Tze-Ping Low

Negative Numbers on the Number Line

Visualization is an important focus in Singapore math and the number line is one tool we used frequently to visualize relationships between numbers. However in 6th or 7th grade, when students are introduced to negative numbers, things can get a bit tricky when dealing with negative numbers on the number line. For example, -3 – …

Comparing Fractions using the Same Whole

A reader raised an interesting question in our previous post on Understanding the Concept of Same Whole in Fractions. Specifically, using a physical interpretation as an example: 3 out of 4 of Ellie’s pencils are red while 5 out of 7 of Tim’s pencil are red. Who has the “greater” fraction? After all, we can …

Double Before-After Bar Model Problem

Sometimes one bar model is not enough. Here’s an interesting double bar model problem using before-after relationships. If Abby gives \$10 to Ben, then they will have the same amount of money. If Ben gives \$20 to Abby, then she’ll have four times as much as he has. How much money does each of them …

Percentage Conversion

If you’re on social media lately, you might have seen this twitter post that has gone viral. This is indeed a percentage conversion identity that can be especially handy when you have to do mental calculations involving percentages. x% of y = y% of x This comes from the fact that percentage is nothing but …

One Bar Model for Two Different Types of Question

We recently came across two entirely different question types and solved them using the exact same bar model. Geometry Type of Question Here’s the first question: The figure below is made up of two overlapping shapes, a triangle and a square. The ratio of the area of the triangle to the area of the square …

We call this an advanced bar model problem. How would you solve this 5th-grade question using bar models? Mr. Lim had some stickers and stamps for his class. The number of stickers was half as many as the number of stamps. After giving each student in the class 3 stickers and 8 stamps, Mr Lim …

Three Meanings of the Minus Sign

We often see bright kids in 5th or 6th grade getting the deer-in-the-headlights look when it comes to dealing with equations with multiple negative or minus signs. Often it is good to stop and think about the different roles the humble minus sign take on in integer arithmetic. In fact, at this level, there are …

Why is it Important to Draw Bar Models Correctly

In the previous post, we talked about two common mistakes in drawing bar models – not aligning the starting points of the bars being compared and having disjoint bars for parts. Here we want to illustrate why it is important for us to draw bar models correctly from the beginning when we first use them …

Common Mistakes in Bar Models

Bar Modeling is a very powerful heuristic in Singapore math. Representing unknown quantities and the relationships between them using rectangular “bars” gives an intuitive and visual representation of the problem. More importantly, when used correctly, representing problem using bar models makes students approach the solution in a systematic and algebraic manner. This empowers even young …

What is Singapore math?

One of the questions we get most often is “What is Singapore math?” and the follow-up question “How is it different from [curriculum]?”. Here is our own definition, interpreted from the point of view of two Singaporeans who grew up in Singapore, went through the public education system learning math using the same concrete-pictorial-abstract techniques, …

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