Sneakers

Task

You are an owner of a sports outlet store. The table shows data about your sneaker sales in a recent week.

Type of Sneaker	Pairs Sold
Adidas®	124
Nike®	64
Tiger®	49
Saucony®	42
Converse High Tops®	21

Next week, you plan to order 36 dozen sneakers.

Explain how you can use the data to decide how many dozen of each type to order.

Alternate Versions of Task

Context

This sixth grade class did some informal and more formal work with percents. It was their first formal academic exposure to percents. We also had worked with fractions, with a very limited introduction to ratios. I realize how important the concept of proportionality is and want to expose my students to many types of problems that deal with data.

What This Task Accomplishes

I wanted this task to assess which students recognized the fact that percents or ratios could help in solving this problem. I would also be able to see which students did not have a working knowledge of proportionality. The data is messy (the number of pairs of sneakers sold last year does not divide to dozens of sneakers evenly). Students have to make decisions about estimating the distribution of pairs of sneakers.

What the Student Will Do

Most students started by changing 36 dozen sneakers to 432 pairs of sneakers. Other students renamed the pairs of sneaker sold last week to dozens. From that point on the strategies varied. Some students recognized that percents could help solve the problem, others used a formal concept of proportions, and others had a more intuitive feeling for proportions. Still others ignored the data and distributed the 36 dozen sneakers evenly.

Time Required for Task

50 minutes

Some students needed more time to write up their reasoning and organize their response.

Interdisciplinary Links

Students can get a sense of what stores must think about as they try to meet their customers' needs and make a reasonable profit.

Teaching Tips

Have calculators available for the computation. It is always interesting to see how students interpret decimal remainders when using calculators.

Suggested Materials

Calculators

Possible Solutions

Answers may vary according to the reasoning and estimating used by each student. Solutions should be close to the findings below:

Adidas® sold 124 out of 300 or about 41% of the sneakers last week. You may want to order 41% of the 36 dozen (or 432 pairs) which is about 14.8 or 15 dozen.

Nike® sold 64 out of 300 or about 21% of the sneakers last week. You may want to order 21% of the 36 dozen which is about eight dozen.

Tiger® sold 49 out of 300 or about 16% of the sneakers last week. You may want to order 16% of the 36 dozen which is about six dozen.

Saucony® sold 42 out of 300 or about 14% of the sneakers last week. You may want to order 14% of the 36 dozen which is about five dozen.

(This leaves only two dozen for Converse® High Tops.)

Converse® High Tops sold 21 out of 300 or about 7% of the sneakers last week.

You may want to order 7% of the 36 dozen which is about 2.52 or two dozen.

Task Specific Assessment Notes

Novice:
The solution has no relationship to the task. It looks like the student divided Adidas® pairs of sneakers in half, but even that strategy is not consistent with the rest of the brands. There is only a limited explanation, but enough to show the student did not understand how to approach the problem.

Apprentice:
Although this student has a reasonable solution, there is no evidence of how those numbers came about. What was the child's strategy or reasoning? If they added "a little more to each" then why were about five dozen added to Adidas® and only four pairs of sneakers added to Converse®? There are too many questions about this child's strategy and reasoning. I would want a conference with this student to see if they could better explain their solution.

Expert:
The solution shows a deep understanding of the problem. The student connected the idea of percents to keep the proportionality of the sneakers sold. This strategy leads directly to a solution. S/he also verified his/her results and realized that strictly rounding would cause his/her total to be too big and made a decision to lower one estimate. There is a clear and effective explanation detailing how the problem is solved. There is precise and appropriate mathematical terminology and notation.