When I say Singapore Math, I do not mean the curriculum/books with this title in the USA. I mean the actual math that Singaporean students are doing day to day. I fell in love with many parts of the Singaporean education system while living there from Dec 2013-July 2016. Because the smell of a bookstore is basically a narcotic to me, I spent a lot of time wandering the stacks of books and picking up mathematics resources and workbooks for my kiddos’ future use, and to use with the students I tutored at the time. I found that the books Singaporean kids used were quite challenging for my students from the international schools, so I became passionate about teaching the highly visual strategies employed in Singapore to solve difficult problems.
Take this one, which I would have previously created a system of equations (Algebra) to solve quite quickly:
There are two numbers which add to 28 and have a difference of 6. What are the two numbers?
The system of equations would be A+B=28 and A-B=6. This would be a fairly easy problem for an Algebra student to solve. But in Singapore? This can be solved by a P2 student, around age 8.
By drawing two rectangles to show one number is bigger than the other, then lining up the end of the shorter one to show the difference of 6, we can more easily understand that without the 6, they are equal. So we do 28-6=22, then divide the 22 in half to get the value of each rectangle. So Number A = 11+6 = 17, and Number B = 11.
Here is another example, this is a higher level year P4 problem in Singapore, for kids about age 10 in Singapore.
Mr. Jones is 4 times as old old as his daughter. His daughter is 2/7 as old as his wife, who is 42 years old. How old will Mr. Jones be next year?
A model of the situation easily shows all the information in the problem. Perfection is not needed for comparing the ages of Mr. and Mrs. Jones, because their ages are related through the daughter, but the daughter’s rectangles needs to match up to each parent’s. Keep in mind this is just one way to model the situation. This method should not be one that is memorized (though many a tuition school in Singapore will help kids to do this). The method’s strength is in teaching a robust and flexible way to visually compare and work with parts and wholes using rectangles. Brain research points out that our visual ability is one of our strongest, so make good use of it when problem solving. I like this method because drawing a picture to represent the problem, especially with a symbol as simple as the rectangle, is an easy first step.
Why is this so important? Because the first step is always the hardest. Once you get that pencil to paper, one thought leads to another and to another, or to a question that leads you to understand the problem more deeply. There is nothing more useless and terrifying than blank paper–this method solves that problem. And as Dr. Martin Luther King Jr. once said, “Take the first step in faith, you don’t have to see the whole staircase, just take the first step.” He wasn’t talking about math in this quote from Testimonies to Freedom: History of the Civil Rights Movement, but it is an important habit to develop when problem solving.
Mathematics can be incredibly difficult because it requires the use of both sides of the brain along with short term, long term, and working memory. No small task for sure. Over my 8 years teaching high school math in the US, and my years of tutoring since, I have seen many a student unwilling to take the first step. Rectangles help. :D
If we take the one number we have been given, 42 for Mrs. Jones’ age, and see that 7 equal units make her age, we divide and get that each unit’s value is 6. Fill that in and work your way up to get 12 for the daughter’s age, then 48 for the father’s age…but we aren’t done! A quick reread of the original problem reminds us that the answer is Mr. Jones’ age next year. So the answer is 49. Ta-dah! LOL. (To make my fancy drawing yourself, go here.)
Nice problem, huh? Multiple steps, all of them concrete, but the overall thinking is complex when taken together. I think these kinds of problems can really stretch students’ abilities, and are worth taking the time to teach or have students wrestle with in class. Bar models are most helpful when working with part and whole concepts, comparisons, fractions, ratios, percents, it’s all interwoven really. This method can even help students solve problems that western students would traditionally use algebra (like systems of equations) to solve! And they do it before Algebra is taught! It truly is a powerful method.
I have created a 40 pack of problems that can be used as a weekly 15-minute enrichment activity in the classroom, or in the home if you want to help your son or daughter to learn this method. You don’t need to have any experience at all; the problems pack comes with an explanatory foreword and a fully diagramed answer key to help you learn to use this method, whether you are a teacher, a homeschool teacher, or just a tiger mom like me. ;) So bookmark this page and come visit again to see what’s new.
Strategies From Singapore: Weekly Problem Solving with Bar Models-Level 1–Purchase and download your digital copy here.
Strategies From Singapore: Weekly Problem Solving with Bar Models-Level 2–Coming this summer
Strategies From Singapore: Weekly Problem Solving with Bar Models-Level 3–Coming this summer
My Free Math Resources
- Little Interactive Math Stories (must use power point to open) for Kindergarten/Grade 1 US, or Year 1 British National Curriculum.
- Math Playground (a great, free math games site) has a bar modeling tool and problems to solve by topic
- A full digital Singapore Math program by Koobits–I haven’t tried this but it looks good. It connects to the local Singapore curriculum and has learning videos, explanations, homework, and assessments, perfect for summer school at home.
- A beginner’s guide to using bar models for kids ages 5-8
- Resources list from a Singapore Math (the US curriculum) trainer’s website