## What are Bar Models?

Bar models are the crown jewel of the Singapore math approach and distinguishing feature. Unlike other math programs, in Singapore math, the C-P-A method is applied extraordinarily well by extending the pictorial stage of learning with special rectangular bar pictures called bar models. Bar models transform a word problem into a picture that shows relationships in a way that children can clearly see them. Rectangular bars are used to represent quantities because they’re easily drawn and divided. Before introducing the drawing stage of bar model diagrams, children are given linking cubes (concrete stage) and rectangular paper strips (pictorial stage) to represent bar models.

Bar model drawing also known as the Model Method is a visual tool developed to help students solve word problems and strengthen conceptual understanding through pictorial representations. Bar models are taught starting in 2nd grade. Each year adds a new level of complexity in applying bar modeling to word problems involving whole number operations as well as fractions, ratios, decimals, and percentages. Most word problems encountered at the elementary and middle school level can be solved with bar models. Because algebraic word problems can be solved with bar models, simple algebraic word problems are introduced as early as 3rd grade.

The bar model method, central to Singapore math teaching, allows for algebraic reasoning, proportional reasoning, and visualization to be developed at an earlier age because more complex problems are introduced at a younger age. Bar models are a math tool that every child should have the opportunity to learn and master. All types of learners benefit from the bar model method.

#### Example 1

#### Example 2

#### Example 3

Here two bars, of lengths 5 units and 1 unit, are drawn to represent the number of chickens and the number of goats respectively. The model shows that the number of chickens is 5 times the number of goats. Given the number of goats (1 unit = 7), students can find the number of chickens (5 units) by multiplication.