Learning Map – Stage 2: Word Problems

Knowing our students is the key to not only meaningful teaching but also effective content literacy instruction. By knowing our students’ talents, cultural experiences, interests, and learning needs, we can ensure our pedagogical decisions are student-centered, empowered, and engaging. As teachers, getting to know our students is just as important as getting to know our learning outcomes and assessment strategies. Forming positive relationships with our students will ensure that students can access and succeed in our content-literacy classrooms!

This week, we will continue building out our Learning Map with an emphasis being placed on getting to know our students and what they are bringing into the classroom. We will be writing about student assets, learning needs, language development, and funds of knowledge while using that information to inform our instructional planning to develop assessments, activities, and content. We were to think about ways to bring our students into the lesson and be creative while doing so!

Focus Group Students

Focus Group Student #2: Single Subject SM

SM is a 10th-grade student. He attended 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 the 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 support 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 with 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 has 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 #3 – ER: EL Learner/Gen. Ed.

“No good deed goes unpunished” is a reflection of this student’s life.  ER was born in Mexico to parents that succumbed when he was 4 years old.  He is in the 7th grade at Rock Hill Middle School, an urban school located in East Los Angeles. As a result, his Los Angeles aunt adopted him along with his four siblings. However, she passed away recently resulting in ER and his siblings being sent to foster parents.  

Due to speaking only Spanish with his parents and aunt, he has limited English proficiency. He takes pride in his Mexican heritage and finds comfort in the experience he shares with many of his peers and their ability to converse in both English and Spanish. He can engage in discussion of the English language with ease but struggles with reading and writing, most notably in the area of decoding. As a result of his foster parents only speaking Spanish, he does not speak English at home and does not receive support in his English language development at home.

ER is a first-generation student who feels connected to the Mexican and Latinx presence and culture present within his community. He is able to communicate with fellow peers and bring his native language with him into the classroom, given majority of the students in the classroom are dual English and Spanish speakers

ER’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. ER maintains a close relationship with his siblings, who offer him support as he transcends adolescence 

ER’s introverted nature limits his interactions with his peers and his chances to work with other students. ER is a bit more introverted than the other students. He maintains a healthy relationship with fellow students and will engage in conversation with them with some consistency – ER’s parents do not speak English and, thus, are unable to assist him in his English language development journey. 

His classwork and curriculum may often not incorporate culturally relevant pedagogy or reflect relatable material, leading to disengagement from the lesson. He is familiar with all letters of the alphabet and their corresponding sounds but struggles in sound blending and decoding of multisyllabic words. As a result, he is hesitant to read out the whole group, given his limited vocabulary

The following is some background on his academic level:

• Limited English proficiency. He can engage in dialogue/discussion of the English language with ease but struggles with reading and writing –
• Reads at a lower first-grade level. 
• His current grade in ELA is an F, but he does have a B in Math and a C in Science. He is passing his PE class with a solid A.

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 9th 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, in 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 include the following: 

• Specialized Academic Instruction
• Accommodations:
  • Direction is given in a variety of waysIncreased verbal response timePreferential seatingVisual/picture supportsCalculator/multiplication tableStudy SheetsExtended time for completing assignments and testsBreaksRepeated review/drillSmall group instructionFidget/sensory object/rocking chairReminders to listen with whole body (eyes on the speaker, body calm and turned toward the speaker, voice quiet)Clarification of abstract/non-literal language
  • Use of self-talk by adults 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 an 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.

The student is an excellent note-taker and benefits greatly from laid-out, color-coded notes. The student then can review these notes with tutors outside of school. Much of classwork is group discussion, 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.

Prior Academic Knowledge Related to Mathematics

Describe what skills students already have coming into this lesson – what are they already know and are able to do as it relates to content area literacy?

