This video demonstrates how to use fraction circles to help students compare the value of several fractions with different numerators and denominators. The use of direct modeling with concrete manipulatives, such as fractions circles, allows students to develop conceptual understanding of fractions before they attempt to compare fractions without concrete manipulatives or pictorial representations. After students have had multiple opportunities to practice comparing fractions with concrete manipulatives, they may be ready to use other strategies such as mental images and reasoning strategies.
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This video illustrates three different models for representing fractions: length, area, and set. Different concrete tools are available to illustrate the different fraction models including fraction tiles, fraction circles, Cuisenaire Rods, Geoboards, and different colored objects such as chips or clips. Many students struggle with fractions; for this reason, students should have multiple opportunities to explore fractions with a variety of models. When students understand how to use concrete models, they will develop the skills that are necessary to develop mental models and reasoning strategies related to fractions. Students should also have the opportunity to use different models to solve the same types of problems and discuss connections between the models.
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.
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 an efficient counting on strategy that students may practice to solve simple subtraction problems without the use of manipulatives.
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 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 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 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.