 Environmentally Friendly  Leigh Nataro
Trig/Calc, difficulty level 2. What dimensions for a given page will use the least amount of paper?
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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 FAB  Annie Fetter
Geometry, difficulty level 2. The measure of one angle in the given picture is x. Using your
knowledge of rhombii and triangles (and other things!), find the
measure of another angle.
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 Finding Fireworks  Annie Fetter
Geometry, difficulty level 2. Do Nasheed and Graciella have enough information to figure out where the
fireworks show is?
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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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 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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 Flatland Soldiers  Terry Trotter
Algebra, difficulty level 1. Find the size of the vertex angle of a soldier in the world of Flatland, a famous book by Edwin A. Abbott.
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 Flying High  Annie Fetter
Geometry, difficulty level 1. Figure out which of two planes is gaining altitude more quickly.
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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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 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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 Frugal Flooring  Marita Paynter
Math Fundamentals, difficulty level 2. Help Graeme determine how many tiles he needs to decorate his new bedroom and whether or not he can afford them.
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 Funny Ducks  Ethel Breuche
Algebra, difficulty level 4. These funny ducks always walk exactly three feet from the lily pond. What is the area of the region bounded by their path?
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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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 Geoboard Gymnastics  Annie Fetter
Geometry, difficulty level 3. Find squares with different areas on a geoboard.
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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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 George's Gutters  Leigh Nataro
Trig/Calc, difficulty level 2. Find the maximum volume of a gutter.
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 Graphing for Area  Judy Ann Brown
PreAlgebra, difficulty level 2. Graph six points and find the area of the resulting hexagon.
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 The Great Flood  Jon Basden
Elementary, difficulty level 3. How much "flood" water did Mr. Basden clean up with his shop vac?
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 The Growing Snowflake  Leigh Nataro
Trig/Calc, difficulty level 4. Find the limit for the area of the Koch snowflake.
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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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 A Holiday Card  Leigh Nataro
Trig/Calc, difficulty level 3. Find the ratio of the red area to the green area as the number of squares approaches infinity.
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 HomeMade Valentine Card  Terry Trotter
Algebra, difficulty level 2. Reuben expresses his affection for his girlfriend by making his own Valentine's Day card, described mathematically.
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 How Are These Equal?  Leigh Nataro
Trig/Calc, difficulty level 2. Solve a trig identity: cot2x  cos2x equals the product of cot2x and cos2x.
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 How Does Your Garden Grow?  Team 7 Red Math Students  Highland Middle School
Elementary, difficulty level 4. Help the HMS students find out how many ways they can arrange their schoolyard garden.
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 How Do You Measure a Mountain?  Leigh Nataro
Trig/Calc, difficulty level 2. Find the height of a mountain based on two angles and the height of a nearby hill.
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 How High Is Enough?  Terry Trotter
Algebra, difficulty level 3. A right triangle is formed by stretching flexible elastic "legs" sufficiently high. How high must that be?
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 How Large Is The Yard?  Leigh Nataro
Trig/Calc, difficulty level 2. Given three sides and two included angles, find the area of my parents' quadrilateralshaped backyard.
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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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 I Get A Kick Out Of Soccer!  Judy Ann Brown
Math Fundamentals, difficulty level 3. How many laps of the soccer field would a team member need to complete to run more than a mile?
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 Integer Triangle Angles  Annie Fetter
Geometry, difficulty level 1. The degree measures of a triangle are x, y, and z, and x, y, and z are
all integers where x < y < z. What's the largest possible value of z?
What's the smallest?
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 Irregular Acreage  Leigh Nataro
Trig/Calc, difficulty level 2. Based on the given information, find the missing length of a lot in the shape of a quadrilateral.
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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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 Judy and Jen's Garden Problem  Terry Trotter
Algebra, difficulty level 2. Judy and her daughter Jen make up math problems while working in their vegetable garden.
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 Kite Construction  Leigh Nataro
Trig/Calc, difficulty level 2. Given some information about the dimensions of a kite, find its area.
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 The Koch Snowflake  Ethel Breuche
Discrete Math, difficulty level 3. Students are asked to find the length of the side of an equilateral triangle that generated the given Koch Snowflake.
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 LawnMowing Chore  Judy Ann Brown
Math Fundamentals, difficulty level 4. Find the area of the yard that Josh, Sam, and Mark must mow.
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 Leaning Ladder  Annie Fetter
Geometry, difficulty level 3. A ladder is leaning against a wall. Explore what happens to the top
of the ladder when the bottom is moved closer or further from the wall.
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