Understanding By Design Lesson Template
Title of Lesson:Solving Multi-Step Inequalities
Grade Level:9th Grade
Curriculum Area:Mathematics (Algebra 1)
Time Frame:45 Minutes
Developed By:Joel Thornton
Identify Desired Results (Stage 1)
Content Standards
4.1.12 B.1 (The Distributive Property)
4.1.12 B.4 (Order of Operations)
4.5 E.1a, 4.5 E.1c, 4.3.12 C.1a, 4.5.B.1a (Solving Two-Step Equations)
4.1.12 B.1 (Solving Multi-Step Equations)
4.3.12 C.1d, 4.3.12 B.2g (Equations with variables on both sides)
4.3.12 D.1a, 1b, 2a, 4.5.E.1b (Equations and Problem Solving)
4.5 E.1d (Inequalities and Their Graph)
4.5 D.4, 4.3.12 D.2a, 4.5.E.1d (Solving Inequalities using addition and subtraction)
4.3.12 D.2a, 4.5 D.4, 4.5 E.1d (Solving Inequalities using multiplication and division)
4.5 E.1a, 4.5 E.2, 4.3.12 D.2a (Solving Multi-Step Inequalities)
Understandings Essential Question(s)
Overarching Understanding
Students will learn how to:
Solve multi-step inequalities with variables on one side.
Solve multi-step inequalities with variables on both sides.
Applying the rules of simplifying the inequality to solve for the given variable.
Overarching
What is the difference between an equation and inequality?
When do we use an inequality?
When do we use an equation?
How do we know if a value is a solution to the inequality?
Topical
What are we solving for in the inequality?
Name the following inverse operation?
Which direction will we shade when we graph the inequality?
Related Misconceptions
When graphing inequalities should an open circle or closed circle be used to represent the solution?
When to reverse the inequality symbol?
When solving an inequality how many possible solution?
Knowledge
Students will know…
Students will be able to…
Solving 1-step equations.
Solving 2-step equations.
Solving multi-step equations.
Solving equations with variables on one side.
Solving equations with variables on both sides.
Solving word problems with equations.
Solving 1-step inequalities.
Solving inequalities with a negative factor.
How to graph inequalities.
Skills
Combine like terms before solving for the variables.
To use the distributive property before solving for the variable.
Solve real-life problems where you compare two situations.
Compare numbers.
Comparing situations.
Applying the rules of inverse operations.
Applying the rules of order of operations.
Assessment Evidence (Stage 2)
Performance Task Description
Goal
My students will be able to solve inequalities by applying their rules of inverse operations and simplifying. Then graph and check their solution.
Role
Assist students in applying previous learned material to solve inequalities.
Audience
Students at their desk and teacher using the overhead projector with transparencies.
Situation
Large group lecture with class notes and examples to guide students on transparencies. Break down to smaller groups during lesson.
Product/Performance
Verbal responses to open ended questions. Students solving practice problems individually. Students completing Lesson Quiz at the end of the lesson as a review.
Standards
See content Standards from (Stage 1)
Other Evidence
Section Quizzes. Chapter Test. Homework assignments. Working in Groups. Students present solutions on the board. Group activities.
Learning Plan (Stage 3)
Where are your students headed? Where have they been? How will you make sure the students know where they are going?
My students are heading to compound inequalities and absolute value equations and inequalities. They have recently learned the rules of solving equations and word problems. My students realize that math is similar to building a house. They need a strong foundation so they can build up to the next level.
How will you hook students at the beginning of the unit?
I will start the lesson with a "DO NOW" of previous material that my students know how to solve. Here they will feel confident and ready to move on.
What events will help students experience and explore the big idea and questions in the unit? How will you equip them with needed skills and knowledge?
I always state the objective for my students. Today I will learn how to solve multi-step inequalities with variables on one and both sides. I will complete 1 example for each type of problem my students will see. Then I have my students work on practice problems individually. Students will complete problems on the communicators to display their answer.
How will you cause students to reflect and rethink? How will you guide them in rehearsing, revising, and refining their work?
