







Subdividing a rectangle into squares 
20180513 

From jeverzyck: A rectangular board is 108cm wide and 156 cm long Equal squares as large as possible
are ruled off this board.Find the size of the square.How many squares are there? Answered by Penny Nom. 





What is the speed of the skateboarder? 
20180213 

From Zack: It takes a skateboarder 20 minutes to get to school, which is 6 km from home. What is the speed of the skateboarder? Answered by Penny Nom. 





Matthew skateboards around the school 
20151209 

From Abigail: Matthew skateboards 4km each hour.
How long will it take him to skateboard around the school yard measuring 300m by 200m.?
Thank you. Answered by Penny Nom. 





A word problem with fractions 
20140326 

From lois: a man has a stack of boards, he cuts 3/5 off each board, after he cuts the boards he finds he has enough pieces left to make 4 boards the length of the original boards. how many boards did he start with. Answered by Penny Nom. 





Area on a dart board 
20101011 

From Robert: A dart board consists of concentric circles and line segment. the radius of the bull's eye is 4 inches and each ring surrounding the bull's eye is 3 inches wide.
a) what is the area of the bull's eye
b) what percent is the bull's eye.
hint there are 4 rings and the bull's eye is divided into 4 (90) degree angles (meaning 1/2 up and down) (1/2 left to right. Answered by Stephen La Rocque. 





Four dots are randomly placed on an 8x8 grid 
20100226 

From bobbym: Four dots are randomly placed on an 8x8 grid, compute the probability
that no row or column contains more than one dot. Answered by Claude Tardif. 





Loading a headboard in a uhaul 
20100120 

From gina: I have a uhaul 9'10" long 4"9"wide 4'7"height I have a headboard 74 inches in height would it fit the box diagonally Answered by Penny Nom. 





Grain of rice on a chess board 
20090330 

From andy: Is there an easy way for my students to find out 8 to the power of 21 to solve the grains of rice doubling investigation on a chessboard? Any suggestions welcome. Thanks very much Answered by Robert Dawson and Claude Tardif. 





The board for a variant of chess 
20090316 

From Adam: I am trying to figure out how big a piece of wood I need for a variant of chess I thought up. The board essentially is a set of 6 concentric rings with an empty space in the center, each ring consisting of 24 spaces  so essentially 6 concentric 24sided polygonal rings made up of trapezoidal spaces. I know the interior angle of the shape (15 degrees), but I can't figure out the size this thing should be.
All I know is that the innermost ring will have the smallest spaces, and that those spaces need to be able to accommodate chess pieces 3/4" wide without them overlapping onto neighboring spaces. That is to say, the short parallel side of the trapezoidal space on the innermost ring should be at least 3/4". But I have no clue how to extrapolate the full diameter of the board from that one measurement. HELP!
Adam Goss
saganth@yahoo.com Answered by Stephen La Rocque. 





The surface area of a cube and rectangular prism 
20090216 

From Mhiko: how to derived the total surface area of a cube and rectangular prism using geoboard?? Answered by Robert Dawson. 





Maximum volume of a box 
20080115 

From Rajesh: A square piece of a cardboard of sides ten inches has four equal peices are removed at the corners, then the sides are turned up to form an open box. What is the maximum volume such a box can have? Answered by Stephen La Rocque. 





Board feet 
20071028 

From Carolyn: Lumber is measured iin board feet, where a board foot in volume of a piece of lumber one ft sq and one inch thick. How many board feet are in a two by four inch that is 10 feet long? Answered by Stephen La Rocque. 





Size of a sphere fitting inside a cone 
20070927 

From Juan: I am supposed to find the largest sphere that
will fit into a cone. I am assuming is a maximizing problem, but I am not sure
of what relation (between a cone and a sphere) to use. Answered by Penny Nom and Stephen La Rocque. 





A 5 by 5 checkerboard 
20070917 

From Darren: Hi, I'm Darren and i have some questions to ask you about this problem:
In a 5 by 5 checkerboard : how many 2 by 2 squares are there,
what other sizes of squares do you need to count and how many of of each size of squares
can you find; how many squares did you find in all Answered by Victoria West. 





