Math Doubles and Squares Fun Time

Thursday, June 23rd, 2016

kids on board out edit2If you teach math, or want to enrich your children’s understanding of numbers, here is a set of activities that children will enjoy while learning a lot.

You may have heard about Multiple Intelligence Theory. One thing it tells us is that we evolved to have intelligence not only in verbal and mathematical learning, which are the main focuses in our schools, but in a number of different areas. That’s why some of us learn better through music, or nature, or art, or bodily movement.

This activity is a kinesthetic (movement-based) way to teach some important number facts. I’ve found that it increases math fact retention in everyone who plays it. One reason might be because it’s more engaging and fun than paper-and-pencil or verbal learning. Who learns well when they’re bored?

I made this project because I teach using Singapore Math, which is the best way I’ve found to teach math. However, the materials don’t focus on teaching basic facts; these are left to the teacher and/or supplementary programs. So I use lots of different activities and resources for teaching the facts; this is one of them.

Learning Objectives
After playing these games, students will be able to remember their basic addition doubles facts and squares (powers of two).

For this set of activities, you will need:

  • Number mat OR sidewalk chalk
  • (We’ll go into how to make the number mat in another step.)
  • Space
  • Number cards: Download squares card and/or addition card PDFs

Step 1 Outdoor Number Mats

Outdoor board

If you have access to asphalt, sidewalk chalk, and decent weather, this is a great activity to get your students outdoors and enjoying learning their math facts.

Just draw your chosen number grid according to the layout in the PDF file, and print and cut out the cards. Instructions for playing the games come in step 3.

Step 2 Indoor Number Mat

times board

This step shows you how to make the Indoor Number Mat. This is a versatile tool to have in your classroom; keep it around for bad weather, and your students may even want to pull it out during recess! You may get some great ideas from them for how to use it.

For this project, you will need:

  • Large piece of fabric, Tyvek, or something else convenient (it could be a good way to recycle canvas used for a stage set). I think the minimum size is about 4′ x 5′.
  • Fabric paint or acrylic
  • Duct tape or ribbon

clothThe first thing I did with my fabric was to fold it in half and see how to split it in twelfths. This was easy given the fold lines in my fabric. If you don’t have this, simply fold twice horizontally, and bring two folds to the middle to make your three. (See diagram.)

cloth with tapeNow use your line-making option to “draw” lines along those folds. I used thinnish strips of duct tape for the vertical lines and the remaining fatter strips for the horizontal ones.

Next, paint the numbers according to the layout inside the boxes in the Grids PDF.
cloth numbers
I chose to use the full length of my fabric and use the top half for squares, leaving the bottom half for addition doubles. I needed to do this partly because I was in a hurry at first and painted just by squeezing acrylic paint directly onto the fabric, so it bled through to the other side. I had planned to use the other side for something else, but that’s no longer possible. If you are more careful, though, or use fabric paint, you can use one side of a smaller piece for the addition and the other side for multiplication.

If you are using a fabric board, I recommend the children play on it with their shoes off.add board

Step 3 Games to Play

class on in board
There are so many possible games to play with these boards. Here are a few I discovered on the first day I tried them with my students.

Doubles Fun Plus or Squares Jump
Note: The idea for the addition doubles jump game comes from Adrian Bruce, an Australian teacher with an awesome website, but all extensions, photos, files, and multiplication-related activities are mine.

1. Children line up.
2. Cards are shuffled. Each child picks a card and tries to solve the problem. If successful, child jumps to the number on the board.
3. Card is returned to the bottom of the pile, and another children gets to try.
4. Play continues until all children have been on the board and have had a chance to solve at least two problems.
marcel jumping
If you are working with a small group of children just learning these facts, have them retry problems they missed until they know them automatically. Not over and over again in a row so that it’s boring, but they won’t mind doing another problem and repeating one they missed a few times because they are having too much fun, in my experience.

Doubles or Squares Fun Around the World Hopscotch
rubyonboardThe idea of this game is to say the equations in order (e.g. “3 x 3 is 9, 4 x 4 is 16, etc.”) while hopping on the successive solutions. Teacher should model how to do this.

I think it’s important in this game that the student says the full equation aloud. This reinforces the equation in their automatic systems. I noticed that directly after the game, my students were using what they had practiced to solve problems.

For young children, once they have practiced with the equations, have them try counting by twos and jumping on the numbers in order.

Discussion Time
This isn’t a game, but an important part of developing the students’ metacognition (higher-level thinking) and discourse (math talk) about these computations. Ask:

  • What do you notice?
  • How can these facts help us figure out a problem?
  • For example, if we know what 7 x 7 is, how can we use that to figure out 7 x 8?
  • Do you notice any patterns?
  • Where are the doubles the same in addition and multiplication, and where are they different?
  • Can you see a pattern where some products are even and some are odd? What are the factors that make them that way? How is this similar or different from addition doubles?
  • With young children, explore odd and even numbers on the addition mat, and then flip it over and have them identify odd and even numbers on the multiplication mat.

Allow the children to explore the concepts. It will make math a lot more meaningful to them.

