Blue/Black Handout Name: _________________________________ “What’s My Rule?” for Geometric Patterns 1) When you cut a circular pizza, each cut goes through the center. 2 cuts Cuts Pieces 1 cut 1 2 2 4 3 4 12 16 3 cuts Fill in the missing numbers in the table. Then write an algebraic expression that describes h ow many pieces you have when you make c cuts. __________________________ pieces Folds Rectangles 2) Fold a sheet of paper in half. Now fold it in half again. 0 1 And again. And again, until you can’t make another fold. 1 2 2 After each fold, count the number of rectangles into which 3 the paper has been divided. Fill in the missing numbers in the table. Write an algebraic expression to name the 4 number of rectangles you have after you have folded the 5 paper k times. 6 ____________________ rectangles k 3) Below are the first 4 diagrams in a pattern made with square blocks. Draw Design 5 in this pattern. Design Design Design Design Design 1 2 3 4 5 a. Create a table for this pattern. b. What is the algebraic expression that describes the rule? ____________ c. How many square blocks will there be … in Design 10? ___________ in Design n? ____________ Solutions: 1) Cuts 1 2 Pieces 2 4 3 6 4 8 6 12 8 16 Folds 0 1 Rectangles 1 2 2 4 3 8 4 16 5 32 6 64 k 2k Fill in the missing numbers in the table. Then write an algebraic expression that describes h ow many pieces you have when you make c cuts. __________2c__________ pieces 2) ______2k______ rectangles 3) Design 5 Create a table for this pattern. Design # of # squares 1 1 2 3 3 5 4 7 5 9 10 19 n 2n-­‐1 What is the algebraic expression that describes the rule? ___Double the design #, then subtract 1____ How many square blocks will there be … in Design 10? _____19___ in Design n? ___2n-­‐1____