Singapore Math Success Stories
In their attempts to improve math skills, US schools have tried to embrace international math programs.
One of the more successful programs is Singapore Math. The Singapore Math curriculum becomes popular due to its consistent top ranking on Trends in International Math and Science Study (TIMSS). Compared with the United States’ rank of ninth and eleventh in third and eighth-grade math scores respectively, Singapore Math ranked top three.
Some US schools found about 20 percentile gains in standardized testing of third graders who have gone through the Singapore Math curriculum. Most students benefit from this program because of its emphasis on understanding number sense, and problem solving. This helps to form a strong foundation for the student, which facilitates math learning in later years.
Singapore Math Worksheets
Students learn by doing lots of practices. Given below are a list of free Singapore math worksheets from Grade 1 to Grade 6 and another list comprising topical worksheets. Click on the links to access the pdf files.
Topical Math Worksheets
Primary 6, 5, 4 CA1 Math Word Problems & Solutions
P6 Math CA1 Word Problem & Solutions - modelled after Nanyang paper
P6 Math CA1 Word Problem & Solutions - modelled after Rosyth paper
P5 Math CA1 Word Problem & Solutions - modelled after Nanyang paper
P5 Math CA1 Word Problem & Solutions - modelled after Nan Hua paper
P4 Math CA1 Word Problem & Solutions - modelled after Rosyth paper
P4 Math CA1 Word Problem & Solutions - modelled after Ai Tong paper
Primary 6, 5, 4 Math CA1 Worksheets
P6 Math CA1 - Whole Numbers
P6 Math CA1 - Decimals
P6 Math CA1 - Fractions
P6 Math CA1 - Percentage
P6 Math CA1 - Measurements
P6 Math CA1 - Word Problems Part 1
P6 Math CA1 - Word Problems Part 2
P6 Math CA1 - Geometry
P5 Math CA1 - Whole Numbers
P5 Math CA1 - Decimals
P5 Math CA1 - Fractions
P5 Math CA1 - Geometry
P5 Math CA1 - Measurements
P5 Math CA1 - Word Problems Part 1
P5 Math CA1 - Word Problems Part 2
P5 Math CA1 - Data Analysis
P4 Math CA1 - Whole Numbers
P4 Math CA1 - Whole Numbers Part 2
P4 Math CA1 - Fractions
P4 Math CA1 - Measurements
P4 Math CA1 - Word Problems Part 1
P4 Math CA1 - Word Problems Part 2
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While the early adopters are home school students, many schools are using it for gifted and talented students or for struggling students. Now Singapore Math is part of core curriculum in 40 American states and a popular Singapore math series is used in 100 over US school districts.
The teaching method is based on a three-step learning process. The three steps are: concrete, pictorial, and abstract. In the concrete step, students learn through manipulation of objects like pens, erasers or clips. In the next step, pictorial representations are used to model the problem. Numbers and symbols are then used in an abstract way to solve the problem. This middle step of using pictorial bar model representation is the unique addition in the learning process.
Unlike traditional US math program which emphasizes learning a number of math principles,
Singapore Math worksheets are based on curriculum that focuses on fewer topics but in greater detail. It is a more balanced approach between the two,
melding old-fashioned algorithms with visual representations and critical thinking.
While American math instruction often relies on drilling and memorization of many skills each year, Singapore math focuses not just on learning but also truly mastering a limited number of concepts each school year. It is not just about getting the right answer, but about how the answer is derived and why it is the right answer.
Adoption of math word problems in US schools
There is a general fear of math word problems among students in the US as they think that word problems are difficult.
It cannot be that children don’t like word problems because they need to find a correct answer.
In fact many of them would like to solve math puzzles.
Children love story problems while in first grade.
These problems have pictures of number of ducks here and number of ducks there and they are required to add them up.
Many children are encouraged during their elementary grades to solve one-step word problems using linear fashion standard approach.
These problems are done at the end of a specific math operation lessons and the method is predictable as it must be using the math operation just taught.
There is a shortage of good word problems in elementary schools. Good word problems are multiple-steps in nature.
It does not necessary need a specific problem-solving strategy. Unfortunately, when teachers are not able to solve such problems, they skip them. Singapore Math worksheets are good resources that contain lots of good word problems.
The worksheets also have answer keys to help teachers.
Types of word problems
One-step word problems
Students may be practicing multi-digit multiplication, subtraction or division calculations.
However the word problems are predictable as they uses the same operation just practiced.
When children practice such standard strategy word problems repeatedly, they manage to be able to get the answers without reading the whole question.
Children eventually will get the impression that word problems can be solved by the routine taught in the textbook. This contrasted with Singapore Math worksheet problems which are more complex and closer to real life problems in daily living.
Example of one-step word problems with a specific operation
The store has 833 cell phone cases in 7 different colors. There is the same amount of cell phone case for each color. How many cell phones cases of each color are there?
Good word problems
One-step problems are good for first and second grades.
When children advance further they need to learn how to solve multi-step problems with gradually increasing degree of difficulty.
Singapore Math worksheets contain good word problems that meet the need of these children.
Example of good problems from Singapore Math worksheets
The total weight of Bala and Mark is 124 kilograms. Mark is 4 kilograms lighter than Bala. What is Mark’s weight?
