This should lead to a discussion of using variables and the nth term. Jeff is using toothpicks to make a row of pentagons as shown above. Find the number of toothpicks it would take to make a row of 10 pentagons Find the number of toothpicks it would take to make a row of 100 pentagons. Then they should make the generalization that for every pentagon they added they needed to add 4 toothpicks. Once they use the formula in the spreadsheet, they may use the fill down feature of the program to find the appropriate number of toothpicks needed for 100 squares.
Students show a depth of understanding, originality, and generalizations.
Students show originality and generalizations, but do not show depth of understanding. OR Students answer three of the four questions correct, with depth of understanding, generalizations and originality present. Students do not show depth of understanding or originality. The teacher will assess the students understanding of open sentences and equations by checking work as the students answer questions in class. This will also come from how well the students are able to answer the open-response question given using patterns and mathematical reasoning.