Rates, Ratios, and Proportions

Prerequisites:

* Understand that percent means part of one hundred and write percents as fractions and decimals

* Understand Concepts of Ratios

* Express Ratios in Different Forms

NYS Content Standards:

* Understand the Concept of Rate

* Express Equivalent Ratios as Proportions

* Distinguish the Difference between Ratio and Rate

* Solve Proportions using Equivalent Fractions

* Verify the Proportionality using the Product of the Means Equals the Product of the Extremes (cross products)

* Read, write, and identify percents of a whole (0% to 100%)

* Solve Percent Problems involving Percent, Rate and base (part, whole, percent)

* Find multiple representations of rational numbers (fractions, decimals, and percents 0 to 100)

* Estimate a percent of quantity (0% to 100%)

* Justify the reasonableness of answers using estimation (including rounding)

* Solve Simple Proportions within Context

Students must KNOW the following definitions:

rate
ratio
percent
proportion/proportionality
equivalence
cross-products

Students will UNDERSTAND:

* Equivalent forms of FDP exist
* Between every two whole numbers there exists an infinite # of fdp
* The decimal and percent systems are based on the number 10
* Different forms (FDP) are more appropriate in particular situations
* Understand the concept of rate
* Understand the concept of ratio
* Understand the relationship/difference between rate and ratio
* Percent problems can be solved using part, whole and/or percent
* Ratio can be a comparison of part-to-part or part-to-whole

Students will be able to DO the following:

* Read, write, and identify percent
* Change fraction, decimal, percents to their equivalent forms
* Estimate a percent of a quantity
* Justify reasonableness of an answer using estimation
* Express equivalent ratios as a proportion
* Distinguish between ratio and rate
* Solve proportions using equivalent fractions
* Use cross-products to verify proportionality
* Solve simple proportions within context
* Solve percent problems using part, whole and/or percent
* Express ratios in different and appropriate form
* Calculate "per unit" rate

Expected Timeline: *Note: Please know that this could change slightly due to unforeseen issues.

Day 1- Percents (as equivalent fractions)
Day 2- Percents (using decimals or proportions)
Day 3- Percent (part, whole, percent NOT base, rate, and percent)
Day 4- Percent continued
Day 5- Proportions (not focused on percents)
Using: Compatible #s, Cross products, and Division
Day 6- Word problems involving proportions
Day 7- Intro to ratios
Day 8- Intro to rates and compare differences between ratio and rate
Day 9- Per unit
Day 10- Review
Day 11-Test

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