Rate of change

Learning Objectives Identify and define rates of change in various real-world scenarios. Calculate unit rates involving decimal quantities using division. Interpret the meaning of a calculated rate of change in context. Solve problems involving constant rates of change where quantities are expressed as decimals. Compare different rates of change to determine which is faster, slower, or more efficient. Accurately perform operations with decimals (multiplication and division) when calculating rates. Ever wonder how fast a snail crawls 🐌 or how much fuel your car uses per kilometer? These are all about how things change in relation to each other! In this lesson, we'll explore the exciting world of 'rate of change,' learning how to measure how one quantity chang...

TermDefinitionExample RateA ratio that compares two quantities measured in different units.60 kilometers in 2 hours is a rate comparing distance to time. Unit RateA rate where the second quantity in the comparison is one unit. It tells you 'how much per one'.If you travel 60 km in 2 hours, your unit rate is 30 km per 1 hour. Rate of ChangeA measure of how one quantity changes in relation to another quantity. It is often expressed as a unit rate.A plant growing 0.5 cm per day is a rate of change. Constant Rate of ChangeWhen the rate of change between two quantities remains the same over any interval.A car traveling at a steady speed of 80.5 km/h has a constant rate of change. Decimal OperationsThe rules and procedures for adding, subtracting, multiplying, and dividing numbers tha...

General Rate Formula $\text{Rate} = \frac{\text{Quantity 1}}{\text{Quantity 2}}$ This formula is used to express how much of Quantity 1 corresponds to a certain amount of Quantity 2. The units of Quantity 1 will be 'per' the units of Quantity 2. Unit Rate Calculation $\text{Unit Rate} = \frac{\text{Total Amount of Quantity 1}}{\text{Total Amount of Quantity 2}}$ To find the unit rate, divide the first quantity by the second quantity. The result will tell you how much of the first quantity there is for *one unit* of the second quantity. Rate of Change (General Principle) $\text{Rate of Change} = \frac{\text{Change in Dependent Quantity}}{\text{Change in Independent Quantity}}$ This principle explains that rate of change is about how much one value (dependent...