Inequalities in the Real-World

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Objective

SWBAT represent real world situation using inequalities and represent those situations graphically.

Big Idea

Hitting The Glass Ceiling... or Floor: Understanding that inequalities describe a type of limitation in a real world situation where you can't go any higher than a given quantity or you can't go any lower.

Curriculum Reinforcer

5 minutes

The curriculum reinforcer, is a daily practice piece that is incorporated into almost every lesson to help my students to retain skills and conceptual understanding from earlier lessons. My strategy is to use Spiraled Review to help my students retain what they learned during the earlier part of the year. This will help me to keep mathematical concepts fresh in the students mind so that the knowledge of these concepts become a part of students' long term memories.

Engagement

5 minutes

For our opening exercise I will have my students participate in an activity where they are given several commands. Each command will limit them in some way shape or form. They will have to carry out each command while taking into consideration that limitation. The commands will be presented on a card of some sort. 

Because my classroom is set up in tables, I will give each student at each table a different card. No student at the same table should have the same card. The cards will have the following scenarios written on them:

  • If you jump, as high as you can, no less than 7 times, how many times would you jump?
  • If you were to walk part of the width of the classroom, and the classroom is 40 tiles wide, to what tile number would you walk?
  • Using a ruler, your teacher wants you to measure an object that is shorter than 25 centimeters but longer than 14 centimeters. How long could your object be?
  • If you were to draw a line that is longer than 10 inches, how long would that line be?
  • You are on a road and there is a sign that says, "speed limit 45 mph" at what speed would you drive?
  • You decide to open up a new savings account. The banking representative tells you that there is a condition to ensuring that you do not incur any fees on this account. That condition is that you have to keep your balance at a minimum of $500. How much money would you keep in your account?

 

Every student will be given a whiteboard paddle to write their answers on. When I read their scenario, they will come to the front of the classroom with their paddles and present their answers. It is my hope that I will get several different answers for most of these scenarios so that we can discuss why each scenario has more than one possible solution. 

After these students have presented their answers and we have had the discussion as to why there is more than one solution to the scenario being presented at that time, I will then ask all students what are some other possible solutions.

This activity is designed to help students to prepare for today's lesson by helping them to see how inequalities can be used in context.

Instruction & Teacher Modeling

10 minutes

Today, I will show my students real-world scenarios that involve inequalities. During instruction, I will ensure that my students understand that the solution will provide a range of answers. Students should be able to locate key words and phrases and understand what those key words and phrases direct them to do.

To do this, I will present my students with two problems that I will work out step by step. One problem is a word problem that involves inequalities. The other problem is one that will require me to work backwards to create an inequality word problem. 

The modeling of these two problems will later serve as a reference to the successful completion of the independent practice. For this reason, all students should be taking notes during this time.

The two problems that I will present and model for my students are as follows:

  1. A company charges $0.10 for each letter engraved. Bobby plans to spend no more than $5.00 on the engraving on a jewelry box. Write and solve an inequality to find the maximum number of letters he can have engraved.
  2. Write a one-step inequality that has a solution greater than 8. Then write a word problem that result in the inequality that you have written with a solution greater than 8.

 

Using these problems, I will allow student to ask questions and address any misconceptions that they may have at this time.

Try It Out

10 minutes

Students will be given 5 minutes to complete 2 inequality word problems that mirror the problems that I modeled for them during the instructional piece of this lesson. During this time, I will be traveling the room answering any questions that the students may have, ensuring that they have a good grasp of the concept and are ready to move on.

The problems that my students will try are as follows:

  1. Joann's parents give her $10 per week for lunch money. She cannot decide whether she wants to buy or pack her lunch. If a hot lunch at school costs $2, write a and solve an inequality to find the maximum number of times per week Joanna can buy her lunch.
  2. Write a one - step inequality that has a solution less than 7. Then write a mathematical scenario that can be solved using the one - step inequality that you have chosen.

 

After the allotted time has elapsed, I will ask my students to provide the solution to the first problem. Then, I will ask three students to provide me with solutions to the second problem. The students that I choose for the second problem will be selected using a purposeful method, in that, they will be chosen to showcase the many different ways that the students could have solved this particular problem. 

Independent Exploration

20 minutes

In today's independent practice, my students will complete two tasks.

TASK #1:

During the first task, I will give my students 4 mathematical scenarios involving inequalities to solve. These mathematical scenarios will be presented to my students on a worksheet and requires my students to write a one-step inequality when given a mathematical scenario and then solve that one-step inequality.

This task is great for a quick assessment as to my students' ability to break down and solve inequality word problems.

TASK #2:

For the second task, my students will be required to write a mathematical scenario involving inequalities in the same manner as what was presented during the instructional portion of this lesson. This is also the same as what the students practiced during the Try It Out portion of this lesson. However, I did make one adjustment. In this task, the students, while given the quantity that must be included in the solution, they will have the autonomy to choose which inequality symbol should accompany that quantity in the solution.

To complete this task, the students will be presented with four quantities in total. For which they must do the following for each of those quantities:

  1. Write an inequality solution using each quantity
  2. Write a one-step equation using each inequality solution that you came up with in step 1
  3. Write a mathematical scenario that is representative of your one-step inequality and its corresponding solution

 

The four numbers that I will give the students are as follows: 6.25, 5/8, 12, and 4

Having the students work backwards to create a mathematical scenario when given only a quantity is very informative, as it pertains to my students' level of mastery when it comes to this concept. I know that if they can create their own mathematical scenarios, then they have truly mastered one-step equations. Being able to work out a scenario demonstrates proficiency but, when you can create a problem on your own, that is exemplary.

Closing Summary

20 minutes

To close out today's lesson, I will choose one student per problem to present.

The students who will present the first four problems will come to the board and write their answers on the board. Then, they will be asked the process that they used to solve their problem. They need to be ready to answer probing questions that I will ask to ensure that they are actually understanding the math behind the problem and not just mimicking my model. And, they will have to be ready to defend their work should they be challenged by me or one of their peers.

The students presenting their scenarios will have much more to articulate and explain. They will need to explain their thinking as they went through the process of completing this task. Their work will be critiqued and analyzed by me, as well as their peers. During their presentation, these students need to be prepared to answer questions and defend their thinking and their solution pathways.