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!)

What can you add?  How do you use 20 frames in your classroom?  Please respond in the comments below!

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.  

Join me each Sunday as we discuss the week's reading and make connections to our own teaching practice.  Leave a comment on this blog post or head over to Facebook and leave your thoughts there.  If you have your own blog and want to write a post about it on your own blog, just leave the link in the comments section.   

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.  

Looking forward to hearing your thoughts and ideas about Chapter 3!  

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.  

Head over to matific.com for more great games that will help your students build conceptual understanding of important math topics! 

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.

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.  

Join me each Sunday as we discuss the week's reading and make connections to our own teaching practice.  Leave a comment on this blog post or head over to Facebook and leave your thoughts there.  If you have your own blog and want to write a post about it on your own blog, just leave the link in the comments section.   

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.
If you have never done a number talk here is my take on the basics.  You are presenting your students with a problem or a few related problems that you will ask them to solve mentally.  As kids find a solution, they give you a signal that they are ready.  I have always had them put their thumb up and bring it to their lips.  I love the idea in this chapter about having them come up with another way to solve the problem while they are waiting and putting up a finger for each additional way.  I can't wait to try this!  When most kids are giving me the ready signal, I first ask for answers.  I record just the numerical answers that kids give me not indicating right or wrong answers.  Then kids can share with a partner or the entire class what their strategy is.  As the teacher, I try to capture what the students are telling me by recording equations, open number lines, diagrams or other tidbits that show their strategy.  Other students get a chance to share their ideas as well and then the strategies are compared and contrasted.  I also like to talk with kids about the efficiency of various strategies.  Wrong answers given serve as a great learning opportunity to find mistakes and help kids think more flexibly about numbers.  Most of the time a number talk will take 10-15 minutes but occasionally my students will be so engaged and excited about their strategies that I will let it go a little longer and offer more problems in the string or increase the complexity of the problems we are solving.

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!



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!



Monday Math Literature: Story Problems with Tacky the Penguin

Happy Monday!  If today is your first day back at work for the year, I hope it is going really well.  I always find January to be the month that my students learn and change the most.  Yesterday, I wrapped up our book study on Children's Mathematics and am looking forward to our new book study starting this Sunday.  We will be looking at Number Talks and from what I read so far, it is going to be another great book!  
For the past few installments of Monday Math Literature, I have been using some of my favorite winter picture books to inspire math story problems.  Last week I shares some problems I wrote for Snowmen At Night.  This week, I have been thinking a lot about penguins and wanted to create some problems to go with Tacky the Penguin.





There are all multiplication and division type story problems to use with primary students. These help students build ideas about equal groups and place value.  
You can grab a printable version of these problems for free on Google Drive

If you use a penguin theme in your classroom you will definitely want to check out this post for some new ideas and a bunch of freebies!

If you like the idea of using story problems with children's literature than make sure you check out these posts:

Children's Mathematics Book Study: Part 5

Welcome to the last installment of our Children's Mathematics book study.  If you are just checking this out, it is certainly not to late to join in!  Grab a copy of the book and head through the posts at your own pace.  If you are looking to join a book study from the start, I will be starting a new on next Sunday on a great new book called Number Talks.  Check out the full posting schedule here.  


Here is the posting schedule for Children's Mathematics:
December 7: Chapters 1- 3
December 14: Chapters 4 & 5
December 21: Chapters 6 & 7
December 28: Chapters 8 - 10
January 4: Chapters 11 - 13

I will post each Sunday morning and share it on my Facebook page.  Please join in by leaving a comment on my blog post or Facebook page.  If you have your own blog and want to write a post about the book that works too!  Add your link in the comments section here.  Thank you to all who shared last week!

Chapter 11: Mathematical Principles Underlying Children's Mathematics


When I was in 7th grade, I remember learning about the commutative, distributive and associative properties.  They were each a section at the beginning of our text book and I remember feeling so confused.  I was learning about these properties in such an isolated, text book driven way that I literally had no idea they were things I had been using to solve math problems my entire life.  I certainly do not want my students to feel this way so as we use Cognitively Guided Instruction I make sure kids are developing a real understanding of the properties of mathematics.  It is truly amazing to see kids develop these big mathematical ideas from experiences and from thinking about how to solve problems.  Having a good understanding of the properties of mathematics and helping kids put equations and words with their ideas is one of the most important jobs a teacher can do in a CGI classroom.  "One way of making these properties more explicit is to introduce notation to record relational thinking strategies so that there is a written record that can be used to discuss a given strategy."  I often find that when kids first start solving problems of a particular type, they might have a mental strategy but will really struggle with how to notate that strategy symbolically.  This is when I step in and write the symbolic notation to go along with their idea.  This seems to really help all kids in the classroom make sense of the strategy.  This chapter also talks about the fact that it is not necessary to use the names of the properties with students but it is important that they understand what the properties allow.  I agree with this but I also almost always use the names of the properties with students, even primary ones.  I think this is because of my own experience learning the names of properties in isolation and not really understanding what that meant. 

Chapter 12: The Conceptual Basis for Cognitively Guided Instruction

This was by far my favorite chapter.  I feel like it really captures what CGI is and what a difference it can make in terms of kids learning to think about the math they are doing rather than just doing it.  The idea that knowledge is connected and that all kids benefit from learning conceptually and building upon what they already know is what I strive for in my teaching every day.  I have to confess that I have already read this chapter multiple times and continue to find gems of understanding each time I read through it.  If this chapter can't prove to folks that teaching conceptually is the way to go than I don't know what can. 

Chapter 13: Conclusion: Keep on Learning

I have so enjoyed reading this book and will continue to provide my students with the benefits of Cognitively Guided Instruction.  I really believe that teachers matter to students more than anything else.  It really does not matter what the standards are, what curriculum you are using or what the administration requires if you don't have good teaching.  A good teacher who listens and understands her students thinking and ideas and facilitates an environment where kids can build upon their intuitive ideas and learn more efficient and elegant ways to solve problems is what every kid deserves.  The standards and curriculum and everything else come second to the power of the teacher and his or her ability to guide students learning.

I hope you have enjoyed reading this book and if you are still haven't read it, I assure you it will be worth your time.