Tiling Rectangles with Integer-Sided Squares Algebra and Perfect Rectangles

Algebra is the mathematics of using letters to represent possible numbers to solve complex problems.

We had the K-3rd graders look at one or two values of square dimension and then fill in the rectangle with all square dimensions using the information given. For example, if a square shared a side with two other squares with dimensions of 3 and 4, that larger square has a dimension of 7. If a square has a dimension that is the difference between a larger square of 10 and a smaller square of 3, its dimension is 7. Then we use a "work around" strategy to complete the puzzle.

Then, each student was encouraged to give the final dimensions of the rectangle but to check all four sides. Opposite sides would have to have equal length. This was a great way for them to check their work.

The 2-5th graders were able to explore doing the same thing with algebraic expressions. So if a square shared a side with two squares of side dimension a and b, it would have a dimension of a + b.

At the end of the exercise, they would solve for the dimensions of the original rectangle and set each opposite side equal to each other. For example if they got 5a = 3b, they could let the value of a=3 and the value of b=5 and then solve the puzzle. Of course, in the above example, a could have been 300 and b could have been 500 but they were encouraged to find the smallest measurement in whole numbers.

Finally, the 5th graders were challenged to find the perfect rectangle where each square dimension was different. 

See all attached pdfs and have fun with algebra.