Math Forum - Problems Library - Pre-Algebra, Geometry in the Plane

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  circumference
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Pre-Algebra
operations with numbers
number sense
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Geometry in the Plane
Problems in this category require students to describe, classify, and understand the relations that exist among two-dimensional objects. They may require students to think in terms of the coordinate plane or understanding of congruence, similarity, the Pythagorean theorem, symmetry, or tessellations.

Some of these problems are also in the following subcategories:

Related Resources
Interactive resources from our Math Tools project:
   Math 7: Geometry in the Plane
The closest match in our Ask Dr. Math archives:
   Middle School: Two Dimensional Geometry
NCTM Standards:
   Geometry Standard for Grades 6-8

Access to these problems requires a Membership.

3-D Vision - Annie Fetter
Pre-Algebra, difficulty level 3. When you fold up the given net of a cube, what shape is formed by the segments on the faces of the cube? ... more>>

All the Similar Triangles - Annie Fetter
Pre-Algebra, difficulty level 3. How would you place points D and E to make similar triangles? ... more>>

Back Yard Trees - Judy Ann Brown
Pre-Algebra, difficulty level 4. How many different quadrilaterals can be formed by joining any four of the nine trees? ... more>>

Bella's Bagel Bakery - Suzanne Alejandre
Pre-Algebra, difficulty level 1. How much more area is covered with cream cheese on the large bagel than on the small bagel? ... more>>

Building Fences - Judy Ann Brown
Pre-Algebra, difficulty level 3. Plan a garden so as to maximize the area surrounded by a 36-yard fence. ... more>>

Building on Water - Judy Ann Brown
Pre-Algebra, difficulty level 4. Find the area of a circular pond not covered by a rectangular building. ... more>>

Canadian Soccer - Judy Ann Brown
Pre-Algebra, difficulty level 2. Find the distance a player runs to complete three "Double V" laps. ... more>>

Chamique the Archer - Mr. Marthinsen's Geometry Class
Pre-Algebra, difficulty level 3. Chamique wants to know the probability of hitting a bull's-eye with a randomly shot arrow. ... more>>

Coloring a Hexagon - Ranjan Rohatgi, Spencer Koerner, Suzanne Alejandre
Pre-Algebra, difficulty level 2. How many different ways of coloring the hexagon are represented in Spencer's drawing? ... more>>

Exploring Area - Judy Ann Brown
Pre-Algebra, difficulty level 4. Find information about Pick's theorem and solve an area problem using this method. ... more>>

Fences for Fido and Friends - Annie Fetter
Pre-Algebra, difficulty level 2. Find the area of each rectangular dog pen. ... more>>

Forming Triangles from a Folding Ruler - Annie Fetter, Suzanne Alejandre
Pre-Algebra, difficulty level 1. Describe the three triangles that can be made with the full length of a 6 foot long folding wooden ruler. ... more>>

Graphing for Area - Judy Ann Brown
Pre-Algebra, difficulty level 2. Graph six points and find the area of the resulting hexagon. ... more>>

Graphs - Suzanne Alejandre, Annie Fetter
Pre-Algebra, 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 y-axes. ... more>>

How Fast Is a Minute? - Suzanne Alejandre
Pre-Algebra, difficulty level 1. How many feet does the tip of the minute hand travel in an hour on the clock on Philadelphia's City Hall Tower? ... more>>

How Wide Is My Garden? - Judy Ann Brown
Pre-Algebra, difficulty level 3. A scale drawing is used to determine the width and area of a garden. ... more>>

I'm a Groundhog? - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Using Suzanne's height, Phil's height, and Suzanne's shadow length, find Phil's shadow length. ... more>>

Lillian's Lines - Lillian Ray and Molly Ribble
Pre-Algebra, difficulty level 3. Students are asked to find how many square panes a path goes through for a window of a given size. ... more>>

Lincoln's Top Hat - Suzanne Alejandre
Pre-Algebra, difficulty level 3. Find the dimensions of a rectangular sheet of paper used to make a paper top hat that has width and height the same. ... more>>

Measuring a Mountain Bike - Annie Fetter
Pre-Algebra, difficulty level 3. Help Annie determine the circumference of her bike tire so that she can accurately set up her new cyclometer. ... more>>

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. ... more>>

Office Tile Choice - Judy Ann Brown
Pre-Algebra, difficulty level 3. Find the total cost of purchasing tiles for my office. ... more>>

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. ... more>>

Paving Stones - Suzanne Alejandre
Pre-Algebra, difficulty level 1. How many stones did Kathy need to buy to pave an area in her yard? ... more>>

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? ... more>>

Picture-Perfect Geometry - Judy Ann Brown
Pre-Algebra, difficulty level 2. Graph four points and name the figure that you have drawn. ... more>>

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. ... more>>

Practicing for the Winter Olympics - Cynthia Paul
Pre-Algebra, difficulty level 2. What is the length of the semicircular path Sonya skates across the ice rink? ... more>>

Quilting Squares - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Help with some quick calculations of the amount of fabric needed for this quilt design. ... more>>

A Quilt Made of Squares - Annie Fetter
Pre-Algebra, difficulty level 3. Using the information given, will the finished quilt be in the shape of a square? ... more>>

Right Triangle, Which Legs? - Annie Fetter
Pre-Algebra, difficulty level 3. Find the possible lengths for the third side of a right triangle given the lengths of the other two sides. ... more>>

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? ... more>>

Shapes Rock - Judy Ann Brown
Pre-Algebra, difficulty level 3. Find the number of diagonals in a polygon of 40 sides. ... more>>

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. ... more>>

Shortcut Savings - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Find a rule to tell how much distance I will save when I take the shortcut. ... more>>

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. ... more>>

Tiling Triangles - Suzanne Alejandre
Pre-Algebra, difficulty level 3. Given the dimensions of a large triangle, find the dimensions of the 25 small triangles that tile it. ... more>>

Timber! - Steve Risberg
Pre-Algebra, difficulty level 3. A tree breaks three-eighths of the way up the trunk, and the tip hits the ground 40 feet from the base of the trunk. How tall was the tree? ... more>>

Twisting Carpet Tiles - Suzanne Alejandre
Pre-Algebra, difficulty level 2. For each of the two floors find the total number of degrees that the sixteen tiles have been rotated. ... more>>

Women's Walkway - Suzanne Alejandre
Pre-Algebra, difficulty level 2. How many bricks would it take to cover the full area of the pattern sample? What's the area? ... more>>

Wondering about Water - Annie Fetter
Pre-Algebra, difficulty level 3. Find the surface area of an Olympic-size ice hockey rink. ... more>>

Wraparound Universe - Jeff Weeks
Pre-Algebra, difficulty level 4. Explore the game of tic-tac-toe using a cylindrical tic-tac-toe board. ... more>>

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