It can’t all be Singapore Math…

This tweet posted by the National Council on Teacher Quality (@NCTQ) caught my eye:


Now, I’ve heard decomposing called “branching” but can’t remember ever seeing this in a Singapore textbook. Where did this problem come from?

It’s nice that NCTQ recognizes Singapore’s Math as “tops in the world.” But it’s discouraging to see methods and terminology that are not a part of the Singapore curriculum attributed to it. Especially in the context of the nasty debate about CCSS. And especially since Singapore’s math curriculum–with its rigor, coherence, and focus–is often cited as a basis for more rigorous standards, including CCSS.

The problem posted is based on the concept of “Number Bonds,” which calls for students to decompose numbers (this is the term used in Singapore and in all major Singapore Math® textbooks distributed in the U.S.). Below, I’ve posted some examples of how this concept is presented in Singapore Math® series available in both the U.S. and Singapore.

This matter points to my BIG concern: As publishers and others adapt Singapore’s Math for the American market, new approaches creep in. These often are not based on the curriculum that helped Singapore’s students go from mediocre to best in the world in a dozen years. I’ve written about this in my comparison of Singapore math textbook series available in the United States.

So my plea to NCTQ: please use examples from an actual Singapore mathematics text when citing the components that make it so successful. And feel free to ask if I can help you find those examples.

Number Bonds problems in Singapore Math® textbooks

Here are some materials covering Number Bonds and “decomposing” numbers from actual Singapore textbooks:

From My Pals are Here, the most-used materials in Singapore:

MPAH 3A Mental Addition

From the U.S. Edition of Primary Mathematics, available in North America since 2003:

PM US 3A Mental Addition

From the Common Core Edition of Primary Mathematics, released in the U.S. market in 2014:

PM CC 3A Mental Addition_0001

And finally, from Math in Focus:




Ugh! One more similar tweet from NCTQ.






New Singapore Math® iPad apps

With new apps being added to Apple’s iTunes store all the time, I’m always on the lookout for ones that advertise themselves with the term “Singapore Math”.

Listed below are some recent additions. I paid for and personally played with all of these in order to offer my candid assessment of each.

You can find these and more Singapore Math-related apps on the Singapore Math® iPad Apps page, which is among the most frequently visited on this site.

Note: I didn’t include the online version of Discovering Mathematics textbooks as they are designed to support the books only.

Archimedes_Roost ipad appArchimedes Roost – $2.99

Kindergarten app based on Singapore Number Bonds and Montessori using parts and wholes and Montessori bead chain and strip board manipulatives. Includes addition and subtraction within 20. Fully narrated for non-readers.

Opinion? Great graphics and engaging activities.  Good number bond and missing addend problems. This is worth $2.99.

Math_Facts_Number_Bonds_iPad_app Maths Facts – $0.99

Four choices: Number Bonds and Fact Families practice to Ten, Addition & Subtraction to Ten. No ability to differentiate or make it more difficult. Addition & Subtraction is find the sum or difference only, no missing addends.

Opinion? Simple and minimal levels. Very basic, froze a couple of times, but only 99¢.

Let's_Count iPad app Let’s Count – Free

For ages 3-6, this is a very basic app with four options. Order quantities of jelly beans from least to greatest, count and label bars to ten, Count beans to ten, match numbers.

Opinion? Well, it’s free and doesn’t take up much memory.

Robin_and_DobPractice Math with Robin and Dob – $2.99

Master addition and subtraction with math whizzes Robin and Dob. 10 levels of each, addition & subtraction, no customizing. The dog pops up when you’ve taken too long and offers help in the form of an abacus, tens and ones place value chart with apples or the problem stacked instead of horizontal. Adorable!

Opinion? While the game is simple and has minimal levels, the basic practice is solid (and adorable!).  This is worth $2.99.

Place Value Cards Place Value Cards iPad appCards – $0.99 each

A number is given and you must show it two different ways, for example if 3 tens and 6 ones is given, you could also make 36 with 2 tens and 16 ones.

  • Level 1: Tens and Ones
  • Level 2: Hundreds, Tens, and One
  • Level 3: Thousands, Hundreds, Tens and Ones
  • Level 4: Hundreds, Tens, Ones, and Tenths
  • Level 5: Tens, Ones, Tenths, and Hundredths

Number_Bond_Cards ipad app Number Bond Cards – $0.99 each

  • Level 1: Ten Frames and
  • Level 2: Number Bonds with missing whole
  • Level 3: Number Bonds with missing part

Opinion? Both of these apps are very simple and have minimal levels. If your child needs this targeted practice you could spend the 99¢.

Crackers_&_Goo iPad app Crackers and Goo – $2.99

Crackers and Goo uses patterns to teach children to identify patterns and see parts of wholes. Flying crackers need to be dragged down to complete the problems. Starts very basic and finishes with rounding then multiplying 898, 899, 900. Yikes! Mental math strategies are explained.

