Area and Perimeter
Lessons in this chapter
About Area and Perimeter
Area and Perimeter introduces two measurements that kids confuse for years, and the chapter separates them by teaching what each one actually counts.
Compute Area using unit squares and multiplication starts with counting squares, then shows why multiplying the sides gives the same answer. Counting first matters: a child who only learns length times width cannot say what the number means or why the units are square.
Find Area of Rectangles and Rectilinear Figures by Splitting handles L-shapes and similar outlines by cutting them into rectangles, finding each area and adding. This is the first time kids break a problem into solvable pieces on purpose, which is a method far more general than the geometry it appears in.
Understand Perimeter as the Length of the Boundary of a Closed Shape and Solve Problems on Perimeter of Polygons cover the other measurement. Perimeter is a distance around and is measured in ordinary units; area is a surface covered and is measured in square units. Keeping those apart is most of what this chapter is for.
Compute Area using unit squares and multiplication, Find Area of Rectangles and Rectilinear Figures by Splitting and Solve Problems on Perimeter of Polygons each open as a worksheet in the page, scored as your child works. Keeping the two quantities apart is the point, so the math problems deliberately mix them rather than keeping each to its own page. Four lessons, all free.
Frequently asked questions
Finding area by counting unit squares and then by multiplying, finding the area of rectangles and rectilinear figures by splitting them up, understanding perimeter as the length of a boundary, and solving perimeter problems on polygons. Area comes first because unit squares make it concrete. It sits in Measurement and Data (3.MD).
Perimeter is the distance all the way around a shape, measured in ordinary units. Area is the surface it covers, measured in square units. They answer different questions.
Because it shows what the number means. A child who starts from length times width can get an answer but cannot explain why the units are square centimeters.
Split it into rectangles, find each area, and add them. Breaking a problem into solvable pieces is the real skill, and it is useful well beyond geometry.
Yes, and it is worth showing. A long thin rectangle and a near-square can have the same perimeter with very different areas, which proves the two measure different things.
Because you are counting squares. An area of 12 means twelve unit squares fit inside, so it is written as 12 square centimeters, not 12 centimeters.