We are trying to show the distributive property using the areas of the rectangles in the picture. remember that the area of a rectangle is with times length. counting the squares of our bigger rectangle, we realize that its width is 6. notice that the width of the bigger rectangle is the same as the width of the blue and green rectangles, so the area of both rectangles, which is the same as the area of the bigger rectangle, will be given by the expression:
6(length of the blue rectangle + length of the green rectangle)
counting squares, we get that the length of the blue rectangle is 6 and the length of the green rectangle is 5, so lets replace those values in our expression:
6(length of the blue rectangle + length of the green rectangle)
6(6 + 5)
we can conclude that the expression shown in the model is 6(6 + 5)
