This video illustrates how manipulatives can be used to show the relation between strategies for subtraction and addition.
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This video shows how manipulatives can be used to explain subtraction using a part-part-whole structure.
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 shows how manipulatives can be used to explain how different combinations of numbers make 10. When students practice putting together and taking apart numbers with manipulatives in different ways they develop a conceptual understanding for composing and decomposing and how numbers are related to one another. Understanding number combinations allows students to develop fluency skills with other operations and assists students with problem solving.
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 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.
This video illustrates the use of an efficient counting on strategy that students may practice to solve simple addition problems without the use of manipulatives. When students use a counting on strategy to solve an addition problem, they must be able to hold one number in working memory; however, an important working memory strategy to teach students and allow students to practice includes using fingers to track counting. Counting on is an efficient strategy that students may use to quickly determine the solution to an addition problem. With enough practice opportunities students will soon be able to perform simple arithmetic without the use of working memory strategies such as finger counting.
This video illustrates the use of an efficient counting on strategy that students may practice to solve simple subtraction problems without the use of manipulatives.
This video describes how to use the partial products strategy with multiplication.
This video illustrates the use of manipulatives to help students practice counting skills such as correspondence and cardinality while applying a counting on strategy.