Toothpick Activity For Unit 6

Task 3 Task #3-Five Squares Problem Objective: The students are to determine how many toothpicks would be needed to make “n” squares.

1st- students will take their toothpicks and make 5 squares, touching only at the ends

2nd- students tell the number of toothpicks they used to make the 5 squares and record their numbers. 3rd- have the students attempt to make 5 squares using a different number of toothpicks than they used originally. Compare the different ways to make 5 squares using the numbers recorded earlier. 4th- now students make 5 squares as shown in the figure below. Tell the students that these 5 squares can be made with 16 toothpicks. Ask the students to determine different ways to count the 16 toothpicks. The counting patterns must be such that another class member can determine how they counted.

Examples: 5 threes + 1 (3 toothpicks on the left (C’s) and 1 on the right end) 3 fives + 1 (top of each square, bottom of each, left of each and 1 on the right) 3 fours + 2 twos (1st, 3rd, and 5th full square – 4 toothpicks, 2nd and 4th – 2 toothpicks in each) 5 fours - 4 (5 complete squares - the 4 toothpicks they share) 8 twos (5 tops and bottoms and 3 twos in the middle) There may be variations of these. Share all the counting patterns the class comes up with. Now inform the class that you want them to use one of the patterns to determine the total number of toothpicks required to make n square. Have them use their “formula” to determine the number of toothpicks in 75 squares.