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Earning and
spending our hard-earned allowance and savings is a topic that intrigues
most of us students. In preparing this series of problems, we considered
the cost of specific food items for the Chicagoland region over the
past century. During the construction of the word problems, we experimented
with presenting information using tables and graphics. We used the
QAR (Question Answer Routines) method to determine how to solve the
problem.
Most of all, we think these problems are fun because there are some historical facts within the question. We liked writing these problems, particularly when we know the "tricks" to getting the right answer--the use of QAR's! The demand for clear thinking and careful writing were very much in evidence.
Step One: Review the Question and Answer Responses by Taffy Raphael.
 Taffy Raphael |
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The information that answers the problem is in the table. You can point to the answer in one of the table's cells. |
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The information needed to answer the problem is in the table, however, you might need to add, subtract, multiply or divide to reach the correct answer. |
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At least part of the information needed to answer the problem is in the table, however, you will need to use your prior knowledge about the topic and add, subtract, multiply or divide to reach the correct answer. |
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The information needed to solve the problem is not in the table; it is information you must have learned earlier--perhaps in science or social studies. However, the information presented in the table may expand your knowledge of the issues and may help you give a clearer, more specific answer to the problem. |
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Step Two: Use the Minimum Wage Table to solve the problems below. The type of QAR has been identified.
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About the Federal Minimum Wage
The Fair Labor Standards Act (FLSA) establishes minimum wage, overtime pay, record keeping, and child labor standards affecting full-time and part-time workers in the private sector and in Federal, State, and local governments. The FLSA requires payment of the Federal minimum wage to all covered and nonexempt employees. Overtime pay at a rate of not less than one and one-half times the regular rate of pay is required for all hours worked over 40 in a workweek .US Dept. of Labor http://www.dol.gov/esa/minwage/q-a.htm |
EXAMPLE: During
the 1960's, a factory worked averaged more than $100 per week for the
first in in United States history for working a 40 hour work week.
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Problem
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QAR
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Answer
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| 1. What was the federal minimum wage in 1960? | Right There | |
| 2. What was the average pay per hour for a factory worker who earned $100 for a 40 hour week during the 1960's:? | Think and Search | |
| 3. What was the difference between his earnings per hour and the minimum wage? | Think and Search | |
| 4 If in 1970 a factory worker earning minimum wage put in an extra day's hours during one 40 hour work week, what would s/he earn for that week? | Author and You (Hint you need to know that overtime was paid at time and a half and that the work day was eight hours long.) | |
| 5. Does an increase in the minimum wage mean that workers will be able to purchase more goods and services? | On Your Own |
Check your answers for this example
Step Three: Use the Chicago Prices Table below to solve the problems students have written. The QAR has not been identified.
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Student Written Problems
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Problem One: Johnny’s Trip to the Major League Baseball Game |
In 1991, Johnny and five friends wanted to go to the major league baseball
game where the Sox were playing against the Cubs. Johnny earned minimum
wage of $4.25/hour.
The average cost of a major league baseball game in 1991 was $8.64. However, he wanted to get seats nearer the field and so he paid $12.50 for each seat. He is paying for all of the tickets. How many hours will he have to work at his minimum wage to pay for all the tickets?
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Problem Two: Dinner at the White House |
A famous movie star, named Max Williams, invited President Franklin D. Roosevelt, his wife the First Lady, Eleanor Roosevelt, Vice-President John N. Garner and the Secretary of State Cordell Hull for dinner in 1941. He bought 2 pounds of apples, 1 quart of beans, 1 pound of steak, 3 loaves of bread, 1 pound of butter, 2 pounds of chicken, 3 pounds of coffee, 2 dozen eggs, 1 pound of flour, 12 quarts of milk, 2 pounds of bacon, 2 pounds of potatoes, and 1 pound of sugar.
1. How much money would the movie star have spent if he bought these items in 1941?
2, How much money would the movie star have spent if he bought the same things and the same amount of the food in 2000?
3. What is the difference in cost between the items purchased in 1941 and 2000?
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Problem Three: Easter Egg Hunt |
A billionaire,
chicken farmer, is having a Easter Egg Hunt. Everyone at the party
will be asked to locate chicken eggs hidden in his mansion and property.
There are 100 people coming to the party. Everyone is to find 20 eggs.
He is going to serve bacon and eggs after the hunt is finished. He plans to
serve each guest 5 eggs. He needs to buy 10 lbs. of pork and 10 lbs. of sugar.
He currently has $10,365 in his bank account.
1. How many eggs does he have to buy for the egg hunt
2 How many eggs does he have to buy to make breakfast?
3. How many eggs does he need in all?
4. How much does his total purchase of eggs cost?
5. How much is his total purchase for the egg hunt and the breakfast?
6. How much remains in his bank account after he pays the bill?
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Problem Four: Joe's BBQ |
1. How much more did a loaf of bread cost in 2000 than in 1960?
2 Joe Franklin wants to have a BBQ in 1990 for 7 friends to celebrate the Fourth of July. He wants to serve hamburger, apples, bananas, bread, milk and coffee. He will need 1/2 pound of meat for each guest as well as 3 quarts of milk, 5 pounds of apples, 4 pounds of bananas, 2 loaves of bread, and 3 pounds of coffee. How much will the BBQ food cost?
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Problem Five: Allison's Surprise Birthday Cake |
Allison is baking a cake for her sister Mary’s birthday who will be 3 years old in 1920. She is inviting 15 of Mary’s friends. Allison needs 5 ingredients for the party cake. If she only has $2.40 and if the total cost for the groceries is exactly $2.40, what 5 ingredients did she buy?
