a great book for K-5 classroom teachers, special educators and math specialists.  It is also a great book for administrators and other educational professionals to read to learn more about what good math teaching looks like.

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
Thank you to all who participated last week!  We certainly had fewer comments than the first week but I am sure this is because folks got busy!   If you missed last week, no worries, just catch up as you have time!

#### Chapter 4 How Do I Design Purposeful Number Talks in the K-2 Classroom?

I particularly want to talk more about the dot images section in the K number talks.  I love using dot images with kids and can't believe I ever taught primary without these.  They are such a great way to build fluency with numbers and really lay the foundation for working with composing and decomposing numbers which is vitally important to students being successful with developing fluency of addition and subtraction facts.  As an interventionist, I often find that first and second graders whose teachers have identified them as needing more work with addition and subtraction facts are the kids who need more work with dot images and other models like 10 frames and rekenreks.  When I pull intervention groups from the classroom or work in classes during Guided Math time, I often will do a number talk with a small group.  By sometimes doing small group number talks, I can differentiate instruction and get to really watch how kids are solving problems.

I love all the models discussed and used in number talks.  Rekenreks are powerful tools and if you don't use these in your classroom yet, than you should!  There are free virtual versions and they are easy to build student size versions using pipe cleaners, cardboard and pony beads.  Ten frames are also fantastic and there are so many ways to use them in the classroom.  In addition to ten frames, I use a double ten frame (aka 20 frame) to extend the power of this model to larger numbers.  These models are important to have in every K-2 classroom and you will find yourself using them again and again during number talks, math centers and for individual student practice.

## Tuesday, January 20, 2015

### Improving Additive Reasoning and Numeracy With 20 Frames

 Clip art by Whimsy Clips
This fall, I shared with you 10 different ways I use 10 frames in the classroom.  Today I want to share with you 10 different ways I use 20 frames with students.  From helping kids identify teen numbers to working on addition and subtraction 20 frames are a very useful tool in the classroom.  Any set of 20 frames will work for these activities.  If you want the ones featured in this post, you can get them here. Most of these activities work well in whole group, small group or individual situations.  The visual model of the 20 frame can support kids who have a fragile understanding and lead to a conceptual model of numbers that they will take with them as they learn more mathematics.  The flexibility of the 20 frame makes differentiating these activities easy to do.  It might look like everyone is working on 20 frames, but the difficulty of what they are doing can range greatly.

#### 20 Frame Flash

This is probably the simplest way to use a 20 frame but can really help build subitizing skills which is the ability to instantly recognize a quantity.  Having students that are confident with what number is displayed on a 20 frame without having to count each time makes the rest of these activities go much smoother!  All you need to do is flash the 20 frame at your students for 1-5 seconds and then put it back down.  When you first start doing this with students you may need to show it longer or give a second peek for some students.  As your students gain experience with this, it will get much quicker.  Make sure you give kids the chance to share with their classmates how they knew the quantity being shown.  This allows all students to hear other students strategies and gives them ideas for how to solve it on their own the next time.

#### Matching 20 Frames and Numerals

This can be great fun as a whole group activity but can also be played in partners or individually.  When playing with a whole group, pass out 20 frame and numeral cards to each kid until you run out and ask them to find the matching number or picture.  Have them stand shoulder to shoulder when ready and review all matches as a class.   Played as an individual or partner game I like to have students spread out all the 20 frame cards and then flip over one numeral card at a time until all matches are found.

#### 20 Frame Memory

Once your students get proficient with matching 20 frame and numeral cards, it can be a lot of fun (and learning!) to play memory with them.  Simply mix all of the 20 frame and numeral cards together, place upside down in an array and flip 2 over at a time until you get a match.  This makes a great math center and is also quite a popular game to take home to play with families since most folks are already familiar with the rules for memory.  I like to keep a few sets in zip top folders ready to go home with students who request them.

#### Sequential and Non Sequential Ordering

Being able to put numbers in order is an important skill and one that is easy to do but often overlooked.  Giving your students a chance to put numbers in order at this level will make it much easier to order numbers later when they are working with much larger numbers.  When I give sequential numbers to kids to order and they have finished I have them read them in order from smallest to largest and then from largest to smallest to me or to a classmate.  This gives them extra practice with the rote counting sequence both forward and backwards and allows them to practicing counting starting from a number other than 1.  You can use either 20 frame or numeral cards for this activity.  Some kids need the visual model of the 20 frame when they are fist starting with an activity like this.

