Area of rectangular shapes and the distributive property - 3rd grade lesson
In this 3rd grade math lesson, I show that AREA has to do with covering a shape with little squares. In other words, area of any shape is always measured in squares (square units).
Area of rectangles can be found by multiplication. In my example rectangle, we count the rows and columns, and then write a multiplication to find the area (5 × 3 = 15 squares).
We also write multiplications and addition to find the area of a two-part rectangular area.
Next, I use a two-part rectangle tiled with squares to show a connection between multiplication and addition — in reality, the distributive property. In symbols, the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. However, we don't use symbols in the lesson — just actual rectangles with side lengths that are small whole numbers. This concept (area model) does prepare students to understand the distributive property later on.
This lesson ties in with the Common Core Standard 3.MD.7, specifically 3.MD.7.a, 3.MD.7.b, 3.MD.7.c, and 3.MD.7.d.
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See also
Math Mammoth Early Geometry — a self-teaching worktext with explanations & exercises for beginning geometry topics (grades 1-3)
Math Mammoth Grade 3 complete curriculum