1
CR 3: Sports Bag
You have been asked to design a sports bag.
 The length of the bag will be 60 cm.
 The bag will have circular ends of diameter 25 cm.
 The main body of the bag will be made from 3 pieces of material; a piece for the curved
body, and the two circular end pieces.
 Each piece will need to have an extra 2 cm all around it for a seam, so that the pieces may be
stitched together.
1. Make a sketch of the pieces you will need to cut out for the body of the bag.
Your sketch does not have to be to scale.
On your sketch, show all the measurements you will need.
2. You are going to make one of these bags from a roll of cloth 1 meter wide. What is the shortest
length that you need to cut from the roll for the bag?
Describe, using words and sketches, how you arrive at your answer.
Samples are from SBAC Content Specification Appendix (Link)
2
Discussion
Sports Bag addresses:
Content Standards 7.G.4, 7.G.6
Practices P1, P4, P5, and P6
Claims 1, 2, and 4
This task involves solving real-world problems involving areas of two-dimensional shapes.
The first task is to recognize that the curved surface of the bag is a rectangle with the length given
and the breadth equivalent to the circumference of the circular end of the bag. This observation,
along with the observation that one must allow for the extra material around the edges of the
shapes, puts the student in a position to make the relevant sketches.
Students are given the diameter of the bag and need to use this to calculate, with the aid of a
calculator, the circumference of the circular ends and therefore the missing dimension of the curved
surface, which is around 78.5 cm.
This means that there will need to be three sketches (two circles and one rectangle) which have the
dimensions (including extra) of 29 cm diameter circles and a rectangle measuring 64 x 82.5 cm.
Part 2 of this task is interesting and requires students to be able to visualize the possibilities to
solve this problem. Starting with the rectangle in the top corner of the roll they can orient it in two
ways. This is the key decision – which way around should it go. With the longer edge along the end
of the roll of cloth there is a wasted strip along the edge and the length of the total piece will be
equivalent to 64 + 29. Here the student could need to see that both circles can fit within the width of
the cloth. However, if the short side (64 cm) of the rectangle runs along the end of the roll there is
room for the two circles alongside the rectangle. In this case the length of cloth is 82.5 cm.
This task demands students work across a range of mathematical practices:
 Make sense of problems and persevere in solving them (P1).
 Model (P4) a situation with mathematical representations.
 Use appropriate tools strategically (P5), in this case to calculate the circumference of the
circle.
 Make use of mathematical structure (P6).
Samples are from SBAC Content Specification Appendix (Link)
3
Rubric Elements
Sports Bag
1.
Points
Circumference of circular ends is one dimension of main body:
C = πd = π x 25 = 78.5 cm
Main body is a rectangle measurements
60 + 4 by 78.5 + 4 = 64 by 82.5 cm
Two circular ends have diameter 29 cm
2.
Draw sketch showing that 1 meter of cloth will make the bag.
1m
64 cm
29 cm
83 cm
1m
Total
Note:
See scoring comments on the “Ms. Olsen’s Sidewalk” task.
Samples are from SBAC Content Specification Appendix (Link)