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Connected Mathematics Project :
Designing Packages

Content Strand:
Measurement

Teacher:
Jim Mamer

School:
Rockway Middle School
Springfield, OH
Grade 7

Project Director:
Yvonne Grant

40 minutes

Designing Packages: Students learn about and experiment with surface area and volume in this lesson from the Connected Math Project. They begin by reviewing previously learned concepts of base, height, width, and length. As employees of the ABC Toy Company, their task is to design a package to house 24 blocks. They are supplied with 24 stacking cubes to explore the different ways the cubes can be put together and packaged. For each package built, they record the dimensions and determine surface area corresponding to that box. Students experience collecting data using manipulatives and devise creative solutions. The concepts of surface area and volume are repeated with each new investigation for each shape. Once students have finished, the class reviews and defines the different methods individual groups used to find surface area. The lesson culminates with the student discovery that as the smaller cubes are put together forming different rectangular shapes, if they are arranged to form a larger cube, the surface area is minimized.


Connected Mathematics Project :
Looking for Squares

Content Strand:
Number

Teacher:
Lisa Brown

School:
Kealing Middle School, TX
Grade 8

Project Director:
Yvonne Grant

35 minutes

Looking for Squares: The goal of this lesson is for students to develop an early understanding of the concept of square root as the length of a side of a square. They begin by finding the area of a square and looking at the dimensions. Students work in pairs to find as many squares as possible that will fit in a 5x5 grid. Finding areas for squares that are not vertical to the grid is perplexing to some students. Those who have mastered the strategy share their procedure and mathematical reasoning with the class. Together the class determines the relationship between area and side length using a variety of examples beginning with area, then beginning with side length. The teacher assesses their strategy and introduces the term square root relating the length of a side to the area of a square. A student inquires about odd numbers and numbers like five, which leads the class into an investigation of estimation strategies for finding square roots.