Sunday, October 19, 2008

Flips, Turns and Area

This week we will be starting a new unit in math. The unit is called Flips, Turns and Area. This unit develops ideas in 2-D Geometry. The following describes the mathematical emphasis for each investigation.

Investigation 1—Motions with Tetrominoes

-Measuring area by covering a flat space with square units
-Finding systematically all possible geometric arrangements of a given number of squares
-Finding patterns for covering a space
-Comparing area of rectangles with different dimensions
-Describing physical motions in precise ways as a series of slides, flips, and turns
-Comparing two shapes to decide if they are congruent or not after using geometric motions—slides, flips, turns—to try fitting one shape exactly on top of the other

Investigation 2—Finding Area

-Measuring area by covering a flat space with square units
-Comparing the area of two shapes by determining if they cover the same amount of flat space
-Comparing shapes to see if they are congruent through motions such as rotation (turns) and reflection (flips)
-Exploring relationships among shapes; for example, a rectangle can be cut into two triangles, each of which is half the area of the rectangle
-Finding the area of complex shapes by cutting them into recognizable smaller units of area such as square units and half units

The following words are vocabulary terms that students will be expected to know by the end of the unit:

Area - The size of a flat surface measured in square units

Congruent - To be the same size and shape

Flip-To turn a figure over

Slide - To move a figure in any direction without rotating it

Turn - To rotate a figure in place

Students will find all of the possible arrangement of 4 squares. These types of shapes are called tetrominoes. Tetrominoes must have "full sides touching." Students will use these shapes to explore the concept of area.

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