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!

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!

Singapore Math Cheat Sheet: Starting a Child Mid-Year

Wednesday, March 13th, 2013

A teacher recently asked me a question: “What do I do with the student who is strong enough in his math concepts, but he has no idea about Singapore Math approaches like number bonds, and he starts our school late in the year?”

For her and other teachers in the same boat, I’m making this “cheat sheet,” which is targeted at elementary school children who start mid-year in Math in Focus or Primary Mathematics.

1. Number Bonds

Number bonds show the ways in which numbers relate to each other. They can also be thought of as “part-whole” pictures, in which you see two or more parts that make up a whole.

To catch a child up with these, you can try one of several things.

a) Sit with the child and a laminated number bond page, and write number bonds in them. Ask the child to create number sentences (equations) from the number bonds. Then have the child fill in the missing number in a number bond with a part, or the whole, missing.


number bond graphic

Whole with two parts

Number sentences:

4 + 6 = 10

6 + 4 = 10

10 – 4 = 6

10 – 6 = 4

With practice, the child will realize that all these facts are related, and that subtraction starts with the whole minus one part, while addition is made of two parts forming a whole. I’ve found it can help students who are struggling with subtraction, especially with those problems missing the whole, for example _____ – 7 = 5. Rewriting these as a number bond can assist the child to see that the whole is what is missing, so she needs to add the two parts.

An article that explains number bonds more in depth can be found at Let’s Play Math.

b) Have the child play number bond games. One of the best I have found is called Number Bonds. It is available for both addition/subtraction and multiplication/division. See my review of these games here.

c) Play other games that involve number bonds. Addition War and Subtraction War, which are outlined in this PDF, are both fun games children love. You can customize them to this need by having the student write the problems that turn up on the cards on a laminated number bond sheet with a dry-erase marker, which will show you how much the child understands about number bonds.

2. Model Drawing

Another feature of the Singapore approach to teaching math that is new to many US teachers in model drawing for problem solving. This is a powerful visual approach, and with practice, it becomes much faster than other ways of solving word problems.

A great resource to learn about model drawing is at To practice free problems using the model drawing approach, head on over to There are also videos on that site that explain the approach, and free iPad apps are available for four different types of word problems here.

For a new student when you don’t have much time to give one-on-one attention, set her up on Thinking Blocks to help her understand how to use this.

3. Place value

The Singapore approach places a heavy emphasis on place value. Many other programs do too, but not all, so you may find this lacking in a new student.

Again, considering that teachers may be too busy to spend a lot of one-on-one time with students, I am providing several electronic resources to teach this.

a) NLVM has some good resources for teaching place value. They require Java to run and can be used on a computer or interactive white board, or you can download their app that doesn’t require Java. Here are links to:

b) Here is an Illuminations lesson plan to play a place value card game.

c) A good iPad app for modeling with place value blocks is Number Pieces.

d) If you do have the time, make your own place value chart and use money or place value blocks to represent tens, ones, and other places your student may be learning. This will help a great deal with his number sense.


That wraps it up for this article, but if you have other questions, suggestions or issues, please let me know in the comments, and I’ll update the article as needed. Thanks for reading!


Pi Day: Pi Music and Classroom Activities

Monday, February 4th, 2013

With March (and spring!) right around the corner, many teachers are already thinking about celebrating Pi Day, or March 14. This is a great day to celebrate how much fun math can be.

I was inspired all over again by this music video using Pi to make music.


pi posterIf you would like to make Pi Day fun for your students, there are lots of fun ideas in this lesson plan, available from Teachers Pay Teachers for $1.99.

I also offer a free downloadable Pi Poster showing almost 1,500 digits of pi. My students always love these. Enjoy!

Free Printable: Money Pinch Strips

Saturday, January 12th, 2013

How is it possible to assess a whole classroom in a moment? One great tool for this is pinch strips. To use these, the children are asked a question, for example, “How much is $1 minus 95¢?” The children then pinch the strips on the segment showing the correct answer – in this case, the nickel – and all hold them up to show the teacher.

