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?

Parts in the series:

Part 1 – Teacher’s Guides

Part 2 – Textbooks

Part 3 – Workbooks

Part 4 – Supplemental materials

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:

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

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)

• Add numbers within 10,000.

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.
  

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

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.

Enjoy!

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:

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” :

How did you solve the problem?

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?

MissKoh.com (The url is actually 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.

(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.

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.