The purpose of these worksheets is to promote thinking. Many of these problems might be difficult to workout using traditional methods, but have elegant solutions that require a little brain power. While most of these problems require a little thought there are several problems are more complex and included for your mathematically gifted students.
There are 4 worksheets in all.
♦ What proportion is shaded? - Based on the information given student have to determine how much of a figure is shaded. These 15 problems are meant to be general representations and therefore don’t have any numbers. Some students may want to add numbers to feel more comfortable with the problems.
Problems 4, 10, 12 – Are slightly more challenging than the other problems.
♦ Brain Scratchers - These problems are great for GT students who need an extra challenge. There are some easier problems near the beginning that don’t require much brain scratching. Problems toward the end require lots of thinking and algebra to solve. All the problems can be solved using high school algebra and geometry skills, but will require in-depth analysis. It is important to keep in mind the hardest problems are challenging and even your brightest kids are likely to struggle on some of them.
♦ Fractals - There a 6 problems looking at areas of fractal type patterns. These problems are like the What proportion is shaded? problems. The answers will be proportions and should be solved using logic.
♦ Area of Circles - Students explore the interesting results of different sized circles can have on area of composite figures.