I prepared these pinch strips for lessons on money, and then I realized other teachers would probably find them useful, so here they are.

These get printed on card stock and can be folded in half to be double sided, or save paper and just print one side. They may be modified for children just learning to identify coins by putting the Tails side on the reverse.

Pinch strips can be used for many types of assessment, including multiple choice questions, using the letters in the questions as the answers in the strip segments.

Download money pinch strips here.

Fun With Blocks: Foundational Geometry

Saturday, September 1st, 2012


In the course of my teaching and tutoring experience, I’ve come across the fact that Americans often fall short of others in geometry1,2. Besides the fact of test scores, I see that in how difficult it is for bright high school students I tutor to grasp certain spatial concepts. In fact, I was recently tutoring one incoming tenth grader, and she was unable to visualize how many cubes were in a stack.

Photo Sep 01, 6 36 27 PM

Recently, I found these foam blocks in packs of 50 for $1.00 at Dollar Tree. I bought a bunch, and they have been so useful for my teaching already. For one thing, I used them to help the tenth grader understand and visualize the geometric/volume concepts I was trying to teach her. Since Singapore Math always teaches from concrete to pictorial to abstract, and she had been missing the concrete experience, I needed to go back to that level to help her visualize what was in the diagrams.

I find that students who played with blocks as children have an easier time visualizing and calculating volume. They help develop the spatial sense. I recommended to several families to buy sets of these cubes just for the children to play with.

One thing I appreciate about Singapore Math is that it starts building geometric understanding at an early elementary level. In fact, I use sixth grade textbooks to teach tenth graders concepts that they are missing.

Today, I was working with an incoming first grader in a kindergarten book. We used the cubes as our concrete manipulative to represent the problems we were doing. (Unifix cubes are another great manipulative, but sometimes they can be hard for little hands to pull apart or put together, especially if they have difficulty with fine motor skills.)

At first the child had a hard time understanding the work, but soon she was doing it with fluency and ease. She was able to compare quantities and see how they connected with the pictures in the book. She also loved playing with the lightweight foam cubes and happily stayed occupied while her mother and I spoke. Hopefully she will spend lots of time building things with blocks and build the neural pathways at the same time that will help her succeed in geometry.

Other school supplies I like and find useful are:

Pilot Frixion pen. This writes like a nice rollerball, and it erases with friction – that is, not a regular eraser, but a piece of rubbery plastic at the end of the pen. It erases cleanly, plus there are no little eraser bits to wipe away, or an eraser to replace.

Sharpie Gel Highlighter: These are a little pricey, but they have some good benefits. One of them is total lack of bleed-through on paper. This is especially important when students have to highlight trade paperbacks with thin pages. Children also like the feel of using the highlighter. It can be used for coloring in a pinch, though it may get used up quickly for the price.

Enjoy your school supply shopping!

Review: Number Bonds Software for Singapore Math

Wednesday, September 14th, 2011


Number bonds software

Crystal Springs Books recently produced a new software program for number bonds practice. This concept is foundational to Singapore Math. Number bonds can be used for everything from addition and subtraction to understanding fractions, and Singapore Math makes great use of them in its teaching.

The software, intended for grades K-2, is a simple Flash-based program. The CD comes with installers for both Mac OS and Windows. The program is small and snappy, even on older or slower computers; I have tried it on a first-generation Macbook Pro as well as two netbooks. I have used the software with young students and demonstrated it in front of a group of teachers, and this is what we found.

The program comes with four different games, ranging from very basic to more advanced. In the first game, Pond Bonds, children must move frogs to the appropriate lily pad to form correct number bonds. In the second game, Bird Bonds, the purpose is to move the appropriate bird to the right hole in the birdhouse. In this one, each bird is labeled with a number. The third game, Which Number, shows number bonds with one of the numbers missing; students must click on the correct number to complete the bond. The final game, Which Bond, gives students a number at the top of the screen, with two number bonds below. The student must click on the correct question mark where the top number should go.

