Perimeter is the total distance around a shape, found by adding the lengths of all its sides. For a rectangle, the perimeter formula P = 2l + 2w (or equivalently, P = 2(l + w)) is a shortcut for adding all four sides. Understanding perimeter means understanding that it measures a one-dimensional boundary -- how much fencing you need for a yard, how much ribbon to wrap around a box. Students should be able to find missing side lengths when given the perimeter, and distinguish perimeter from area.
Have students measure the perimeter of real objects: desktops, books, the classroom. Walk the perimeter of the playground. Use string to trace around shapes, then measure the string. Practice with irregular shapes (add all sides) before introducing rectangle shortcuts. Pair perimeter problems with area problems so students learn to distinguish the two.
You already know multi-digit addition — adding numbers with regrouping across multiple columns. Perimeter is a measurement application of that skill: the total length you'd travel if you walked all the way around the outside of a shape. Perimeter is always a linear measurement (one-dimensional), meaning it's measured in the same units as individual side lengths — inches, centimeters, meters, and so on.
For any shape, the method is always the same: add up all the side lengths. A triangle with sides 5, 7, and 9 centimeters has a perimeter of 5 + 7 + 9 = 21 cm. An irregular hexagon with sides 4, 3, 6, 4, 3, and 6 feet has a perimeter of 4 + 3 + 6 + 4 + 3 + 6 = 26 feet. For a rectangle, because opposite sides are equal, you always have two lengths and two widths, so the formula P = 2l + 2w is simply a faster version of adding all four sides. A rectangle with length 8 and width 5: P = 2(8) + 2(5) = 16 + 10 = 26 units. You can also think of it as adding one length and one width, then doubling: P = 2(l + w) = 2(13) = 26.
Perimeter is often confused with area, especially when both are introduced in the same unit. The key distinction: perimeter measures the boundary (the path around the edge), while area measures the interior (the space inside). If you fenced a yard, you'd buy fencing based on perimeter. If you carpeted that yard, you'd buy carpet based on area. Same yard, completely different questions. Perimeter is measured in feet or meters; area is measured in square feet or square meters.
A useful problem type is finding a missing side length when you're given the perimeter. If a rectangle has perimeter 30 cm and one side is 9 cm, what is the other side? You know P = 2l + 2w, so 30 = 2(9) + 2w, which gives 30 = 18 + 2w, so 2w = 12, w = 6. Your multi-digit addition and basic equation sense both apply — perimeter problems are arithmetic problems wrapped in geometry.