Gold Seal Lesson:
Going Camping

Copernicus Education Gateway

Subject:

Mathematics

Grade:

5-8

ICLE Standards:

Patterns and Functions: Given visual, arithmetic and geometric (including exponential) situations:

1. identify patterns

2. generate rules using algebraic symbols where appropriate

3. formulate a prediction or make a decision

Statistics: Represent and explain information through tables, graphs, spreadsheets, algebraic expressions and verbal descriptions.

Performance Task:

You are a member of a group of campers going on a camp out. When you arrival at the campsite, you will be given a piece of string 60 meters long and four flag poles with which to mark out a rectangular boundary for your group's campsite. Your group has decided to pitch their tent next to a river, which means the string will be the boundary on just three sides of the campsite. Your task is to plan the campsite prior to your arrival. Your plan must include a picture of the campsite and a table showing all the possible lengths and widths (integral dimensions only) of the boundary for the campsite. Identify any pattern(s) you see in your table. In your math journal record the pattern(s) you found and give a complete description of how the length of the boundary changes as the width increases. Write an algebraic expression that would generate the length, given any width.

Using technology, find all the possible areas enclosed by the boundary (using only whole number lengths and widths) and create a spreadsheet to display this information. Draw a graph to show the relationship between the area enclosed and the width of the rectangle.

As a camper you are interested in having as much space (area) as possible. From your investigation, determine the length and the width of the boundary that will give you the largest space. Record these dimensions in your math journal and explain any relationship you see between the length and width of the boundary that produces the maximum area. Do you think this relationship could be generalized for any length piece of string? Explain your response.

Knowledge / Skills:

Perform operations with signed (positive and negative) numbers, including decimals, ratios, percents, and fractions.  (m1)

Understand the best procedures for statistical data collection, organization, and display.  (m5)

Understand the use of variables in expressions such as 4x, x+2, and 2x-1, solve for the variable, and know how to represent expressions such as "twice the number" or "four more than the number" using variables. (m7)

Compute the perimeter and area of two-dimensional figures. (m13)

Use the technique of dimensional analysis to convert units of measure (e.g., convert km/hr to m/min). (m33)

Use writing as a tool for learning in formats such as learning logs, laboratory reports, note-taking, and journals. (ela40)

Rubric:

4 Points = The student independently completes all aspects of the task. His/her work is neat, accurate, complete, and well organized. The student’s entry in his/her math journal is neat and well presented. The student is able to make a correct conclusion from his/her data and is able to propose a generalization to the problem situation. He/she is able to skillfully communicate his/her findings both orally and in writing.

3 Points = The student needs some assistance to complete all aspects of the task. His/her work is neat and well organized, but some minor conceptual and procedural errors occur in his/her work. The student’s entry in his/her math journal indicates some uncertainty about the concepts involved in the problem situation. He/she does make a correct conclusion, but has difficulty expressing this in writing. He/ she needs help to make and justify a probable generalization of the problem.

2 Points = Even with assistance the student is unable to complete all aspects of the task. He/she puts forth the effort, but lacks understanding of major concepts in the problem situation and has difficulty expressing himself/herself both orally and in writing. Several errors occur, not only in conceptual understanding, but also in computation. The student has difficulty using technology to create a spreadsheet. The student’s conclusion and generalization were vague and unclear.

1 Point = The student does not complete the task. He/she shows little understanding of the concepts involved and demonstrates an inability to analyze and solve the problem. The student’s work is incomplete, poorly organized and inadequately recorded and presented. The student makes no attempt to use technology in the solution of the problem. The student puts forth little effort to find a solution to the problem.

Keywords:

ALGEBRA
ALGEBRAIC OPERATIONS
EQUATIONS
PATTERNS AREA
QUADRILATERALS
PERIMETERS
GEOMETRY 
CHARTS
GRAPHS
INFERENCE
MEASUREMENT
PROBLEM SOLVING
TABLES
TECHNOLOGY INTEGRATION 
JOURNAL

Grades:

Kg [] - 1 [] - 2 [] - 3 [] - 4 [] - 5 [x] - 6 [x] - 7 [x] - 8 [x] - 9 [] - 10 [] - 11 [] - 12 []

ICLE Application:

D

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