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:

USp25USp26USp27

Standards Edition Workbook 3A:

STp48STp49STp50

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:

MPAHp29 MPAHp30

Shaping Maths Activity Book 3A part 1:

SMp31 SMp32

Were you expecting less practice in the materials from Singapore?

Parts in the series:

Part 1 – Teacher’s Guides

Part 2 – Textbooks

Part 3 – Workbooks

Part 4 – Supplemental materials

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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:

USp24 USp25 USp26

Standards Edition Textbook 3A:

STp50 STp51 STp52

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:

MPAHp28 MPAHp29 MPAHp30 MPAHp31

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:

SMp32 SMp33

Which materials would you choose for your third grade classroom? Share your opinion in the comments!

Parts in the series:

Part 1 – Teacher’s Guides
Part 2 – Textbooks
Part 3 – Workbooks
Part 4 – Supplemental materials

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.

PMUS

PM-St

MPAH

SHAP

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:

PMUSp22

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

  • Add numbers within 10,000.

PMStp74

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.

MPAHp40

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.

SHAPp56

Shaping Maths: Addition (p. 56)

  • 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.

Next in the series:

Part 2 – Textbooks
Part 3 – Workbooks
Part 4 – Supplemental materials

Singapore Math Tests..from Singapore

MissKoh

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 advertises itself as “Your Online Test Center” From the About Us page:

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.

add

subtract

multiply

divide

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!

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