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.
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3 comments:
Joel-
One piece that would help anchor this for kids would be an understanding of why inequalities are important. You outline a sequenced plan of instruction, but WHY is it important for students to know and then understand this? What would understanding of an inequality look like?
As a non-math person, I agree with Barry in saying I'd want to know why inequalities are important. Additionally, under the assessemnt evidence I would encourage you to create a role for students to take on, meaning place students into a real life situation where inequalities are necessary to solve a problem, and in turn, they have to present that solution to their audience.
It's hard for me to come up with a math situation for the "real problem", but to give you an idea of what I'm talking about, it's as if in English I would have students pretend to be reporters and write an article to be published in the local newspaper; hence it's a real life situation.
On the other hand, I like your other evidence - working in groups and have students write solutions on the board is a good way to monitor their understanding and at the same time allow students to teach each other. Good job!
Joe,
I think your lesson was well thought out. In my school, we have communicators. In essence, they are small white boards which allow us to have students practice while we are teaching. This affords us the ability to make sure that they are on task during the whole period. Great job with the content standards as well!
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