 Dissecting Shapes  Annie Fetter
Geometry, difficulty level 3. 1) Take the irregular shape shown and, making just two cuts, turn it into a square. 2) Take a square and, using four cuts, make five smaller equal squares whose total area is t he same as the original.
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 Divided Rectangle  Annie Fetter
Geometry, difficulty level 1. A rectangle is divided into four rectangles with areas 45, 25, 15, and x. Find x.
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 Drawing a Kite Plan  Annie Fetter
Geometry, difficulty level 3. Given a picture of a kite plan, figure out the radius of the circle that creates the curved section.
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 Drawing Out a Decagon  Annie Fetter
Geometry, difficulty level 2. Extend sides AB and IH of the regular decagon ABCDEFGHIJ until they intersect. What is the measure of the acute angle at this intersection?
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 Equal Area & Congruence  Annie Fetter
Geometry, difficulty level 2. If two triangles are congruent, they have the same area. Is the converse true?
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 Equilateral Triangles and Circles  Annie Fetter
Geometry, difficulty level 2. Two vertices of an equilateral triangle are on the diameter of a circle whose area is 49 pi. The other vertex is on the circumference of the circle. What's the largest possible area of the triangle?
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 Examining an Octagon  Annie Fetter
Geometry, difficulty level 3. Describe the rectangles that you would need to put on the sides of a square in order to be able to end up with a regular octagon when you connect the outside vertices of the figure.
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 Explanation Only!  Annie Fetter
Geometry, difficulty level 4. Prove that x/(1x) = 1/x in the given picture.
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 Exploring Area  Judy Ann Brown
PreAlgebra, difficulty level 4. Find information about Pick's theorem and solve an area problem using this method.
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 Extending the Enneagon  Annie Fetter
Geometry, difficulty level 3. Extend the sides AB and ED of the regular enneagon ABCDEFGHI until they intersect. What is the measure of the acute angle at this
intersection? Extend sides AB and EF. Now what's the measure of that acute angle at the
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 Finding Formulas for Medians from Edgelengths  Annie Fetter
Geometry, difficulty level 3. Write a formula for finding the median of a triangle in terms of the three sides of the triangle.
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 Finding the Base of a Trapezoid  Annie Fetter
Geometry, difficulty level 3. Given trapezoid ABCD, with AD one base and BC the other and a 60 degree angle at CDA. If CD is 26sqrt3/3 meters, BC is 7 meters, and the area of the trapezoid is 130 square meters, what's the length of AD?
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 Finding the Side of a Parallelogram  Annie Fetter
Geometry, difficulty level 3. In parallelogram ABCD, the bisector of angle ABC intersects AD at point P. PD is 5, BP is 6, and CP is 6. What's AB?
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 Finding the Volume of a Box  Annie Fetter
Geometry, difficulty level 2. If the areas of the top and front of a box are 252 and 105 square inches, respectively, and the surface area of the box is 834 square inches, what's the volume of the box?
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 Find the Area of This Square  Annie Fetter
Geometry, difficulty level 2. Given a square split into four pieces, one with an area of 35 and the other with an area of 8, find the area of the whole square.
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 Find the Largest Equilateral Triangle  Annie Fetter
Geometry, difficulty level 3. Two vertices of an equilateral triangle lie on a diameter of a circle whose area is 36pi cm^2, and the third vertex lies on the circle. What is the largest possible area of the triangle?
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 Find the Perimeter  Annie Fetter
Geometry, difficulty level 3. In the given picture, DB and DC are both 20 inches. What's the perimeter of triangle FDG?
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 Find the Volume of a Box  Annie Fetter
Geometry, difficulty level 2. Given the surface area of three sides, find the dimensions and volume of a rectangular box.
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 Find This Angle  Annie Fetter
Geometry, difficulty level 3. Given triangle ABC, where E is on AB and DB is perpendicular to AE. AC = BC, angle ACB is twice the measure of angle CBD, and angle DBE = 90 degrees. What is angle CBD?
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 Fix This Picture  Annie Fetter
Geometry, difficulty level 2. Figure out what's wrong with this picture that includes a circle and a rhombus.
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 Folding a Piece of Paper in Thirds  Annie Fetter
Geometry, difficulty level 3. Show that the given folds mark a piece of paper exactly in thirds.
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 Folding Postage Stamps  Annie Fetter
Geometry, difficulty level 2. Fold a block of eight postage stamps, as indicated, along the perforations and without tearing, so as to form a single pile with the stamps numbered consecutively from top to bottom.
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 The Folding Ruler  Annie Fetter
Geometry, difficulty level 2. Describe all of the possible triangles that can be made with the full length of a 6 foot long folding wooden ruler.
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 Framed!  Annie Fetter
Geometry, difficulty level 3. Given a triangular painting with dimensions 20 x 14 x 10, and three different ways you could frame it, which frame will take the least amount of material?
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 A Gardening Puzzle  Annie Fetter
Geometry, difficulty level 2. If a rectangular garden were 2 feet wider and 3 feet longer, it would be 64 square feet larger. If it were 3 feet wider and 2 feet longer, it would be 68 square feet larger. What are the dimensions of the garden?
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 Geometric Algebra?  Annie Fetter
Geometry, difficulty level 2. Given a geometric picture that illustrates the fact that a(a+b)=a^2+ab, explain what the second picture illustrates.
