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Highway Robbery

  • Lesson
6-8
1
Number and Operations
Kimberly Rubin
Alexandria, VA

The National Bank of Illuminations has been robbed! Students apply their knowledge of ratios, unit rates, and proportions to sort through the clues and deduce which suspect is the true culprit.

In this lesson, students assume the role of a detective investigating a bank robbery. Students wear police badges from a party store or that you make, and use four clues to help them apprehend the thief.

Below is a suspect matrix with the clue values needed to make a particular suspect the actual thief. Before class, choose one, and fill in the blanks on the Clue Sheet Overhead.

overhead Clue Sheet Overhead 

The information you put on the overhead will lead the students to your chosen thief.

Suspect Matrix 

Roy G. Biv Jen Eric Matthew Matics 
Clue 1 Question 1: 15 cmClue 1 Question 1: 13.2 cmClue 1 Question 1: 15 cm
Clue 2 Question 2: 25 poundsClue 2 Question 2: 25 poundsClue 2 Question 2: 32 pounds
Clue 3 Question 5: 16 miles/gallonClue 3 Question 5: 9 miles/gallonClue 3 Question 5: 8 miles/gallon
Polly Hedron Evan Number Al T. Tude 
Clue 1 Question 1: 13.2 cmClue 1 Question 1: 13.2 cmClue 1 Question 1: 15 cm
Clue 2 Question 2: 32 poundsClue 2 Question 2: 25 poundsClue 2 Question 2: 32 pounds
Clue 3 Question 5: 8 miles/gallonClue 3 Question 5: 25 miles/gallonClue 3 Question 5: 16 miles/gallon
The Suspect List Activity Sheet summarizes what is known about each person.
You can also create your own suspect list, using people you make up or people you know, such as other teachers or classmates. Having two or three possible values for each characteristic makes it easier to have students find suspects to match their calculations.

Give each student a pretend police badge as they enter the classroom. You can find them at most party stores, or make them yourself. Address the class as if they are a police academy with an opening statement like, "Detectives, we have received an urgent email from the captain of police. We have been chosen for this task because of our superior math skills. I have created a copy of the note for everyone."

 3128 surveillance 

Give students the option of working in pairs or individually. Groups larger than two tend to result in students being off-task with an unequal distribution of work.

Pass out the Clue Sheet Activity Sheet to each student and place the Clue Sheet Overhead on the board.

pdficon Clue Sheet Activity Sheet 

Lead a class discussion about the clues. Ask, "What they would do with ___ pounds of quarters?" or "If the perpetrator's car gets ___ miles per gallon, do you think he/she is very far away?" Some students, especially students whose first language is not English, may not be familiar with the vocabulary words perpetrator, apprehend, and deduction. As you read the letter, pause to ask for volunteers who can define each of these words.

  • Perpetrator- a person who committed the crime
  • Apprehend- to arrest someone
  • Deduction- to reach a conclusion
Then, have students fill in the blanks in Questions 1, 2, and 5.

Review conversions that students will need to solve problems: 12 inches in 1 foot, 4 quarters in 1 dollar. Suggest that students write word ratios to write a proportion. For example, Question 1 compares the centimeters in the photo to the inches in reality. A word ratio would be photo/real or centimeters/inches. Remind students that for these word ratios, all "photo," or "centimeter," measurements must be in the numerator. All "real," or "inch," measurements must be in the denominator.

Be conscious that proportions are not required to solve Questions 3, 4 or 5. Alternate solution methods can lead to the correct results, so if you want students to use proportions, clearly state so.

Pass out the Suspect List Activity Sheet. Read the Question 1 of the suspect list out loud with the class and let them know that they can work with both the clue sheet and suspect list at the same time to find the perpetrator.

3128 mugshot 5

Polly Hedron
Apprehended in Harrisburg, PA
With $640
Height: 5'6"

Monitor students' work, and listen for students who are struggling. Students may have problems correctly answering Question 1. Some students will leave their answers as decimals, but the suspect list does not have decimal heights. Ask, "Do any of your answers match the answers on the suspect list? What do you notice about the answers on the suspect sheet?"

[They are in feet and inches.]
"So what do you have to do?"
[Convert the decimal into inches.]
The most common problem will be students' making the decimal the number of inches, like 5.5 feet must be 5 feet 5 inches. Ask, "How many inches are in half a foot?"
[6 inches.]
"What should the height be?"
[5 feet 6 inches.]
Remind them to multiply 12 inches by the decimal part of their answer to find the number of inches.

