Visualization: The student represents problems visually, connects concrete and abstract representations of problems, and creates numeric data from visuals.
Singapore Math focuses on helping students visualize problems, making it different from other math programs. Using manipulatives and creating pictorial representations of mathematical problems play key roles in building conceptual understanding and algebraic reasoning. In Grades K-1, students draw direct representations of objects (e.g., drawing balloons for a word problem about balloons) and use number bonds to represent fact families.
In Grades 1-5, place value charts are used as a visual way to show the value of an operation. See the Place Value page for more information about place value charts.
Starting in Grade 2, the key visualization tool used is the bar model, used to show what is happening mathematically in real-world problems (also known as story problems or word problems).
What is Bar Modelling? Part 1
What is Bar Modelling? Part 2
Note: Current students should be comfortable with the previous year's models in order to build upon them for more complex problems. As you will see below, most problems can be solved using one of two categories of models: Part-Whole or Comparison. Additionally, some problems may require multiple models, but these will be some combination of Part-Whole and Comparison models.
Many students may be able to solve simpler problems in the abstract form (i.e., using just numbers and symbols), so feel they don't need to draw a representation of these problems. However, problems increase in complexity as the curriculum progresses, and students may need to build on earlier models to solve new problems. It is very important that students are fluent in the early models, thus students should be drawing models for every real-world problem (unless noted by the teacher).
Models represent the problem, not necessarily the answer (though sometimes the answer can be seen once the problem is visualized). Make sure that your model contains all of the elements described in the problem. It often helps to model the problem one sentence at a time.
Practice is crucial! It will take a lot of drawing and practice with the different types of models to understand the power of modeling. Once you get it, it's an amazing problem solving tool and transfers quite nicely to understanding how algebra works.
Thinking Blocks from Math Playground offers a nice selection of problems to solve using bar models. This is a great way to learn how to use bar models without having to draw them.