Singapore Math word problems

Making math masters: A brief overview of Singapore Math®

March 16, 2012 by Cassy Turner 10 Comments

My students love math class. In fact, many will tell you math is their favorite subject. Why? They’ll tell you it’s because Singapore math is fun. I’d say it’s because once they understand how math works, they become confident in their abilities. So what exactly is Singapore math?

Wait, math from Singapore? Isn’t that some little island in Asia?

Primary Mathematics is based on a program of study introduced by the Ministry of Education in Singapore in 1981, a time when Singapore’s students were middling in math. Fifteen years after the adoption of its new Primary Mathematics Syllabus, Singapore students led the world in global Math achievement tests (Singapore topped international rankings first in 1995, and again in 1999, 2003 and 2007).

The Singapore math success story—from mediocre to world-class in a generation—is no secret. The curriculum provides students with a solid foundation in mathematics by focusing on visual understanding, connections, number sense, mastery, and word problems.

Concepts in Singapore Math® are taught in a concrete – pictorial – abstract sequence

Hands-on manipulatives or real life objects are used to demonstrate the concept, then students use and create pictorial representations. This interim visual step is typically missing from many curricula used in the U.S. It provides a transition from the words to an abstract algorithm. The goal is always to use the concrete and visual components to get to a standard algorithm.

To gain number sense, students are taught to make connections between topics. While first graders will still work on “fact families”, Singapore math also uses a pictorial representation called a “Number Bond” to help students see the connections between addition and subtraction.

Fact Families: Number Bonds:

Understanding numbers and operations is critical to mathematics

Singapore materials focus on place value to provide a deep knowledge of numbers. As students work with and manipulate numbers, they work towards fluency by learning and using mental math strategies.

For example:

“If I know that 7 and 3 make 10, I could solve the problem of 47 + 8 by breaking the number 8 apart into 3 and 5. Adding the 3 to 47 gives me 50, then I can easily add on 5.”

These mental math skills show flexible thinking and provide a “check” students use when the algorithm is learned. I was in a first-grade classroom last week where the teacher was talking about addition and subtraction strategies with her students. They were working with numbers like 9 + 5 and the teacher had asked the students how they got their answers:

“I counted on from 9”
“I took 5 apart to 1 and 4 and made a ten first”
“I used automaticity!”

To get to mastery, students work on focused concepts and skills. U.S. curricula are typically criticized for being “A mile wide and an inch deep”. Topics continually spiral and “It’s ok if kids don’t have their multiplication facts memorized this year, we’ll reteach them again next year.”

And next year and next year…

Not so with schools using Singapore Math®. In first grade, students will learn multiplication of twos and threes within 40. In second grade, they’ll master multiplication and division by 2,3,4,5 and 10. Each year builds on the prior foundation and extends student understanding. By the end of third-grade students will have mastered all of their multiplication tables as well as multiplying and dividing by a single digit. Yep, they will even become proficient with the dreaded “long division algorithm”.

Understanding problem solving

Another component of mastery is the ability to take what you already know and apply it in a new context. Remember being tortured in school with story problems? The heart of the Singapore curriculum is an emphasis on problem-solving — and that means word problems. They are incorporated throughout the materials to provide context to each topic as it’s taught. The key to solving these begins with a bar model or pictorial representation of the word problem. For instance:

1) Ginny has 40 cherry and grape gumballs in all. She has 24 cherry gumballs. How many grape gumballs does she have?

2) Ginny has 24 gumballs. She has 3 times as many gumballs as Paul does. How many gumballs does Paul have?

3) 2/5 of the students in a class are boys and the rest are girls. There are 35 students in the class. How many boys are in the class?

4) The ratio of the number of boys to girls in a class is 2:3. After 6 boys join the class, the ratio becomes 5:6. How many boys were in the class at first?

This is a sixth-grade problem from a unit on changing ratios. Can you see the answer? Note that the number of girls doesn’t change.

1 unit = 6 boys

4 units = 24 boys

Mastering Math Makes Math Fun!

Singapore Math® is a great foundation for elementary math success. Working with teachers in their classrooms, I see the impact the materials have on students every day. Singapore math can help make every child in every classroom a competent and confident mathematics student.

