Learning Map Stage 2: Multi-Step Inequalities

This week we thought about the funds of knowledge our students bring into the classroom based on their experiences. What do we mean by funds of knowledge? All of the knowledge and experiences that they have before they enter our classroom! As teachers, we utilize cultural identities, language/linguistic assets, interests, and experiences when planning literacy activities for our students. When we learn and embed our students’ funds of knowledge into our learning activities, we understand more about how they learn, how they implement ideas, how they share their comprehension, and how to support them best. Dr. Yosso’s Cultural Wealth Model addresses six forms of cultural capital students of color experience in college. We also observed and analyzed this model in our K-12 environments by learning about the communities our students came from, their families’ assets, goals and dreams, communication skills, and how they navigated their world. The more we know about our students’ funds of knowledge, the better equipped we are to embed that knowledge and integrate it into teaching via texts and other literacy activities.

Our learning map continued this week as we wrote about our students’ assets, the content/activities of our lesson, and some of our assessment ideas. Our learning map provided opportunities for students to develop oral and written communication skills, access high-level text, and practice proficiency in new vocabulary. We were to remember that we were teaching our content and literacy – together! In Week 3, we had an opportunity to implement our completed learning map with a group of students!

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Focus Group Students (Examples / Case Studies)

Focus Group Student #2: Single Subject SM

SM is a 10^th grade student. He attended a traditional schooling for middle school and transferred from the same district. He has a very strong sense of self and appears to be comfortable in his own skin. He talks about his family and how much they have helped him and supported him. Being the oldest child, he has a sense of responsibility within this family. SM has been through very tragic life experiences including parental divorce, child abuse, homelessness, gang violence, and more. SM has been able to hold down a steady job at McDonald’s. He has a strong passion for music and rapping where he is able to express his emotions. He also loves to draw which helps him de-stress. SM’s fascination for cars and racing is utilized and implemented in the class as an incentive to try his hardest and produce his best effort and work. SM continuously strives to work on given tasks and assignments during allotted classroom time. He is currently at or above grade level in all academic subjects.

SM has been approaching staff to inquire about means to improve his classroom assessment scores in hope of achieving higher grades. He has involved a peer in the routine of going to teachers during lunch to ask for makeup work. Student still shows a need for supports initiating academic conversations with peers during group collaboration. SM is a bit more extroverted than the other students. He maintains a healthy relationship with fellow students in extracurricular activities and will engage in conversation them with some consistency. SM’s parents do not speak English and thus, are unable to assist him in his English language development journey. Gap identification indicates SM is limited English proficiency. He can engage in dialogue/discussion of the English language with ease but struggles with reading and writing. He reads at a lower first grade level.

Focus Student #5 (JB Special Ed.)

J.B. is a male, EL student with autism who receives specialized academic instruction (special education) services within a collaborative setting (general education). He is currently in the 9^th grade attending Johnson High School.  He learns best when using headphones and playing with a fidget. J.B. is working on self-regulation and self-advocacy. J.B. could benefit from taking notes online and additional instruction on math. He learns best when in a separate setting and with timed breaks. He is interested in computers and technology.  

JB comes from a single parent home with his mother and no siblings.  He lives in San Diego, CA, the Lincoln Park neighborhood.  He has transferred from different schools but within the same district about five times.  His mom is very supportive of his work and makes sure his work completion is on pace.

His IEP goals include the following:

• By annual review, when prompted by an adult Jacob will demonstrate an increased ability to take perspectives by identifying how his conversation partner might feel about Jacob’s own verbal and nonverbal communication and implementing a better alternative in 80% of opportunities with minimal adult support.
• By February, when given a vocational task, Jacob will demonstrate the ability to stay on task for 15 minutes and complete the task with no more than 2 prompts, in 2 of 4 core classes as measured by teacher observations.
• By February 2020, when given a set of 10 problems requiring division single-digit divisor and multiple digit multiplication, Jacob will solve with 80% accuracy in 3 out of 4 trials as measured by student work samples or teacher kept data.

His IEP Services and Supports including the following: 

• Specialized Academic Instruction
• Accommodations:
  • Direction given a variety of ways
  • Increased verbal response time
  • Preferential seating
  • Visual/picture supports
  • Calculator/multiplication table
  • Study Sheets
  • Extended time for completing assignments and tests
  • Breaks
  • Repeated review/drill
  • Small group instruction
  • Fidget/sensory object/rocking chair
  • Reminders to listen with whole-body (eyes on speaker, body calm and turned toward speaker, voice quiet)
  • Clarification of abstract/non-literal language
  • Use of self-talk by adult to make their own perspective clear (i.e. “I feel frustrated because students are talking”)

JB is independent and does not ask for help. He is self-motivated and will advocate for himself for breaks, etc. Possibly related to his autism, J.B. tends to spend most of his time by himself, rather than in groups or in large settings. He avoids social interaction and does not hold membership within the classroom.