16 levels with 5 mini-levels on each

  • Grades K-1: game levels 1-4
  • Grades 2-3: game levels 5 – 7
  • Grades 4-5: game levels 8 – 11
  • Grades 5 and up: game levels 12 – 16

Opinion? Great, if repetitive, practice. Turn the volume down on the annoying music. I can’t see kids playing this for long, but it is more of a “game” than typical flash cards. I dig this app, but not sure about young students.

Visual_Math_Word_Problems_iPad_app Visual Word Problems  – $4.99

Designed to help 1st and 2nd grade school children to visualize, understand and solve basic addition & subtraction word problems, this is a guided, easy to use app for early learners. I really like how prompted the steps are to maneuver through the program and that the default option is to have the app read the problems aloud. The animated word problems that use actual pictures of cows, oranges and apples are fabulous. They are laid out as a definite precursor to the bar modeling that begins in grade 3.

Opinion? Worth the $4.99, but this is not a game. If you would like your child working some basic addition & subtraction word problems, here’s your app.

Xyla_and_Yabu_iPad_App Xyla and Yabu  – $0.99

Help Xyla and Yabu trade gems back and forth by learning to add and subtract with number bonds. Use the relative sizes of number bond bars representing parts and wholes to develop number sense while solving word problems. Understand and become automatic at using tens, doubles, and other recurring patterns with numbers.

Each number bond is presented in the context of a word  problem. After mastering sums up to 20 (14 activities), kids explore similar patterns with sums up to 100 (13 activities), for 10 levels in all. There is no option to have the app read the problems aloud. In numbers to 20, there is a picture and a bar hint, in numbers to 100, just some bar hints. After the beginning levels, three possible answers are given.

Opinion? Best 99¢ you can spend on a word problem app for grades 1-2 working with parts and wholes to 100. Of course, Thinking Blocks is still free.

Math_Master_Bingo iPad app Math Master Bingo – Free to download, 99¢ in-app purchase for unlimited play.

Practice your four operations with Bingo. Choose the operands rang and the operation. (% is used for ÷). Answer questions until you get five in a row.Every 5 problems, it asks you to upgrade. Has two buttons on homescreen to send you to Facebook, only one for Twitter

Opinion? Constantly asks to post to Facebook, I’d pass.

Jingle's_Puzzle iPad app Jingle’s Puzzle – $1.99

For grades 3-6, the website claims this app is designed Singapore primary school’s mathematics model methods.  Good luck with that. This is a problem-solving, logic game. Sums are listed on teh left and top of an array and some of the squares are filled in. Students find the pattern and complete the grid.

Opinion? I think the words of the single reviewer say it best: “VERY confusing…Not for young child…There is NO app support. I want a refund.”

Math_Olympiad_by_KooBits  Math Olympiad – Free for first 6 problems, then $15.99 per level to unlock.

Designed for 8-12 year olds, this app has official competition questions from the Asia Pacific Mathematical Olympiad for Primary Schools. And the 6 problems that are included are exactly the types of problems seen on the U.S. version of the Math Olympiads for Elementary & Middle Schools.

Opinion?  This might be a great purchase for Math Olympiad teams looking for new problems. The levels are less expensive than the books in the MOEMS store.

HeyMath! ipad app Hey Math from Singapore – Subscriptions from $0.99

Videos and practice with multiple levels from Singapore’s #1 online learning site. Hey Math! is an official Partner of the Academy of Singapore Teachers. They also  make Factorama – which my 17 year old son loves to challenge me on.

Opinion? This is a very good iPad version of the online site. The videos are very directed and the practice is like an online worksheet. 

Smartest_Singapore_iPad_app Smartest Singapore – Free

Online learning game for Singapore primary school children. Students play in 60 second speed challenges in languages, mathematics and general knowledge. There is no way I could see to customise this app to focus on mathematics. You need to choose a Singapore primary school in order to register and there is no option for “other” or “homeschool”. If you’d like to study up on topics, there is an option. Choose from activities,  animals, food, Geography, Plants, the MRT (subway in Singapore, Singapore history & famous people or a language. you never know when the Chinese word for bricklayer may come in handy.

Opinion?  Pass. Unless you want your child deciding if a picture is of Chimgan Mountain in Uzbekistan or Global Geoparak in Hong Kong. Game portion works about 50% of the time.

Math_Mastery! iPad appMath Mastery! – Free

Secondary and Middle school topics. Supports, who also declares itself the “leading online Mathematics E-Learning system in Singapore”. Must be a registered user of Ace Learning to use.

Opinion?  No need to download unless you already subscribe to Ace Learning.

Math_Exam_Revision_Kit Math Exam Revision Kit – Free

Also by ACE-Learning Systems and so must be registered to get the full app. Secondary and Middle school topics including notes, questions with guided solutions and more practice questions.

Opinion?  No need to download unless you already subscribe to Ace Learning.

Matholia iPad apps Matholia iMath tools & Essential Practice – Free to download, paid subscription to access

For grades 1-6, Matholia is an another online mathematics learning portal providing pupils, teachers and parents with dedicated content based on the latest primary maths syllabus from the Singapore Ministry of Education – or you could get the U.S. version. Try the program free for 7 days with a code, then you must subscribe to continue. Ther are practice learn and games option available on the desktop version as well as Singapore math tools and virtual manipulatives for differentiated interaction.

