MP7: Look for and make use of structure.
I can use what I know to solve new problems.
Task
My Work
The width of the rectangle piece of cloth needed is 64cm, 60cm (length of bag) + 4cm (extra material needed for seams).
The length of the rectangle piece of cloth needed is 82.54cm, 78.54cm (circumference of the circle pieces) + 4cm (extra material needed for seams).
The diameter of the 2 circle pieces of cloth is 29 cm, 25cm (diameter of the circular end of the bag) + 4cm (extra material needed for seams).
To determine the shortest length of a 1 meter wide roll of material to make the bag, I arranged the pieces in 2 variations. In the first arrangement, the bag would require about 83cm of the 100cm width and 93cm of length. In the second arrangement, the bag would require 93cm of the 100cm width of the roll and about 83cm of length.
The second arrangement makes the best use of the roll of material and requires the shortest length of the roll, about 83cm.
Reflections
I started this task by making sketches that included all measurements that the problem provided, explicitly and implicitly. Then I had to determine the circumference of the circular ends of the bag to find the length of the rectangle needed to make the body of the bag. Just as the standard reads, "step back for an overview and shift perspective", I had to arrange the pieces within another area (the 1 meter wide roll), making sure to rule out options that would not fit in the given area.
The difficulty of this task comes from the details of actual pattern making - adding 2cm on all sides to allow for seams, and from recognizing that the side length of the rectangle comes from the circumference of the circular ends. These are pieces of the task that may cause students to struggle. The second part of the task may lead students to believe that they need to determine the area of the pieces of material in order to solve the problem, causing extraneous work for the student.
To make this task more engaging, I might have manipulatives for students to physically move around in different arrangements. This might also be a fun task to complete in a pair or group of 3. A lower floor could be achieved by simplifying the task, providing students with manipulatives, and by cutting out the seam allowance detail. A higher ceiling might include cost and quality information about different materials and asking students to decide which material, or combination of materials, they would use to make a bag for themselves or to make bags they could sell. This could lead to discussions of product quality and profit potential. Additional bag details such as zippers, other closures, bag straps, or handles might also be a factor in the material size needed and the cost to make the bag.