Theme:
Ratio and Proportion
Objective:
To create an experience of ratio and proportion.
To solve problems using proportion.
Material:
Scissors, construction paper in different colors, pencils, rulers, question sheet.
Key Question:
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—How does Mathematics work in construction?
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—How much Mathematics will the Plumber, Cement Masons, Architects and other construction workers need in order to be proficient and successful in their jobs?
Background Information:
Construction workers must make careful plans in the form of budgets, time schedules, and blue print (scale drawing of projects). They need to know how to measure and they must have a working knowledge of ratios and proportion and scales. Cement Masons are faced with the job of ordering, mixing, and pouring cement to complete projects. They need to know the area of the cement work to be completed.
They much decide how much cement is needed for the job? How many cement trucks must be scheduled for the job? They must also decide the ratio of men to cement trucks for the job. They also need to have a working knowledge of ratio and proportions. The customers interested in the overall cost of the job. He needs to know Mathematics to decide if the estimates given by the various construction workers are cost effective.
Method:
Simulation to encourage brainstorming for imagination, and innovation.
Management Suggestions:
Divide class into groups of three or four.
Activity:
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—Each group will be given a pair of scissors, 6 sheets of construction paper in 6 different colors and one question sheet.
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—Instruct group to divide the task.
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—Each group must fold, then cut the construction paper in the following way:
(figure available in print form)
Yellow is folded/cut into two equal pieces.
Green is folded/cut into four equal pieces.
Red is folded/cut into three equal pieces.
Orange is folded/cut into six equal pieces.
Blue is folded/cut into eight equal pieces.
White is left whole.
Each group prepares the pieces, then uses them to answer the questions of the question sheet.
Sample Questions from Activity Sheet
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1. Write a fraction that compares one piece of green to the total number of green pieces.
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2. Write a fraction that compares two pieces of blue to the total number of blue pieces.
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3. Are these fractions equivalent?
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When each group had completed the assignment, teacher leads out in a sharing discussion which should highlight the following concepts:
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(1) A ratio is the comparison of two numbers by division e.g. numbers of yellow pieces to orange pieces is 2:6 or 2/6
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(2) A proportion is an equation that equates tow ratios e.g. 1/4(green)=2/8 (blue)
Follow up activity to test for comprehension will include questions that require students to write a proportion by setting the ratios equal, then solving that equation.
Sample Questions:
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1. Two men can paint a house in five days, How long will it take one man to do the job if he works at the same rate?
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2. If one out of five people use Colgate Cavity Fighting Toothpaste, how many people will be expected to use this brand in a city of 30,000 people?
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3. Find the perimeter of the room shown on the scale drawing if 1 cm->5m.
(figure available in print form)