Opinion?  No need to download unless you already subscribe to Matholia.

Mathematical_Quickies_&_Trickies_Ipad_app Mathematical Quickies & Trickies -$9.99

Designed for students in grades 6 and up, this is an ipad version of a book of math and math puzzlers. From the Amazon description:

Mathematical Quickies & Trickies contains more than 300 non-routine problems to enhance students’ problem-solving skills…Mathematical Quickies & Trickies would appeal primarily to students and teachers looking for some fertile trick and tricky questions; mathletes preparing for local and regional contests and competitions; problem solvers longing to be challenged by questions whose obvious solutions are never the correct ones for what offhand appears to be true is false.

More_Mathematical_Quickies_&_Trickies_ More Mathematical Quickies & Trickies  – $9.99

Opinion? Cheaper than the books. 


2048_SG_Army_iPad_app 2048 SG Army  – Free

Version of 2048 in which you match tiles to earn your way through the Singapore Armed Forces

Opinion? Probably not for your typical child. I made it through the ranks to Staff Sargent through sheer luck. Stick with the regular numbers version.


Save the Date! Singapore Mathematics Fall 2014 Seminars

My brain exploded!

Here are the just-released Fall 2014 dates for my BER seminars “How to Use the Best Strategies from Singapore Mathematics to Strengthen your Math Instruction”  and  “Boost Students’ Math Problem Solving Skills Using Singapore Model Drawing” 

Boost Students’ Math Problem Solving Skills Using Singapore Model Drawing” (BER)

A whole day of problem solving with Singapore Bar Modeling PLUS that handbook for your own home enjoyment! (- with the answers and fully worked solutions!)


“How to Use the Best Strategies From Singapore Mathematics to Strengthen Your Math Instruction” (BER) – I’ll update this post when the registrations are available. UPDATED 8/16/2014

2015 dates – I’ll update this post with links when the registrations are available. 

This overview of Singapore Math® strategies will put your students on the road to success with number sense, computation and problem solving.  (Plus you a get a handy-dandy handbook!)


Your city not on the list? Contact me and I can bring my Singapore Math® workshop(s) to your school or district – email Cassy (at)

Pre-orders open for Primary Mathematics Common Core Edition

PMCC and DMCC As I previewed last week, the new Primary Mathematics Common Core Edition is now available for 2014-2015 school year.

Primary Mathematics Common Core Edition maintains the proven Singapore approach to teaching and learning mathematics, with a focus on the Concrete to Pictorial to Abstract (CPA) method and use of strategies including bar modeling.

We are currently accepting pre-orders for Primary Mathematics Common Core Edition and Earlybird Kindergarten Common Core Edition. Materials will be available to ship starting in mid July 2014. We will arrange the delivery for a time convenient to your school.

Want more information? Schools can request a price list, review sample chapters, and get info on  pre-ordering materials with this form.

Dimensions Math Common Core is also available for grades 7 & 8.


Singapore Math Common Core Edition debuts at NCTM Conference

Cassy Turner

Thanks to Pearson for my cool caricature. Looks just like me, doesn’t it?!

I’ve just returned from an invigorating week at the National Council of Supervisors of Mathematics (NCSM) and National Council of Teachers of Mathematics (NCTM) conferences in New Orleans. Expect some posts soon that will share interesting things that I learned.

Common Core Edition of Primary Mathematics

First off, the new Common Core aligned editions of Primary Mathematics were available at the Singapore Math, Inc.® booth and they looked great! If you’re currently using the California Standards Edition of Primary Mathematics, don’t panic! The company will continue to carry the materials. However, once you see the Common Core Edition, you’re probably going to want to switch. [Using the U.S. Edition? You’re good to go with some supplementing, but you’re used to that already.   😉  ]  Copies of the new materials are not available for preview yet, but I’ll be posting some more info and sample lessons as they do become available.

Good news! Looks like there will be a Primary Digital component to the program as well.

I don’t know about anyone else, but I’m a little Common Core-d out. It seems like EVERY session at both conferences had to reference the Common Core to get accepted. Thank goodness that Primary Mathematics is already fairly well aligned  to Common Core. [Don’t believe me? Here’s Achieve’s analysis.] In perusing the new Primary Mathematics Common Core books, I noticed that content was not moved to higher grade levels, just because that’s where it was in the CCSS-M. They’ve kept the integrity of the sequence, added a few review lessons to meet CCSS-M at grade level and provided an unprecedented level of potential student questioning and discourse in the Teacher’s Guides.

I thought I’d leave you with one of the Japanese Puzzles from a fabulous session at NCTM presented by Jeffrey Wanko called Puzzling It Out: Teaching Inductive Reasoning. Have fun!

Use the three examples of Mirror puzzles and their unique solutions shown below to determine both the goal and the rules that govern Mirror puzzles.Mirrors_Puzzles