July 6, 2013

Solving Unknown Perimeter Mysteries

Mystery Perimeters Freebie Lesson

Perimeter is a pretty simple concept to grasp, but finding unknown sides of irregular polygons can be challenging for kids. Solving these types of problems requires the ability to think logically and somewhat abstractly. Fortunately, we can help students make the transition from concrete to abstract with a hands-on lesson that allows them to make those connections.

Earlier this week I finished writing Exploring Perimeter, a CCSS aligned, comprehensive resource for teaching perimeter. When I finish a new book, I like to offer a free sample lesson, and I selected Mystery Perimeters to share as a freebie. This lesson presents the unknown side problems as “perimeter mysteries,” a fun twist on a traditional assignment. You can download the lesson from my TeachersPayTeachers store, but be sure to return to this blog post to pick up some valuable tips for using this activity. The free version of Mystery Perimeters uses inches, but the one you’ll find in Exploring Perimeter also includes a variation that uses centimeters.

Tips for Teaching Mystery Perimeters
When I was almost finished with Exploring Perimeter, I recruited some field testers and reviewers to ensure that the book was rock solid. Joy Darden, an upper elementary teacher in NC, shared some really useful tips for teaching the Mystery Perimeters lesson, and I want to pass them along to you.

When Joy introduces this lesson, she shows her students how to identify the pairs of opposite parallel sides by coloring them the same color. All horizontal sides are colored one color and vertical sides are colored a different color. In the illustration on the right, all vertical lines are outlined in green and the horizontal lines are in blue. If you project the demo page onto an interactive whiteboard, you can use your colored drawing tools to demonstrate. You can also give students their own copies of this page and colored pencils to follow along and practice with you.

Next, Joy shows her students how they can use addition and subtraction to find the missing sides. Having the lines color coded helps them to decide which ones are needed to determine the lengths of each missing side. For example, in the top polygon, you can find the length of the missing horizontal line by subtracting 3 inches from the total length of the opposite side, which is 5 inches, to arrive at a length of 2 inches. In the bottom polygon, you can add the lengths of the known vertical sides on the left, 2 inches plus 1 inch, to arrive at a length of 3 inches for the missing side. After students figure out the missing sides, they add to find the total perimeter as usual.

Another way to solve missing side perimeter problems is to divide the polygon into rectangles as shown on the Mystery Perimeters Demo Hints page shown on the right. By dividing the polygon into rectangles, you can infer the lengths of the missing sides. You can also combine the color-coding strategy with this method.

Another reviewer, Ann Sullivan, pointed out that with some of the more complex shapes, you may have to divide the shape into more than three rectangles. Yet the basic concept is still the same.

If this kind of reasoning is too difficult for your students, you can display the demo page that shows the figures on a 1-inch grid. Because the polygons are drawn to scale, you can also have your students measure the sides with a ruler to find the missing lengths. (Note: When you print the pages, make sure the printer settings are set to "Actual" and not "Fit to Page." If your printer shrinks the pages, the polygons will not be accurately drawn to scale.)

Remember that you can download this Mystery Perimeters lesson, absolutely free, from my TeachersPayTeachers store.

Exploring Perimeters – Step by Step
If you like Mystery Perimeters, why not preview Exploring Perimeter to see what the entire book has to offer? All thirteen lessons include a teacher direction page with Common Core Standards, printables, and answers.

Exploring Perimeter is organized in sequential order according to skill level to make it easy to teach perimeter for deep understanding. When you develop these concepts in a step-by-step manner, students are far more likely to grasp those concepts and retain them. As one student who tested the materials said, "Last year I got every one wrong when you had to find the missing number. This is much easier to figure out because it goes one part at a time."  Now that’s high praise indeed!


  1. I love the color coding idea! Why didn't I think of that? Genius!

  2. I have taught grade 6 for two years and i really liked colour coding idea for colouring horizontal and vertical lines, superb!


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