For Clue 4, students use their answers from Clue 3 and measure the scale line in centimeters and use a proportion to calculate how far to measure on the map to find the perpetrator's city. Be prepared to help students read a ruler. Remind them that the smaller lines represents millimeters, which are 0.1 centimeters.

Have students submit their papers when they can identify the thief. Have students share who they think is the perpetrator. If students disagree, have them explain why their answer is correct. Or the teacher could ask what changes in the clues could lead to any of the other suspects.

 

Assessment Options 

  1. Have students work in groups to create their own mysteries. Each student is responsible for creating at least one clue. Groups swap mysteries and solve.
  2. Have students work backwards. Assign different suspects to different students to create their own sets of clues. Then, students can swap and try to find the new perpetrator.

Extensions 

  1. The thief escaped the police and was able to make way toward his home in Corpus Christi, Texas. Have students determine whether the perpetrator can make it within 24 hours before an arrest. Students should use the same gas mileage used in the Clue Sheet, but using current gasoline prices. Using a map of the United States have students plot the quickest route from the hideout city to Corpus Christi. They need to consider state speed limits and whether the culprit has to make any stops. Using proportions and the formula d = rt, students conclude whether the thief escapes and justify their conclusions mathematically.
  2. The thief had some accomplices to help him pull off the crime. The original plan was to split up the money. The thief was to receive 65% of the loot. Accomplice A was to receive 30% of what was left. Accomplice B was to receive 15% of what is left after Accomplice A and the thief each get their share. Accomplice C gets the rest. Students should calculate how much each accomplice gets. 
 

Questions for Students 

1. How did you know when to use a proportion to solve a problem? 

[Student answers may vary. Students might say that they saw that two objects were compared.] 

2.If you did not use a proportion, how did you solve the problems? 

[Students may have solved using a method similar to a proportion without setting one up. In the unit rate problems, students may have simply multiplied or divided.]  

3. What are some things in real life that would have affected the answers you got? 

[Questions 2 and 3 assume that all the quarters weigh exactly the same. Question 6 assumes that the car was getting 25 miles per gallon. Gas mileage varies based on driving conditions, such as speed.] 

4. What is a tip you can give a student who is struggling setting up their proportion? 

[Look for the two different units in the problem or the two different objects being compared. Then write a ratio using those words to help to organize the information.] 

5.Does it matter what variable you choose to represent the missing value? [No.] Why not? [No matter what letter you choose for the variable, the answer will remain the same.] 

Teacher Reflection 

  • Was students' level of enthusiasm/involvement high or low? Explain why.
  • How do you think the grouping of your students affected their learning?
  • What were some of the ways the students illustrated that they were actively engaged in the learning process?
  • For those students who chose to work in pairs, how did you ensure that each group member was participating rather than one person completing all the work?
  • Did the lesson help students deepen their understanding of proportions? How?
 

Learning Objectives

Students will:

  • Practice computation of ratios, unit rates, and proportions.
  • Apply skills to an authentic context.
  • Develop problem solving and deductive skills.

Common Core State Standards – Mathematics

Grade 6, Ratio & Proportion

  • CCSS.Math.Content.6.RP.A.1
    Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, ''The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.'' ''For every vote candidate A received, candidate C received nearly three votes.''

Grade 6, Ratio & Proportion

  • CCSS.Math.Content.6.RP.A.2
    Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, ''This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.'' ''We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.''

Grade 7, Ratio & Proportion

  • CCSS.Math.Content.7.RP.A.1
    Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction (1/2)/(1/4) miles per hour, equivalently 2 miles per hour.

Grade 7, Ratio & Proportion

  • CCSS.Math.Content.7.RP.A.3
    Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Grade 7, The Number System

  • CCSS.Math.Content.7.NS.A.3
    Solve real-world and mathematical problems involving the four operations with rational numbers.

Grade 7, Expression/Equation

  • CCSS.Math.Content.7.EE.B.3
    Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

Common Core State Standards – Practice

  • CCSS.Math.Practice.MP1
    Make sense of problems and persevere in solving them.
  • CCSS.Math.Practice.MP2
    Reason abstractly and quantitatively.
  • CCSS.Math.Practice.MP4
    Model with mathematics.
  • CCSS.Math.Practice.MP5
    Use appropriate tools strategically.
  • CCSS.Math.Practice.MP7
    Look for and make use of structure.