The following is JB’s academic information:

• SBAC Math – Far Below Basic
• SBAC ELA – Far Below Basic
• MAPs (Measurement of Academic Performance) Fall ‘19
• Mathematics – 204
• ELA – 220
• ELA Grade – F
• Math Grade – F

J.B. doesn’t want people to think of him differently, so he doesn’t accept help often. This results in sustained struggle with academics, such as math which typically leads to him “shutting down.” His desire to be independent and not receive help has impacted his attendance, which has resulted in negatively impacting his ability to self-regulate as well as his grades.

Focus Student #6 A.S. Bilingual

A.S. is a 10th-grade student. She is new to the region and has little connection to the students and community here. Her mother recently had to spend a few weeks in the hospital, and A.S. needed to be sent to Arizona for the duration. She struggles academically due to chronic absenteeism, with the additional weight of being an English learner with all English curriculum. 

AS and her family are bilingual: Spanish and English. Dad, Mom, and Angel all have varied levels of fluency in both languages.  AS’s family is multi-ethnic: Central American and Mexican.  Both parents have different religious practices. She tends to spend most of her time by herself during her appointment hours for coursework at her resource center. She avoids social interaction and does not hold membership within the classroom likely due to her chronic absenteeism as a result of her anxiety.

Student is an excellent note-taker, and benefits greatly from laid out, color-coded notes. Student then can review these notes with tutors outside of school. Much of classwork is group discussion, and so this student may need extra prep to feel they can participate effectively. Assessment data shows that AS is an English Language Learner and has Limited English Proficiency. She will grow frustrated and upset if she perceives work as too difficult for her to complete. Parents both speak limited English, but Spanish is primarily spoken at home. Gap Identification indicates

• Mathematics
• Operations and Algebraic Thinking
• Area of Need
• Statistics and Probability
• Strength
• Reading
• Literature
• Vocabulary Acquisition and Use
• Informational Text

During class A.S. is a student who benefits from taking notes. A.S. is successful at self-advocacy and usually asks for help when she needs it. She could benefit from additional time in the classroom and direct one-on-one support for her academic fluency. 

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Write a Description of Students’ Assets and Learning Needs (Whole Class)

Prior academic knowledge related to the specific content you plan to teach

Describe what skills students already have coming into this lesson – what are they already able to do?

SM (10th Grade Student)

1. Academic Skills:
   • Currently at or above grade level in all academic subjects.
   • Strong passion for music, rapping, and drawing.
   • Fascination for cars and racing, used as an incentive in the classroom.
2. Work Ethic and Responsibility:
   • Holds down a steady job at McDonald’s, demonstrating a good work ethic.
   • Sense of responsibility as the oldest child in the family.
3. Interpersonal Skills:
   • More extroverted than other students.
   • Maintains a healthy relationship with fellow students in extracurricular activities.
   • Engages in conversation with peers with some consistency.
4. Language Skills:
   • Limited English proficiency but comfortable engaging in spoken English.
   • Struggles with reading and writing and reads at a lower first-grade level.

J.B. (EL Student with Autism, 9th Grade)

1. Learning Preferences:
   • Learns best when using headphones and playing with a fidget.
   • Benefits from online note-taking and additional math instruction.
   • Interested in computers and technology.
2. Social Skills:
   • Independent and self-motivated learner.
   • Tends to spend most of his time alone and avoids social interaction.
   • Successful in self-advocacy and asks for help when needed.
3. Academic Performance:
   • Far Below Basic performance in SBAC Math and ELA.
   • IEP goals include improving perspective-taking, task completion, and math accuracy.
4. Support Needs:
   • Receives Specialized Academic Instruction with various accommodations.
   • Reluctant to ask for help, impacting attendance and academic performance.

A.S. (10th Grade English Learner)

1. Language Skills:
   • Bilingual in Spanish and English.
   • Excellent note-taker, benefits greatly from color-coded notes.
   • Limited English proficiency and experiences frustration with challenging work.
2. Cultural and Family Background:
   • Multi-ethnic background (Central American and Mexican).
   • Both parents have different religious practices.
   • Spanish is primarily spoken at home.
3. Learning Preferences:
   • Successful at self-advocacy and usually asks for help when needed.
   • Benefits from laid out, color-coded notes and reviewing them with tutors.
4. Challenges:
   • Chronic absenteeism and struggles with academic fluency.
   • Anxiety related to academic challenges and social interaction.