This project was originally published on It is all my original work.

Hangout On Air tonight, 8:00 Eastern time

Wednesday, April 6th, 2016

I’m offering a last-minute Hangout On Air tonight to discuss some multiplication and division quick tips. Just half an hour of your time. I’m sure it will be worth it!

Math Play!

Independent Common Core Math Curriculum Reviews

Wednesday, March 4th, 2015 graphic

Click on thumbnail to go to site

I’m pleased to report that an independent non-profit organization,, is reviewing new Common Core math curricula. I sometimes get asked about my opinion about the different options, but it’s hard to respond when there are so many new materials that I haven’t seen, and I am only one person. While the reviews don’t address every curriculum, they do address many of the available Common Core options. If your district is considering adopting a curriculum, please consider the detailed reports here.

They also have a graphic that shows the alignment in a visual format. Click the thumbnail to view it.

To toot my own horn a bit, Eureka Math (also available on, of which I was on the second and fifth grade writing teams, is getting the highest praise of any of the curricula reviewed so far here, especially at the elementary level. I am no longer connected with the company, or any curriculum company, for that matter, so you can believe me when I say that I joined the teams because of the quality of their approach, pedagogy, and curriculum team excellence. While there are still kinks to work out, I think the curriculum is top quality.

In case you are interested in professional development, I do offer that to schools and other groups. Please feel free to contact me to inquire.

Getcher Epic Pi Day T-shirt Here!

Tuesday, March 3rd, 2015

Pi Day Shirt on Zazzle

Pi Day Shirt on Zazzle

Hot off the presses, a new design is available to celebrate Pi Day 2015! Order soon to get yours in time, or order yours later to commemorate the fact you were there.

They could also make great prizes for Pi Day celebrations, drawings, or math fairs! Shirts in many colors, mugs, hats, even baby-wear and ties are available.

Free Downloadable Pi Poster

Free Downloadable Pi Poster

If you would just like a freebie, download my Pi Poster. And for classroom activities, visit this site to get them for $1.99.

Happy Epic Pi Day!!


Thursday, February 19th, 2015

Ever since I heard this story, I’ve been working to change my communication with children about what is important. I think this comic says it better than my soapbox speeches. And you can substitute anything else for math, but I chose math because I hear that all the time.

*If you’re stuck on helping your child with a concept, try or other sites like to refresh your skills and make learning fun for both of you.

For more on why this is important, see this Scientific American article titled The Secret to Raising Smart KidsIt has some citations to research showing why this is so important at the bottom of the article.

Also, if I dare mention it, this is why I think Common Core State Standards Mathematical Practice 1 (CCSS MP.1), Make sense of problems and persevere in solving them, is so essential. The way we have gone on historically has led to a lack of perseverance, but changing our values and how we speak about them can turn it around.

Feel free to share, and teachers and presenters, please feel free to use these comics in your work. Let me know if you do and how they came across if you feel like it.

And as always, please comment below!

New Eureka Math Books Available

Friday, December 6th, 2013

Common Core Mathematics
Yesterday, an exciting package came in the mail: the first two published modules of the Common Core math curriculum for Grade 2, complete with my name on the inside! Even though it was only listed for Grade 2 (I’m writing on the Grade 5 team too), it was nice to see my name on another publication.

While all of the modules can be downloaded and printed for free from EngageNY, it may save money and time for schools to buy the printed books. Print editions are available from Great Minds, or you can order individual books for homeschooling, enrichment, or preview from Amazon.

creditsI’m proud to be part of writing such a strong curriculum with powerful roots in Singapore Math approaches!

Have questions about the curriculum? Leave them below in the comments, and I’ll answer them as well as I can, and if I don’t know, I’ll do my best to find out the answers!

Websites and Apps from NYSCATE 2013 Presentation

Tuesday, November 26th, 2013

Here is a list of websites and apps demonstrated during my session at NYSCATE 2013. where you can download the full curriculum modules for free. access Eureka, the interface for the full math curriculum modules.

Number Pieces (Free): Virtual Base 10 blocks and whiteboard

AL Abacus ($1.99): Virtual abacus, sometimes called a Rekenrek

10 Frame Fill (Free): Basic ten-frame game/app.

Virtual Manipulatives! (Free): Fraction, decimal and percentage tiles

Teaching Table ($2.99): Smartboard-like manipulatives and interactivity for math presentations

Number Bonds: Addition & Subtraction to 99 ($1.99): Number bonds app for composing and decomposing numbers

Bugsy Kindergarten Math ($2.99): Fun game to practice K-1 skills

Splash Math website & apps ($9.99 per grade level): Adaptive Common Core-aligned math practice, with individual users

Numberland ($2.99): Montessori-based early numbers practice

Marble Math ($2.99): Game-interfaced math practice with choice of levels & subjects

Hands-on Equations ($4.99): Learn to solve for a variable step-by-step from concept to procedure

Thinking Blocks (All apps free): Solve word problems while making models interactively

Conceptua Math: Online tools and curriculum for math. Very strong for fractions.

Common Core Standards Viewer (Free): Interactive Common Core standards viewer with flow from one to the next



Meet me at NYSCATE!

