Slides and Handouts from my NCSM/NCTM Presentations

NCTM model session It was so fun to present not one, not two, but three, sessions at recent national math educators’ annual conferences in Boston.

At both the NCSM and NCTM**, Lauri Susi and I presented “Strip Models, Tape Diagrams, and Bar Models, Oh My!” Slides that accompanied that presentation are online. Some slides don’t have the bar models on them as we drew them in during the session.


NCTM Singapore Math Presentation

In addition, at NCTM I presented an Exhibitor Workshop entitled: Filling Knowledge Gaps with Critical Singapore Math® Approach (Gr. 3-5). Thanks! Singapore Math, Inc. for inviting to speak on your behalf!

**National Conference of Supervisors of Mathematics and National Council of Teachers of Mathematics

Dispatches from 2015 National Math Educator Conferences

This week, I’m attending the 2015 Annual Meetings of the National Council of Supervisors of Mathematics (NCSM) and the National Council of Teachers of Mathematics (NCTM) in Boston. I presented Strip Models, Tape Diagrams, and Bar Models, Oh My! at NCSM on Tuesday and will do a similar session at NCTM on Thursday. I’m excited to share some resources that are now available!

conceptua-logo New bar modeling tool! Conceptua Math has a beta version of their bar model tool available to review. Check it out at
They welcome your feedback.

kakoomaGreg Tang has a fun fact automaticity practice app – and it’s a game! And there are iPad apps! Visit Greg Tang Math for Kakooma. Greg claims the record for the addition puzzle is 8 seconds, set by a student.

RodelRodel Foundation in Arizona has released a fabulous new book that schools will want in their library: Math Power: Simple Solutions for Mastering Math.  This handbook is full of visuals and is written in English and Spanish. Here’s a page chock full of great definitions and pictorial models:

Math Power

Handouts from my sessions:

NCSM: #232 Strip Models Tape Diagrams Bar Models Oh My!

NCTM: #126 Strip Models Tape Diagrams Bar Models Oh My!

NCTM: #494.3 Filling in Knowledge Gaps: Critical lessons across grade levels 1-3 for students in grades 4-6



Looking for the Best Singapore Math® Materials?

InformationOr resources to help students?

These new pages should help.

Every year, I respond to hundreds of inquiries from teachers, administrators and parents seeking more information about the Singapore Math curriculum.

Some want to learn more about Math from Singapore and why it is so successful. Others are looking for specific resources to use in the classroom or for home enjoyment. Others still are seeking to a higher level of knowledge so they can be more effective math coaches or trainers.

I’ve added three new pages to Singapore Math Source to steer you to the best available books for a variety of needs:

Singapore Math® Editions – at a GlanceWhich series should I buy? See all your options.

Best Books to Support Singapore Math in the ClassroomSupplemental books for use with students.

Best Books for Grown-Ups Wanting to Learn Singapore Math: Title says it all, doesn’t it?

-Image via Indexed

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.