• Basic Arithmetic Skills: Students usually have a strong understanding of fundamental arithmetic operations such as addition, subtraction, multiplication, and division and are familiar with working with fractions, decimals, and percentages.
• Algebraic Foundations: Most students are familiar with basic algebraic concepts such as variables, simple equations, and inequalities and can manipulate these expressions.
• Geometric Concepts: Students typically possess foundational knowledge of geometry, such as understanding various shapes, the basic properties of these shapes, and fundamental concepts like perimeter, area, and volume.
• Numerical and Graphical Data Interpretation: Students typically possess skills in interpreting basic graphs and charts, recognizing trends and patterns in data, and performing fundamental statistical calculations such as mean, median, and mode.
• Mathematical Vocabulary and Language: Students understand key mathematical terms, including those specific to algebra, geometry, and basic statistics, enabling them to use them in problem contexts.
• Problem-Solving Skills: Students typically possess varying levels of math proficiency but can follow multi-step procedures to solve problems.
• Reading Comprehension: Students can read and comprehend texts, which is crucial for understanding word problems. They can identify key information in a text and understand instructions or descriptions.
• Basic Logical Reasoning: Students have acquired fundamental logical reasoning skills that allow them to construct or follow logical arguments and draw inferences based on given information.
• Experience with Technology: Many students are familiar with using basic technology, such as calculators and computers, which can aid in solving mathematical problems.Collaborative and Independent Work: Students are familiar with both group work and independent assignments.

English Language Proficiency Levels

List students and their CELDT or ELPAC levels.

• SM (Focus Student #2) – Level 3 (Developing): SM can converse in English but requires assistance with reading and writing, particularly in academic settings.
• ER (Focus Student #3) – Level 2 (Emerging): ER faces significant challenges reading and writing in English due to his limited proficiency. Although he can communicate at a basic level in spoken English, he struggles with decoding and comprehending written English. This indicates a need for significant support in English literacy.
• JB (Focus Student #5) – It is not possible to accurately determine JB’s CELDT or ELPAC level based on the provided information, as his primary challenges are related to autism rather than English language proficiency. Although his language proficiency may align with his grade level, his learning strategies and support differ due to his autism.
• A.S. (Focus Student #6) – Level 2/3 (Emerging/Developing): A.S. is bilingual and has difficulties with chronic absenteeism. Additionally, she has an all-English curriculum, which has likely resulted in her having only a basic to fair command of English. Although she may be able to converse, she requires support in academic English, particularly in reading and writing.

Cultural and Linguistic Resources and Funds of Knowledge

Cultural resources and funds of knowledge

SM (Focus Student #2)

• Family and Community Responsibilities: SM has developed resilience, responsibility, and maturity due to being the oldest child in the family and experiencing significant life challenges.
• Interest in Music and Art: SM’s interest in music and art, particularly rapping and drawing, can be utilized as tools for self-expression and creativity in learning activities.
• Work Experience: SM’s work experience at a fast-food restaurant has provided practical skills in time management, customer service, and basic financial literacy.

ER (Focus Student #3)

• Bilingual and Bicultural: ER’s ability to speak both Spanish and English and his connection to his Mexican heritage provides a valuable linguistic and cultural perspective and can help foster a sense of identity and pride.
• Experiences of Resilience: Having faced significant personal losses and transitions, ER brings a depth of resilience and adaptability.
• Interest in Cars and Racing: This fascination can be tapped into for learning, using real-world examples related to mechanics or physics that resonate with his interests.

JB (Focus Student #5)

• Technological Affinity: JB’s interest in computers and technology can be a significant asset, especially in a math classroom where technology can be used for simulations, calculations, and visualizations.
• Self-Regulation Skills: JB’s ability to advocate for his own needs and his work on self-regulating behaviors can be harnessed to create a learning environment that he finds comfortable and conducive to his learning style.

A.S. (Focus Student #6)

• Multilingual and Multicultural Background: A.S.’s bilingualism and multi-ethnic heritage provide her with a rich cultural and linguistic background, which can be an asset in learning and understanding diverse perspectives.
• Strong Note-Taking Skills: Her proficiency in note-taking is a valuable academic skill that can aid in her learning process, and she can share this technique with peers to help them in their learning process.
• Family Experiences and Challenges: The challenges faced due to her mother’s health issues, and her experience of being away from home could have fostered resilience and independence.

Linguistic resources and funds of knowledge

SM (Focus Student #2)

• Conversational English Proficiency: SM’s ability to engage in dialogue and discussion in English, despite struggles with reading and writing, indicates strong verbal communication skills.
• Expressive Skills in Music and Art: His passion for music, particularly rapping, suggests a strong sense of rhythm and an ability to express ideas creatively, which can be a powerful tool for learning and communication.

ER (Focus Student #3)

• Bilingual Abilities: ER’s ability to speak Spanish and English can aid in understanding complex concepts when translated between languages, providing a bridge for learning new vocabulary and concepts in English.
• Cultural and Linguistic Connections: His connection with the Mexican and Latinx community offers a rich linguistic and cultural perspective, which can be harnessed in collaborative learning settings.

