 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.
...more>>
 Good Fences  Lisa Lavelle
Math Fundamentals, difficulty level 3. Design a fence that will keep the animals happy.
...more>>
 Graphing for Area  Judy Ann Brown
PreAlgebra, difficulty level 2. Graph six points and find the area of the resulting hexagon.
...more>>
 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.
...more>>
 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?
...more>>
 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.
...more>>
 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'.
...more>>
 Lost at Sea?  Annie Fetter
Geometry, difficulty level 2. Help Darius and Skip figure out whether they're in the United States
or Canada using the bearings Skip takes.
...more>>
 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.
...more>>
 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?
...more>>
 Measuring Cylinders  Annie Fetter
Geometry, difficulty level 2. Help Ian measure his stove pipe and his propane tank.
...more>>
 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?
...more>>
 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.
...more>>
 Mirror Musing  Suzanne Alejandre
PreAlgebra, difficulty level 3. Using the information given in a picture of Hagrid and Baby Norbert, find out how tall each of them is.
...more>>
 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?
...more>>
 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.
...more>>
 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.
...more>>
 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.
...more>>
 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?
...more>>
 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?
...more>>
 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.
...more>>
 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
...more>>
 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.
...more>>
 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?
...more>>
 Pentagon Puzzle  Annie Fetter
Geometry, difficulty level 1. Explore the interior angles of pentagons.
...more>>
 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.
...more>>
 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?
...more>>
 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.
...more>>
 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?
...more>>
 Pizza Pie  Judy Ann Brown
PreAlgebra, 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.
...more>>
 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?
...more>>
 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.
...more>>
 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.
...more>>
 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.
...more>>
 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?
...more>>
 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
...more>>
 Pythagorean Circles  Lillian Ray
Geometry, difficulty level 3. Figure out the relationship between the area of three regions in this
construction
of "Pythagorean circles".
...more>>
 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.
...more>>
 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.
...more>>
 Replacing the Football Field  Annie Fetter
Geometry, difficulty level 2. Will a regulationsize NCAA soccer field fit inside an equalquadrant 400meter track?
...more>>
 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.
...more>>
 Riz's Route  Richard Tchen & Steve Risberg
PreAlgebra, 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?
...more>>
 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?
...more>>
 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?
...more>>
 Shine On Harvest Moon  Judy Ann Brown
PreAlgebra, difficulty level 2. Find the area of the largest circle that can be cut from a nineinch by twelveinch sheet of paper.
...more>>
 Shortcut Savings  Suzanne Alejandre
PreAlgebra, difficulty level 2. Find a rule to tell how much distance I will save when I take the shortcut.
...more>>
 Shotgun Targets  Annie Fetter
Geometry, difficulty level 2. Figure out how large to make the inner circle of this shotgun target.
...more>>
 The Speed Skating Oval  Annie Fetter
Geometry, difficulty level 2. Find the radii of the turns of a 400 meter speed skating oval.
...more>>
 
