This video demonstrates how to use benchmark fractions, such as ½, to compare fractions with unlike denominators. When students show that they are proficient comparing fractions using concrete manipulatives or pictorial representations, they may be ready to compare fractions using reasoning strategies without representations. For beginners and for students who struggle, it may also be important for teachers to model to students how to check their work using other tools, such as fraction tiles.
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This video demonstrates how students can practice determining equivalent fractions with different denominators using fraction circles. Students can explore this concept by comparing different representations of the same value against a whole fraction circle. After students have found one representation of the same fraction (3/6), teachers can encourage students to find another representation (4/8). Teachers can then ask students to discuss the patterns that they see in the different representations of the same value.
This video demonstrates how students can practice finding equivalent fractions with different denominators using fraction tiles. Students can explore this concept by stacking fraction tiles to determine the multiple representations of the same value, such as 1/2. Once students have found one representation of the same fraction (4/8), teachers can encourage students to find another representation (3/6). Teachers can then ask students to discuss the patterns that they see in the different representations of the same value.
This video shows how to use the set model to represent fractions, such as 1/2. In the set model, the whole is represented by a set of objects, such as two-colored chips. Individual chips within the set, represent the fractional parts. It is important that students be exposed to the set model because fractions in real-world settings are often represented this way.
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 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.