Teacher resources and professional development across the curriculum

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Teaching Math: A Video Library, K-4

Arrays and Fractions

Video Overview

Students discuss how they use fractions in their everyday lives. Students investigate fractional parts of a set by using square tiles to build arrays that represent wholes of different sizes. They are told they will be working with arrays and are asked to divide the arrays into equal parts to represent fractions. Students work in pairs on a task card that states the size of an array that they are to build and two fractions that they must show in each array. Each pair is asked to record its work on graph paper. During this task, students use mathematical language and symbols for fractions and arrays. They also form mathematical connections among concepts of addition, area, multiplication, division, and fractions. Once students have completed the task, the class reconvenes and students discuss the task and their problem-solving approaches.


Using Arrays to Investigate Fractions

  1. What were the mathematical connections in the lesson?

  2. Ms. Dale1s class discussed real-life fractions at both the beginning and the end of this lesson. How could real-life examples also be brought into the developmental portion of the lesson when students were using arrays?

  3. Identify the students1 understanding and misunderstanding of arrays and fractional parts of sets. How could you have addressed any misunderstandings?

  4. Why do you think Ms. Dale asked students to divide the array of fourteen tiles into fifths?

  5. Describe the mathematical language used in the lesson and its meaningfulness for students.

  6. What other mathematical ideas can be modeled and investigated by using arrays?


Teaching in Multigrade Classrooms

  1. This classroom includes students from first through third grade. Identify the pros and cons of multigrade classrooms.

  2. What planning and instructional issues must be addressed when teaching a multigrade class?

  3. What was the mathematical content in this lesson? How was this content appropriate for students in a multigrade classroom?

  4. How accessible and challenging was the task for students in the class? Identify the different levels of the students1 understanding. List criteria to consider for selecting and developing tasks for all students in multigrade classrooms.

  5. How did the use of manipulatives and diagramming facilitate the students1 understanding in this lesson? Cite additional ways in which various materials can facilitate students1 understanding at different levels.

  6. Compile a list of ways to plan for assessment in a multigrade classroom.


Extension

Other Fraction Models

Develop other ways to model fractions. Your ideas might include pattern blocks, geoboards, base-ten blocks, grids, Unifix cubes, circular units, and real-world examples. Cite the pros and cons of each model. Which models demonstrate parts of regions or areas, parts of sets, parts of lengths, or combinations of these? Which models can be easily connected to decimals? How can these models be connected to one another?



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