# Category Archives: Math Resources

Web sites and materials to support math.

## Comparing Singapore Math Materials: Workbooks

In Part 1 and 2,  I shared examples from the Teacher’s Guides and textbooks from four sets of materials used in Singapore and the United States.

The materials are all from the third grade level:

1. Primary Mathematics U.S. Edition (2003)  from SingaporeMath.com
2. Primary Mathematics Standards Edition (2008)  from SingaporeMath.com
3. My Pals Are Here Maths (2007) obtained in Singapore from Marshall Cavendish Education
4. Shaping Maths (2007) obtained in Singapore from Marshall Cavendish Education

Following are the practice pages from each workbook that correspond with the lesson on addition within 10,000 that introduces regrouping in the hundreds. As before, each thumbnail links to a full-sized file.

Once again, there are minimal differences between the U.S. and Standards editions of Primary Mathematics.  Problem #1 changes pictures from towels hanging on a clothesline to boats. Problem #2 has one small change. The equation for  letter B changes from  4107 + 5 to 4105 + 5. Finally, on problem #4, “Weihua” becomes “Will”

U.S. Edition Workbook 3A:

Standards Edition Workbook 3A:

The My Pals Are Here Workbook is perforated and 3 hole punched. Perforated pages would be a great change to make to the Primary Mathematics workbooks! Neither My Pals Are Here nor Shaping Maths have any word problems tied to this practice lesson, in fact, there are very few word problems in the books at all.

My Pals Are Here Workbook 3A Part 1:

Shaping Maths Activity Book 3A part 1:

Were you expecting less practice in the materials from Singapore?

## Site has moved…

Bigger and better things to come – change your bookmarks to Singaporemathsource!

## Comparing Singapore Math Materials: Textbooks

In Part 1, I shared some examples from the Teacher’s Guide from four sets of materials used in Singapore and the United States.

The materials are all from the third grade level:

1. Primary Mathematics U.S. Edition (2003)  from SingaporeMath.com
2. Primary Mathematics Standards Edition (2008)  from SingaporeMath.com
3. My Pals Are Here Maths (2007) obtained in Singapore from Marshall Cavendish Education
4. Shaping Maths (2007) obtained in Singapore from Marshall Cavendish Education

Following are the pages from each textbook unit on addition within 10,000  that introduces regrouping in the hundreds. As before, each thumbnail links to a full-sized file.

There are minimal differences between the U.S. and Standards editions. The Standards edition is in color and there are two additional prompts asking students to estimate their answer first, then check for reasonableness. The first example shows regrouping in the hundreds. Problems 1-5 ask students to recall addition with regrouping the ones or tens or hundreds.

U.S. Edition Textbook 3A:

Standards Edition Textbook 3A:

My Pals Are Here includes two pages of instruction, another page with directions to a game and a final page exploring regrouping in the hundreds. Problem 5b on page 29 is the only problem that demonstrates  regrouping in both the ones and hundreds places,  although students are only asked to find the missing ones value in one addend.

Note the example #2 on page 29 that spells out the concept in words  (5 hundreds + 8 hundreds). This is a great reminder of how teachers can model this concept in a classroom and is included in the Teacher’s Guide for Primary Math both U.S. and Standards editions ( 7 ones + 5 ones = 1 ten 2 ones).

My Pals Are Here Textbook 3A:

The Shaping Maths lesson is two pages of slightly more abstract description than My Pals Are Here. Place value disks are used instead of images of base-10 blocks.

Shaping Maths Coursebook 3A:

## Comparing Singapore Math Materials: Teacher’s Guides

### First in a four-part series

I thought it might be interesting to provide examples of how a lesson is presented in four different sets of Singapore Math materials. Part 1 compares the materials where a lesson begins – the Teacher’s Guide. The rest of the series will include textbooks, workbook and supplemental materials.

All four sets of materials are listed below. The two editions of Primary Mathematics are currently in use throughout the United States. My Pals Are Here and Shaping Maths are currently in use in Singapore.

This overview doesn’t include the Math in Focus series by Marshall Cavendish and exclusive United States distributor Great Source (A division of Houghton Mifflin Harcourt)  which will be available soon in the United States.  Representatives at the NCTM Conference in Washington, D.C. stated that the Math in Focus content is based on the  Singaporean edition of  My Pals Are Here, with U.S. money and measurement the main additions. A listing of key topics can be found on the Great Source site.

