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The following are a few manipulatives that might be used at the elementary level.
Concrete models can help students represent numbers and develop number sense; they can also help bring meaning to written symbols and can be useful in building place-value concepts.
You should try to "get inside students' heads" as they work with concrete materials by asking questions that elicit their thinking and reasoning.
According to learning theory based on psychologist Jean Piaget's research, children are active learners who master concepts by progressing through three levels of knowledge--concrete, pictorial, and abstract.
The use of manipulatives enables students to explore concepts at the first, or concrete, level of understanding.
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They then add the fractional parts to find the sum.