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Allison’s
Surprise Birthday Cake
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| cheese | 0.42 |
| eggs per dozen | 0.71 |
| cornmeal | 0.07 |
| tea | 0.70 |
| coffee | 0.40 |
| flour | 0.71 |
| butter | 0.63 |
| milk | 0.15 |
| sugar | 0.20 |
| bread | 0.12 |
| beans | 0.12 |
| prunes | 0.29 |
| pork | 0.38 |
| rice | 0.17 |
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Problem
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QAR
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Answer
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| 1. What was the federal minimum wage in 1960? | Right There | $1.00 |
| 2. What was the average pay per hour for a factory worker who earned $100 for a 40 hour week during the 1960's:? | Think and Search | $2.50 |
| 3. What was the difference between his earnings per hour and the minimum wage? | Think and Search | $1.50 |
| 4 If in 1970 a factory worker earning minimum wage put in an extra day's hours during one 40 hour work week, what would s/he earn for that week? | Author and You (Hint you need to know that overtime was paid at time and a half and that the work day was eight hours long.) | $83.20 |
| 5. Does an increase in the minimum wage mean that workers will be able to purchase more goods and services? | On Your Own |
A NOTE OF CAUTION: How
can we find prices of popular items through the centuries to
make comparison charts? Morris
County Library's Food Timeline |
To get this
answer we found out that since Johnny was going to pay for 5 other
people and himself he would have to pay for six people so he would
have to buy 6 tickets. So we did 6*$12.50=$75.00.
Now we had to figure out how long he would have to work to get that much money.
To do that we did guess and check strategy. Our first guess was 20 hours *
$4.25 = $85.00. That was too much money. Then we lowered it to 17 * $4.25 which
was $72.25. That was too little. Then we tried 18 * $4.25 which was $76.50
that was $1.50 too much. ($76.50-75.00 = $1.50)
He will need to work at least 19 minutes of an additional hour to pay for the
tickets. Therefore he had to work 18 hours and 18 minutes and 45 seconds. Realistically,
he would work 18 1/2 hours.
1. Add the cost of the items, multiplying by the number of items purchased. $6.10
| 1941 | 2000 | |
| 2 pounds of apples | $0.12 | |
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1 quart of beans |
$0.10 | |
| 1 pound of steak | $0.38 | |
| 3 loaves of bread | $0.21 | |
| 1 pound of butter | $0.41 | |
| 2 pounds of chicken | $0.64 | |
| 3 pounds of coffee | $0.75 | |
| 2 dozen eggs | $0.78 | |
| 1 pound of flour | $0.05 | |
| 12 quarts of milk | $1.80 | |
| 2 pounds of bacon | $0.74 | |
| 2 pounds of potatoes | $0.08 | |
| 1 pound of sugar | $0.06 |
2. In 2000, the bill was $37.97
| 1941 | 2000 | |
| 2 pounds of apples | $0.12 | $1.88 |
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1 quart of beans |
$0.10 | $0.60 |
| 1 pound of steak | $0.38 | $1.44 |
| 3 loaves of bread | $0.21 | $2.79 |
| 1 pound of butter | $0.41 | $2.48 |
| 2 pounds of chicken | $0.64 | $2.10 |
| 3 pounds of coffee | $0.75 | $9.09 |
| 2 dozen eggs | $0.78 | $1.82 |
| 1 pound of flour | $0.05 | $0.29 |
| 12 quarts of milk | $1.80 | $8.16 |
| 2 pounds of bacon | $0.74 | $6.24 |
| 2 pounds of potatoes | $0.08 | $0.66 |
| 1 pound of sugar | $0.06 | $0.42 |
3. The difference in price between 1941 and 2000 is $31.87
1. Multiply 100 times 20 to find the number of eggs--2000. One hundred people finding 20 eggs each would total 2000 eggs.
2. Multiply 100 times 5 to find the number of eggs 100 people would eat if each ate 5 eggs. The number is 500.
3. Add the answer to questions one and two. The total is 2500.
4. To determine the total purchase price, determine the number of dozen eggs needed. 2500 divided by 12 which rounds to 209 dozen eggs.
To get the total purchase price for the eggs,multiply 209 by $1.15. This totals $204.35
5. To determine the total cost, find the total cost of the pork (10 times $1.95=$19.50) and the cost of the sugar (10 X .40 = $4.00). Add these costs to the cost of the eggs. $204.35 + $19.50 + $4.00 = $263.85
1. The difference between the price of bread in 1960 and 2000 was $0.74.
2.
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Joe's
BBQ Grocery List
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| Item | Cost | Amount | Total |
| hamburger | $1.57 | 4 pounds | $6.28 |
| apples | $.78 | 5 pounds | $3.90 |
| milk | $0.73 | 3 quarts | $2.19 |
| bananas | $0.42 | 5 pounds | $2.10 |
| bread | $0.66 | 2 loaves | $1.32 |
| coffee | $2.77 | 3 pounds | $8.31 |
The total cost is $24.10
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Allison’s
Surprise Birthday Cake
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| cheese | 0.42 |
| eggs per dozen | 0.71 |
| cornmeal | 0.07 |
| tea | 0.70 |
| coffee | 0.40 |
| flour | 0.71 |
| butter | 0.63 |
| milk | 0.15 |
| sugar | 0.20 |
| bread | 0.12 |
| beans | 0.12 |
| prunes | 0.29 |
| pork | 0.38 |
| rice | 0.17 |
The five ingredients are: eggs, flour, butter, milk, and sugar. The cost of the cake is exactly $2.40
Bibliography:
Mesmer, H.A.E., and Hutchins, E.J. (2002). Using QAR's with charts and graphs. The Reading Teacher, 56, 21-27.
The Value of a Dollar: Prices and Incomes in the United States 1860-1999. (2000). Edited by Scott Derks. Lakeville, CT: Grey House Publishing.
Reviewed,
2003
J. Beyersdorfer