Math Problem Comparison

Teachers often ask, “What’s the difference between (the textbook I’m using now) and Singapore Math textbooks?” While there are many answers, I’d like to direct you to a resource that has been pointing out some differences  for over a year.

Once a week, Lefty (as in left-brained) over at Out In Left Field posts assignment comparisons between either a traditional math program or Singapore Math and various reform math textbooks.

From the original post:

Math problems of the week: Reform Math vs. other math

We’ll pair up a specific assignment drawn from this set with a specific assignment drawn either from a traditional series like McGraw-Hill, or from the foreign series most popular in America: Singapore Math.
I’ll try to pick assignments that take place at approximately the same point in the school year.  For example, I might choose two assignments from the first few weeks of first grade, or from the last few weeks of second grade, or from approximately 2/3 of the way into third grade.

At the end of many posts are some thought provoking Extra Credit questions. Some examples:

  • Which problem set involves more rote repetition of a given algorithm?
  • Which problem set is more accessible to children with language impairments?
  • Discuss how the two problem sets reflect the cultural and political differences between American and Singaporean societies.

Although many of the sample problems come from Singapore Math, there are also comparisons to traditional math books from the 1920s.


Grade 6 Word Problem Solutions

Earlier this month, I posted the following problem from a Nanyang Primary School 2007 Preliminary Examination I found at

A mixture, weighing 100 kg is made up of 2 chemicals A and B in the ratio of 7:3. When some volume of Chemical A evaporates, the content of Chemical A is reduced to 60% of the new mixture. What is the mass of the mixture now?

I thought I’d share how my son worked the problem:

chemical wp

He knew that if he multiplied 40% x 2.5, he’d get 100% so:

2.5 x 30 kg = 2.5 x 40%

75kg = 100%

I used a different drawing for “after” :

chem after

How did you solve the problem?

World Metrology Day

I know you’re on the edge of your seat.

World Metrology Day is celebrated annually on May 20, the anniversary of  the international agreement on units of measurement finalized at the Metre Convention in Paris, France in 1875.

World Metrology Day (WMD) commemorates the signing of the treaty and it is a day when all the countries in the world that enjoy the benefits of a single, coherent system of measurements, traceable to the International System of Units (SI), celebrate the scientific, technological, and economic achievements that this treaty has enabled for more than a century.

There are only 3 countries in the world that have not officially recognized the metric system: Liberia, Myanmar, and the United States.

Great news for students struggling to remember how many ounces in a pound, feet in a mile, or cups in a gallon. According to Elizabeth Gentry of the National Institute of Standards and Technology(NIST):

The United States is undergoing a subtle transition to the International System of Units (SI), commonly known as the metric system.

Learn about events in Gaitherburg, MD and Boulder, CO as well as celebrations around the world at the official WMD2009 site.

You were wondering: “What is Metrology?”

From Coastal Calibration Laboratories:

Definition 1): Metrology is the science of measurement.

Definition 2): Metrology is the science of weights and measures used to determine the conformance of an item to technical requirements. Metrology also includes the development of standards and systems for absolute and relative measurements.

Want to learn more about Metrology?


First visit? Check out the most popular pages:

  • Direct links to placement tests & recommended supplements –  Curriculum Materials.
  • Websites that support & supplement Singapore Math –  Math Links.
  • Download materials from trainings – Handouts.
  • AIR & TIMSS Reports – Resources

Singapore Math Tests..from Singapore

MissKoh (The url is actually is a website supported by Singapore’s Straits Times. If you click on the academic year, then the grade level you are interested in, you will be brought to a page of mid-year and final semestral papers as well as a few continual assessment papers, all from top schools in Singapore. For example; select 2008 and Primary 6 and you are offered test papers for English, Chinese, Maths or Science from 5 schools. (You need to register for some of the schools)

Go back to the 2007 Academic year and find tests through the second year of Junior College. All assessments are scans from actual school papers, so expect some rough looking pdfs.

My 8th grader and I had a great time working our way through some challenging word problems on a test.  For your mathematical enjoyment, here’s one from the Nanyang Primary School 2007 Preliminary Examination:

A mixture, weighing 100 kg is made up of 2 chemicals A and B in the ratio of 7:3. When some volume of Chemical A evaporates, the content of Chemical A is reduced to 60% of the new mixture. What is the mass of the mixture now? advertises itself as “Your Online Test Center” From the About Us page: is set up to create awareness for “The Straits Times School Pocket Money Fund” to help students from low income families who cannot even afford a proper meal during recess…

Most of the these students do not have extra revision materials to revise, so we hope you can help by sharing your printouts with them if you know of any such friends in school.

Singapore Math Training Sessions


(Image courtesy of Indexed.)

I’ll be presenting “How to Use Strategies from Singapore Math to Strengthen your Math Instruction” in Cincinnati on May 13, Atlanta on May 14 and in New Jersey on May 20 & 21, 2009. You can read more about these 1 day seminars and register through the Institute for Educational Development.