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English language proficiency levels (Standard English learners and English learners)

List students and their CELDT or ELPAC levels

Student	CEDLT	ELPAC
SM	Early Intermediate	Early Intermediate
JB	Advanced	Advanced
AS	Early Advanced	Intermediate

Cultural and linguistic resources and funds of knowledge

Cultural resources and funds of knowledge

SM (10th Grade Student):

SM brings a wealth of cultural resources and funds of knowledge to the learning environment. His strong passion for music and rapping reflects a deep cultural connection and showcases artistic skills contributing to cultural expression within his community. His love for drawing is another valuable cultural resource, highlighting his creative abilities and potentially offering unique perspectives rooted in his cultural background.

SM’s work experience at McDonald’s demonstrates a fund of knowledge related to employment, responsibility, and work ethic. As the oldest child, he has a strong sense of responsibility, which, coupled with the support from his family, forms an additional fund of knowledge that contributes to his understanding of family dynamics and community support.

J.B. (EL Student with Autism, 9th Grade):

J.B. brings a set of unique cultural resources and knowledge to the educational setting. His profound interest in technology is a valuable cultural resource, reflecting his potential knowledge and skills related to technological advancements within his community. Additionally, J.B.’s tendency to spend most of his time alone may be attributed to cultural perspectives on individuality and personal space within his background. His success in self-advocacy represents a fund of knowledge related to understanding and expressing personal needs, potentially influenced by cultural perspectives on self-expression.

A.S. (10th Grade English Learner): A.S. brings a wealth of cultural knowledge and resources to the educational setting. Being bilingual in Spanish and English, she is an important resource in navigating different language communities and understanding cultural nuances. Her multi-ethnic background, which includes Central American and Mexican heritage, adds diverse cultural perspectives, traditions, and practices to her community. Additionally, her note-taking skills, particularly with color-coded notes, reflect knowledge of effective learning strategies and organizational skills rooted in her cultural context. Her understanding of family dynamics, including parents with different religious practices, provides additional cultural insight.

Linguistic resources and funds of knowledge

SM (10th Grade Student):

SM possesses a unique combination of linguistic abilities and knowledge. Despite having limited English reading and writing proficiency, he demonstrates comfort and creativity in spoken English, primarily through his passion for music and rapping. SM’s ability to express emotions and experiences through music and drawing showcases a distinctive form of linguistic and artistic proficiency. Furthermore, his work experience at McDonald’s involves practical use of the English language, contributing to his knowledge in the context of employment and everyday communication.

J.B. (EL Student with Autism, 9th Grade):

Being bilingual, J.B. has excellent proficiency in English and another language, which suggests a diverse linguistic background. His interest in technology implies exposure to specialized vocabulary and language related to this field. Additionally, J.B. has demonstrated his ability to express personal needs effectively, indicating communicative competency. His individualistic tendencies may reflect a distinct understanding and expression of language within his cultural and personal context.

A.S. (10th Grade English Learner):

Being fluent in English and Spanish, A.S. is adept at navigating multiple language communities and understanding cultural nuances. Her note-taking skills are exceptional, with her use of color-coded notes being an example of a linguistic resource that goes beyond language comprehension to effective learning strategies and organizational skills. A.S.’s multi-ethnic background, including Central American and Mexican heritage, adds to her linguistic repertoire. Furthermore, her understanding of family dynamics, such as parents with different religious practices, suggests nuanced communication skills and a depth of cultural and linguistic understanding.

Prior experiences and interests related to the content

How might you incorporate or build on their experiences and interests as assets to this lesson?

SM (10th Grade Student):

Music and Rapping: When teaching a lesson, it can be beneficial to incorporate music and rhythm to increase student engagement. You can do this using educational songs or rhythmic activities related to the lesson content. Additionally, you can provide opportunities for students to express the concepts they have learned through music or rap. This can involve creating lyrics or a rap that summarizes the lesson’s key points.

Drawing and Artistic Passion: Incorporating visual elements into the lesson can help SM leverage his drawing skills and better understand the concepts. Encourage him to create diagrams or visually represent ideas to aid his understanding. Additionally, incorporating art projects that relate to the lesson content can be helpful. These projects could include creating visual representations or drawings that connect to the subject matter.

Interest in Cars and Racing: Relate lesson concepts to cars and racing, showcasing practical applications. For example, use physics concepts in the context of racing or explore the technology behind modern vehicles.

J.B. (EL Student with Autism, 9th Grade):

Technology Interest: Integrate technology, such as educational apps, simulations, or interactive online resources, into the lesson related to the content. Also, explore coding activities or logic puzzles aligned with J.B.’s interest in technology.

Individualistic Tendencies: Provide opportunities for independent projects or research within the lesson framework. This allows J.B. to explore concepts at his own pace and in-depth.

Self-Advocacy Skills: Offer choices in assignments or learning paths. Allow J.B. to advocate for tasks that resonate with his interests, fostering autonomy.

