- How Many Angles? - Annie Fetter
Geometry, difficulty level 2. Given a picture of two parallel lines and two transversals, how many
different angle measures are represented by the 14 labeled angles?
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- An Inscribed Circle - Annie Fetter
Geometry, difficulty level 2. Find the radius of a circle inscribed in a right triangle with legs of
5 units and 12 units.
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- A Line of Reflection - Annie Fetter
Geometry, difficulty level 2. Find the equation of the line of reflection for triangle ABC and its
image, A'B'C'.
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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 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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- 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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- Mirror, Mirror - Annie Fetter
Geometry, difficulty level 2. In the given image, the green polygon is a reflection of the purple
polygon. Find the equation of the line of reflection.
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- Mirror Musing - Suzanne Alejandre
Pre-algebra, difficulty level 3. Using the information given in a picture of Hagrid and Baby Norbert, find out how tall each of them is.
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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 "Matt-mowing" work?
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- Mowing Madness - George Miller and Lisa Lavelle
Math Fundamentals, difficulty level 2. Using a special "Matt-mowing" technique, find the dimensions of the last rectangle to be mowed in a 48 ft. by 64 ft. yard.
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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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- Nautical Navigation - Annie Fetter
Geometry, difficulty level 2. Help the sailors of the Kaleidoscope figure out what time
they'll pass the lighthouse and how far from the lighthouse they'll be
at that time.
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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 10-inch target, what are the odds that his shot will be in the 6-inch circle?
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- Painting a Carousel - Annie Fetter & Car Talk
Geometry, difficulty level 2. Help Liam and Thomas figure out the area of the deck of a carousel
using only one measurement.
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- A Parallelogram Dissection - Annie Fetter and Everyday Math Grade 3
Geometry, difficulty level 3. Cut the given parallelogram along the dotted lines and rearrange the
three resulting triangles to form what seems to be a square. What
needs to be true of the original figure in order for the resulting
figure to actually
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- Partial Area - Judy Ann Brown
Pre-algebra, difficulty level 3. Find the area of the portion of the circle that is not included inside the inscribed square.
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- Peanut's Back Yard - Jonathan Bauer
Pre-algebra, 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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- The Perimeter of an Octagon - Annie Fetter, with thanks to the Texas Education Agency
Geometry, difficulty level 3. What's wrong with this picture of a regular octagon? Can you fix
what's wrong and find the perimeter?
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- Picking an Area Formula - Annie Fetter
Geometry, difficulty level 2. Find the area of a polygon on a grid and figure out which of four
formulas, incorporating points on the interior and points on the
boundary, calculates its area correctly.
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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
x-coordinate of the point will be less than the y-coordinate?
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- Pizza Pie - Judy Ann Brown
Pre-algebra, difficulty level 3. Use the given information to decide how many slices of the small pizza would be equal to or greater than 3 slices from the large pizza.
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- Playing with a Pentadecagon - Annie Fetter
Geometry, difficulty level 2. Extend the sides AB and ED of the regular pentadecagon ABCDEFGHIJKLMNO
until they intersect. What is the measure of the angle at this
intersection?
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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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- 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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- Proving PD - Annie Fetter
Geometry, difficulty level 3. AOD is a diameter of the circle with center O. B is any point on the
circle that isn't A or D. A tangent is drawn to the circle at point B.
A line is drawn through O parallel to AB, meeting the tangent at P.
Prove that
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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?
...more>>
- A Quickie Triangle Puzzle - Sasha Sokolsky
Geometry, difficulty level 2. Find the length of the unknown side of this triangle using knowledge of special right triangles.
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- A Rectangle Dissection - Annie Fetter
Geometry, difficulty level 3. Cut the given rectangle into three pieces as indicated by the dashed
lines. Rearrange the pieces to form a square, and explain why the
resulting shape actually is a square.
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- Replacing the Football Field - Annie Fetter
Geometry, difficulty level 2. Will a regulation-size NCAA soccer field fit inside an equal-quadrant 400-meter track?
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- Reza's Circle - Reza Kassai
Geometry, difficulty level 2. OC is the radius of a circle and has a length of sqrt2 units. DE is
the perpendicular bisector of OC. BA is tangent to the circle at A. DC
= CB. Find the length of AB.
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- Riz's Route - Richard Tchen & Steve Risberg
Pre-algebra, difficulty level 3. Where is Riz standing when he realizes it would be the same distance to
continue walking
on the longer path as it would be to turn around and take the shortcut?
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- The Rolling Triangle - Annie Fetter
Geometry, difficulty level 3. Equilateral triangle ABC sits on top of unit square DEFG so that AC is
coincident with DE. The triangle is rotated around the outside of the
square until it returns to the top edge. How far did point A travel?
...more>>
- 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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- Seeing Stars - Annie Fetter
Geometry, difficulty level 2. Find the measure of the angle at the "star points" of a "regular star"
when the star has five sides. How about when the star has eight sides?
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- Shine On Harvest Moon - Judy Ann Brown
Pre-algebra, difficulty level 2. Find the area of the largest circle that can be cut from a nine-inch by twelve-inch sheet of paper.
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- Shotgun Targets - Annie Fetter
Geometry, difficulty level 2. Figure out how large to make the inner circle of this shotgun target.
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- The Speed Skating Oval - Annie Fetter
Geometry, difficulty level 2. Find the radii of the turns of a 400 meter speed skating oval.
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- Splitting a Plane - Annie Fetter
Geometry, difficulty level 3. What's the greatest number of regions into which you can split a plane using six lines?
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- Splitting Space - Annie Fetter
Geometry, difficulty level 4. What's the greatest number of regions into which you can divide space using four planes?
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- Splitting up a Triangle - Annie Fetter
Geometry, difficulty level 4. Take any triangle ABC. Construct D and E as the midpoints of BC and
AB, respectively. Now construct DF and EF, where F is any point on AC.
How are the areas of the triangles related to the area of the
quadrilateral?
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- Square in a Right Triangle - Annie Fetter
Geometry, difficulty level 3. In the given picture, square DEFG is inscribed in a right triangle ABC (with right angle at B) with DG on AC, E on AB, and F on BC. If AD is 14 and GC is 29, what's the area of the square?
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- Squares on Squares - Annie Fetter
Geometry, difficulty level 3. Let P be the center of a 16" x 16" square as well as a vertex of
another 16" x 16" square that pivots freely around P. What is the
largest possible value for the area where these two squares overlap?
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- A Stellar Garden - Bill Marthinsen
Pre-algebra, difficulty level 3. Martha Stewart wants to rebuild her ugly garden. She needs help calculating the areas in the new garden.
...more>>
- Symmetry Surprise - Annie Fetter, Suzanne Alejandre
Pre-algebra, difficulty level 3. Identify the types of symmetries of each of three patterns.
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- A Tangent Square and Circle - Reza Kassai
Geometry, difficulty level 3. The square and circle below are tangent at one point and meet at four
other points, as shown in the picture. If the side of the square is 8
units long, what's the radius of the circle?
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- Teresa's Tiles - Kristina Lasher
Math Fundamentals, difficulty level 3. How many square tiles does Teresa need to cover her bathroom floor?
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