This video demonstrates how to use fraction circles to compare the value of fractions with unlike denominators. This example compares 5/6 and 5/8. In this example students can see that 5/6 is greater than 5/8. This will help them understand that although 8 is larger than 6, sixths are larger than eighths in fractions. Using fractions circles allows students to develop a solid conceptual understanding of how to compare fractions correctly.
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This video demonstrates how to use fraction tiles to explore how different fractions can be equivalent to the same value, such as 1/2. It is important for students to understand that fractions have multiple representations because they can apply this knowledge to compare fractions, especially fractions with unlike denominators. For example, students can use the benchmark of 1/2 to determine that 1/4 is less than 4/6 by knowing that the equivalent fractions of 1/2 include 2/4 and 3/6.
This video demonstrates how to use fraction tiles to explore how different fractions can be equivalent to the same value, such as 1/5 and 2/10. It is important for students to understand that fractions have multiple representations because they can apply this knowledge to compare fractions, find common denominators, and perform computation with fractions.
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 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 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 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 illustrates the use of manipulatives to help students practice counting skills such as correspondence and cardinality while applying a counting on strategy.
This video shows how manipulatives can be used to explain multiplicative problem structures to students who are just beginning to use multiplication strategies.
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.