Group Activity Cards

 Use groups of 3. Materials: Graph paper, colored markers Street Smarts

Each group member draws 10 street maps like the one shown below on their grid paper. Each line represents a street, so where two lines intersect is the location of a street corner. The object of this activity is to determine how many different paths there are from the starting point to any street corner, given that you are only allowed to move downward, either to the left or to the right.

• Begin with the first row of intersections below the starting point. On one of the maps in your group, use colored markers to show that there is only one path to each of these intersections. Then write the number 1 by each of these intersections.
• Move on to the next row of three intersections. On a different map, use colored markers to show the number of paths to the left most intersection and then the right most intersection. On another map, show the number of paths to the middle intersection in this row. Again, indicate the number of paths to each intersection with a number beside the intersection.
• Continue to the fourth row with four intersections. Use at least three maps to show the number of paths to each of the intersections in this row, numbering each intersection appropriately.
• Go on to the fifth row following the same procedure.
• On a single master map, record your findings for the number of paths to each intersection point through the fifth row. Do you see a pattern that will generate the next row of numbers? If so, explain the pattern and apply the rule to generate the number of paths for each intersection point in the next three rows. If not, continue using the procedure described above to calculate the number of paths to each intersections.
• Compare your findings with those of the rest of the class.