Write an inequality to represent each of the following ...



This Lesson Lab was created by Diane Farmer & Mike Allred (Perkins Middle School; Akron, Ohio. June 2000)

Subject: Pre-Algebra / Algebra

Grade: 7/8

Time: 3- 40 minute periods

Strand: Problem-Solving Strategies; Algebra; Data Analysis

Topic: Margin of error in radar devices

Objective: By transforming data from a real world situation learners will develop a representative inequality, graph it, and make interpretations and predictions. (OPO #5, #12)

Learners will demonstrate in writing an understanding of deductive reasoning based on data analysis. (OPO #12)

Materials: Explorer Plus, or higher, calculator

Graphing or spreadsheet software

Internet access (optional)

Worksheet

Margins of Error in Radar Speeding Devices

Concept:

Define inequalities and interpret data using graphs, tables, and numerical representations.

Draw reasonable conclusions based on data analysis.

Learning Objectives:

1. By transforming data from a real world situation learners will develop a representative inequality, graph it, and make interpretations and predictions. (OPO #5, #12)

#5 Solve problems and make applications involving percentages

#12 Read, interpret and use tables, charts, maps and graphs to identify patterns, note trends and draw conclusions.

2. Learners will demonstrate in writing an understanding of deductive reasoning based on data analysis. (OPO #12)

#12 see above

Project/ Task:

Working with calculators in pairs, learners will complete a table of values representing the maximum and minimum vehicle speeds derived from the given percentage of error of a radar gun. From the table, learners will formulate a generalized inequality for the maximum and minimum car speeds, graph the data, (with available tools, i.e. ClarisWorks, Excel; TI-73) and predict the speed at which an officer would pull a driver over for speeding.

Assessment:

Informal observation: Percentages, inequalities, graphs; math tools used Type I

Problem solving/ reasoning; math dialogue or communication Type II

Formal: Accuracy of tables and graphs; formulation of inequalities; Type I

Written explanations Type II

Learning Strategies:

This LessonLab is designed for three days or a block period with seventh and/or eighth graders.

Day 1

Learners will begin working on an exercise page "Warming up your Engines" to stimulate thought about inequalities. (5 minutes). Review warm-up activity (5 minutes). As a whole group consider the problem presented in the LessonLab and answer questions 1 and 2. ( 5 minutes) In pairs, using the calculators, learners will complete the table and questions 4 and 5. (If necessary quickly review the percent function on the calculator). ((15 minutes)

Review table and questions 4 and 5 as a class. (5 minutes)

Day 2

Review #5 (the inequality derived from the table). Briefly discuss the format of the graph given in #6. (5 minutes) Learners will work in same pairings to complete the graph and questions 7 and 8. (20 minutes) Learners will share their results with the whole class. (10-15 minutes) Assignment: complete the extension. (time permitting, begin in class)

Day 3

Final assessment: in class, learners will complete the enrichment problem on the worksheet using the technology available in the classroom (i.e. computers, calculators, internet) and then to investigate other applications of margin of error calculations and/or radar devices.

Classroom and Information Management:

This LessonLab is designed to be used in a classroom where students are seated in pairs. The facilitator will serve as a timekeeper. Materials required are the lab sheet, calculators, (Explorer Plus and up) and if possible computers/ calculators with graphing and internet capabilities.

Sharing:

Small and large group debriefing occurs throughout this lesson as the teacher facilitates the lab. Input from learners, parents, teachers, administrators is welcome to enhance learner's development of the concept.

Results:

The class culmination is the particular data representations (i.e. graphs, tables, web searches), created throughout the LessonLab.

Tools and Resources:

Explorer Plus or above, calculators;

Graphing software or spreadsheet;

Internet access (optional)

Worksheets

Do and How:

Learners will use the Radar Reading lab sheet to analyze data.

Learners will use computers/calculators to create graphs, tables.

Learners may use the internet to search for information related to the topic.

Warming up your engines

Write an inequality to represent each of the following sentences.

1. Farmer Bob has more wheat than his cow. ___________________________

2. Larry is taller than Moe, but shorter than Curly. _______________________

3. Rapunzel’s hair is at least as long as Juliet’s. __________________________

4. Either Mike ate no more than 2 tacos or no less than 2 hamburgers.

(hint: use 2 inequalities) ______________________________________

Write a sentence that describes each inequality.

5. 4 < 9 ___________________________

6. 9 > 4 ____________________________

7. z = b __________________________

8. 5 < x < 10 ___________________________

9. b ( -73 _______________________________

ready to roll!!

RADAR READING LAB

A police officer was using a radar gun to measure the speeds of cars in a 35 mph zone. The radar gun has a margin of error of 12%.

1. Caravan: What numerical value does not change in this situation? ( the constant)

2. What value will change in this situation? (the variable)

3. Pick up a passenger: Complete the table below for the given radar readings:

|Radar reading |Margin of |Error (mph) |Minimum speed |Maximum speed |Compound inequality |Range (max-min) |

| |error (%) | | | | | |

|38 |12% |4.56 |33.44 |42.56 |_ _ _ _ _ _ _ |9.12 |

|42 | | | | | | |

|37 | | | | | | |

|45 | | | | | | |

|33 | | | | | | |

4. What mathematical operations were used to complete the table?

5. Write an inequality or inequalities representing a car’s actual speed if the radar gun detects a speed of x miles per hour.

6. Use the information from the table to complete the following graph

Car 5

Car 4

Car 3

Car 2

Car 1

31 33 35 37 39 41 43 45 47 49 51

7. Using the graph, try to determine which cars the police officer will pull over for speeding.

8. The police officer wants to stop only the cars he/she is sure are speeding. At what

radar reading will the officer pull a car over? Justify you answer mathematically

and explain it in complete sentences.

Driving Solo: (complete individually)

Extension: Using the same radar gun, determine what reading would necessitate an officer pulling a car over in a 20 mph zone?

In a 65 mph zone?

Show your work with a graph, inequality, or table for each speed zone.

Enrichment: An officer of the State Highway Patrol uses a laser gun to detect speeders. The error for this machine is only 4%. In a 35 mph zone, what reading would require a speeding ticket. Justify your conclusion with a written explanation that is supported by a graph, table or algebraic inequality.

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