This video illustrates the use of manipulatives to help students practice counting skills such as identifying a set within a set of objects, correspondence, and counting on in order to determine the cardinality of a set of objects.
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This video uses manipulatives to review common counting errors that many students who struggle with counting exhibit. When students make counting errors such as coordination errors, omission errors, and double counting errors, it suggests that they do not have a solid foundation of one-to-one correspondence with counting. Allowing students multiple opportunities to practice counting with a set of objects presented in a line will help students refine skills in correspondence. Students may also commit errors related to reciting the correct counting sequence. If students have not mastered the stable orders of numbers, they will not be able to correctly apply other counting skills; therefore, students should be provided with multiple opportunities to practice the verbal count sequence.
This video illustrates the use of manipulatives to provide students with multiple opportunities to practice counting skills such as rote counting, correspondence, and cardinality.
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 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 lattice multiplication. Although the lattice multiplication strategy eliminates regrouping while solving the problem, it requires careful construction of the lattice (it needs to be the correct size), correct placement of the numbers (above or below the lattice line), and a solid understanding of place value. The lattice strategy uses place value by partitioning multi-digit numbers into smaller parts and it may not be an efficient strategy for students to use if they do not understand how multiplication works. However, learning this strategy with whole numbers may benefit students as they begin to multiply decimals as lattice multiplication is an efficient tool to use with decimals.
This video illustrates the use of manipulatives to help students practice counting skills such as correspondence and cardinality while applying a counting on strategy.
This video illustrates how manipulatives can be used to explain the commutative property of addition to students. Understanding that the order in which two numbers are added does not change the result supports basic fact fluency and students’ thinking related to problem solving. For example, when students understand how the commutative property works and if they have mastered a basic fact such as “3 + 1” then they have also mastered the basic fact of “1 + 3.”
This video illustrates how to use the partial quotient strategy to divide. To correctly use the partial quotient strategy, students need to have strong recall skills in division and multiplication facts. Students rely on this knowledge to partition the larger quantity that is being divided, into smaller and more manageable numbers. The partial quotient strategy is an alternative strategy for students who have not yet mastered the steps of the traditional algorithm.
This video reviews to how use the traditional algorithm to solve multiplication with regrouping.