#### Roll and Build

If you have 20 sided dice, this is sure to be a class favorite.  There is something so engaging to young children about dice games and this is no exception.  If you do not have 20 sided dice or want kids to practice building a specific set of numbers on the 20 frame blank dice are an easy way to differentiate.  If you don't have blank dice or are looking for something very engaging, you can make an origami cube and use that for your blank dice.  All you need to do is roll the dice and fill in the number you rolled on a blank 20 frame.

#### Odd and Even Sort

The concept of odd and even is important for kids to develop and it always seem like they need more exposure to it.  using the 20 frames for this sort is great because kids can see if each dot has a pair or if there is one left over.  This is great for a whole group activity where each kid has a card and you sort onto 2 sides of the room.  It also works well in a math station or for an individual activity.  It is simple as sorting into 2 piles.  Of course, I always follow up this sort with picking one or two cards from a pile and asking kids how they knew those numbers were even or how they knew they were odd.

#### Flip and Fill

This game is a great one to use to check in with how kids are doing with 20 frames.  It is very similar to roll and build but this time they are using the numeral cards to flip over and fill in the 20 frame.  When you do it this way, you know students will be getting the numbers 11-20 (unless you decide to limit it further) and can really practice those teen numbers.  I like to laminate blank 20 frames and have kids flip over the numeral card and fill in the number on their 20 frame.  If the cards are laminated, they can use a dry erase marker for this which they love.  You will see some kids erase the dots each time while others quickly figure out that they only need to erase or add some each time as the numbers change.

#### Close to 30

I love using this game with kids who are showing proficiency with adding single digit numbers and are ready to be introduced to the idea of adding larger numbers.  This game is great played in pairs and makes an excellent math center.  Each student flips over 2 cards and finds the sum.  Then they figure out how far away from 30 their answer is.  The person whose answer is closest to 30 wins both cards.  You can have kids make a simple record sheet to go along with this.  My students like to circle their answer when they win by being the closest one to 30.  I love how this is a gentle introduction to double digit addition and works on the concept of comparing numbers all in a game format.

I love having 10 and 20 frames in the classroom and find that these cards, along with the cards in my place value deck are used in about 75% of the games and activities I do with my intervention students.  There is just something about the visual model combined with the flexibility of these cards that make them engaging and effective.

Looking for more?  Check out my complete set of 20 frame playing cards and activities! (THIS SET IS 50% OFF FOR THE FIRST 48 HOURS!)

## Saturday, January 17, 2015

### Number Talks Book Study: Part 2

Welcome to week 2 of our book study on Number Talks.  This is a great book for K-5 classroom teachers, special educators and math specialists.  It is also a great book for administrators and other educational professionals to read to learn more about what good math teaching looks like.

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
Thank you to all who participated last week!  We had a great discussion and many folks left insightful comments and shared ideas.  I love the enthusiasm I am seeing for this great book!

### Chapter 3: How Do I Develop Specific Strategies in the K-2 Classroom?

Now that we know what a number talk is and how to prepare for them, it is time to dig in to the specifics of using number talks in the K-2 classroom.  Here are the four goals for K-2 number talks.

#### Developing Number Sens

This one gets covered by almost every number talk.  The whole process of sharing  and comparing solutions and deciding if they are reasonable develops number sense.  Since number sense is the foundation for conceptual understanding of all mathematics its importance can not be overemphasized.  Knowing if a solution is reasonable should not be taught separately in an estimation unit but should rather be part of everyday mathematics instruction.

#### Developing Fluency with Small Numbers

Not developing fluency with small numbers is one of the biggest obstacles I find kids who struggle in math face.  I will often be asked to work with a second or third grader who is struggling and much of it can be traced back to not having fluency with small numbers.  If kids don't get fluency at this level, they can not develop fluency with larger numbers or other operations.  "Fluency is knowing how a number can be composed and decomposed and using that information to be flexible and efficient with solving problems."

#### Subitizing

Subitizing can be one of the most fun things for kids (and adults!) to practice.  There are so many engaging ways to give kids a chance to subitize.  If you are new to the idea of subizing you can read more about it here or check out my favorite subizing app.

#### Making Tens

"Making groups of ten provides a link to developing and understanding place value and our system of tens."  Kids need lots of opportunities to practice grouping things into tens.  In my school, we are big fans of 10 frames and using Counting and Estimating Routines to help kids think in tens.

