This video shows how manipulatives can be used to explain addition using a part-part-whole structure.
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This video illustrates the use of manipulatives to help students practice solving story problems that require the use of counting skills such as correspondence, cardinality, and counting on. When students practice solving story problems with manipulatives, they are able to apply mathematics skills, such as counting, in a real-world context. The application of strategies and skills in a real-world context makes learned mathematics knowledge meaningful.
This video illustrates the use of manipulatives to help students practice number relations skills. When numbers are represented with manipulatives as sets, students develop a concrete understanding for comparing quantities. Students must possess a deep understanding of number relation skill including identifying more, less, and equal quantities prior to mastering higher-level skills such as number operations.
This video demonstrates how to use base-10 blocks to help students solve division problems that cannot be solved with automatic retrieval. The use of direct modeling with concrete manipulatives to demonstrate division allows students to visualize the division of a quantity into equal groups. Students should have multiple opportunities to practice division with manipulatives to develop an understanding of the steps for regrouping and dividing quantities into equal groups. While students may have moved on to traditional algorithms with other operations (e.g., subtraction) they may still require the use of concrete manipulatives with learning division.
This video shows how to use an area model to solve a multi-digit multiplication problem. An area model can serve as a visual representation of the partial products multiplication strategy. Using an area model may be a good option for students who have not yet gained a conceptual understanding of how regrouping works or how the partial products strategy works. The area model method can serve as a visual guide for students until they are ready to use traditional algorithms.
This video demonstrates how to use base-10 blocks to help students solve multiplication problems that cannot be solved with automatic retrieval.
This video demonstrates how to use base-10 blocks and a place value chart to help students subtract multi-digit numbers that require regrouping.
This video illustrates the use of manipulatives to help students practice correspondence and tracking objects as objects are counted in different ways. When children understand that objects may be counted in any order (e.g., left-to-right, right-to-left, in a random fashion) they have developed an understanding of the order irrelevance counting principle. Counting objects in many different ways also allows students to practice tracking objects as the objects are counted to make sure that each objects is counted once and only once, regardless of the order in which the object is counted.
This video describes how to use the partial products strategy with multiplication.
This video illustrates how to use the traditional addition algorithm with regrouping.