Learning with Manipulatives

Symphony 3-tier ModelStudents use on-screen manipulatives to solve problems. The manipulatives provide a concrete representation of mathematical concepts and number relationships; students readily grasp these concepts, because the manipulatives illustrate them in a tangible way. This solidifies the mental model and inspires learning.

Understanding Symbols

Symphony 3-tier ModelThe program helps students to understand the meaning of symbols by associating them with manipulatives. Students create number sentences based on the manipulatives and arrange them accordingly. This enables students to correlate the concepts with the abstract notation symbols used to represent them.

Mastering Number Facts

Symphony 3-tier ModelImmediate recall of number relationships can be achieved when students develop a solid conceptual understanding of their underlying concepts. Addition, subtraction, multiplication and division facts are practiced in timed activities, and students are challenged to solve problems correctly in five seconds or less.

Solving Word Problems

Symphony 3-tier ModelStudents solve word problems and apply the same concepts and skills they mastered earlier in the program. The word problems model real-world situations, emphasize the relationships between manipulatives and symbols and clarify the relationships between them.

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