### Models and Tools

Here is a short list of models that should be available and used in every K-2 classroom
- Dot images
- Rekenreks (number rack)
- Five, Ten and Twenty Frames
- Number Lines
- Hundred Chart

I am happy to say that we have all of the above models at out students' fingertips.  We do a slight variation on the number line in K+1 and use a number path.  Stay tuned for a future blog post about the difference between a number line and a number path and what the research says about introducing number lines to early.

### Using Real Life Contexts

Math is a part of real life and it is our job to help kids see that.  Providing them with a context is at the heart of helping kids see why learning math is important.  It helps kids think of mental images and evaluate the reasonableness of the answers.  Math should not be something you are taught with naked numbers and then asked to practice in a context.  Give kids a contextual problem and let them develop an understanding of the mathematics.  If you want to read a lot more about why this is important, check out our Children's Mathematics Book Study.

### You Oughta Know About Matific

Today I am linking up with Buzzing with Mrs. McClain for the You Oughta Know blog hop.  I am so excited to share this treasure of a math site with you today.  This is going to be one you don't want to miss!

In the last few  years, my school has shifted from having overhead projectors to having digital projectors and/or smart boards in every room.  This new technology has been amazing and I am always on the look at for more ways to use this technology with students.  This past summer, I discovered Matific, a website designed to help teachers of K-6 math.  The site is free to use (you do have to sign up for a free account to access it all).

The website (there is also an app) consists of mini interactive games designed to teach a specific math concept in a fun and engaging way.  The mini games, called episodes are organized by grade and Common Core strand.  There are also "worksheets" which are easy for kids to fill out on the computer and click submit to see if their answers are correct.  If you teach K-6 math, this is a website that you are definitely going to want to check out!

Here is a tiny sampling of some of the things Matific has to offer.

 This is bees and flowers from the Kindergarten menu.  It is a fun way for young children to learn about more and less.  You can pick the bees up and match them to the flowers in this episode,

 This is Out on the Tiles from the second grade section.  You pick up and drag squares to cover the rectangle and find the area.  The idea of area is pretty new to second graders and this is a fun way to work on tiling to fill in the rectangle.  It is very interesting to watch kids who have done this episode a few times find ways to be more efficient and to figure out the area without tiling the entire shape.  This leads to kids constructing their own knowledge about area and designing their own shortcuts.
 This is What's Your Angle I from the fourth grade section.  This is a great introduction to using protractors to measure.  There is also a what is your angle II that steps up the difficulty.  You will find on Matific that there is often a series of episodes that get progressively more challenging around a particular topic.  I really like this because I can have some students working on level 1 while others work on level 2 or 3 as they are ready.
 This one is Volume Fraction from the sixth grade section.  I love doing these episodes with upper elementary students because they often feel like they are to mature for other hands on manipulatives.  Matific lets them have hands on experience in a fun and engaging way.  The hands on practice is such an important part of conceptual understanding.

Grab yourself a big cup of coffee or a nice cup of tea, and check out what these other great blogs are saying in the You Oughta Know blog hop.

## Saturday, January 10, 2015

### Number Talks Book Study: Part 1

Welcome to week 1 of our book study on Number Talks.  This is a great book for K-5 classroom teachers, special educators and math specialists.  It is also a great book for administrators and other educational professionals to read to learn more about what good math teaching looks like.

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
If you are looking for a general overview of what Number Talks is all about, check out this short article from the author, Sherry Parrish

#### Chapter 1: What is a Classroom Number Talk

This is my first time reading this book but I started using number talks with my students 3 years ago.  Our district had done some excellent math professional development and the teacher leading the professional development was a big fan of number talks.  I learned a lot about getting kids to share mental strategies and which types of problems and problem strings bring out the strategies I want my students to be proficient with.  Making a commitment to using number talks in the classroom has changed my teaching for the better over the last few years.  In many ways I feel like adding number talks has been the single most important change to my teaching practice.  I have always seen value in mental math and flexible thinking.  I used to do some mental math exercises and problem strings with my students once in a while as kind of a change from the regular schedule.  Now however, I use number talks as a cornerstone of my instruction and see mental math and flexible thinking as the building blocks to developing a strong conceptual understanding.