The materials are all from the third grade level:

1. Primary Mathematics U.S. Edition (2003)  from SingaporeMath.com
2. Primary Mathematics Standards Edition (2008)  from SingaporeMath.com
3. My Pals Are Here Maths (2007) obtained in Singapore from Marshall Cavendish Education
4. Shaping Maths (2007) obtained in Singapore from Marshall Cavendish Education

Most people will display the cover of a book. You get the title, authors and little else. The back of the book,  however, contains more interesting information. (Exception? The Primary Mathematics-U.S. Edition) These are from the 3A Teacher Guides and provide a brief overview of each series. For your reading ease, each thumbnail links to a full-sized file.

For comparison, I will be using the first lesson in the 3A materials from the unit on addition within 10,000  that introduces regrouping in the hundreds. All materials use the term “renaming” except My Pals Are Here, which uses “regrouping”.

Below are the names, pages and the stated objectives for the lesson from the corresponding Teacher’s Guide along with one page as an example:

Primary Mathematics-U.S.: Adding Ones, Tens, Hundreds and Thousands (p. 22)

Primary Mathematics-Standards: Adding Ones, Tens, Hundreds and Thousands (p. 74)

• Review of addition of numbers up to 3 digits.
• Adding thousands with another number up to 4 digits with renaming once.

My Pals Are Here: Addition With Regrouping in Hundreds (p. 40)

• Add two 4-digit numbers with regrouping in hundreds using concrete representation.
• Show regrouping of hundreds to thousands and hundreds.
• Carry out vertical column addition by adding the hundreds first then the thousands with regrouping in the hundreds place
• Add without place value charts.

• To add 4-digit numbers with renaming once.
• To add 4 digit numbers with renaming more than once.

Both My Pals Are Here and Shaping Maths have a larger sized Teacher’s Guide (A4 size). This allows the publisher to include each page from the textbook, surrounded by:

My Pals Are Here: instructional objectives, instructional procedures, key concepts, materials, additional activities, individual work, heuristic for problem solving and thinking skills

Shaping Maths:  objectives, lesson, materials, classroom organisation, vocabulary, general learning difficulties, IT, notes and textbook practice

The Teacher’s Guide for Primary Mathematics – Standards provides much more guidance.  The layout of the material is more familiar to most teachers and looks a bit more like a typical American teacher manual.  Although the Standards Edition provides California Standards, it would be easy to correlate these to another state’s standards. As a design, I like the spiral binding that allows the book to lay flat.

As we will see in the rest of the series, you should not choose a set of materials based on the Teacher’s Guide alone.

## Singapore Math Tests..from Singapore

MissKoh.com (The url is actually http://www.MissKoh.info) 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?

Misskoh.com 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.

## 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 MathFun.com (maker of the Witzzle Pro) along with some engaging free puzzles to keep your number sense on its toes.

## 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.

SingaporeMath.com 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!

## Why Singapore is another model for teaching excellence

The Christian Science Monitor is running a series entitled “What Makes a Teacher Good?” that includes articles on teacher pay, teacher training, and lessons from international schools. An example of a strong international education system is highlighted in the article: Why Singapore is another model for teaching excellence that discusses the way Singapore ensures that their teachers are truly highly qualified. Three U.S. visitors to Singapore were interviewed. Steven Paine, the superintendent of West Virginia’s schools:

asked a Singapore official about the basis of their math curriculum, she cited a standards framework put out by the National Council of Teachers of Mathematics – in the United States. West Virginia’s curriculum takes guidance from the same source, Mr. Paine says. “So the question remains, why is it that they lead the world in student achievement? I think it’s because of their teacher quality,” he says.

While teacher quality is a part of the success that Singapore has experienced, curriculum is another large  part. The Singapore official may have cited the NCTM standards, however it’s clear that Singapore’s Ministry of Education has created a more refined framework document. The NCTM’s Principles and Standards for School Mathematics runs 402 pages for elementary and secondary while Singapore’s Ministry of Education can cover both primary and secondary in a concise, content-rich 82 pages.

From the NCTM online access for Principles and Standards:

From the MOE primary syllabus (Primary 1 is 1st grade):

As a teacher, which set of 1st grade standards would you prefer to follow?

