IM Alg1.6.1 Lesson: A Different Kind of Change
Look at the patterns in the 3 tables.
What do you notice? What do you wonder?
Noah has 50 meters of fencing to completely enclose a rectangular garden in the backyard.
Draw some possible diagrams of Noah’s garden. Label the length and width of each rectangle.
Find the length and width of such a rectangle that would produce the largest possible area. Explain or show why you think that pair of length and width gives the largest possible area.
Plot some values for the length and area of the garden on the coordinate plane.
What do you notice about the plotted points?
The points and each represent the length and area of the garden. Plot these 2 points on coordinate plane above, if you haven’t already done so. What do these points mean in this situation?
Could the point represent the length and area of the garden? Explain how you know.
What happens to the area when you interchange the length and width? For example, compare the areas of a rectangle of length 11 meters and width 14 meters with a rectangle of length 14 meters and width 11 meters.
What patterns would you notice if you were to plot more length and area pairs on the graph?