Five pages on why the area of a split rectangle is the distributive property. On page 1 each rectangle is drawn in unit squares and a line splits it in two: students write the area inside each part, then fill in the equation in three steps (5 × 8 = 5 × (5 + 3) = 5 × 5 + 5 × 3 = 25 + 15 = 40); one rectangle is split across its rows. Page 2 leaves out the squares: students split a 2-digit number into tens and ones on top of the model (6 × 14 = 6 × (10 + 4)), and on the last two a 3-digit number into hundreds, tens and ones, three parts to add. Page 3 has area models with numbers missing: a side length to find from an area, the side both parts share, a part's area from the total, a part from the whole side, and one with two missing. Page 4 has ten equations with one number missing, such as 8 × (10 + □) = 80 + 56, then three rectangles to match to the one equation that shows them. Page 5 splits both numbers into tens and ones, so 12 × 14 is four parts, and ends with two rectangles to split any way that makes the work easier (the key shows one way). Every page starts with a worked example.
Draw a 6 by 14 rectangle on grid paper and count the squares together; it takes a while. Then draw a line after 10 columns and ask what two facts the class sees now. Write 6 × 14 = 6 × (10 + 4) = 60 + 24 under it and point to each number in the picture. On page 5, compare students' own splits: 7 × (10 + 6) and 7 × (8 + 8) give the same area.
Look for rectangles at home: a sheet of stickers, a tiled floor, a muffin tin. Ask your child to cover part of it with a hand and say the two facts they see, then add them. Bigger rectangles work too: a 4 by 23 patio is 4 by 20 and 4 by 3.
This pack supports the following Common Core State Standards for Mathematics:
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How the area of a rectangle shows the distributive property: a rectangle split into parts has the same area as its parts added, so 6 × 14 = 6 × (10 + 4) = 60 + 24. Students find the area of each part of split rectangles, write the equations, find missing side lengths and areas, and split rectangles of their own.
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