A. Unit Overview:
- Content Area: Pre-Algebra
- Unit Title: Solving and Writing Equation and Inequalities
- Target Course/Grade Level: Math/5th grade
- Instructor’s Name: Dee Niederberger
- School: Pennsauken Intermediate School
- Date: July 23, 2011
- Unit Summary: Solving and Writing Equations and Inequalities will begin with solving one step addition and subtraction equations. From there the students will move on to solving one step multiplication and division equations. Number lines will then be introduced and the students will graph equalities and inequalities on number lines. Finally, tables and values will be interpreted to find patterns and create equations for the set of table values.
- Primary interdisciplinary connections: Science, Language Arts
- 21st century themes: Financial, Economic, Business, and Entrepreneurial Literacy
- 21st century skills: Critical Thinking and Problem Solving
- Unit Rationale: Solving and Writing Equations and Inequalities will set the foundation for solving and making equations. The students will also gain an understanding of the use of inequalities. Students will further analyze numbers to describe and create patterns using tables, simple equations and graphs.
B. Learning Targets :
Common Core Standards :
- Write and interpret numerical expressions.
- 5.OA.1. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
- 5.OA.2. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.
- Analyze patterns and relationships.
- 5.OA.3. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.
2. Standards for Mathematical Practice
- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.
3. Unit Essential Questions:
- How can an equation be solved using addition and subtraction and multiplication and division?
- How can inequalities be graphed on a number line?
- How can a rule be written for a pattern to complete a table?
- How can equations be written to solve problems?
4. Unit Enduring Understandings:
- Properties of equality and inverse operations can be used to solve addition and subtraction equations and multiplication and division equations. The solutions can be checked by substitution.
- Patterns can help identify the relationship between quantities.
- Real world problems can be solved with equations to determine profit, expenses, revenue, rates etc.
C. Evidence of Learning:
- Summative Assessments
- Unit Test
- Unit Project Factoid
- Formative Assessments
- Exit Cards
- Quick Checks
- Independent practice
- Student responses
- Teacher observations
D. Equipment / Resources
- Equipment / Technology needed throughout the Unit:
- SMART board
- Document camera
- Manipulatives (colored chips, marbles, and scale)
Teacher Resources: Envision MATH program, Topic 15, Pearsonsuccess.net
E. Lesson Plan Topics / Titles:
Lesson 1: Solving addition and subtraction equations
Lesson 2: Solving addition and subtraction equations part 2
Lesson 3: Solving multiplication and division equations
Lesson 4: Solving multiplication and division equations part 2
Lesson 5: Inequalities on the number line
Lesson 6: Patterns and equations
Lesson 7: Problem solving: write an equation
Lesson 8: Unit Review
F. Teacher Notes about Lesson Plans
- Begins with an activity to connect to Previous Knowledge and to Student Interest / Preferences.
- Includes High Quality Curriculum – See Teacher Resources – D2
- Includes Flexible Grouping via:
- Scavenger hunt
- Think-Pair- Share
- Tic -Tac -Toe Choice Board
- Cooperative learning groups
- Leveled Homework
- Whole class
- Independent Practice
- Provides Respectful Tasks within a Supportive Learning Environment via Multiple Means. (see next page)
G. Universal Design for Learning Options
- Multiple Means of Representation
Guideline 1: Provide options for perception
Guideline 2: Provide options for language, mathematical expressions, and symbols
Guideline 3: Provide options for comprehension
- The Mathematics Glossary uses multiple means of representation to explain and reinforce concepts. Multiple exposures to vocabulary and symbols through various forms of representation increase depth of knowledge. This free online glossary defines mathematical terms and concepts through text, images, and examples relating to real world applications http://www.ronblond.com/MathGlossary/
2. Multiple Means of Action and Expression
Guideline 4: Provide options for physical action
- AIM are specialized formats of curricular content that can be used by and students with print-disabilities. They include formats such as Braille, audio, large print, and electronic text. The audio and the electronic text formats are excellent examples of providing options in the mode of physical response for students who have difficulty turning pages or holding a book.
Guideline 5: Provide options for expression and communication
- SAM Animation is software designed to give students the power of making stop-action movies to share their ideas and understanding. The software is easy to use and provides a unique experience for students to explore challenging problems in any subject through creating animations.
- SAM provides a unique and engaging way for students to communicate their ideas http://www.samanimation.com/
Guideline 6: Provide options for executive functions
- Elona Hartjes shares the insights, resources, and practical classroom strategies that have earned her A Teacher of Distinction Award.
- Elona's post "Helping my students set goals the smart way" offers ideas on effective goal-setting.
3. Multiple Means of Engagement
Guideline 7: Provide options for recruiting interest
- Industrial Revolution Tic-Tac-Toe - Learn how two teachers from Columbus East High School in Columbus, IN created a unique way for students to choose projects on the Industrial Revolution. These teachers won the U.S. Innovative Teachers Forum and went on to the Microsoft Worldwide Innovative Teachers Forum in Brazil to represent the United States. Industrial Revolution Tic Tac Toe is a great example of providing students with individual choice. Encouraging students to choose from different projects increases student creativity and engagement. http://vimeo.com/6104437
Guideline 8: Provide options for sustaining effort and persistence
- Use touch equivalents (tactile graphics or objects) for key visuals that represent concepts. Touch equivalents allow the use of tactual sensory options to access the information as typically available visually or verbally.
Guideline 9: Provide options for self-regulation
- This website addresses the coping brain, coping challenges and coping skills and tools. It is geared toward parents and educators of pre-teens and addresses the varying ways one can cope and learn to cope. The site is also rich with resources and activities.
- This website is loaded with tips on how to scaffold students' coping skills and strategies! http://www.copingskills4kids.net/
H. Online Resources :
The following websites were used in preparing additional strategies, accommodations, and modifications in the above lessons: