In this topic, students will:
use rations to describe the relationship between two quantities
use bar diagrams and double number line diagrams to model ratio relationships
use multiplication and division to find equivalent ratios
solve problems by finding equivalent ratios
use ratio tables to compare ratios
compare ratios to solve problems
represent equivalent ratios on graphs
use ratio tables and graphs to solve problems
use rates to describe ratios in which the terms have different units
use rates and unit rates to solve problems
use ratio reasoning to compare rates and solve problems
use unit rates to solve problems involving constant speed
use unit rates to solve problems involving unit price
solve unit rate problems using an equations
use mathematical modeling to represent a problem situation and to propose a solution
test and verify the appropriateness of their math models
explain why the results from their mathematical models may not align exactly to the problem situation
use ratio reasoning and conversion factors to convert customary units of measure
Vocabulary:
Ratio - a relationship in which there are y units of a quantity for every x units of a quantity
Terms - single numbers, variables, or the product of a number and variables
Circumference - the distance around a circle
Diameter - The distance from one point on a circle through the center to another point on the circle
Equivalent ratios - ratios that are the same when we compare them
Pi - The ratio of a circle’s circumference to its diameter
Rate - a ratio that compares quantities with unlike units of measure
Unit rate - a unit rate compares a quantity to 1 unit of another quantity
Unit price - the price of a single item
Constant speed - When the speed of an object remains the same - it does not increase or decrease
Conversion factor - a number used to change one set of units to another, by multiplying or dividing
dimensional analysis - a problem-solving method that uses the fact that any number or expression can be multiplied by one without changing its value