A.S. (10th Grade English Learner):

Bilingualism: Celebrate A.S.’s bilingualism by incorporating both English and Spanish into the lesson. This could involve bilingual materials, discussions, or writing activities.

Excellent Note-Taking Skills: Share A.S.’s effective note-taking strategies with the class. Encourage collaborative notetaking or provide templates that align with her color-coded approach.

Multi-Ethnic Background: Integrate content that connects with A.S.’s multi-ethnic background. Explore literature, history, or cultural aspects that resonate with Central American and Mexican heritage.

Lesson management structure

What behavioral expectations will you model and expect?

Active Listening:

I will actively listen when students, colleagues, or guests speak, demonstrating the importance of attentive listening.

I expect students to actively listen during discussions, group activities, and when instructions are given.

Participation:

I will participate enthusiastically in class activities, discussions, and collaborative projects.

I expect students to actively engage in class activities, share their thoughts, and participate in discussions.

Responsibility:

I will consistently demonstrate responsibility by completing tasks and assignments with diligence.

I expect students to cultivate a sense of responsibility, emphasizing the importance of committing to academic tasks.

Effective Communication:

I will model effective communication, both verbally and in written expression, to provide a clear example for students.

I expect students to develop and refine practical communication skills, focusing on improving reading and writing proficiency.

Respectful Interaction:

I will model respectful interactions with peers, teachers, and others to set a positive tone in the classroom.

I expect students to actively foster a positive and inclusive atmosphere by treating others with kindness and respect.

Self-Advocacy:

I will model self-advocacy by expressing my needs and preferences clearly and confidently.

I expect students to observe and learn self-advocacy skills, expressing their needs and preferences effectively.

Social Interaction:

I will demonstrate positive social interactions during group activities, providing an example for students to follow.

I expect students to actively participate in group settings, gradually increasing social interactions in a structured and supportive environment.

Collaboration:

I will model effective collaboration and teamwork during group projects, providing a demonstration for students.

I expect students to engage in collaborative efforts actively, fostering a positive and inclusive environment that values everyone’s strengths and contributions.

Inclusivity:

I will create an inclusive environment that values diversity and different perspectives.

I expect students to value and embrace diversity in their classmates’ backgrounds and experiences.

Flexibility:

I will demonstrate flexibility in adapting to the needs of individual students.

I expect students to recognize the need for varied support strategies and encourage a flexible approach to learning.

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Content of the Lesson

What do you expect students to deeply understand about the lesson? What do you expect students to retain after the lesson and use in future learning?

Deep Understanding During the Lesson:

Understanding of Multi-Step Inequalities: Students should grasp the concept of multi-step inequalities, understanding that they involve a series of operations to isolate a variable.

Procedural Competence: Students should be able to skillfully apply the steps involved in solving multi-step inequalities, including addition, subtraction, multiplication, and division.

Application of Mathematical Properties: Students should demonstrate an understanding of mathematical properties, such as the addition and multiplication properties of inequalities, and apply them appropriately during problem-solving.

Problem-Solving Skills: Students should develop problem-solving skills to choose appropriate strategies and steps to solve different types of multi-step inequalities.

Retention and Future Application:

Transferability of Skills: Students should retain the ability to apply the principles learned in solving multi-step inequalities to more complex mathematical problems in the future.

Connection to Real-World Scenarios: Students should recognize and apply the concept of multi-step inequalities to real-world situations, making connections between mathematical concepts and everyday scenarios.

Integration with Algebraic Concepts: Students should integrate the knowledge gained in solving multi-step inequalities with other algebraic concepts, such as linear equations and systems of equations.

Critical Thinking: Students should develop critical thinking skills, allowing them to analyze problems, make informed decisions about the steps needed, and justify their solutions.

Continuous Learning: Students should see the lesson as part of a continuous learning process, building on their understanding of inequalities to tackle more advanced algebraic concepts in subsequent lessons.

What misunderstandings or misconceptions do you expect students might have from the lesson?

Direction of the Inequality Symbol: Students might struggle with the direction of the inequality symbol when performing operations on both sides of the inequality.

Order of Operations: Students may forget or misapply the order of operations, leading to errors in solving multi-step inequalities.

Combining Like Terms: Students might struggle with combining like terms accurately, especially when dealing with multiple variables or constants.

Distributive Property: Students may forget to apply the distributive property correctly, leading to errors in simplifying expressions.

Confusion with Absolute Values: Students may encounter confusion when dealing with absolute values within inequalities.

Forgetting to Check Solutions: Students might neglect to check their solutions after solving the inequality, potentially leading to incorrect answers.

Inconsistent Sign Errors: Students may make inconsistent sign errors when combining terms or applying operations.

What knowledge and skills do you expect students to have after engaging in the lesson?