JB (Focus Student #5)

• Communication Preferences: While specific linguistic abilities are not detailed, understanding and accommodating JB’s preferred modes of communication, especially considering his autism, can enhance his learning experience. This might include more visual or kinesthetic communication methods.

A.S. (Focus Student #6)

• Bilingualism and Biculturalism: A.S. has access to a broad spectrum of linguistic and cultural knowledge as a bilingual student from a multi-ethnic background, allowing her to understand diverse perspectives and learn more complex concepts.
• Effective Note-Taking in Two Languages: A.S.’s proficiency in note-taking, potentially in both English and Spanish, is a valuable skill that can aid her own learning and can be shared with peers as a learning strategy.

Prior Experiences and Interests Related to Mathematics

How might you incorporate or build on student experiences and interests as assets in this lesson?

• For SM: I can integrate SM’s passion for music and art into the curriculum by creating assignments that allow him to compose math-related songs or rap verses. I can also encourage him to use his drawing skills to represent mathematical concepts visually. In addition, I can include real-world problems related to vehicles, aligning with his interest in cars, to make the content more relevant and engaging for him.
• For ER: I can incorporate ER’s Mexican heritage into my word problems, using scenarios or cultural references that resonate with him. I can also design bilingual problems to leverage his language skills, connecting his linguistic abilities with mathematical problem-solving.
• For JB: I can use JB’s interest in technology by incorporating technology-based math problems and using interactive software for problem-solving. To accommodate his need for structured learning environments, I can provide clear, step-by-step instructions and visual aids to help him break down complex problems.
• For A.S.: I will leverage A.S.’s strong note-taking skills by having her create ‘math guides’ for different types of word problems, which can also serve as resources for her peers. I can also include word problems reflecting cultural and linguistic diversity, making the content more inclusive and relatable for her.

General Strategies:

• I can encourage collaborative work where students like SM and ER can blend their artistic and linguistic skills in group projects. This fosters peer learning and allows them to appreciate diverse perspectives.
• I can personalize some aspects of the lesson, allowing students to choose problems or projects that align with their individual interests or experiences.
• I can connect math problems to real-world scenarios that are relevant to my students’ lives, enhancing the practicality and relatability of the lessons.

Lesson Management Structure

What behavioral expectations will you model?

• I will model respect and inclusivity in all my interactions. I will show respect for all student responses, encourage diverse opinions, and demonstrate how to appreciate the different backgrounds and abilities in my classroom.
• I will actively participate in the learning process, showing enthusiasm for the subject matter. I will model how to engage with the material, asking probing questions and demonstrating curiosity to encourage students to do the same.
• I will demonstrate responsibility for my actions and decisions as an educator. I will hold myself accountable for providing clear, structured instructions and timely feedback, setting an example for students to take responsibility for their learning.
• I will model patience in understanding and solving complex problems, showing students that taking time to work through difficult concepts is okay. I will encourage perseverance, demonstrating that challenges in learning are opportunities for growth.
• I will actively engage in collaborative activities, showing how to work effectively in teams. I will demonstrate active listening, constructive feedback, and cooperative problem-solving.
• I will model good organizational skills, showing how to keep materials and notes in order. I will also demonstrate effective time management, ensuring that classroom activities are planned appropriately and deadlines are met.
• I will maintain a positive attitude towards teaching and learning, even when facing challenges. I will offer encouragement and positive reinforcement to students, fostering a supportive and motivational classroom atmosphere.
• I will demonstrate self-regulation techniques, such as taking deep breaths before responding to challenging questions or situations. I will also incorporate brief mindfulness exercises at the start or end of class to help students center their attention and manage stress.