All seminars will be “buzzword” free!

These are the only public sessions I’ll be doing until the 2009 – 2010 school year.

Thinking about a field trip to see the world’s top-scoring math in action? There are just a few spots left for this July’s Singapore Math Summer Program.

Flash Cards designed for Singapore Math

(Whether they meant to or not!)

Here are samples from the four decks I purchased at NCTM from Dr. Frank Wang’s booth. The cards are available from (maker of the Witzzle Pro) along with some engaging free puzzles to keep your number sense on its toes.





NCTM Takeaways

The National Council of Teachers of Mathematics Annual Meeting and Exposition (NCTM) has ended and I wanted to share a few quick items regarding Singapore Math.


First off, Houghton Mifflin’s division Great Source premiered their new Singapore math series. Called Math in Focus, the textbooks are hardbound (and are heavy!) and the Teacher’s Editions appear quite comprehensive. This series looks like an American textbook series. I chatted with Patsy Kanter, one of the authors, as well as Shar Hammet, the head of the mathematics division for Houghton Mifflin, and they feel that they’ve kept the true essence of the curriculum while adding value to a classroom teacher.  I hope to procure a grade level to review and share. At each grade level, the series includes:

  • Student Book A and Student Book B
  • Workbook A and Workbook B
  • Teacher’s Edition
  • Extra Practice (Blackline Masters)
  • Assessment (Blackline Masters)
  • Reteach (Blackline Masters)
  • Enrichment (Blackline Masters)
  • Manipulatives

You can download a sample lesson from the first grade.



The Singapore Model Method for Learning Mathematics was available from the Marshall Cavendish booth and will be available next month from Written by the Ministry of Education, this book ( or monograph, as they refer to the publication) is designed to serve as a resource book on the Model Method:

The main purpose is to make explicit how the Model Method is used to develop students’ understanding of fundamental mathematics concepts and proficiency in solving basic mathematics word problems.

Although I’ve just begun reading the book, it appears to be a comprehensive overview of the Model Method and provides examples for both basic and quite challenging word problems.

The table of contents (click to enlarge):

Model Method

And a sample page 77 from Appendix A:

model method example

Finally, there were 4 presentations on Singapore Math at the NCTM:

  • Singapore Math Sixth Graders Solve Harder Problems than the Eighth-Grade NAEP by John Hoven
  • Every Child Counts, and Every Child Can Count! Strategies from Singapore Classrooms by Ban Har Yeap
  • Taking the Problem out of Word Problems with Singapore’s Model-Drawing Approach by Char Forsten
  • What’s so Good About Singapore Math – An exhibitor workshop by

ALL four Singapore Math sessions were oversubscribed, with disappointed attendees listening outside at the door. Dr. Yeap’s session saw people lining up 40 minutes beforehand to get a seat!

Challenging Word Problems series discontinued

The Singapore Math series: Primary Mathematics Challenging Word Problem from EPB Pan Pacific is being discontinued. Get your copies while you still can! According to the publisher, these books are:

“Highly recommended for capable students as a source of interesting review and challenging word problems”

If you’ve ever used the books, you know what a loss this will be to future users. While the books may be relics compared to the current Singapore Syllabus, one can’t help wonder if the changes in the “Teach Less, Learn More” syllabus in Singapore haven’t contributed to the country’s ever so slight drop on the most recent TIMSS. may have most books in the series available through summer, although it sounds like Primary 3 is in short supply.

For your problem-solving enjoyment, here’s a sample from the end of the Primary 6 book – Challenging level:

Cindy had four times as many postcards as Annie. After Cindy gave 20% of her postcards to Jane and Annie gave 10% of her postcards to Jane, the number of Jane’s postcards increased by 75%. If Jane had 252 postcards in the end, how many postcards did Cindy have at first?

Have fun!

(Cross-posted at Kitchen Table Math – The Sequel)

Grade 4 Word Problem

An interesting word problem was recently posted at the SingaporeMath Yahoo group. The original poster wrote for help solving it without algebra and mentioned that it was from the Primary 4 books. This seems a little advanced compared to the problems in the text and workbooks. I believe the problem could be from the Challenging Word problems series, which provides answers only.

There are 285 teachers and students in the hall. 5/6 of the students and 1/3 of the teachers went out of the hall. There is an equal number of students and teachers left in the hall. How many teachers were there in the hall at first?

If 5/6 of the students and 1/3 of the teachers went out, there would be 1/6 of the students and 2/3 of the teachers left in the hall.

Begin with the end result:


2/3 of the amount of teachers is equal to 1/6 of the amount of students. For every unit of students, there are 2 units of teachers.

Then let’s work back to how many there were at first:


There are 285 people divided into 15 units.
285 ÷ 15 = 19 people per unit.

There were 3 units of 19, or 57 teachers in the hall at first.

Then, to check out work, let’s find out how many students there were at first.
12 units x 19 people in each = 128 students

128 students + 57 teachers = 285 teachers and students were in the hall at first.

How can you extend the problem?