Sunday, November 24th, 2013

I’m excited to be presenting at NYSCATE on Tuesday morning, the last session of the conference. Even more exciting, my session is receiving a lot of attention; looks like we’ll have a packed house!

I’ll be showing off Eureka, Common Core, Inc.’s excellent interface for the New York State math curriculum. I’ll also be demonstrating a number of apps and a few websites that can be useful in conjunction with common core math. Hope to see you there, but if not, check here for links to handouts and apps!

Also, the reason for the long quiet on my blog is that I’ve been busy writing curriculum for A Story of Units, the New York elementary math curriculum. Now that this is winding to a close, I’ll have more time for other things, like this website. Let me know if I can help you!

Quick Tip for Teachers: Organize Your Manipulatives

Saturday, August 3rd, 2013

One of the biggest challenges many teachers face when adopting a manipulative-heavy math curriculum, where pretty much every lesson starts with a hands-on component, is how to manage the pieces without sacrificing half the lesson time. Here is one way that may help.pencil case number disks

1. Buy, or ask each parent to buy, as many extra pencil cases as you need for the manipulatives. These cases are usually inexpensive, $1 each or less. Make sure you ask for the kind with the window and for three-ring binders.

2. Have a set of number disks (or color tiles, or play money, or whatever) per child. Sort the parts into plastic baggies if there are a lot of them, or just put them in together.

3. Use a permanent marker to label the pencil case with each child’s name.

4. Keep all the pencil cases in an easily-accessible place, so when it’s time to use that manipulative, each child, or classroom helpers, can easily find and distribute them.

5. Make each child responsible for putting his/her manipulatives back into the pencil case.

End result: hours of prep work and many classroom minutes lost reduced to just a few minutes of taking out and putting back!

Some teachers may want to group each child’s pencil cases onto a book ring, using the grommet holes in the pencil case. Others may want to place all of the same kind of manipulative into organizing baskets for distribution during a lesson.

Have other great classroom organizing or time-saving ideas? Post them in the comments below!

More Math Apps for iPad: Singapore Math and Common Core

Saturday, July 6th, 2013

It’s been a while since my last post on iPad apps, and in the meantime a lot has happened. For one thing, I have downloaded and tried quite a number of math apps. I’m going to start a round-up of some of the most useful apps as I have time.

number bondsFirst up: exciting news! The Number Bond software, that I lamented being only on Mac or PC for so long, is now ported to iOS. As far as I can tell, having downloaded only the addition/subtraction version, it’s pretty much exactly the same as the computer version.

This has its pros and cons. Pros: the familiar interface, its simplicity, and the fact that it does one thing – it teaches number bonds at different levels. Cons: In light of the outstanding, more powerful software out there, it takes advantage of very few of these features. For example, it is not adaptive, meaning the difficulty does not change with the user’s proficiency. It also does not save user data, something the better educational software is doing (as I’ll discuss later), even emailing it weekly to the parent or teacher if desired. It also has a few bugs to iron out, which I’m sure will happen soon.

So would I recommend it? Yes, as a practice tool for a child at home or as a station in the classroom – but I would love to see it get more developer attention and become more powerful.

Download Number Bonds: Addition & Subtraction to 99

Next up: AL Abacus

For anyone teaching/homeschooling with Singapore Math or a Common Core curriculum, such as Eureka Math, or working with a child with a math learning disability, you will find  that the Slavonic Abacus, or Rekenrek, is incredibly useful for teaching number sense and place value. It breaks down numbers into groups of five and ten, which are easy to manipulate mentally, not least because our hands are right in front of us since we are in the womb, with five fingers each (otherwise known as digits!). While having the concrete manipulative is ideal for sensory feedback, sometimes teachers want to project the abacus to a group, or show a demonstration to a small group. This is where the iPad version, AL Abacus, comes in.

AL Abacus to 100This app is a Slavonic Abacus with two modes. The first is the side with numbers to 100. To access this side, hold the abacus in landscape (horizontal) mode. When all the beads are to the right, it is like pressing “C” (or Clear) on a calculator. To reset all the beads, just tilt the iPad to the left – exactly like on a real abacus. Just slide single or groups of beads to the left to add, subtract, multiply, or divide within 100.

AL Abacus to 1000sThe second side is accessed by turning the iPad to portrait, or vertical, orientation. In this mode, you can work with numbers to 1000, with different columns of beads representing the different place values. This can be a very powerful, easy tool for computing whole numbers through the thousands. To reset the beads, just lift the iPad up, and the beads all fall to the bottom.

Incidentally, this second side was designed by Dr. Joan Cotter, who did her doctoral dissertation using it. Her website, with additional resources, including how to use the AL Abacus, is

This is an almost perfect representation of a physical version of the abacus. There are only two things missing, in my view: the sound of the beads clicking together, which would be great sensory feedback.

Download AL Abacus – Activities for Learning, Inc.

Since this tool is new to many people, here are some other resources besides just the iPad version.

Do you have other ideas or resources for teaching number bonds or using the Rekenrek? Post them in the comments!


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