ERPB - Proportional Relationships Module Overview
Proportional Relationships Module Overview
Introduction
In this module, students will learn to represent proportional relationships and scale drawings within real-world contexts. They will learn to translate measurements and distances into maps or scale drawings or find actual measurements and distances from scale drawings. Students will learn to use scale factor to determine area and perimeter of similar figures. Next students will continue using proportional reasoning to explain why the slope, m, is the same between distant points. Finally, students will use proportional relationships to solve multi-step ratio and percent problems presented in applicable situations. This will include multistep percent application problems as students learn to find percent of increase and decrease and use the formula: I = PRT to solve interest problems.
Essential Questions
How are distances and measurements translated into a map or scale drawing?
- How do I determine the appropriate scale for the area (such as my yard or school) that I am measuring and mapping?
- How can scale factors, ratios, and proportions be used to represent the relationships that exist between similar figures?
- How can scale factors, ratios, and proportions be used to solve problems related to similar figures?
- How do I use similar triangles to explain why the slope, 𝑚, is the same between any two distinct points on a non-vertical line in the coordinate plane?
- How can I use proportional relationships to solve multistep percent problems?
- How can you use measures of center and variability to compare two populations?
- How can you use a sample to gather information about a population?
- How can samples be used to make predictions about a population?
- Why is a random sample more reflective of the population than other means of sampling?
Key Terms
The following key terms will help you understand the content in this module.
Dilation- A dilation is a transformation that changes the size of an object, but not the shape.
Enlargement- An enlargement is a dilation with a scale factor greater than 1.
Reduction- A reduction is a dilation with a scale factor less than 1 and greater than 0.
Scale Factor- The scale factor is the factor by which a figure is enlarged or reduced and can be written as the ratio of any two corresponding lengths in two similar geometric figures. Note - The ratio of areas of two similar figures is the square of the scale factor. The ratio of volumes of two similar figures is the cube of the scale factor.
Similar Figures-Figures are similar if
- The measures of the corresponding angles are congruent
- The ratio of the lengths of their corresponding sides are equal
Congruent-Objects have the same shape and the same size
Similar-Objects have the same shape
Slope-How steep a line is. The steeper the line, the greater the slope. It can be found using “rise/run” or
Principal-The initial amount of money borrowed or saved.
Percent of Change (increase and decrease)-The percent of change describing and increase or decrease in a quantity.
Simple Interest-a fixed percent of the principal. It is found using the formula I = Prt, where P represents the principal, r the rate of interest, and t the time.
Tax-Money collected by the government based on income, sales, and other activities
Markups and Markdowns-The amount the retailer increases (Markups) or decreases (Markdowns) the price compared the original price paid by the retailer.
Gratuities/Tips-A percent added to the cost of the service.
Commission-A fee made to the person who makes a sale.
Discount-A percent that is subtracted from the cost of an item.
Sales Tax-The tax on the sale of an item or service. It is a percent of the purchase price and is collected by the seller.
Sample-part of the population
Population-The entire group being studied or surveyed.
Random Sample-A sample in which every individual of the population has a chance of being chosen and is representative of the entire population.
Biased Sample-A sample that does not fairly represent the population
Convenience Sample-A sample based on members of the population that are readily available.
Stratified Sample-A sample drawn from a number of separate subgroups of the population, rather than at random from the whole population, in order that it should be representative.
Systematic Sample-A type of sampling method in which sample members from a larger population are selected according to a random starting point and a fixed, periodic interval.
Sample Mean-The mean or average of the sample data.
Population Mean-The mean of average of the population.
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