 Measuring the Circumference of the Earth  Annie Fetter
Geometry, difficulty level 3. At our office on the autumnal equinox, the angle formed by the sun's rays and a stick is 40 degrees. If our office is 2749 miles from the equator, what's the circumference of the Earth?
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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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 MiniMall Measurements  Claire Mead
Math Fundamentals, difficulty level 2. Use given measurements of the stores in the minimall to find the area
and dimensions of
other stores.
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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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 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 Pie, Anyone?  Annie Fetter
Geometry, difficulty level 2. How big a pie pan would you need if you made twice as much dough as you would need for a 9inch pan?
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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 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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 My Mom Rocks!  Annie Fetter
Geometry, difficulty level 3. Help my mom decide if she's buried the stones in her new garden deep enough.
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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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 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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 Office Tile Choice  Judy Ann Brown
PreAlgebra, difficulty level 3. Find the total cost of purchasing tiles for my office.
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 Olympic Softball  Annie Fetter
Geometry, difficulty level 2. Should the pitcher's rubber in Olympic softball be behind the line drawn from third base to first base, or in front of it?
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 Olympic Target Shooting  Annie Fetter
Geometry, difficulty level 2. Given that a shooter is equally likely to hit any point on a 10inch target, what are the odds that his shot will be in the 6inch circle?
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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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 Painting a Cube  Annie Fetter
Geometry, difficulty level 3. A large cube, made up of smaller cubes, has some of its faces painted. When it's taken apart, 24 of the small cubes have no paint on them. How big was the large cube, and how many of its faces were painted?
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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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 Peanut's Back Yard  Jonathan Bauer
PreAlgebra, difficulty level 3. Peanut, the overexcited dog, makes 40 laps around a stake and travels a total distance of 1 mile. If his bowl of water is 20 feet away from the stake, can he get a drink?
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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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 Picking a Point  Steve Risberg
Geometry, difficulty level 2. A point is randomly selected from within the rectangle having vertices
at (0,0), (2,0), (2,3) and (0,3). What's the probability that the
xcoordinate of the point will be less than the ycoordinate?
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 Picking Painted Cubes  Annie Fetter
Geometry, difficulty level 2. A large cube, composed of smaller cubes, is painted on all sides. The edge length is five small cubes. It's then broken apart and the smaller cubes are put in a bag. What are the odds that a chosen cube is painted on three
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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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 Pi Day Treats  Judy Ann Brown
PreAlgebra, difficulty level 3. Help Mrs. Granville and Mrs. Germain plan a Pi Day celebration.
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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 Blocks  Annie Fetter
Geometry, difficulty level 4. A large cube is made up of 13 double cubes like the smaller one shown, plus a single cube. What color is the single cube, and where does it have to be?
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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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 Point P Perambulates  Annie Fetter
Geometry, difficulty level 3. Find the length of the path of a vertex of an equilateral triangle as that triangle rotates around the inside of a square.
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 Points, Lines, and Planes  Annie Fetter
Geometry, difficulty level 3. Determine the number of lines defined by 5 or 6 points, and the number of planes defined by 4 or 5 points. Expand this for N points.
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 Precision Paper Folding  Annie Fetter
Geometry, difficulty level 3. After folding down two corners of a rectangular piece of paper, explain what the resulting angle measure will always be.
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 Proofs Without Words  Annie Fetter
Geometry, difficulty level 2. Drawings can 'prove' mathematical statements. What picture would prove what (a + b)^2 is equal to? How about (a + b)(c + d)?
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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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 The Protean Perimeter  Annie Fetter
Geometry, difficulty level 3. Given isosceles triangle ABC, with AC=AB=5 inches and angle CAB greater than or equal to 60, what's the perimeter of the triangle if all the edgelengths must be integers?
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 The Puzzling Parallelogram  Annie Fetter
Geometry, difficulty level 3. Draw a parallelogram ABCD with AB=10. Draw EF with E between A and B and F between C and D such that EF divides the area of ABCD in half. If EF=4, what is FD?
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 Quad Query  Annie Fetter
Geometry, difficulty level 2. Given quadrilateral ABCD, with E the midpoint of AB and F the midpoint of AD. The area of FAEC is 13. What's the area of ABCD?
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 Quilting Squares  Suzanne Alejandre
PreAlgebra, difficulty level 2. Help with some quick calculations of the amount of fabric needed for this quilt design.
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 Regional Ratios  Annie Fetter
Geometry, difficulty level 2. A regular hexagon and an equilateral triangle have the same perimeter. What's the ratio of their areas?
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 Replacing the Football Field  Annie Fetter
Geometry, difficulty level 2. Will a regulationsize NCAA soccer field fit inside an equalquadrant 400meter track?
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 Returning to Napoleon's River  Annie Fetter
Geometry, difficulty level 3. A soldier stands on the bank of a river and uses his cap to measure its width. How far off will he be if he drops his head even one degree?
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 The Return of the Parallelogram I  Annie Fetter
Geometry, difficulty level 3. Given parallelogram ABCD, with AB=10, and E on AB and F on CD. If EF is 4, what is the area of ABCD?
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 The Return of the Parallelogram II  Annie Fetter
Geometry, difficulty level 3. Draw a parallelogram ABCD with AB=10. Draw EF with E between A and B and F between C and D such that EF divides the area of ABCD in half. If EF=4, what is the area of the parallelogram?
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 Rotating a Triangle  Annie Fetter
Geometry, difficulty level 2. Given a triangle on a coordinate grid, find the new coordinates of the vertices if you rotate the triangle 90 degrees about the origin.
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 Running a Mile on a Metric Track  Annie Fetter
Geometry, difficulty level 4. How far out from the rail on a 400 meter track would you have to run to cover 440 yards?
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 Save the Lake!  Annie & Tom Fetter
Geometry, difficulty level 2. How far does the water level drop if you take 900,000 gallons of water out of a lake with a surface area of 334 acres?
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 Scintillating Similarity  Annie Fetter
Geometry, difficulty level 2. Given a triangle with sides of 3, 4, and 6. What is the perimeter of the smallest triangle that is similar to the first one and has one side with length 12?
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