Describe in detail what you need	I need s do now mini lesson and exit ticket for 7th grade proportional reasoning to solve problems
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Introduction

Proportional reasoning involves understanding the relationship between two or more quantities that change in proportion to each other. In middle school, students learn how to use proportional reasoning to solve problems in various contexts. In this mini lesson, we will cover the basics of proportional reasoning and provide some examples of how it can be used to solve problems in 7th grade.

Proportions and Ratios

A proportion is a statement that two ratios are equal, such as:

2/5 = 8/20

Here, the two ratios are 2/5 and 8/20, and they are equal. We can use proportions to solve problems involving unknown quantities. For example:

If 3 pies are shared equally among 12 people, how many pies will be needed to feed 24 people?

3/12 = x/24     // where x is the number of pies needed

Cross-multiplying, we get:

12x = 72

Solving for x, we find:

x = 6

Therefore, we need 6 pies to feed 24 people.

## Direct and Inverse Proportions

In some cases, two quantities are directly proportional, meaning that as one quantity increases, the other quantity also increases. For example, if the speed of a car is directly proportional to the distance it travels, then:

Speed = Distance/Time

In other cases, two quantities are inversely proportional, meaning that as one quantity increases, the other quantity decreases. For example, if the time it takes to complete a task is inversely proportional to the number of people working on it, then:

Time = k/Number of People

Here, `k` is a constant that represents the amount of work that needs to be done.

## Exit Ticket

1. What is a proportion?
2. How can we use proportions to solve problems?
3. What is the difference between direct and inverse proportions?

Submit your answers in the comments section below.