Knowledge:

Understanding of Multi-Step Inequalities: Students should comprehend the concept of multi-step inequalities, recognizing that they involve a series of operations to isolate a variable.

Order of Operations (PEMDAS): Students should be familiar with and apply the order of operations (PEMDAS) when simplifying expressions within multi-step inequalities.

Distributive Property: Students should understand and apply the distributive property when dealing with expressions containing parentheses.

Rules for Absolute Values: Students should be familiar with the rules and strategies for solving inequalities involving absolute values.

Inverse Operations: Students should grasp the concept of using inverse operations to isolate the variable and solve for the unknown in multi-step inequalities.

Solution Checking: Students should understand the importance of checking solutions by substituting them back into the original inequality to verify their accuracy.

Skills:

Solving Multi-Step Inequalities: Students should be able to solve multi-step inequalities systematically, applying appropriate operations to isolate the variable.

Applying Inequality Symbols: Students should correctly use the inequality symbols (>, <, ≥, ≤) when expressing relationships between expressions.

Combining Like Terms: Students should effectively combine like terms, especially when dealing with expressions containing variables and constants.

Analyzing and Interpreting Solutions: Students should be able to analyze and interpret the meaning of solutions in the context of the given problem or real-world scenario.

Translating Word Problems into Inequalities: Students should demonstrate the ability to translate word problems into mathematical inequalities, identifying the appropriate operations to solve them.

Applying Mathematical Properties: Students should apply mathematical properties, such as the addition and multiplication properties of inequalities, appropriately during problem-solving.

Critical Thinking in Problem-Solving: Students should develop critical thinking skills, making informed decisions about the steps needed to solve different types of multi-step inequalities.

Recognizing Patterns in Solutions: Students should be able to recognize patterns in the solutions of various multi-step inequalities and apply similar strategies to new problems.

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Assessment / Checking for Understanding

What essential questions will you ask to determine if students are not meeting, meeting, or exceeding the learning goal(s) of the lesson?

Not Meeting the Learning Goals

Conceptual Understanding

Question: Can you explain the key steps involved in solving a multi-step inequality?

Indicators for Not Meeting: Difficulty articulating the sequential steps or demonstrating a lack of conceptual understanding.

Procedural Application

Question: Can you solve a multi-step inequality and isolate the variable using the correct operations?

Indicators for Not Meeting: Inconsistent application of operations, frequent errors in the solution process, or reliance on memorization without understanding.

Error Analysis

Question: If an error is made in the solution process, can you identify and explain where the mistake occurred?

Indicators for Not Meeting: Difficulty recognizing and analyzing errors, indicating a limited ability to self-assess and correct mistakes.

Meeting the Learning Goals

Application to Real-World Scenarios:

Question: How would you apply the concept of multi-step inequalities to represent a real-world situation?

Indicators for Meeting: Demonstrating an ability to connect the mathematical concept to practical scenarios, showcasing a transfer of knowledge.

Problem Variation:

Question: Can you solve a multi-step inequality when the structure of the problem is slightly altered?

Indicators for Meeting: Successfully adapting problem-solving strategies to address variations in problem structures.

Explanation of Solution Process:

Question: Explain the reasoning behind each step when solving a specific multi-step inequality.

Indicators for Meeting: Providing clear and coherent explanations, demonstrating a deep understanding of the solution process.

Exceeding the Learning Goals:

Generalization of Concepts:

Question: How would you generalize the principles learned in multi-step inequalities to solve more complex mathematical problems?

Indicators for Exceeding: Demonstrating an ability to extend the learned concepts to tackle advanced mathematical challenges.

Connection to Other Algebraic Concepts:

Question: How does the knowledge gained in solving multi-step inequalities connect to other algebraic concepts you’ve learned?

Indicators for Exceeding: Exhibiting a comprehensive understanding of how the current lesson integrates with and enhances broader algebraic principles.

Application to Critical Thinking:

Question: In what ways can critical thinking be applied when solving multi-step inequalities, and why is it important?

Indicators for Exceeding: Offering insightful perspectives on the role of critical thinking, showcasing a high-level understanding of the subject matter.

What will students do to demonstrate achievement of content during the lesson? Identify the UDL Principle Guidelines incorporated.

Problem-Solving Stations

Activity Description:

I will create stations with different types of multi-step inequality problems.

Students move through the stations, solving problems collaboratively.

UDL Principle Guidelines Incorporated:

Multiple Means of Representation: Provide visual and auditory representations of problems at each station.

Multiple Means of Engagement: Allow for flexible groupings, enabling students to choose partners or work independently.

Real-World Application Project

Activity Description:

I will assign a real-world scenario that requires creating and solving a multi-step inequality.

Students present their solutions and explain mathematical reasoning.

UDL Principle Guidelines Incorporated:

Multiple Means of Representation: Offer a variety of real-world scenarios to cater to diverse interests and backgrounds.

