Answer:

The perimeter of the 12^th shape will be 38. (To model this problem, some students will draw the shapes and count the sides to determine the perimeter. Others will use the pattern blocks to create the shapes and count the sides. Others may look at the table and add 3 to the previous perimeter to get the perimeter for the next number. Some may see the general pattern that the perimeter for any number can be determined by multiplying the number by 3 and adding 2.)

Teacher Notes:

Students in grades 3–5 can model a variety of situations, including geometric patterns, real-world situations, and scientific experiments. Sometimes they will use their model to predict the next element in a pattern. At other times, they may make a general statement about how one variable is related to another variable: for example, if a sandwich costs $3, you can figure out how much any number of sandwiches costs by multiplying that number by 3. In modeling situations that involve real-world data, students need to know that their predictions may not always match the observed outcomes for a variety of different reasons. Students should also begin to understand that different models for the same situation can give the same results.9

9 National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics (pp. 162–163). Reston, VA: Author.