1 Match Stick Problems and Puzzles: Connecting Geometry, Algebra, and Problem Solving By Patty George Cerritos College

2 Match Stick Triangles Here is a triangle made of 3 match sticks. A track of two triangles looks like this. A track of three triangles looks like this.

3 Problem 1 How many match sticks would it take to make a track of 500 triangles?

4 Look for a Pattern: Deconstruct the Information in the Chart TrianglesMatch Sticks 13=3 25=3+2 =3+2(1) 37=3+2+2 =3+2(2) 49= =3+2(3)

5 Make a Generalization TrianglesMatch Sticks 13=3 25=3+2 =3+2(1) 37=3+2+2 =3+2(2) 49= =3+2(3) n3+2(n-1)

6 Solution to Problem 1 You would need f(500)=3+2(499)=1001 match sticks to create a track of 500 triangles.

7 A Square Match Stick Unit Suppose a square match stick unit is defined to be a square with one match stick per side.

8 A Track of Square Match Stick Units A track of two square match stick units would look like this. A track of three square match stick units would look like this.

9 Problem 2 How many match sticks would you need to create a track of 500 square match stick units?

10 Make a Generalization SquaresMatch Sticks 14=4 27=4+3 =4+3(1) 310=4+3+3 =4+3(2) 413= =4+3(3) n4+3(n-1)

11 Solution to Problem 2 It would take 1501 match sticks to create a track of 500 squares.

12 Problem 3 How many match sticks would you need to make a track of 500 rectangles in which each rectangle is two match sticks long and one match stick wide? Is there more than one answer?

13 Problem 4 How many match sticks would it take to make a 20 by 20 match stick square that is made from joining square match stick units? Here is a 2 by 2 match stick square.