The games follow the progression of Concrete > Pictorial > Abstract, which is known to lead to student success. Picking up a kicking frog and dropping it on the lily pad, or hearing it splash in the water, triggers concrete sensory feedback, especially when used with a touch screen or interactive white board. Moving birds with numbers on them starts to combine the concrete with the abstract, and the shapes of the holes in the birdhouse mirror the shapes of the number bonds in the next levels. The final two levels use the pictorial and abstract levels to good effect.

The software has several options for customization. For each game, you can set a numerical range, a time limit, and a number of players. Be aware, though, that if you go with the defaults, it may be a recipe for failure; the time limit is set to lowest, and the numbers are set to the highest range, meaning even a very fast adult can’t get a very high score. I wish the defaults had been reversed. On the other hand, if you need to move students quickly through stations, the fast pace can be good. The fastest time may not allow adequate time for learning, though. Once you set the settings for a game, they stay that way until you change them.

One area where this software is lacking is educational feedback for the player. On the early games, if you miss a question, you can go back and try again, but you don’t receive any clues about what went wrong. On the higher games, if you miss one, too bad; you can’t even try again. I would like to see some sort of helpful feedback when mistakes are made.

When you have one player set, the score for the player is displayed at the end of the game. For more players, the others have to sit through each entire set until the scores are displayed at the end. I think more interactive game play would be nice. There is no way to save scores in the software, either. I would recommend that teachers create individual score sheets for students to keep track of their scores and how they improve over time, so they compete against themselves, not against others.

Since the software is Flash-based, it cannot run on iOS devices. I hope they develop a version for that platform soon.

UPDATE: As of March 2013, an iOS version is available! Read the review here.

Conclusion: Highly Recommended
Number Bonds is a simple, inexpensive software package that can provide extra addition and subtraction practice in the classroom or at home. Children find it fun and engaging, and it provides good composing and decomposing practice, as well as mental addition and subtraction. I would use it for a wider age range of children; it can be helpful for differentiating, like with more advanced preschoolers and upper elementary students who need foundational number bond practice. It would be nice if the software had a few more features, but I’m sure those features would take away from the software’s speedy response on older hardware. For best results, it should be run on a touch device, so it would be great if it could be installed on iOS or Android in the future.

Not expensive
Site license available
Small and fast
Good educational design (concrete > pictorial > abstract)
Fun for children
Range of levels and challenges
Compatible with a wide range of desktops and laptops
Singapore math-based!

Not enough feedback on mistakes
Can’t save score data
Settings need to be reset when first played
Not a true multiplayer game
Needs teacher introduction to be most effective (not stand-alone)
Teachers need training to make the most of it, but program-based help is minimal

NCTM Illuminations 2011

Wednesday, September 7th, 2011



This summer I gave a three-hour workshop on Singapore Math model drawing at the NCTM Illuminations Institute in Reston, VA. This was a fun workshop with a great group of people, and we accomplished a lot of model drawing practice and understanding.

I was pleased to see recently that the workshop received a couple of mentions on the web. One is on the thinkfinity site, which is run by Verizon and which I first joined after attending ISTE 2011. The other is from one of the participants, who wrote a blog post mentioning it.

If you are interested in seeing what I can offer your school, please be sure to contact me.

Which Singapore Math series should I use?

Tuesday, May 17th, 2011


Singapore Math is a rising trend in math education in schools and with homeschoolers, for the simple reason that it works. As an experienced Singapore Math teacher and trainer, I often get the question, “Which Singapore Math series should I use?” This question is posed by both teachers and homeschooling parents, and as more series enter the market, the choice becomes more challenging. In this article, I will present the pros and cons of each current series as I see them. Please feel free to contribute your views in the comments below.

Singapore Math, US Edition, published by Marshall-Cavendish:

This edition has been around the longest in the US. The main difference from the curriculum Singapore was using until recently is that this edition includes some additional problems using US measurements (feet, miles, pounds, etc.). This is the series that Singaporean students used when they scored highest on the TIMSS (international) test.