Answers to Word Problems

1) Ginny has 16 grape gumballs

2) Paul has 8 gumballs

3) There are 14 boys in the class

4) There were 24 boys in the class at first

Bar Models generated from ThinkingBlocks.com

Filed Under: Implementing Singapore Math, Masters, Math Resources Tagged With: Model Method, number bonds, Singapore Math curriculum, Singapore Math word problems

Singapore Math Must-Know Word Problems

June 9, 2010 by Cassy Turner 3 Comments

From publisher Frank Schaffer and Singapore Asian Publications comes a series of books: Singapore Math: 70 Must-Know Word Problems. From the back cover:

This book is designed to help students master word problems, which are often tricky and challenging…This book is perfect for students familiar with Singapore Math and for those who just need extra practice with word problems.

The 70 Must-Know Word Problems books are marked by levels that are considered a grade above for the U.S. market. For example, the Level 6 book claims to be appropriate for students in grade 7 and the Level 4 book is listed as appropriate for students in grade 5. If your child has been learning with Primary Mathematics and you’d like to pick up one of these workbooks, you should probably pick up the level that correlates to their current grade. Meaning, if your child is currently working their way through the Level 4 Primary Mathematics textbook, then the level 4 70 Must-Know Word Problems book will work as a supplement. The problems in the books are extra practice type problems, designed to give students similar to the ones in the Primary Mathematics textbooks. If you student is look for something harder, you might want to consider the Challenging Word Problems for Primary Mathematics series.

The 70 Must-Know series does not follow the Primary Mathematics lesson progression, the questions jump between concepts. Questions #3 and #47 in the Level 6 book, for example, are both on Volume. Question #2 & 5 cover the four operations with money and Question #4 is on percentages, so you may need to verify that a topic has been covered in class if your planning on using the book at home. The books have little instruction, however they do include a four page Introduction to Singapore Math (be forewarned, it’s written in six-point font!). Each problem has its own full page for work and there are fully worked solutions included in the answer key.

Here’s Question #70 from the Level 4 book. It’s listed in the table of contents under “Addition, Subtraction, Multiplication and Division of Whole Numbers”.

At a movie, 1/4 of the people in the theater were men, 5/8 were women and the rest were children. If there were 100 more women than children, what was the total number of people in the theater?

And Question # 48 from Level 6:

A box contained some red, blue, and green markers. For every 5 red markers, there were 2 blue markers. For every 3 blue markers, there were 5 green markers.

(a) Find the ratio of red markers to blue markers to green markers.

(b) When 6 red markers were removed from the box, 3/7 of the remaining markers were red markers. How many markers were left in the box?

Singapore Math: 70 Must-Know Word Problems was $12.99 at my local Barnes and Noble and Borders stores. The easy accessibility of these books make them great for parents looking for additional problems for their students. Teachers looking to use these materials in class need to keep on mind that these books may already be in their students’ homes!

Filed Under: Math Resources, Singapore Math Problems Tagged With: Singapore Math resources, Singapore Math word problems

Problem Solving and Literature

December 14, 2009 by Cassy Turner 1 Comment

Denise at Let’s Play Math has written up a some fourth grade level multi-step word problems (and provided bar model solutions) based on C. S. Lewis’ The Lion, the Witch and the Wardrobe. She concludes:

…as word problems become more complex, the bar diagrams offer significant help for students who struggle with the question, “What do I do?” Diagrams make visible the abstract relationships between numbers, enabling the student to decide which arithmetical operation makes sense in the context of the problem.

This is the fourth installment of her series on Pre-Algebra Problem Solving. Other posts use Mr. Popper’s Penguins and Poor Richard to illustrate problem solving using bar models in earlier grades.

Enjoy!

Filed Under: Math Resources, Singapore Math Problems Tagged With: Singapore Math word problems

Word Problem Progression

December 2, 2009 by Cassy Turner Leave a Comment

These word problems come from Practice A in the 5B Standards Edition Textbook (p. 68). This particular practice follows six lessons on “Percentage” and “Writing Fractions as Percentages”. Notice how the challenge progresses through the seven problems.