Splitting A Circle Evenly 
20061220 

From Joe: I'm trying to make a game board and instead of having it square, I would like to give it a curve (the game is Parcheesi). The attached diagram is pretty much completed (done in AutoCAD). What I would like to know is how to manually find the points that intersect the red line. In other words, evenly split the semicircle into 8 pieces. Answered by Penny Nom. 





How many squares are there on a checkerboard 
20061217 

From Tania: how many squares are there altogether on the checkerboard (including the 64 small squares)? Answered by Penny Nom. 





A board is cut into two pieces... 
20060711 

From DeAnna: A 102" board is cut into 2 pieces. One piece is two times the length of the other. Find the lengths of the two pieces. Answered by Stephen La Rocque. 





How many 16 foot 2 by 4's are there in a 1000 board feet of lumber. 
20060208 

From Fred: how many 16 foot 2 by 4's are there in a 1000 board feet of lumber. Answered by Penny Nom. 





The length of a cut 
20040917 

From Florita: My daughhter, who is a 9th grader is attempting to cut a piece of wood after determining the length of the cut for the hypotenuse. These are the measures:
a=4squared, b=6squared.
She determined that c should equal 52. But when she measured the actual piece to be cut, c measured 39.5 inches! Can you offer any insight as to what she is doing wrong? I have suggested that she may be working with an Acute rather than a Right angle . But she insists that it is a Right angle after using a "framing square". Answered by Claude Tardif. 





Geoboards 
20040109 

From Elissa: What is a geoboard? I have a young girl in grade eight math who has a math
question using a geoboard. Answered by Diane Hanson. 





Room and board fees 
20031129 

From Jennifer: A certain university wishes to determine room and board fees for the next academic year. For the current year, the fee is $3600 per student and 1800 students are living in the residence halls. Past data suggests that for every $300 increase in the semester fee, 200 fewer students will choose to live in the dorms. There are also costs to the university associated with the residence halls. The fixed costs total $2,000,000 per semester. the variable costs are currently $1000 per student but will fall $100 per student for each decrease of 100 students. Your task is to help the university determine the optimal fee. Assume linear relationships between the number of students and the fee and between the number of students and the cost per student Answered by Penny Nom. 





Cutting a board 
20030120 

From George: A person has a sheet of board which he saws into two (2) pieces. The length of the first piece is two thirds the length of the original board, while the length of the second piece is four feet longer than the first piece. How long was the original board? (the length is defined as the longer of the two sides of the board) Answered by Penny Nom. 





Squares on a chess board 
20010411 

From Tom: It was once claimed that there are 204 squares on an ordinary chessboard (8sq. x 8sq.) Can you justify this claim? "PLEASE" include pictures. How many rectangles are there on an ordinary chessboard? (8sq. x 8sq.) "PLEASE" include pictures. Answered by Penny Nom. 





Calculator and telephones keypads phones 
20000627 

From Thomas Smith and Veronica YatesRiley: On a keyboard, why is the number "7" on the top of the keypad as opposed to the number "1" at the top a telephone keypad? Answered by Penny Nom. 





Cutting a board into 8 equal pieces 
19991021 

From Brittany: Jamie wanted a board cut into 8 equal pieces. The Lucas Lumber Co. charges 60 cents for cutting a board into 4 equal pieces. How much will it charge for cutting Jamie's board? Answered by Claude Tardif. 





How many squares are on a chessboard? 
19991020 

From Tchilco: How many squares are on a chessboard? Answered by Penny Nom and Claude Tardif. 





Geometry patterns lesson plans 
19981231 

From Vicki: hi,,, my name is Vicki and I am a new 5th grade teacher.... Anyway, I'm supposed to come up with a lesson plan to  Explore patterns that result from cominations of "reflections, rotations, and translations of geometric figures.
The plan is to include:  writing/metacognition, assessment strategies, interdisciplanary connections, supplemental materials, or textbook, and Bloom's taxonomy level.
Any help you could give would be greatly appreciated. Thanks Answered by Jack LeSage. 

