Math problems for grade 8 geometry
Problem sets in PDF format that address objectives of the Measurement and Geometry strands of the North Carolina Standard Course of Study for Mathematics, Grade 8.
What makes a good problem?
- A problem should be non-routine — that is, a student can’t simply isolate the numbers and calculate but must give the numbers some meaning. - A problem should help students foster their mathematical reasoning.
- The problem should include follow-ups that elaborate from a special case to a generality — for example, from finding the perimeter of a string of 2, 3, 4 adjacent hexagons to a string of n hexagons.
- John A. Van de Walle, in "Reform vs. the Basics: Understanding the Conflict and Dealing with It," defines a good problem as “any task or exploration for which the solution has not been explained, that begins where kids are (with their ideas), that is challenging mathematically, and for which justification and explanations for answers, methods, and results are understood to be the responsibility of the students.”
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- Problem centered math
- Why students must build their own understanding of mathematics if they are to be able to use it in the real world, and how teachers can guide them in doing so.
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These problems were created or compiled by participants at LEARN NC’s May 2001 Problem-Based Mathematics workshop at the North Carolina Center for the Advancement of Teaching in Cullowhee, N.C. They address various objectives of the Spatial Sense, Measurement, and Geometry strand (Goal 2) of the North Carolina Standard Course of Study for Mathematics, Grade 8.
The problems are available in PDF format except where otherwise noted. (The free Adobe Acrobat Reader is required to view PDF files.) To view a problem, click on its title; to view the text of relevant curriculum objectives, click on the numbers of the objectives.
Relevant goals and objectives are listed in parentheses after the title of each problem set and refer to the 1999 version of the mathematics Standard Course of Study.
Area, Surface Area, and Volume: Selected Problems
A set of 6 problems involving manipulation of sides of squares, rectangles, and rectangular solids and explaining resulting changes in area, surface area, and volume. Solutions provided. By Retella Jones and Grayling Williams, Durham County Schools. Based on problems from http://www.mathcounts.org and from the collection of Grayson Wheatley, Professor Emeritus, Florida State University.
Fencing Problems
A set of 8 related problems involving building of fences around various sizes of garden plots. Solutions provided. By Randy Harter, Buncombe County Schools.
Gardening Problems
A set of 3 related problems involving manipulation of sizes of garden plots and construction of boxes from sheets of given sizes. Illustrations provided. By Pat Sickles, Durham Public Schools.
A Pile of Gold
Comparison of volumes of containers of various shapes. Illustrations provided. By Holley Merschat, North Buncombe Middle School, Buncombe County.
Circles and Regular Polygons
Using a spreadsheet to explore relationships between sizes of inscribed and circumscribed circles. By Randy Harter, Buncombe County Schools.
PE Storage Box
A set of 7 related problems involving the visualization and manipulation of boxes of different sizes and their contents. By Jeanne Joyner, North Carolina Department of Public Instruction.
Manipulating Pyramids
Finding surface area and volume of a pyramid from given dimensions; understanding the relationship between changes in various dimensions of the pyramid. Illustration provided. By Wayne Drummond, Owen Middle School, Buncombe County.
Pythagorean Problems
A set of 5 real-life problems requiring use of the Pythagorean Theorem. Solutions provided. By Brent Bustle, Troutman Middle School, Iredell-Statesville Schools.
Explaining the Area of a Triangle
From a triangle with given dimensions, explain three different ways of computing the area. Illustration provided. By Wayne Drummond, Owen Middle School, Buncombe County.
Overlapping Triangles
Comparison of areas of various triangles in a complex diagram. Illustration provided. By Wayne Drummond, Owen Middle School, Buncombe County.
What’s My Rule?
A game to help students understand the concept of adding squares and their square roots. This makes a good way to begin a lesson on the Pythagorean theorem. By Brent Bustle, Troutman Middle School, Iredell-Statesville Schools.
Visualizing Halves (PDF file|Web page)
Students examine diagrams to determine whether exactly half is shaded. Could be used as a warmup exercise. By Grayson Wheatley, Professor Emeritus, Florida State University.
