 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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 The Length of Larry's Rectangle  Larry Sue
Algebra, difficulty level 2. Larry wants to know the length of his rectangle. Can you help him?
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 Let the Sunshine In  Leigh Nataro
Trig/Calc, difficulty level 2. Find the dimensions of a window designed to let in the maximum amount of sunshine.
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 Lost in Space  Lisa Lavelle
Math Fundamentals, difficulty level 4. Figure out how big an error the engineers made when they mixed up their units.
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 Lucie and Daryl's Bike Ride  Terry Trotter
Algebra, difficulty level 2. A sister and brother who ride bikes provide us with a math challenge concerning distance, rate, and time.
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 Lucky Lettuce Land  Kainoa Trotter, et al.
Math Fundamentals, difficulty level 3. Help Farmer Lucky fence his lettuce land.
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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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 The Mad Hatter's Gone!  Leanne Gater
Math Fundamentals, difficulty level 4. Explore a coordinate plane and help the Cheshire Cat find his favorite cheese.
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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 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 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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 Managing a Mall  Leigh Nataro
Trig/Calc, difficulty level 2. Find how many square feet there are in a quadrilateralshaped store.
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 Marsha's Triangle  Marsha Hurwitz
Algebra, difficulty level 3. Find the area of an isosceles triangle whose two legs are on the x and y axes and whose hypotenuse passes through the point (c,d).
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 Measuring the Matterhorn  Annie Fetter
Geometry, difficulty level 2. Use some right triangle trigonometry to calculate the height of the
Matterhorn at Disneyland.
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 The "Middle" Triangle  Annie Fetter
Geometry, difficulty level 2. In rectangle ABCD, E is the midpoint of BD, F is the midpoint of ED, AD is 10 cm, and AB is 20 cm. What's the area of AEF?
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 Midpoint Magic  Terry Trotter
Algebra, difficulty level 4. Connecting the midpoints of a general quadrilateral yields a special new foursided figure. What is it?
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 A Minor Arc Subtended by a What??  Annie Fetter
Geometry, difficulty level 2. A chord of a circle is the hypotenuse of an isosceles right triangle whose legs are radii of the circle. The length of the chord is 6 times the square root of 2. What is the length of the minor arc subtended by the chord?
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 Missing Angle Mystery  Terry Trotter
Algebra, difficulty level 2. Help Detective Sam Spade solve a robbery of valuable polygons from Mrs. Hempstead's famous collection.
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 The Mobius Band  Annie Fetter
Geometry, difficulty level 2. Build a Mobius band and explain what happens when you cut it up.
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 More Mowing Madness  George Miller and Lisa Lavelle
Math Fundamentals, difficulty level 4. Where should Matt and Georgette change places to evenly split their "Mattmowing" work?
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 More Tangents!  Annie Fetter
Geometry, difficulty level 3. Given a square ABCD inscribed in a unit circle. AB is extended to P, where PC is tangent to the circle. Find the length of PD.
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 Mowing Madness  George Miller and Lisa Lavelle
Math Fundamentals, difficulty level 2. Using a special "Mattmowing" technique, find the dimensions of the last rectangle to be mowed in a 48 ft. by 64 ft. yard.
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 Mowing My Lawn  Annie Fetter
Geometry, difficulty level 3. My lawn is 75 feet by 42 feet, my lawn mower cuts 18 inches at a time. I am mowing in a circular pattern, and have finished part of the lawn. That part took me 8 minutes. How much longer will I have to mow to finish the
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 Name This Quadrilateral!  Annie Fetter
Geometry, difficulty level 3. A quadrilateral is drawn on a piece of paper. It has one pair of opposite sides congruent, the other pair not congruent, and a pair of opposite angles that are supplementary. What is this figure, and how do you know?
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 Napoleon's River  Annie Fetter
Geometry, difficulty level 2. A soldier uses the visor of his cap to measure the distance across the river.
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 Nets of a Cube  Annie Fetter
Geometry, difficulty level 2. When you fold up the given net of a cube, what shape is formed by the segments on the faces of the cube?
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 The New Rug  Lisa Lavelle
Elementary, difficulty level 3. Find the number of squares needed to cover the Reading area.
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 Nine Congruent Rectangles  Annie Fetter
Geometry, difficulty level 2. Nine congruent rectangles form a larger rectangle whose area is 720 units^2. What's the perimeter of the large rectangle?
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 The Ninja Mission  Steve Earth
Trig/Calc, difficulty level 4. Find the measurement of a spike's angle, given the star's perimeter.
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 Office Tile Choice  Judy Ann Brown
PreAlgebra, difficulty level 3. Find the total cost of purchasing tiles for my office.
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 One Area  Many Solutions  Leigh Nataro
Trig/Calc, difficulty level 2. Find the area of a triangle given the coordinates of its vertices.
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 One Last Bit of Fun  Annie Fetter
Geometry, difficulty level 3. In parallelogram ABCD, the bisector of angle ABC intersects AD at P. If PD=5, BP=6, and CP=6, what is the value of AB?
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 Overlapping Squares  Annie Fetter
Geometry, difficulty level 3. Two squares, one 8 cm on a side and the other 10 cm, overlap. A corner of the 10 cm square is anchored at the middle of the 8 cm square and can rotate around that point. What are the maximum and minimum areas they'll overlap?
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 Partial Area  Judy Ann Brown
PreAlgebra, difficulty level 3. Find the area of the portion of the circle that is not included inside the inscribed square.
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 Patterning a Shotgun  Annie Fetter
Geometry, difficulty level 2. Construct a circular target with nine regions of equal area, with one a circle in the middle and spokes going out to the edge. If the whole circle is 6 feet in diameter, what will the diameter of the inner circle be?
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 Pentomino Cubes  Annie Fetter
Geometry, difficulty level 3. Given the 12 pentominoes, explain which ones can't be used as the basis for the net of a cube. Then take three of the ones that will work and explain where you can attach the sixth square to make the full net.
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 A Picture Is Worth A Thousand Words  Leigh Nataro
Trig/Calc, difficulty level 4. Find the ratio of the area of the overlapping region to the area of nonoverlapping regions of two circles.
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 PicturePerfect Geometry  Judy Ann Brown
PreAlgebra, difficulty level 2. Graph four points and name the figure that you have drawn.
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 Play Ball!  Annie Fetter
Geometry, difficulty level 2. Figure out how to scale down parts of a basketball court so that it's "woman sized," assuming that the average men's college player is 6'3" and the average woman is 5'6".
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 Playing with Matchsticks  Annie Fetter
Geometry, difficulty level 2. Thirteen matchsticks are arranged to make six equal regions. Take away one of the matchsticks and arrange the remaining twelve so that they still make six equal regions.
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 Playing with Paint  Annie Fetter
Geometry, difficulty level 2. Explain what threedimensional solid would make a given "trail" if it were dipped in paint and rolled on the floor.
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 Pondering Pantographs  Annie Fetter and Lillian Ray
Geometry, difficulty level 3. Why does a pantograph work?
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 A Problematic Pizza  Leigh Nataro
Trig/Calc, difficulty level 2. Find the area of a specific region of a circle based on given information.
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 Product Max  Leigh Nataro
Trig/Calc, difficulty level 2. Find the maximum value for two numbers whose sum is a.
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 Proofs Without Words I  Annie Fetter
Geometry, difficulty level 2. Explain how these pictures and algebraic expressions are related. Draw your own picture that illustrates an algebraic concept.
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 Proofs Without Words II  Annie Fetter
Geometry, difficulty level 2. Based on a simple example that illustrates the distributive property, explain what the second picture illustrates.
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