Math Model, Series Model for Third of Square or Triangle
cults3d
What do most kids think of when you ask them about simple fractions such as one half, one third, etc. I have used series models to stimulate discussions about fractions and some of the beautiful ideas behind them. There are numerous nice models or processes available for exploring these concepts with students. Here are two examples that work well for teaching one third (1/3). The side length is approximately 50mm; the wall is 1mm thick and can be made 5mm or 10mm high, depending on your preference. Question: What happens when you add up all the squares/triangles with bottoms if we let the pattern continue indefinitely, ignoring the walls between them? In general, consider a real number R, where R is greater than one. Then, the sum of an infinite series can be calculated using the formula 1 / (R - 1). However, what does it look like in specific cases?
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