MP4: Model with mathematics.

First, I wrote down all of the given information and re-created the picture of the stained glass window on paper so that I could write on it.

Next, I found the areas and perimeters of each of the pieces that make up the window. I found the total area of the window to be 10 square feet. I used the formula for the area of a circle to determine that the clear glass had an area of 7.86 square feet. Then I subtracted the clear glass from the total glass to find that the colored glass has an area of 2.14 square feet. The joining material (around the partial circles and the vertical pieces) had a total length of 39.42 feet and the frame around the perimeter of the window had a total length of 14 feet.

Once I had determined the areas of the stained glass and clear glass and the lengths of joining and framing materials, I multiplied those figures by the cost of each material to determine the costs of those materials. Then I added all of the costs of the individual materials together to find the total cost, about $94.22.

The students raised $100 to pay for the materials needed for the window. This means they had enough money to cover the cost of the materials.

With this task, we must assume that the students do not have to pay for extra pieces of glass, joining material, and framing material that may be wasted as scrap.

This task presents a real-world problem of determining required amounts and costs of materials to produce a product. The task involves basic operations of addition, subtraction, and multiplication. As math practice standard 7 states, "a student might use geometry to solve a design problem...", this task requires the use of formulas - area of a rectangle, perimeter of a rectangle, area of a circle, and circumference of a circle. Standard 7 also states, "use a function to describe how one quantity of interest depends on another." This task uses unit costs to determine total costs of materials and could have been written as and determined using function notation.

The difficulty of this task comes from the partial circles. First, determining that there are 12-quarter circles + 14-half circles = 10 full circles. Students may struggle with the idea of determining the area of the colored glass pieces because they have an irregular shape. With time to explore and discuss the problem, students should arrive at the strategy of subtracting the clear glass from the total glass to find the amount of colored glass.

This task is an authentic, real-world problem that students will likely engage with, but even more if they are allowed to choose a stained glass pattern from a selection of patterns.

A teacher could lower the floor of this task by creating a design with squares and rectangles, which tend to be easier for students. It may also be easier for students to break the problem down into its 5 separate sections. The stained glass task could be made more challenging and/or more engaging by having students create their own stained glass window designs that meet criteria such as: minimum/maximum amounts of colored or clear glass, budget constraints, minimum window size, etc.