While this problem is nothing spectacular, one needs only to minus 4 kg from total weight 124-4 =120 kg and divide 120 kg by two, which equals 60kg. Therefore Bala weighs 64 kg and Mark 60 kg.
Singapore Math worksheets’ problems test students’ ability to analyze and use multi-step approach.
However in the US, this kind of problems is only introduced in the ninth grade during algebra lessons and solved using algebraic equations.
Objective of word problems
The first purpose of Singapore Math worksheets is to train children in math skills required in everyday living, for example shopping problems.
Another reason is to develop the child’s ability in logical and abstract thinking.
Singapore Math worksheets encourage use of pictorial diagrams such as bar models to visualize the problem.
Thirdly, real-life scenarios help motivate students to participate.
To achieve all these goals, lots of practices are required.
Problem solving plan
There are four common sense steps in math problem solving process.
The steps are: understanding the problem, devising a plan, carrying out the plan and looking back.
We should emphasize the first and last steps, but should not compartmentalize the problem solving into the two simples steps of devising and carrying out the plan.
With challenging problems from Singapore Math worksheets, the problem solving process may become iterative,
i.e. adopting one strategy, doing mental check, then correcting and doing it over again with another strategy.
Students must understand that the steps are not sequential.
One might make a plan, carry it out and then unexpectedly having to go back to step one to try to understand the problem correctly.
Problem solving strategies
According to Polya’s book on How to Solve It, the general strategy is to draw a picture of the problem,
find a pattern, solve a simpler problem, work backwards or act out the problem.
Students can make use of bar models used in Singapore Math worksheets as part of the pictorial process.
Bar models are useful quantitative tools that help students to visualize the problem.
Students’ thinking should not be limited to one given strategy or some pre-established recipe but
rather to let them use various problem solving strategies naturally when attempting challenging problems weekly.
Teachers need not feel apprehensive about problem solving. They should find some good problems such as Singapore Math worksheets’ problems for students to solve.
They can discuss the solutions, explain the various strategies and solve the problems together in class.
The critical success factor is to have lots of practices in solving problems.
What others say?
Martin said that Singapore Math had been an excellent curriculum for his sons and
that Singapore Math worksheets prepared them extremely well for high school math.
Shanda commented that overall she loved Singapore math’s way of doing math.
She added that the only thing she had not mentioned was that level 6 worksheets were very challenging.
She remarked that level 6 was almost entirely reviewed and the word problems got pretty intense and fun if you liked math.
Bell shared that he had been very pleased with the Singapore Math worksheets for grades 1-5.
He continued that it had served his son well and when compared with other more gifted children he scored higher on a variety of standardized tests.
Erika observed that the approach to teaching math was vastly different from the way
she had been taught math in public school and that Singapore math worksheets were far superior, in her opinion.
She agreed with other reviewers who noted that the emphasis in Singapore Math was on deep conceptual knowledge of mathematical concepts, rather than learning by rote.
Elizabeth mentioned that Singapore Math worksheets’ problems solving were structured and enabled a certain thinking process to the point of mastery.
She said that the scope of content was somewhat narrow, and incorporated many word problems.
Bar modeling is a pictorial method used to solve word problems in arithmetic.
Bar Models can be used to solve word problems involving addition and subtraction. The models could also be used to analyze multiplication or division word problems.
Given here are some word problem examples found in Singapore Math worksheets that demonstrate the use of bar models.
Problem Solving with Bar Models
1. The total mass of three sofas is 218 kg. The first sofa is twice as heavy as the second sofa. The third sofa is 14 kg heavier than the second sofa. Find the mass of the third sofa.
2. Chris had $243. He spent 2/3 of his money on a bag and some money on a book. He had $21 left. How much money did he spend on the book?
3. Sam is 45 years younger than his grandmother. Last year, his grandmother was 4 times as old as he was. How old will Sam be when his grandmother reaches 65 years old?
4. A tie costs twice as much as a belt. A briefcase costs $80 more than a tie. The total cost of a tie, a belt and a briefcase is $2530.
a) What is the cost of a belt?
b) What is the total cost of a tie and a briefcase?
Singapore Math Syllabus
Grade 6 syllabus includes topics such as fractions, percentage, ratio, speed, measurement (area, circumference, perimeter and volume of cube & cuboid),
geometry (figures and nets), data analysis and algebra.
Grade 5 syllabus includes topics such as whole numbers (up to 10 million, four operations, order of operations),
fractions (division, four operations), decimals (four operations), percentage and ratio.
The next set of topics are measurement (length, mass and volume, area of triangle, volume of cube & cuboid), geometry (angles, triangle, parallelogram, rhombus and trapezium), data analysis (average of set), fractions (four operations), percentage, ratio, speed (distance, time and speed) and measurement (area, circumference, perimeter, volume of cube & cuboid). Last 3 topics are geometry (figures, nets), data analysis (pie charts) and algebra
Grade 4 syllabus includes topics such as whole numbers (up to 100,000, multiplication & division, factors and multiples),
fractions (mixed numbers & improper fractions, addition & subtraction, fraction of a set and multiplication)
and decimals (up to 3 decimal places, addition & subtraction and multiplication & division).
It also includes topics like measurement (time, money, area and perimeter), geometry (perpendicular and parallel lines, angles,
rectangle and square, symmetry and tessellation) and data analysis (tables, line graphs).