This document outlines instructional content and strategies for teaching students about proportions and rational numbers using a scenario about a lawn mowing business. It includes anticipatory questions to engage students, details about three employees and the lawns they cut each day, proportions calculations for the lawns cut each day and in total, instructions for writing checks and filling out a check register, calculating employee paychecks, and a scenario about fixing or replacing a broken lawnmower where students calculate costs with different discount rates. Modifications are suggested to assist weaker students and provide additional challenges for stronger students.

1. Instructional Content and Strategies Organizer
Instructional Content
• See attached worksheet, “Representing Equivalent Rational Numbers” for Anticipatory Set/Introduction.
• Proportion questions for Anticipatory Set/Introduction:
o “What proportion of your cards are red?”
o “What proportion of your cards are black?”
o “Add together the proportion of your cards that are black with the proportion of your cards that are red. What do you get?”
o “What proportion of the group’s cards are red?”
o “What proportion of the group’s cards are black?”
o “Add together the proportion of the group’s cards that are black with the proportion of the group’s cards that are red. What do you get?”
• Powerpoint Slide # 1:
o “Imagine you are the owner of a summer lawn mowing service. You have three employees.”
• Powerpoint Slide # 2:
o “This is Joe’s first summer working for a lawn mowing service. He earns $10 per lawn. He cut 2 lawns on Monday, 3 and ½ lawns on Tuesday, and ½
lawn on Wednesday.”
• Powerpoint Slide # 3:
o “This is Stacy’s third summer working for you. She earns $15 per lawn. She cut 3 lawns on Monday, 4 lawns on Tuesday, and 2 lawns on Wednesday.”
• Powerpoint Slide # 4:
o “Marcus has been working for you for five summers now. He earns $20 per lawn. He cut 5 lawns on Monday, 3 lawns on Tuesday, and 4 lawns on
Wednesday
• Powerpoint Slide # 5:
o “10 total lawns were cut on Monday. Out of the lawns cut on Monday, what proportion did Joe cut? Stacy? Marcus?”
 Answers:
• Joe: 2/10 = 0.20 = 20%
• Stacy: 3/10 = 0.30 = 30%
• Marcus: 5/10 = 0.50 = 50%
o “10.5 total lawns were cut on Tuesday. Out of the lawns cut on Tuesday, what proportion did Joe cut? Stacy? Marcus?”
 Answers:
• Joe: 3.5/10.5 = 1/3 = 0.333 = 33.3%
• Stacy: 4/10.5 = 0.381 = 38.1%
• Marcus: 3/10.5 = 0.286 = 28.6%
o “6.5 total lawns were cut on Wednesday. Out of the lawns cut on Wednesday, what proportion did Joe cut? Stacy? Marcus?”
 Answers:
• Joe: 0.5/6.5 = 0.077 = 7.7%
• Stacy: 2/6.5 = 0.308 = 30.8%
• Marcus: 4/6.5 = 0.615 = 61.5%
o “How many total lawns were cut on Monday, Tuesday, and Wednesday combined?” Answer: 27 total lawns.
o “What proportion of the total lawns did Joe cut? Stacy? Marcus?”
 Answers:
• Joe: 6/27 = 0.222 = 22.2%
• Stacy: 9/27 = 0.333 = 33.3%
• Marcus: 12/27 = 0.444 = 44.4%

