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Mathematics in Context Project:
Looking At An Angle

Content Strand:
Geometry

Teacher:
Tanya Sanchez

School:
Garcia Elementary Phoenix, AZ
Grade 7

Project Director:
Meg Meyer

35 minutes

Looking At An Angle: The Mathematics in Context curriculum is designed so that lessons begin with a meaningful context and the math is extracted from that context. The context here involves a ladder positioned against a building, what it does, and for whom and when would a ladder be needed. The class moves outside where they help the school janitor position a ladder. By directing the positioning of the ladder, students see and describe how the angles and distances made by the ladder change when the ladder moves from an unstable position to a safe and stable position- underscoring the mathematical focus of this lesson - the tangent ratio. Back in the classroom, students draw triangles representing the ladder against the wall and examine the relationships amongst distance, height, and angles of the resulting triangles. They discover that the height-to-distance ratio is a measure of steepness affected by the size of an angle. The lesson culminates with students plotting a steepness graph to determine the necessary height-to-distance ratio for a ladder to be safe and stable.


MathScape Project:
String Shapes & Shaping Up

Content Strand:
Geometry

Teacher:
Retella Jones

School:
Rogers-Herr Middle School
Durham, NC
Grade 6

Project Director:
Susan Jannsen

40 minutes

String Shapes & Shaping Up The MathScape curriculum empowers middle school children with the use of manipulatives, hands-on activities, and investigations that push kids beyond identification of geometric shapes to thinking critically about their geometric properties and relationships amongst those properties. In this lesson, students are beginning to explore the properties of sides and angles in quadrilaterals. In the first activity, they are given clues that describe properties of geometric shapes. Working together in small groups, they use a loop of ribbon pulled tight to create different shapes. They adjust the sides and angles of the ribbon shape to form figures that match the properties in their clue. Students then partner up to play the Side-Angle Game, which is played with 2 stacks of cards - one consists of clues about sides, the other gives clues about angles. Players pick a card from each stack and put the clues together to draw shapes that meet both properties. Then it's back to group-work with ribbons in the Animated Shape Game. Here students standing in groups of four each hold a point in the ribbon to form a shape. They are given a clue as to the properties of another shape they are to make and must decide who is going to move where to make that shape. The lesson demonstrates students exploring options, questioning themselves and others, and communicating their strategies with mathematical vocabulary.