The perimeter of a shape is the length of the lines that form its sides. Since 3rd graders measure the perimeter of polygons, they will identify the length of intersecting line segments.
MA.3.GR.2.3 – Solve mathematical and real-world problems involving the perimeter and area of rectangles with whole-number side lengths using a visual model and a formula.
Dimensions of Measurement
Perimeter is a 1-dimensional measurement of length.
It provides a good foundation to build an understanding of the 2-dimensional measurement of area in 3rd and 4th grade. In 5th grade, students work with the 3-dimensional measurement of volume.
Perimeter also provides the opportunity to review many 3rd grade-level mathematical skills and concepts at different levels of sophistication.
Concrete Experience
The best place to start teaching perimeter is using measurement tools like rulers and measuring tapes to physically measure and label the sides of polygons in inches or centimeters. They add the side lengths, and the perimeter is their sum.
Students can then progress to using the properties of shapes to make observations about side lengths without having to measure each side. For example, regular polygons like equilateral triangles and squares have equal sides. Once one side length is known, it can be multiplied by the number of the shape’s sides.
Rectangles and parallelograms have equal, opposite sides. The length of the equal sides can be added (w + w + l + l = p), or the length and width can be multiplied by 2 and added together (2w + 2l = p).
Missing Side Lengths
The study of perimeter can also be used to reinforce student understanding of division. If a square has a perimeter of 16 cm and 4 equal sides, its side length can be found as multiplication with a missing factor:
4 equal sides x ? = 16 c
Of course, an equivalent equation is dividing the perimeter by the number of equal sides:
16 cm (divided by) 4 equal sides = 4 cm
If the perimeter of a rectangle is 24 inches and it is 11 inches long, a combination of subtraction and division can be used to find the missing width, reinforcing multi-step problem solving skills.
24 inches – (11 inches x 2 sides) = 2 x width
24 inches – 22 inches = 2 inches
2 inches divided by 2 equal sides equals 1 inch per side.
The rectangle is 11 inches long and 1 inch wide!
Different Learning Styles
Geometry and measurement are an opportunity for students who struggle in other academic areas to shine! The hands-on work and spatial nature of working with shapes may be less confusing than other mathematical tasks. The consistent work with repeating whole-number measurements will also build fluency and confidence over time.
3rd graders who are linear thinkers may enjoy systematically finding all of the possible rectangles with a certain perimeter, like 100 cm. The least whole-number side is 1 cm, which will take 2 cm of the 100. That leaves 98 cm to be divided in half for the length, which will be 49 cm. One centimeter per side can be moved from the length to the width at a time, until students reach the 25 cm square. Then, measurements start to repeat but with the rectangles oriented in the other direction.
Standards
Florida’s B.E.S.T. standards focus on the measurement of perimeter in rectangles because it can then be compared and contrasted with area, once students learn that concept. Common Core and TEKs are broader and include common polygons.
I encourage teachers and parents to fully explore the measure of perimeter of a variety of polygons for the reasons listed in this article. It can also help students develop a deeper understanding of area once they realize polygons besides rectangles and squares also have an area, they are just more complicated to calculate.
Whichever route you decide to take with your 3rd grade learner, a solid foundation in their understanding of perimeter measurement will prepare them for many more complex geometric and measurement concepts in the years to come!
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