Write a text according to the following request...Do now, practice and exit ticket for the following learning objective: students will be ab...
Describe in detail what you needDo now, practice and exit ticket for the following learning objective: students will be able to define inverse proportionality and understand how it differs from direct variation and proportionality
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Do Now

  1. What is direct variation?
  2. What is proportionality?
  3. Give an example of a situation that demonstrates direct variation.

Practice

Read the following scenarios and decide whether they represent direct variation, proportionality, or inverse proportionality. Write your answer on a piece of paper.

  1. Sarah drives her car at a constant speed of 60 mph. The distance she travels is directly proportional to the time she spends driving.
  2. The amount of money you pay for a product is directly proportional to the number of items you purchase.
  3. The time it takes to complete a task is inversely proportional to the number of people working on it.
  4. When the temperature decreases, the volume of a gas decreases proportionally.
  5. The force required to stretch a spring is directly proportional to the amount of stretch.

Exit Ticket

Answer the following questions in complete sentences:

  1. What is the difference between direct variation and proportionality?
  2. Give an example of a situation that demonstrates inverse proportionality.
  3. How can you identify whether a situation represents direct variation, proportionality, or inverse proportionality?

Answers

Do Now

  1. Direct variation is a mathematical relationship where two variables are directly proportional to each other. This means that if one variable increases, the other will also increase in proportion to the first variable.
  2. Proportionality is a mathematical relationship where two variable are proportional to each other. This means that if one variable increases by a certain factor, the other will also increase by the same factor.
  3. An example of direct variation is the relationship between the number of hours you work and the amount of money you earn. The more hours you work, the more money you earn.

Practice

  1. Direct Variation
  2. Proportionality
  3. Inverse Proportionality
  4. Proportionality
  5. Direct Variation

Exit Ticket

  1. Direct variation is a mathematical relationship where two variables are directly proportional to each other, while proportionality is a mathematical relationship where two variable are proportional to each other. The difference is that in direct variation, the two variables increase or decrease together, while in proportionality, the two variables change in proportion to each other.
  2. An example of inverse proportionality is the relationship between the amount of time it takes to complete a task and the number of people working on it. The more people there are working on the task, the less time it will take to complete.
  3. You can identify whether a situation represents direct variation, proportionality, or inverse proportionality by examining how the two variables relate to each other. If they change in proportion to each other, the situation represents proportionality. If they increase or decrease together, the situation represents direct variation. If one variable increases while the other decreases, or vice versa, the situation represents inverse proportionality.