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 equalsided 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?
TriSquare 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 rhombusshaped backyard.
Same Area: Triangle & Square: Construct a triangle that always has the same area as a square.
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