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 Geometry XGames  Annie Fetter
Geometry, difficulty level 2. Given triangle ABC, with D on AB and E on BC. AC is 39 units, AD is x units, DB is 9 units, DE is 13 units, and BE is x units. If triangles ABC and EBD are similar, what's x, and what's the length of CE?
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 Go Fly a Kite!  Annie Fetter
Geometry, difficulty level 2. If you're flying a kite 75 yards away from 70 foot tall trees, how much line would it take to get to the top of the trees? What if the kite moved up so that was 65 yards away? What would the angle be? And more!
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 Going Global  Annie Fetter & NCTM's WLME
Geometry, difficulty level 2. Look at Shakespeare's Globe Theater from a mathematical standpoint  figure out the interior angle of an icosagon and calculate how many people could stand in the "field" in front of and around the stage.
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 Graphs  Suzanne Alejandre, Annie Fetter
PreAlgebra, difficulty level 3. Match the descriptions to the graphs. Explain how to find one of the points on each graph and give the labels for the x and yaxes.
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 The Hexagonal Cross Section of a Cube  Annie Fetter
Geometry, difficulty level 3. Explain how to get a hexagonal cross section of a cube. If the cube has edgelength one, what are the area and perimeter of the hexagon?
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 A Hexagon and a Triangle in a Circle  Annie Fetter
Geometry, difficulty level 2. A regular hexagon and an equilateral triangle are both inscribed in the same circle so that the hexagon and the triangle share three vertices. The radius of the circle is 10 units. What is the area of the region between the
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 Hippocrates' Lunes  Annie Fetter
Geometry, difficulty level 3. ABC is half a square inscribed in a semicircle. Then a semicircle is constructed on AB. BD is then constructed, the perpendicular bisector of AC, and triangle ABD is shaded, as is the part of the outer semicircle that's
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 How Wide Is My Garden?  Judy Ann Brown
PreAlgebra, difficulty level 3. A scale drawing is used to determine the width and area of a garden.
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 Intersecting Circles  Annie Fetter
Geometry, difficulty level 3. What is the maximum number of times six circles of the same size can intersect? In other words, draw six circles of the same size on a piece of paper  what is the maximum number of intersections your drawing can have?
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 Jill and Jimmy  Soap Bubbles  Annie Fetter
Geometry, difficulty level 3. You're given two spheres with centers 14 cm apart. If the two spheres intersect in a circle whose radius is 12 cm, and the radius of one sphere is 13 cm, what's the radius of the other sphere?
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 Journey Through Outer Space  Annie Fetter
Geometry, difficulty level 2. How many Earths can fit in Uranus?
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 Large Cube and Painted Faces  Annie Fetter
Geometry, difficulty level 3. Unit cubes form a larger cube. Some faces of the larger cube are painted. When the large cube is taken apart, 24 of the unit cubes have no paint on them. How big was the large cube and which of its faces were painted?
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 Learning About GPS  Annie Fetter
Geometry, difficulty level 4. What percentage of the surface of the earth can be seen by a satellite orbiting at an altitude of 20,200 km? Are the Global Positioning System satellites "geosynchronous"?
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 The Length of a Belt  Annie Fetter
Geometry, difficulty level 3. The diameters of two wheels are 18 cm and 12 cm and their centers are 30 cm apart. A belt goes around them and crosses 18 cm from the center of the big wheel. How long is the belt? How do you know you're right?
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 Mad About Medians?  Annie Fetter
Geometry, difficulty level 3. The medians drawn from the vertices of the acute angles of a right triangle are 5 and sq root of 40. What is the length of the hypotenuse?
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 Magic Coins  Annie Fetter
Geometry, difficulty level 3. How come you can fit a quarter through a hole the size of a dime? Find a pair of coins in another system of money that could be used as "magic coins"  the "biggest" and "smallest" coins for which this would work.
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 Make a Square!  Annie Fetter
Geometry, difficulty level 3. Make two cuts in the given figure and rearrange the pieces to make a square.
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 Making a Map  Annie Fetter
Geometry, difficulty level 3. Given a list of relationships between five different objects, explain which ones you could uniquely place on a map.
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 Making a Quilt of Squares  Annie Fetter
Geometry, difficulty level 4. Figure out the dimensions of some closely packed squares.
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 Making a Six Pointed Star  Annie Fetter
Geometry, difficulty level 3. Take a circle of paper. Explain how to fold it so that you can make just one cut and get a "perfect" sixpointed star.
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 Making Pie Crust  Annie Fetter
Geometry, difficulty level 3. How would you change the recipe for a 9inch pie crust to make an 11inch pie crust?
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 Making Scalene Triangles  Annie Fetter
Geometry, difficulty level 2. A scalene triangle has sides of 8, x, and 19. The sides are listed in order from smallest to largest. What are all of the possible integer values for x?
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 Making Triangles I  Annie Fetter
Geometry, difficulty level 2. Take a scalene triangle. The lengths of the sides, in size order, are 5, x, and 15. What are the possible integral values for x?
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 Making Triangles II  Annie Fetter
Geometry, difficulty level 2. Given a scalene triangle with sides, listed from shortest to longest, of 6, x, and 16, what are all the possible integer values for x?
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