Content of the Lesson

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

• I expect students to develop robust skills in dissecting word problems. They should be able to identify key information, discern what the problem is asking, and differentiate between necessary and extraneous details.
• I want students to retain a fundamental understanding of how to translate a verbal problem into a mathematical equation or expression. This skill involves recognizing mathematical operations and relationships described in words and representing them numerically or algebraically.
• I expect students to understand how to apply various mathematical principles, whether it’s algebra, geometry, or basic calculus, to solve problems. This involves computational skills and understanding how and why particular mathematical methods or formulas are used.
• Students should retain different strategies for approaching and solving complex problems. This includes breaking down a problem into smaller, manageable parts, using logical reasoning, and exploring multiple methods to find a solution.
• A deeper understanding of critical thinking and reasoning in mathematics is expected. Students should be able to follow through a logical sequence of steps to solve a problem and justify their solutions with clear reasoning.
• I want students to be adept at clearly articulating their problem-solving process and solutions, both in writing and orally. This includes using proper mathematical terminology and presenting their thoughts in a structured and coherent manner.
• It’s crucial that students see the relevance of what they are learning. I expect them to understand how mathematical problem-solving skills apply in real-life situations and how they can use these skills outside the classroom. Finally, I hope students retain a sense of confidence in their ability to tackle challenging problems and a mindset that embraces mistakes and setbacks as part of the learning process.

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

• Students might misunderstand the actual question being asked in the word problem, especially if it’s phrased in a complex or unusual way. They might focus on irrelevant details or miss key information necessary for solving the problem.
• Some students might take certain phrases or terms too literally without understanding their mathematical context. For instance, misinterpreting phrases like “less than” or “product of” could lead to incorrect mathematical representations.
• A common misconception can occur in translating narrative descriptions into mathematical equations or expressions. Students might incorrectly associate certain words with mathematical operations or misplace variables and constants.
• When dealing with problems that involve measurements, students might ignore or mix up units (like meters, liters, and grams), leading to calculation errors or misinterpretation of the problem’s requirements.
• Students might apply the wrong mathematical principle or formula to a problem, either from misunderstanding the problem or not recalling the correct mathematical concept.
• Some students might think that there is only one correct way to solve a problem and might not explore other valid methods or strategies that could lead to the solution.
• After learning a particular type of problem, students might overgeneralize and try to apply the same pattern or solution method to different types of problems, which may not always work.
• Students who lack confidence in their math skills might feel overwhelmed or anxious when facing complex word problems, leading them to give up too quickly or not try different approaches.
• Even if students understand the conceptual part of the problem, they might make simple arithmetic errors in their calculations, leading to incorrect answers.
• Some students might struggle with abstract thinking required in certain mathematical problems, especially in algebra or problems that require visualization of geometric concepts.

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

• Students should be adept at breaking down complex word problems into manageable parts, identifying key information, and determining the steps needed to find solutions.
• They should be able to accurately translate descriptions from word problems into mathematical equations or expressions, understanding how language corresponds to mathematical symbols and operations.
• Students should have a better grasp of applying various mathematical principles, such as algebraic formulas, geometric reasoning, and basic calculus concepts, to solve problems.
• They should demonstrate improved analytical skills, being able to approach problems logically, think critically about their methods, and reason through solutions.
• Students should be able to clearly articulate their problem-solving process and solutions, both in writing and verbally, using appropriate mathematical vocabulary and logical structuring of their explanations.
• They should recognize how the mathematical concepts learned can be applied to real-life scenarios, seeing the relevance of mathematics beyond the classroom.
• Students should exhibit improved skills in working both collaboratively in groups and independently, leveraging peer insights during collaborative work, and applying individual critical thinking in solo tasks.
• They should show improved accuracy in performing calculations, whether they are simple arithmetic or more complex computations, with an understanding of the importance of precision in mathematical solutions.
• Students should display increased confidence in their ability to tackle challenging problems and a resilient mindset that views difficulties as opportunities for learning and growth.
• They should demonstrate competence in using various tools and resources, such as calculators, graphs, and technology, effectively as aids in solving mathematical problems.
• By the end of the lesson, the goal is for students to have solidified their mathematical understanding and problem-solving skills and developed a positive and proactive approach to learning and applying mathematics.

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?

To Guage Understanding and Interpretation:

• Can you identify the key elements and variables in this word problem?
• What do you think is the main question or challenge this problem asks you to solve?

To Guage Understanding of the Translation of Word Problems into Mathematical Language:

• How would you translate the scenario described in the word problem into a mathematical equation or expression?
• What mathematical operations and relationships are implied in this text?

To Guage the Application of Mathematical Concepts

• Which mathematical principles or formulas are applicable in solving this problem and why?
• Can you explain how you applied these concepts to reach your solution?

To Guage Analytical and Critical Thinking

• What strategy did you use to approach this problem, and why did you choose this strategy?
• How did you verify that your solution is reasonable or accurate?

