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.





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.

Manipulatives Make the Math Concrete

Manipulatives and Models
From a school that introduced Math in Focus materials this fall comes a great image of a fourth grader working with manipulatives to understand both algorithms and bar modeling. The class is learning long division. Number disks are a vital part of developing number sense in Singapore curricula.

Parnassus pennies
Another school is using Primary Mathematics and the class is doing the first lesson in multiplying and dividing by twos (Count by Twos). Students hadn’t used a lot of manipulatives before. This student excitedly exclaimed:

Hey, this is really useful!

Comments from observing teachers provided some interesting insights:

Wow, it sure is loud!

You can use a pre-cut sheet of felt from the craft store, or a laminated mat to help deaden the sound of working with louder manipulatives.

My kids would be bored to tears with this activity.

And she’s right, they would have. Her students were the higher ability group and need fewer concrete examples to understand the concept. (Note, not zero concrete examples, just fewer)

Number Discs
The red, white, orange discs with large numbers and the square set are available at as well as many online stores. The set with the smaller numbers is sold in conjunction with Math in Focus materials from Houghton Mifflin and corresponds to the colors used in the textbooks.

Looking for more on manipulatives? Check out this post: If I had a million dollars, ok $1000…

If I had a million dollars, ok $1000…

Recently, I received a question from an excited teacher who had just received a grant to spend on her classroom: “If you had a $1000 dollar grant and taught second grade, what would be the most important pieces of Singapore Math you’d buy?”

If I had a million dollars, ok $1000… here are two scenarios.

#1 Using the curriculum in 2nd grade as your main curriculum

  1. A classroom set of the 1B & 2A textbooks @ $9.00 each, so if you had 24 students + 1 for your self: 25 x $18 = $450
  2. Possibly a set of the 2B textbooks: 25 x $9 = $225
  3. A Teacher Manual for 1B, 2A & 2B: 3 x $21 = $63
  4. A workbook for reference and problem ideas for 1B, 2A & 2B = 3 x $9 = $27
  5. Challenging Word problems level 1 & 2: 2 x $8.50 = $17.00
  6. Intensive Practice: 1B, 2A & 2B: 3 x $8.80 = $26.40
  7. Process Skills in Problem Solving: $10.70
  8. Math Sprints Masters, Levels 1 & 2: 2 x $31 =$62
  9. Elementary Mathematics for Teachers by Parker & Baldridge: $29
  10. Place Value Strips: $12.50

That’s $625.80

I’d spend the rest on linking cubes, base-10 blocks, place value disks or other manipulatives and containers to keep them organized.

Keep in mind that for Number Disks/Place Value Disks you’ll need about 20 each of ones, tens and hundreds disks per student or pair of students sharing. Many companies sell these:

Place Value Disks, 100 Ones DisksPlace Value Disks, 100 Ones Disks

Place Value Disks - 100 Tens DisksPlace Value Disks – 100 Tens Disks

Place Value Disks (1-3): HundredsPlace Value Disks – 100 Hundreds Disks

#2 Using Singapore Math to Supplement another core curriculum:

  1. Start a library at your school with one set of the textbooks and workbooks for every grade level at the school as reference (4 per grade level)  x $9.00 each book – k-6 would be $36 x 7, k-5 would be $36 x 6
  2. A Teacher Manual for each level:  $21 each book, 2 books per grade level = $42 per grade level
  3. Challenging Word problems are $11 each and there are 6 levels (1-6)
  4. Process Skills in Problem Solving vary in cost from $10.20 to $12.80 – levels 1-6
  5. SpeedMaths Level 1 – 4: $8.20 each (no higher than level 4!)
  6. Math Sprints Masters, Levels 1 -5: 5 x $31
  7. Elementary Mathematics for Teachers by Parker & Baldridge: $29 several copies for staff
  8. The Singapore Model Method for Learning Mathematics: $29 for grades 5 & up
  9. Teaching of Whole Numbers by Dr Yeap Ban Har, Singapore’s renowned math educator, $30.50
  10. Bar Modeling A Problem-solving Tool also by by Dr Yeap Ban Har, for lower elementary. $30.50
  11. Place Value Disks: get plenty of ones, tens and hundreds. $15.95 per 100 disks
  12. Place Value Strips: $12.50 and other manipulatives (if you don’t already have them on campus).

What did I miss? Are there any books or tools that you consider “must-haves” in your Singapore Math classroom?

Seeking Singapore Math Assessments?

A recent visitor left this comment:

I am part of a team of first grade teachers at my school. We are piloting Singapore Math this year. We are creating assessments and were looking for ready-made assessments to genuinely fit the curriculum.

One of the challenges for a classroom teacher using the U.S Edition is that there aren’t any assessments ready-made. The Standards Edition of Primary Mathematics has assessments, however they won’t correspond directly to the U.S. Edition Materials.

Keep in mind that if you write the questions, you can tailor them to the objectives of your lessons. Are you assessing for basic competency? Are you assessing for deeper understanding? Additionally, for a teacher-created assessment, you need to create an answer key. I frequently hear from teachers who tell me, “Well, I gave this test, but all I have is the answer and I’m not sure how to work the problem.”

That being said, I know teachers’ time is valuable. Many teachers use questions from the Review sections of the textbook. Other basic questions from Intensive Practice books or practice problems from the Challenging Word Problems books could be used as well.

Be sure to save any well-written assessments for future use. After one year of working with the materials, you should have a good bank of assessments for future years.

One site that offers Singapore test paper problems for free (with registration) is Old School. At the first grade they have several mid-year and end-of-term papers available. Teachers can select the questions, either short answer or multiple choice, and create an assessment.  Additionally, you can choose problems from a list of topics. Topics for first grade are:

  • Addition and Subtraction
  • Combination Questions (3%)
  • Comparing and Ordering numbers (13%)
  • Division (1%)
  • General (1%)
  • Graphs (5%)
  • Measurements (7%)
  • Multiplication (3%)
  • Notation and Place values (9%)
  • Shapes and Patterns (12%)

Would you be interested in a test bank of questions? How about a place for sharing some teacher-made tests?