# Other Topics ## Sine, Cosine and Tangent in the Four Quadrants

Remember this picture? We used it to remember the signs of the three primary trigonometry ratios – Sine, Cosine and Tangent in the four quadrants. Each letter (of ASTC or CAST) represents the trigonometry function that is positive in each quadrant, e.g. Cosine is positive in the 4th quadrant etc., and All three are positive … ## 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 – … ## 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 …

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