2. • Powerpoint Slide # 6: Explain how to write a check
o “First, put the current date on the check.”
o “Then, write out the name of the person that will be receiving the money through the check on the line titled ‘Pay to the Order of’.”
o “Next, write the dollar amount next to the dollar sign.”
o “Next, write out the dollar amount in words on the next line.”
o “On the ‘For’ line, write the reason for writing the check. Ex: Paycheck October 3 – 10.”
o “Finally, sign your name on the line at the bottom right of the check. This authorizes the recipient to take the check to a bank and receive cash for the
amount specified.”
• Powerpoint Slide # 7: Explain how to fill out a check registry
o “The check number in this exercise is 101. However, with a real checkbook, check numbers will increase by 1 each time.”
o “Write down the same date that you wrote on the check. This is especially important when pre-dating or post-dating checks.” Ask for any questions
about pre-dating and post-dating checks.
o “The ‘Check Paid To’ column should be the same name that you wrote on the check next to ‘Pay to the Order of’.”
o “The check amount must be exactly the same that you wrote on the check. This should be recorded as the subtraction of this amount from the current
balance. If you were depositing a check that someone had written to you into your account, this amount would be a deposit amount, or an addition to
the current balance.”
o “The beginning balance for this exercise is $5000.”
• Powerpoint Slide # 8:
o “Assuming no taxes are withheld, use the per lawn rates of each employee to compute their paychecks.”
o “Write appropriate paychecks for each employee based on all three days of work.”
o Answers:
 Joe: $10(6 lawns) = $60.
 Stacy: $15(9 lawns) = $135.
 Marcus: $20(12 lawns) = $240.
• Powerpoint Slide # 9: “Your newest employee, Joe, ran over a stump and broke one of the lawn mowers.”
• Powerpoint Slide # 10:
o “A new lawn mower costs $200. It will cost you $180 to fix the old lawn mower.”
o “Stores occasionally offer discounts to encourage consumer purchasing.”
o “A discount is a percentage of the total cost subtracted from the total cost to give you the discount price.”
o “For example, a discount of 40% would be .40(200) = $80 off of the total price. The resulting discount price, when given a discount rate of 40%, would
be $120.”
o “What discount would the store have to offer for you to buy a new lawnmower instead of having the old one fixed?” (Answer = 10% discount).
o “In order to figure this out, we will be working in groups with different discount rates in each group.”
• Powerpoint Slide # 11:
o “As a group, figure out the resulting discount price from the discount rate offered.”
o “Then, as a group, decide whether it would be more cost effective to buy a new lawnmower with the given discount, or to get the old lawnmower
fixed.”
o “Write an appropriate check to ‘The Mower Store’ if you choose to buy a new mower. Fill out an appropriate check to ‘Moe’s Lawn Service’ if you
choose to fix the old mower.”
o Answers:
 Group 1: No discount – price is still $200.
 Group 2: 5% discount rate - .05(200) = $10 off the original price $190 discount price.
 Group 3: 10% discount rate - .10(200) = $20 off the original price $180 discount price.

3.  Group 4: 15% discount rate - .15(200) = $30 off the original price  $170 discount price.
 Group 5: 20% discount rate - .20(200) = $40 off the original price  $160 discount price.
Instructional Modifications to ASSIST
Weakest Students
Major Instructional Strategies
Instructional Modifications to CHALLENGE
Strongest Students
• The very weakest students should be put in
group #1 where there is no discount,
therefore less necessary computation.
• Help students compute the amount for each
paycheck by setting up the proper equation
and allowing them to work for the answer:
o Joe: $10(6 lawns) = $60.
o Stacy: $15(9 lawns) = $135.
o Marcus: $20(12 lawns) = $240.
• Help students set up the proper proportion
equations before solving.
• Collaborative learning (group work).
• Reflective and leading questioning.
• Repetition.
• Student demonstration of knowledge
(presentation to the class).
• Application to real life.
• Authentic Assessment
• Students that finish their group assignment
before others should compute answers using
other groups’ discount rates.
• Students should use the proportion of total
lawns cut for each individual employee to
estimate how many lawns they cut on Thursday.
Compute the resulting change in each
individual’s paycheck.
• Assuming the company earns $50 per lawn cut,
compute the amount of profit earned on
Monday, Tuesday, and Wednesday. Then
compute the total profit for all three days
combined.
• Add these profits to the check registry and
compute the resulting ending balance.
• Based on the results of the activity, which
employee should cut one extra lawn if you want
to spend the least amount of money?