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.
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This video demonstrates how to use base-10 blocks to help students solve multiplication problems that cannot be solved with automatic retrieval.
This video illustrates the use of manipulatives to help students practice counting skills such as correspondence and cardinality. When students practice counting with manipulatives they learn to recognize that number names are stated in a standard order, each number word is paired with one and only one object, and the last number stated in the sequence tells the number of total objects counted in the set. It is important for students to master skills such as correspondence and cardinality, because a strong foundation in counting is necessary for students to learn other skills such as number relations.
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.