Multiple Means of Action and Expression: Allow students to choose how they present their solutions (e.g., written report, oral presentation, or visual display).

Interactive Online Simulations

Activity Description:

I will utilize online platforms or simulations to present multi-step inequalities in a dynamic and engaging way.

Students will interact with and solve multi-step inequalities online.

UDL Principle Guidelines Incorporated:

Multiple Means of Representation: Provide visual and interactive representations of inequalities through the online platform.

Multiple Means of Engagement: Cater to different learning preferences by offering both visual and auditory cues within the simulation.

Peer Teaching and Reflection

Activity Description:

I will have students work in pairs to teach each other how to solve specific types of multi-step inequalities.

Students will reflect on their teaching experience.

UDL Principle Guidelines Incorporated

Multiple Means of Action and Expression: Allow students to choose how they present their teaching (e.g., written explanation, demonstration).

Multiple Means of Engagement: Encourage collaboration and peer teaching to foster a supportive learning community.

Formative Quizzes with Immediate Feedback

Activity Description:

I will administer short quizzes throughout the lesson, providing immediate feedback to guide students in correcting errors.

Students will quickly understand correct answers, learn from mistakes, and address any misconceptions in real-time.

UDL Principle Guidelines Incorporated:

Multiple Means of Representation: Present questions in various formats, including multiple-choice, short answer, and graphical representation.Multiple Means of Action and Expression: Allow students to choose the format in which they receive feedback (e.g., written comments, verbal feedback).

How will you know students understand the content? What evidence will you collect? Identify the UDL Principle Guidelines incorporated.

Observations during Collaborative Activities

Evidence Collection:

I will observe students working collaboratively on problem-solving activities related to multi-step inequalities.

UDL Principle Guidelines:

Multiple Means of Engagement: Observing how students actively engage with their peers during collaborative activities provides insights into their understanding.

Exit Tickets or Reflection Journals

Evidence Collection:

I will use exit tickets or reflection journals where students summarize the key concepts learned in the lesson.

UDL Principle Guidelines:

Multiple Means of Representation: Students can choose how they express their understanding, whether through writing, drawing, or a combination of methods.

Concept Maps or Graphic Organizers

Evidence Collection:

I will ask students to create concept maps or graphic organizers illustrating the relationships between different steps in solving multi-step inequalities.

UDL Principle Guidelines:

Multiple Means of Representation: Providing visual tools allows students to represent their understanding in diverse ways.

Peer Teaching and Feedback

Evidence Collection:

I will facilitate peer teaching sessions where students explain multi-step inequality concepts to their peers, followed by peer feedback.

UDL Principle Guidelines:

Multiple Means of Action and Expression: Students can express their understanding through teaching and receive feedback from diverse perspectives.

Interactive Whiteboard or Virtual Platforms

Evidence Collection:

I will use interactive whiteboards or virtual platforms where students can visually solve and explain multi-step inequalities.

UDL Principle Guidelines:

Multiple Means of Representation: Visual and interactive platforms cater to various learning styles.

Student-Generated Questions

Evidence Collection:

I will have students generate questions related to multi-step inequalities and answer questions posed by their peers.

UDL Principle Guidelines:

Multiple Means of Engagement: This activity engages students in both creating and responding to questions, fostering deeper understanding.

Formative Quizzes with Immediate Feedback

Evidence Collection:

I will administer formative quizzes with immediate feedback to gauge students’ comprehension and identify areas of improvement.

UDL Principle Guidelines:

Multiple Means of Action and Expression: Quizzes can be designed with various question formats to accommodate different learning preferences.

Performance-Based Tasks

Evidence Collection:

Assign performance-based tasks where students apply multi-step inequality concepts to real-world scenarios.

UDL Principle Guidelines:

Multiple Means of Engagement: Real-world tasks appeal to different interests and backgrounds, engaging students in meaningful applications.

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Structured Student Learning Activities

What activities will the students be involved in during the lesson to support their achievement of the learning goal(s)? Identify the UDL Principle Guidelines incorporated.

Guided Problem-Solving Exercises

Activity Description: Walk students through step-by-step solutions to multi-step inequality problems, providing explanations and demonstrations.

UDL Principle Guidelines:

Multiple Means of Representation: Visual and verbal explanations cater to different learning preferences.

Multiple Means of Engagement: Engages students with clear, guided examples to build confidence.

Collaborative Group Work

Activity Description: Assign students to small groups to solve multi-step inequalities collaboratively. Each group member has a specific role, such as a scribe, solver, and checker.

UDL Principle Guidelines:

Multiple Means of Engagement: Collaboration encourages active participation and diverse perspectives within the group.

Multiple Means of Action and Expression: Assigning specific roles allows students to contribute based on their strengths.

