# Tze-Ping Low  ## 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 … ## 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 … ## 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, … ## Fraction Multiplication as Scaling

Multiplication as Scaling is usually taught at the end of the 5th grade, in preparation for rates and proportions in 6th grade. In the 5th grade Common Core, it is listed as (CCSS.Math.5NF): 5NF.5. Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the basis of the … ## Fractions and Decimals

Fractions and decimals both serve the same purpose of describing parts of a whole, i.e. they are two ways of expressing non-whole values. Up to 4th grade, students learn fractions and decimals as separate topics and once comfortable with both formats, they should start to appreciate the relationship between the two. Why is Understanding the Relationship …

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