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Background Information for Teachers

The following resources offer insights into the arithmetic and geometry underlying the Curriculum Focal Points for fifth graders. Each is an online workshop session designed for K-8 teachers who are looking for deeper understanding of mathematical content. The workshops were developed by Learning Math as free, college-level courses for educators.

Meanings and Models for Operations In this session, you can explore some of the laws that govern the basic operations, including division. Interactive mathematical models aid in examining division as inverse multiplication, as do questions for teacher discussion.

Solids Through these activities, developed for teachers, you will build and and manipulate the Platonic solids, exploring their properties and some of the geometric relationships between them. Other investigations focus on nets and cross sections of solids.

Measurement Relationships This workshop begins with an examination of the relationships between area and perimeter but goes on to the proportional relationship between surface area and volume and some of its applications. For instance, you will construct boxes and use graphs as you try to find the dimensions of the rectangular prism that holds the maximum volume. Video segments of teachers working on this activity lead to further discussion in this session from Learning Math: Measurement.

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