  • Short, focused textbooks and workbooks.
  • Clear graphics.
  • Emphasis on mental math.
  • Clear sequence from one book to the next.
  • Follows the best of the Singaporean teaching model.
  • Fits the Common Core State Standards well (see this article).
  • Decent Homeschooling Guide, from what I hear.


  • The measurement units don’t follow the Singaporean teaching model; that is, they don’t thoroughly teach one type of measurement before moving on to the next, rather mixing US and metric together. This can cause confusion in students.
  • For American teachers, teacher’s manual may be inadequate without further training.
  • Doesn’t come with assessments; I used the Practices and Reviews in the textbook for this.
  • Needs supplementation with math facts practice.
  • Children going from this edition to public school may be missing some subjects, but stronger in others.
  • Must be ordered online; shipping is high.

: This is my preferred series despite its shortcomings, which can be easily overcome with a little knowhow and creativity.
Buy here:, Inc.

Singapore Math, Standards Edition, published by Marshall-Cavendish:

This edition was created to meet the California learning standards. It is more colorful than the US Edition and covers slightly different topics each year. A comparison chart showing the scope and sequence of the two is available here. This series has been approved by the California State Board of Education.

  • Designed like the US Edition, with most of the same pros.
  • Thorough Teacher’s Guide.
  • Comes with Assessments.
  • Decent Homeschooling Guide, from what I hear.


  • One of the strengths of the Singapore Math curriculum is its focus on mastery of fewer subjects per year. This edition repeats the mistake of many US-designed curricula by putting in too many subjects per year so there is less time for each.
  • Must be ordered online; shipping is high.

Overall: Recommended if the child is in California or the state has similar standards to meet.
Buy here:, Inc.

Math in Focus
, distributed by Houghton Mifflin Harcourt:

This series is new to the US market, and Houghton Mifflin has Americanized it, with the typical large-sized teacher guides, a variety of student books, and manipulatives, packaged in typical school bundles. I have seen the company at trade shows and looked at the materials there, and have requested samples, but none have been forthcoming, so I have not been able to test them out until now. I just discovered the online sampling website they provide, but it’s slow, and I can’t try it out with my students. So while I have been able to see the series to some extent, this review is less in depth than others.


  • Easiest for US public school teachers to adapt to, with explicit guides and scripts.
  • Flows better to the middle school/high school Singapore curricula.
  • Wide variety of differentiation options.


  • Expensive.
  • Scores in Singapore went down after they implemented this program.
  • Less emphasis on mental math.
  • Books are larger with more complicated/busier graphics, potentially distracting from the learning process. I like the drawings, but combining them with photos can be confusing.

Overall: Recommended for teachers who don’t have prior experience using Singapore Math. For those who do, I need more experience with this program to recommend it or not, but I would stick with the US Edition for now. Homeschooling parents are better off with one of the series from
Buy here: Houghton Mifflin Harcourt

Singapore Math Practice
, published by Frank Schaffer Publications:

This series appeared in bookstores a year or two ago, and I made a beeline to it with interest. I put it down almost immediately, though. It appears to capitalize on the popularity of Singapore Math without a thorough understanding of its best principles and practices.

  • Readily available in bookstores
  • May provide extra practice in addition to using one of the other series, but use with caution.


  • Promotes the use of calculators too early, a big no-no in my book.
  • Problems have mistakes and are not well designed.

Buy here: or in bookstores like Barnes & Noble

Video: MSNBC Report on Singapore Math Model Drawing

Monday, May 9th, 2011


MSNBC ran a piece on May 3 about third-grade students learning math using Singapore Math. This report outlines the importance of model drawing for problem solving, and of parent understanding to be on board with it.

The report is well done, except it gives the mistaken impression that the only thing that makes Singapore Math unique is the model drawing approach. I used to think that too, but now I know better; developing number bond-based numeracy is at least as essential, as are other elements of the curriculum.

View the video below:

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