In this activity students will examine data table that represent the hourly and annual mean salary of bookkeeping, accounting, and auditing clerks over twelve years, 1997-2008. The students will graph the data, determine the line of best fit for given data (graph it and determine its equation). Students will also use the identified line of best fit to predict a clerk’s salary in year 2010.
Compare and contrast the life styles of Mr. Cratchit in Dickens’ time and Mr. Cratchit today.
Students will use proportional reasoning to estimate original Mr. Cratchit’s wage in terms of US money.
Students will identify a function that best describes a change in a salary earned by a clerk given data from year 1997 – 2008.
Students will calculate the percentage of change in salaries of 1843 Mr. Cratchit and the 2011 Mr. Cratchit.
Students will predict future salaries based on the function they identified, assuming the same rate of change applies in the future.
Use attached file Modern Mr. Cratchit Worksheet
(5-10 minutes) Have students read the description of Mr. Cratchit (his office, house, salary, life, personality…) as illustrated in “A Christmas Carol”. Depending on the reading competences, 5-10 minutes should be enough for all students. Also, tell them to respond to the included questions to check their understanding.
(5 minutes) After about 10 minutes, let students share their responses to the questions. Even though most students are familiar with “A Christmas Carol”, they might not remember Mr. Cratchit and the details included in the reading. This will ensure that all students have the same background knowledge.
The reading indicates that Mr. Cratchit was a clerk in the Scrooge and Marley’s counting house. Actually, it was never specified what “counting house” means. So, we will assume that Scrooge and Marley Company was some type of money landing or accounting company or a bank. Hence, we will assume that if Mr. Cratchit lived today, he would be the bookkeeping, accounting, or auditing clerk.
(15 minutes) Divide students in groups of 3-4. Let students examine how a bank clerk salary changed over time. Tell them to plot the data using graphing calculator and to estimate what would Mr. Cratchit earn today. Let groups work on their own, but if they are not sure how to estimate salary other than guessing from the graph, ask them if there is another way they could use to predict the value from the data. They should be able to state that they could find the line of best fit – a function that describes the data best, to get a better prediction.
If a graphing calculator is not available for students, they can plot data on a graphing paper and examine whether this function would be linear, quadratic, cubic, exponential, logarithmic…
(15 minutes) Let students share results. They might have decided to use different functions to model the data. Discuss which one of them seems to be the best fit or to give the best estimate of today’s Mr. Cratchit salary. Compare this estimate to he actual average salary of the bank clerk.
Assignment: Given the estimate of the Mr. Cratchit’s salary, have students describe what kind of life he could afford (where he lives, what does his house look like, what type of car (if any) he has, etc.). Students will have to research monthly expenses for a household of 8 in order to complete the assignment.
Create a graphical representation of the given data
In writing describe how the bank clerk salary changed over the years, based on the graph they created (when was the greatest/smallest increase in salary, was it ever constant, etc.)
Generate mathematical model – function, that describes the data best, and use it to predict future salaries
On their own:
Using their investigation at school, students will write an essay describing a life of Modern Mr. Cratchit.