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The Ratio of Circumference to Diameter: Students measure the circumference and diameter of circular objects. They calculate the ratio of circumference to diameter for each object in an attempt to identify the value of pi and the circumference formula.

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Distributing and Factoring Using Area: In this lesson, expressions representing area of a rectangle are used to enhance understanding of the distributive property. The concept of area of a rectangle can provide a visual tool for students to factor monomials from expressions.

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Classic Middle-Grades Problems for the Classroom: This lesson presents two classic problems (Mangoes Problem and Sailors and Coconuts) that can be represented and solved in several different ways. Middle-grades students work in groups on the problems to promote communication of mathematical ideas, and a variety of classroom solution attempts are described.

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Measuring Up: This 7-lesson unit explores the concepts of proportional reasoning, ratio, and indirect measurement. Students engage in a variety of activities that involve taking their own measurements, exploring different ratios, and examining similar figures. Students convert measurements into customary and metric units. These activities immerse students in problem solving, reasoning, and making connections to real-life situations.

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#### Discovering Gallon Man

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Grid & Percent It: In this lesson, students use a 10 × 10 grid as a model for solving various types of percent problems. This model offers a means of representing the given information as well as suggesting different approaches for finding a solution.

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#### Grid and Percent It

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Area Formulas: In this 4-lesson unit, students use the area formula for a rectangle to discover the area formulas for triangles, parallelograms, and trapezoids. Students also consider irregular figures whose areas can be determined by estimation or decomposition.

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#### Discovering the Area Formula for Triangles

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Math Vocabulary Bingo: This lesson provides students an opportunity to assess their understanding of mathematical vocabulary as they relate to key concepts from the five content areas. Through the use of a familiar game format, Bingo, students will identify numbers 0‑75 that correspond to mathematical descriptions from math vocabulary clue cards.

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#### Math Vocabulary Bingo

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Sorting Polygons: Students identify and classify polygons according to various attributes. They then sort the polygons in Venn Diagrams, according to these attributes. Extensions to fundamental ideas about probability and statistics are also included.

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#### Sorting Polygons

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Barbie Bungee: The consideration of cord length is very important in a bungee jump—too short, and the jumper doesn’t get much of a thrill; too long, and ouch! In this lesson, students model a bungee jump using a Barbie® doll and rubber bands. The distance to which the doll will fall is directly proportional to the number of rubber bands, so this context is used to examine linear functions.

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