#### Chapter 2: How Do I Prepare for Number Talks

Location: I most often do number talks by having kids gather on the rug in front of the white board.  Things might get a little squished but I like to have the students close to me so I can hear them sharing their ideas when we do a partner share.  This is the time where I can listen in and think about which students I want to share with the entire class.  When all students are close to me, it is amazing how many conversations I can listen into at once.  I also like how changing the location mixes up who is paired up with who each day.  My students greatest teachers are each other and I like to keep things fresh!

Wait Time: Most teachers THINK they give plenty of wait time, myself included.  When I was doing my master's program this is one of the things I worked on in great detail though observations and video.  I thought my wait time was excellent and it really was only 2-3 seconds.  Extending my wait time was super uncomfortable for both my students and me but now it is the new normal.  Along with my other formative assessment strategies, waiting until kids have time to think has really helped increase the achievement of all the learners in my classes.

Think-Pair-Share: To me this is the backbone of number talks.  I get the chance to hear kids strategies and decide who I want to share with the entire group.  ALL of my students get a chance to articulate how they solved the problem.  My students get a chance to practice listening and understanding someone else's strategy.  I love the pair-share aspect and do it with almost every problem.  When pair-share time is finished, I often ask a pair to share each other's strategies.  Partner A tells me what partner B did to solve the problem and partner B tells me what partner A did.  Holding kids accountable for their partner's idea has really increased engagement during pair-share time.

Recording Student Thinking: It is your job as the teacher to record students ideas on the white board while they are sharing their thinking.  It can be very intimidating the first few times, especially if you are not used to hearing a lot of different ideas.  I still sometimes struggle to understand and capture a students idea but I try to tell myself to stop teaching and start listening.  Listen to what your student is saying, ask questions and let the class work as a team to figure out how each student solved the problem.

Keeping Students Accountable: For me, the best way to keep kids accountable is by giving an exit question.  Even though my students sit close to me, I listen hard and work my best at making sure everyone is getting it, some kids are just so good at faking it.  Giving an exit ticket is a painless and efficient way to see what strategies kids are using and who is completely lacking a strategy.  I often just give kids one problem and a quarter sheet of scrap paper.  I write the problem on the board and ask them to solve the problem and show me how they got their answer.  Because they are used to seeing me record their thinking with number sentence, open number lines and diagrams they are usually pretty good about being able to capture their strategy on paper.  I collect the papers and take a minute right then (usually) to sort the exit tickets by strategy.  I take particular note of those students who do not have a strategy so I can address that with a small group number talk during Guided Math groups.  I also take particular note of any strategies that were super efficient or something I want shared with the entire class.  I might start the next class by showing a few of the exit tickets on the projector and having kids try to tell me how they problem was solve based on what they see on the paper.

I love how number talks have changed learning in my classes and can't wait to read more and refine my approach.  How about you?  What are your thoughts on setting up and starting number talks?  Have you tried it yet?  How did it go? Please respond in the comments below!

## Tuesday, January 6, 2015

### Fun with Combinations of 5, 10 and 20

If you are a regular follower of this blog, you might be tired of me talking about combinations of 5, 10, 20 and 100.  I spend a lot of time making sure students are fluent with these ideas and am always coming up with more ways to make sure students get the practice they need with these facts.  Today is no exception.  Over the holidays, I spent lots of time with my nieces and nephews and one of them had a fun looking paper cup they were playing with.  All it is is a balloon that has been tied off and had the tip snipped off.  Take a paper cup and cut the bottom out of it.  Stretch the balloon over the cup and you have a little popper.  I used the regular 9 oz paper cups for this but depending on what objects you want to pop and if you are working on numbers to 5, 10 or 20, a bigger or smaller cup might work out better for you.

Let's say you are working on combinations of 10.  Give each student a popper cup and 10 pom poms.  I made sure each kid had 10 of the same color so there wouldn't be arguing and let them get to work! They pull on the tied end of the balloon and release.  Some of the pom poms will pop out and some will stay in the cup.  This is a great time to ask questions about how many came out and how many are still left in the cup.

After a few rounds of popping, you can have kids make a simple record sheet and record their combinations.  These can be done as addition or subtraction equations or in a table format.

Here are a few other things we have put in the poppers to work on number ID, shape ID and coins!

If you try these with your students remember that pom poms are a lot lighter and softer than other materials.  If you have a large class or are short on space, stick with the pom-poms!