At the end of the lesson, I will give the students a Lesson Quiz which is a review of the entire lesson. Each students completes 1 problem at a time on the communicators. They must show me the correct answer before moving to the next. Students use their class notes to help them solve each problem. Students are reviewing each problem and completing it themselves while having fun using the communicators.
How will you help students to exhibit and self-evaluate their growing skills, knowledge, and understanding throughout the unit?
Throughout the lesson I call on all of my students to answer at least one question. The questions could be basic to complex. It is also review questions from previous material.
How will you tailor and otherwise personalize the learning plan to optimize the engagement and effectiveness of ALL students, without compromising the goals of the unit?
After the lesson is complete and students have a good understanding of the basic rules and procedures for solving multi-step inequalities, I will play a game. The game is when students are put in teams. Each team is completing against each other. Teams are put in rows and given 1 communicator and they will solve multi-step inequalities. Each member will solve only 1 step and pass it to their teammate until the problem is complete. The first team to have the correct answer receives bonus points. Here students are reviewing the lesson and having fun.
How will you organize and sequence the learning activities to optimize the engagement and achievement of ALL students?
I start with basic problems and progress to more difficult ones. The previous problems are also used to help answer the next problem. Students are excited to get the correct answer in the beginning and see how they can apply the basic problem when they get to a complex one. Also students need to practice the problems as the lesson moves on.
Wednesday, October 29, 2008
Wednesday, October 1, 2008
Pink
I decided to read Chapter 9, which focused on MEANING. MEANING is one of the six senses that Daniel Pink elaborated in his book. The six senses are essential in supporting the R-Directed side of the brain to complement our L-Directed reasoning.
MEANING has forced a new approach called logotherapy, which became an influential movement in psychotherapy. "Logos" the Greek word for meaning. MEANING is more then a definition according to Frankl "man’s main concern is not to gain pleasure or to avoid pain but rather to see a meaning in his life." The main goal in one’s life or drive is the pursuit of meaning. To find the MEANING is a drive that all human beings hold. It is possible to find MEANING through suffering or without any situation of hardship. Think about your life if it had no meaning.
Pink talked about two practical ways to begin the search for MEANING, which is spirituality and happiness. There is a strong relationship between the brain and spiritual experience. Such as reduced stress, heart disease and cancers. Spirituality shows us that life has some higher purpose and that will help lead to MEANING. Happiness will lead to the MEANING because an individual will look towards the good and fight off negative feelings. Pink explained three levels, which are "Pleasant Life", "Good Life" and "pursuit of meaning". When you reach the "pursuit of meaning" you know your highest strengths and you use them.
Pink ended with a summary of a best-selling book "Who Moved My Cheese?" The moral of the story is that change is inevitable, and when it happens, the wisest response is not to wail or whine but to suck it up and deal with it. This lead to the idea of a labyrinth where your goal is to follow the path to the center, stop and turn around and walk back out. So when you walk into the labyrinth, you begin to see your life because the purpose is the journey itself.
MEANING has forced a new approach called logotherapy, which became an influential movement in psychotherapy. "Logos" the Greek word for meaning. MEANING is more then a definition according to Frankl "man’s main concern is not to gain pleasure or to avoid pain but rather to see a meaning in his life." The main goal in one’s life or drive is the pursuit of meaning. To find the MEANING is a drive that all human beings hold. It is possible to find MEANING through suffering or without any situation of hardship. Think about your life if it had no meaning.
Pink talked about two practical ways to begin the search for MEANING, which is spirituality and happiness. There is a strong relationship between the brain and spiritual experience. Such as reduced stress, heart disease and cancers. Spirituality shows us that life has some higher purpose and that will help lead to MEANING. Happiness will lead to the MEANING because an individual will look towards the good and fight off negative feelings. Pink explained three levels, which are "Pleasant Life", "Good Life" and "pursuit of meaning". When you reach the "pursuit of meaning" you know your highest strengths and you use them.
Pink ended with a summary of a best-selling book "Who Moved My Cheese?" The moral of the story is that change is inevitable, and when it happens, the wisest response is not to wail or whine but to suck it up and deal with it. This lead to the idea of a labyrinth where your goal is to follow the path to the center, stop and turn around and walk back out. So when you walk into the labyrinth, you begin to see your life because the purpose is the journey itself.
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