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recommended investigations

Constructing Quadrilaterals 1: Given two parallel lines, form various quadrilaterals.

Diagonals of Quadrilaterals: Explore the properties of the diagonals of various quadrilaterals.

Quadrilaterals Inscribed Inside Quadrilaterals: Explore properties of quadrilaterals constructed using the midpoints of the sides of given quadrilaterals.

Mystery Quadrilaterals: Classify a quadrilateral by making measurements in a dynamic construction.

Transformers: Make a quadrilateral into a triangle without changing its area.

Optimal Quadrilaterals: Determine the largest area of a quadrilateral for a given perimeter.

Double the Fun: Determine ways to double the dimensions of quadrilaterals.

Equal Sides: Construct an equal-sided quadrilateral inside a trapezoid or other quadrilateral.

Isosceles Trapezoid: Investigate properties of an isosceles trapezoid.

Two Squares: Explore the relationship between length and area.

Transforming Triangle: What is the perimeter of a rectangle formed from an equilateral triangle?

Water Stop: How far does Paul walk to get a drink of water?

Rectangle Squares: Given the perimeter of a rectangle, find its area.

Dividing Rectangles: Find the possible areas of a rectangle that is formed from a larger integral rectangle.

Almost a Square: What rectangle can you form that is close in shape to a square?

Tri-Square Trios: Find pairs of triangular numbers whose sum is a square number.

Rectangular Percents: Compare a rectangle's area when its length and width are changed.

Tripling Perimeter: Find the length and width of a rectangle.

Penning for Pony: What are the dimensions of the largest rectangular pen Ted can make for his pony?

Minimum Perimeters: Find the minimum perimeter for a rectangle with a given area.

Triangle in a Quadrilateral: Given the ratio of a quadrilateral's length to width, find the ratio of the area of a special shaded region to the area of the quadrilateral.

Constructing Squares: Can you construct a square that has twice the area of another square?

Biggie Size It: If the area of a square increases by a certain amount, how long is an edge of the original square?

Land Dispute: Help settle a dispute over land between Squaresville and Centerville.

Folding Squares: Use the perimeter of a rectangle to determine the area of a square.

Increasing Area: If the area of a rectangle increases, how much does its length and width increase?

Triangle or Square: Dissect a triangle into four parts so that it can be rearranged into a square.

Rhombus and Circular Pool: Find a way to build the largest circular pool in a rhombus-shaped backyard.

Same Area: Triangle & Square: Construct a triangle that always has the same area as a square.

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