Interactive Whiteboard Practice

Activity Description: Use an interactive whiteboard or digital platform where students can practice solving multi-step inequalities by dragging and manipulating equations.

UDL Principle Guidelines:

Multiple Means of Representation: Visual and interactive platforms provide diverse representations of problems.

Multiple Means of Engagement: Appeals to digital learners and allows for hands-on engagement.

Real-World Scenario Applications

Activity Description: Present students with real-world scenarios that require setting up and solving multi-step inequalities (e.g., budgeting, time management).

UDL Principle Guidelines:

Multiple Means of Engagement: Real-world scenarios connect the lesson to practical applications and students’ lives.

Multiple Means of Action and Expression: Encourages creativity in applying math to solve everyday problems.

Peer Teaching and Feedback

Activity Description: Allow students to take turns explaining multi-step inequality concepts to their peers and provide constructive feedback.

UDL Principle Guidelines:

Multiple Means of Engagement: Promotes peer interaction and active learning.

Multiple Means of Action and Expression: Gives students opportunities to express their understanding through teaching.

Formative Quizzes with Immediate Feedback

Activity Description: Administer short quizzes during the lesson to assess understanding, with immediate feedback provided for each question.

UDL Principle Guidelines:

Multiple Means of Representation: Quizzes can include various question formats catering to diverse preferences.

Multiple Means of Action and Expression: Allows students to demonstrate their understanding and receive timely feedback.

How will you group students and manage group work to support student learning? Identify the UDL Principle Guidelines incorporated.

Grouping Strategy: Employ flexible grouping that allows students to work in various configurations, such as pairs, small groups, or larger teams.

UDL Principle Guideline: Multiple Means of Engagement: Flexible grouping accommodates diverse learning preferences and social interactions, promoting student engagement.

Grouping Strategy: Assign different roles within each group, such as a scribe, solver, checker, and reporter. Rotate roles to ensure everyone experiences various responsibilities.

UDL Principle Guidelines: Multiple Means of Action and Expression: Providing roles ensures students can contribute based on their strengths and preferences, fostering a sense of autonomy.

Grouping Strategy: Consider students’ interests and strengths when forming groups. Encourage students to share their interests, which can guide group topic selection for real-world applications.

UDL Principle Guidelines: Multiple Means of Engagement: Incorporating student interests into group work promotes engagement by connecting the lesson to their personal passions.

Grouping Strategy: Clearly communicate the group’s objectives, expectations, and shared goals. Ensure that each group understands its purpose and tasks.

UDL Principle Guidelines: Multiple Means of Representation: Providing clear instructions and objectives in various formats ensures that all students understand their roles and responsibilities.

Grouping Strategy: Use diverse criteria for grouping, such as mixed abilities, learning styles, or personalities. Occasionally mix up group compositions to encourage interactions with a range of peers.

UDL Principle Guidelines: Multiple Means of Engagement: Diverse grouping criteria promote social interaction and cooperation among students with varying backgrounds and abilities.

Grouping Strategy: Allocate structured time for collaboration within groups. Provide clear guidelines on when group work begins and ends.

UDL Principle Guidelines: Multiple Means of Action and Expression: Structured collaboration time ensures students can express their understanding and contribute to the group.

Grouping Strategy: Encourage peer feedback and self-assessment within groups. Students can provide constructive feedback to their peers and reflect on their contributions.

UDL Principle Guidelines: Multiple Means of Action and Expression: Peer feedback and self-assessment offer multiple ways for students to express their understanding and self-regulate their learning.

Grouping Strategy: Be prepared to address collaboration challenges promptly, such as conflicts or communication difficulties, and provide guidance for effective teamwork.

UDL Principle Guidelines: Multiple Means of Engagement: Supporting collaboration challenges ensures all students can engage effectively in group work.

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Instruction to Support Learning

What instructional strategies will support student learning through multiple modalities? How will you use gradual release? Identify the UDL Principle Guidelines incorporated.

Gradual release: State, specifically, what you will do to model your instructional strategy (I do), how you will engage the children in order to receive immediate feedback on what they are understanding and learning (We do), and how will you specifically ask the children to apply this understanding and learning (You do). 

I Do (Teacher Modeling)

During the initial phase of the lesson, I will play the role of the instructor to demonstrate the concept of multi-step inequalities. To begin, I will introduce the fundamental idea, and provide clear explanations and illustrative examples on the board. For instance, I may present a problem such as “2x – 5 > 7” and guide the students through each step of the solution process, emphasizing the importance of isolating the variable. Additionally, I will utilize questioning techniques to verify comprehension periodically. I will ask questions such as “Can someone explain why we’re adding 5 to both sides in this step?” or “What happens to the inequality sign when we multiply or divide by a negative number?” to ensure students understand the key concepts.

