Investigation and student accountability is extremely important in education today. Students need to be challenged! They will learn so much more by discovering the formulas rather than me just placing the formula on the board! While talking to my intern about not finding anything cool dealing with recursive sequences, I got an idea. I wanted my kids to find a pattern and develop the arithmetic and geometric recursive formulas using the information that they already know. I created a cut and paste activity where students had to match the sequence, the type, the common difference/ratio, the explicit formula, and the recursive formula. From that, I hoped that students would be able to see a pattern! On a note card, I had them answer three questions...describe any patterns that you see, write a general recursive arithmetic formula, and write a general recursive geometric formula. The students did an awesome job until they were asked to produce the general rec...
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