## What’s the difference?

### Singapore Math U.S. v. Standards edition

When I was in Singapore two years ago, Marshall Cavendish unveiled the new primary Mathematics Standards edition materials and there were murmurs of concern throughout the room. The general consensus was that the books looked too big; they must have added so much material that the series will look just like any American curriculum. There are added pages and concepts. Schools and homeschooling families that have a choice (sorry California, no choice for you) will want to review the materials thoroughly before purchasing.

Let’s back up a bit. Why did Marshall Cavendish/SingaporeMath.com decide to create the Standards edition? From the SingaporeMath.com website:

Primary Mathematics Standards edition is an adaptation of Primary Mathematics to meet the Mathematics Contents Standards for California Public Schools, adopted by the California State Board of Education in 1997 for grades 1-5 as one of the approved textbooks. It is similar to the US edition but has some rearrangement of topics and some added units, primarily in probability and data analysis, negative number, and coordinate graphing.

A side-by-side comparison of the scope and sequence of the two curricula appears on the SingaporeMath.com website. Of note, there are Extra Practice books for both series as well as Teacher Guides. Home Instructor Guides are available for the U.S. edition and the following Standards edition levels: 1A, 1B, 2A, 2B, 3A and 3B. 4A will be available in the summer of 2009. The Standards edition has comprehensive tests books for each level. Although the distributors state that materials are not interchangeable between the editions, anyone willing to do a bit of work will find that the test books can be adapted to the U.S. materials. If you enjoy this overview and  would like to see one for another grade level, feel free to email me.

Prompted by a comment by Ali in VA, I took a look, book-by-book, at the 1st grade materials and found a few differences. Please do not make your decision on edition based on just the 1st grade materials. The curriculum is sequential, and spirals with mastery.  I would not, therefore, advise jumping between the two different editions.

Minor changes to the series include the numbering of units in the textbook and exercises in the workbook. I believe that it organizes the materials better for teachers. Added to each of  the textbooks are a glossary and index. Added to each workbook are 33 pages of Math at Home activities. Pictures have been used occasionally in place of clip art, a few names have been changed, color added, number bonds are now circles, not squares, etc. Starting with the unit Numbers to 40, the colors on the place value strips have been standardized. Ten strips are always pink, ones are blue. (You can purchase Place Value Strips or make your own from sentence strips.)

More important changes include the addition of concepts. The following concepts were added in the first grade textbooks with complementary additions for practice in the workbook exercises and reviews.

1A Units:

1. Position & Direction -lesson has been added to the unit on Ordinal Numbers.
2. Shapes –lesson has been added that focuses on vocabulary: flat, stack, roll, slide, corners, sides.
3. Capacity – three lessons on comparing and measuring in non-standard units.

1B Units:

1. Graphs – Lesson on tally charts and bar diagrams has been added.
2. Numbers to 40 – lesson on counting by 2’s.
3. Time – two lessons: Before & After & Estimating Time.
4. Numbers to 100 – one lesson on addition with the vertical algorithm, one with subtraction (without renaming).

Now, having gone though through all four books, literally page-by-page, I could ONLY find one page in the U.S. edition that was omitted from the Standards edition.

Additions and eliminations duly noted, here are a couple of quirky difference between the editions.

Two pages from the same exercise – U.S. edition on the left, Standards on the right.

And two pages from the textbook. U.S. edition on the left, Standards on the right.

Finally, it looks like school starts 2 hours later in the Standards edition. Again U.S. edition on the left, Standards on the right.

## Personal Whiteboards

In the post about Number Strings, I referred to a student’s “personal whiteboard”.  I use whiteboards throughout the day as a way of informally assessing students.

Instead of a store bought whiteboard, I prefer to provide students with a customized version.

1. Start with a glossy page protector, a box of which which can be purchased inexpensively on eBay or at Sam’s Club or Costco.
2. Insert a brightly colored sheet of card stock. Card stock makes the whiteboard a little sturdier and by using color on one side, I can instantly tell when the entire group of students is ready.
3. Add appropriate pages. In the first grade, I might have a pre-made number bond page ready to go. When I’m teaching a lesson on adding or subtracting, I’ll insert a place value chart.

By keeping a classroom set of these on the shelf with the student textbooks, they would last an entire school year. Here are some printables to get you started:

You can find information on Alexandria Jones’ Pharaoh’s Treasure in the picture at Let’s Play Math.

These are also great for games and learning centers…

Sudoku, Kenken, Contig or

Or any of the international logic games on the handouts page of this site.