Introduction to Ratios & Proportions
Key Points:
Key Points:
 A ratio is a comparison between two quantities
 "FOR EVERY..." OR "FOR EACH..." are words to begin your description of a ratio.
 Three different ways to write a ratio (fraction, colon : or the word "to")




Comparing Ratios Using Ratio Tables & The Structure of Ratio Tables
Key Points:
Key Points:
 Know how to identify both additive and multiplicative structure of a ratio table
 Use the structure to make additional entries in the table and to solve problems


Finding Missing Values in a Ratio Table
Key Points:
Key Points:
 A ratio table is a table of equivalent ratios
 A ratio is often used to describe the relationship between the amount of one quantity and the amount of another quantity as in cases of mixtures or constant rates.



Equivalent Ratios
Key Ideas
Key Ideas
 How to create a tape diagram using ratios
 Write ratios in numerous ways using words demonstrating part to part, part to whole, and whole to part
 What total quantity does a tape diagram represent?
 What are the values of each individual part in a tape diagram?


Steps to Solving Problems Using Two Tape Diagrams
 Read the problem
 Determine the 1st ratio and write it down
 label and draw a tape diagram
 Find the second ratio
 label and draw the second tape diagram
 Determine which value goes into each equal sized section and fill out all the sections (you may have to divide)
 Solve the question/problem and write your answer in a complete sentence
The Value of a Ratio
Key Points:
(Finding the value of ratios is similar to simplifying fractions)
Key Points:
(Finding the value of ratios is similar to simplifying fractions)
 Find the Greatest Common Factor between both/all numbers within the ratio
 Draw your arrows (optional)
 Divide each number in the ratio by the GCF (greatest common factor)
 Ask: Can you find any other numbers that can go into both of the values? If you cannot, you have the value of the ratio.
Unit Rates & Unit Price
Key Ideas:
Key Ideas:
 When comparing ratios, remember to find the Unit Rate for each ratio first.
 To find a Unit Rate, you want to find the rate for ONE.






Comparing and Computing Unit Rates
Key Ideas:
Key Ideas:


Measurement Conversions and Rates


Constant Rate of Change
Key Points to Remember:
Key Points to Remember:
 For each Ratio A:B you should associate the ordered pair (A, B) which can be plotted on a coordinate plane.
 Notice that all points lie on a line through the origin.
 The coordinates in the line satisfy y=kx, where k is the value of an associated ratio (the constant rate of change)


From Ratio Tables, Equations, and Double Number Line Diagrams to Plots on the Coordinate Plane
Key Points to Remember:
Key Points to Remember:
 Students associate each ratio A:B with an ordered pair (A,B)
 Students take the ratios and create ordered pairs, then graph the points on a coordinate plane
Creating equivalent ratios using Number Lines
1. Construct one number line to represent the first quantity
2. Construct another number line to represent the other quantity
3. Label both number lines with the names of the quantities
4. Plot the equivalent ratios on your double number line
5. Solve the problem/question