We Do (Guided Practice):

Moving on to the next phase, we will commence with guided practice, where students will actively solve multi-step inequalities collaboratively. I will provide a set of problems for the students to work on in pairs or small groups while I circulate around the classroom, offering assistance and observing students’ problem-solving processes. The objective of this stage is to encourage interaction among students, allowing them to learn from one another and practice applying the concepts they’ve learned. I will facilitate class discussions during this phase, encouraging students to share their approaches and solutions, while addressing any common misconceptions or challenges that may arise. Immediate feedback will be a crucial component of this phase.

You Do (Independent Practice):

During the final stage, students can showcase their proficiency in multi-step inequalities through independent practice. I will provide them with a set of problems that are in line with the concepts covered during the guided practice sessions. Students will be encouraged to solve the problems independently and check their work for accuracy. Additionally, they will be prompted to reflect on their problem-solving strategies to develop their metacognitive skills and self-assessment.

As the teacher, I will evaluate and analyze the independent practice work submitted by the students to assess their comprehension of the concepts. This assessment data will help me to refine my teaching approach and tailor it to the individual needs of each student while addressing any misconceptions they may have.

UDL Principles Employed

Multiple Means of Representation: In the “I Do” phase, I will employ multiple means of representation by using verbal explanations and written examples on the board to introduce the concept of multi-step inequalities. During guided practice (“We Do”), diverse problem-solving approaches will be encouraged, accommodating different learning preferences.

Multiple Means of Engagement: The gradual release model promotes engagement through active participation in each phase, from teacher modeling (“I Do”) to collaborative problem solving (“We Do”) and independent practice (“You Do”). Group work in the “We Do” phase fosters social interaction and cooperation, appealing to students with varying backgrounds and abilities.

Multiple Means of Action and Expression: In the “You Do” phase, students will be given opportunities for independent problem-solving, allowing them to express their understanding in their preferred manner. The model encourages self-checking and reflection, promoting metacognition and self-assessment.

What resources, materials, and/or educational technology will you or your students use during the lesson?

Whiteboard or Chalkboard: Traditional whiteboards or chalkboards will be used for teacher modeling (I Do) and collaborative problem-solving (We Do). These provide a visible platform for working through examples and explanations.

Markers, Chalk, or Whiteboard Pens: Writing tools will be used on the whiteboard or chalkboard to illustrate equations, inequalities, and problem-solving steps.

Paper and Pencils: Students will need these basic materials to jot down notes, work through problems independently, and engage in collaborative activities.

Printed Worksheets: Guided practice and independent practice worksheets will be distributed to students to practice solving multi-step inequalities.

Real-World Scenario Materials: To introduce real-world applications, materials such as budgeting worksheets, time management scenarios, or hypothetical situations may be used to create a context for problem-solving.

Interactive Whiteboard or Projector: An interactive whiteboard or projector can display digital versions of problems, solutions, and interactive activities, enhancing visual representations.

Laptops or Tablets: If available, students may use laptops or tablets to access digital resources, complete online practice problems, or engage with educational software.

What adaptations and accommodations, including, as appropriate, assistive technologies, will support individual student learning needs beyond the UDL supports built into the lesson?

Extended Time for Assignments and Assessments: Provide students with additional time to complete assignments and assessments if they have documented learning disabilities or conditions that require extra time.

Alternative Formats for Content: Offer content in alternative formats, such as audio recordings, digital texts, or large-print materials, to accommodate students with visual or reading impairments.

Assistive Technology Tools: Integrate assistive technology tools like speech-to-text software, text-to-speech applications, or screen readers to support students with various disabilities.

Individualized Instruction: Tailor instruction to meet students’ individual learning needs by providing additional explanations, practice, or alternative approaches to challenging concepts.

Note-Taking Assistance: Provide students with note-taking assistance, such as access to peer notes, note-taking apps, or using scribes when handwriting is challenging.

Visual Supports: Utilize visual supports like graphic organizers, charts, diagrams, and visual schedules to aid comprehension and organization for students with learning differences.

Flexible Seating and Physical Accommodations: Offer flexible seating options or physical accommodations for students with mobility impairments or sensory processing needs.

Modified Assessments: Modify assessments to align with individual students’ needs, including alternate assessment formats, simplified language, or adjusted difficulty levels.

Alternative Assignments: Allow students to choose or create alternative assignments that align with their interests and strengths while addressing learning objectives.

Peer Support: Assign peer mentors or classroom aides to provide one-on-one support and guidance for students who require additional assistance.

Individualized Goals and Progress Monitoring: Set individualized learning goals for students and regularly monitor their progress to ensure they are making meaningful strides in their learning.

Collaboration with Specialists: Collaborate with special education teachers, speech therapists, occupational therapists, and other specialists to provide targeted support.