To Evaluate the Communication of Solutions

• Can you clearly explain your solution process for this problem?
• How would you justify your answer to someone who might approach the problem differently?

To Evaluate the Ability to Apply Concepts to Real-World Application

• How can you apply the concepts learned from this problem to real-world situations?
• Can you give an example of where you might encounter a similar problem outside of the classroom?

To Evaluate Reflection on the Learning and Problem-Solving Process

• What challenges did you face while solving this problem, and how did you overcome them?
• What part of the problem-solving process did you find most difficult, and what part did you find easiest?

To Test the Demonstration of Advanced Understanding

• Can you think of a different method to solve this problem, and what would be its advantages or disadvantages?

• How might this problem be modified to make it more complex, and how would you approach this new challenge?

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

• Group Problem-Solving Sessions (Multiple Means of Engagement): Students will work in small groups to solve a set of word problems. This fosters collaboration and peer learning, allowing students to engage with the content in a social context.
• Individual Practice (Multiple Means of Action and Expression): After group activities, students will solve different word problems individually. This allows them to apply the strategies they’ve learned independently.
• Use of Technology (Multiple Means of Representation): Students will utilize technological tools like graphing calculators or educational software to help visualize and solve problems.
• Interactive Whiteboard Exercises (Multiple Means of Representation and Action/Expression): Using an interactive whiteboard or smartboard, students can visually map out their problem-solving process and receive immediate feedback.
• Class Discussion and Reflection (Multiple Means of Engagement): Students will participate in class discussions where they can share their solutions and problem-solving strategies and reflect on their learning process.

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

• Student Participation in Group Activities (Multiple Means of Engagement): Observations of student participation and interaction during group problem-solving sessions. I will note how students discuss, collaborate, and contribute to solving problems.
• Individual Problem-Solving (Multiple Means of Action and Expression): Collection of individual work where students solve word problems independently. This will provide insight into each student’s ability to apply learned strategies.
• Use of Technology and Tools (Multiple Means of Representation): Observing how students use technology like graphing calculators or educational software to solve and understand problems. Their ability to effectively utilize these tools is indicative of their understanding.
• Responses on Interactive Whiteboard (Multiple Means of Representation and Action/Expression): Tracking student responses and problem-solving methods on the interactive whiteboard, looking for accuracy and understanding of the concepts.
• Class Discussions and Reflective Exercises (Multiple Means of Engagement): Assessing students’ contributions to class discussions and their reflections on learning experiences, challenges faced, and strategies used.
• Formative Assessments (Multiple Means of Representation): Regular quizzes or short assessments to check for understanding. This will include problems varying in difficulty and style.
• Student Self-Assessments (Multiple Means of Engagement): Collecting student self-assessments where they evaluate their own understanding and progress. This can provide insights into their perception of their skills and knowledge.

Structured Student Learning Activities

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

• Interactive Warm-Up Exercise (Multiple Means of Engagement): Starting with a quick interactive warm-up where students solve a simple word problem related to real-life scenarios.
• Group Problem-Solving Sessions (Multiple Means of Engagement and Action & Expression): Students work in small groups on a set of word problems, encouraging collaborative learning and peer support.
• Use of Technology (Multiple Means of Representation): Integration of technology such as graphing calculators or educational apps to visualize and solve problems.
• Individual Work and Practice (Multiple Means of Action & Expression): After group work, students engage in individual problem-solving to apply the strategies they learned.
• Interactive Whiteboard Demonstrations (Multiple Means of Representation): Using an interactive whiteboard for problem-solving demonstrations allows students to map out problems visually.
• Class Discussion and Reflection (Multiple Means of Engagement): Facilitating class discussions where students share their solutions and thought processes and reflect on their learning.
• Formative Assessments (Multiple Means of Assessment): Conduct short quizzes or in-class assignments to provide ongoing assessment of understanding.
• Incorporation of Student Interests (Multiple Means of Engagement): Including word problems that align with students’ interests and real-world experiences to enhance relevance and engagement.

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

• Diverse and Flexible Grouping (Multiple Means of Engagement): I will create groups that are diverse in terms of abilities, interests, and learning styles. This diversity ensures that students can learn from each other’s strengths and perspectives. This aligns with providing multiple means of engagement by fostering a community of learners where students can benefit from diverse talents and perspectives.
• Purposeful Group Roles (Multiple Means of Action & Expression): Assigning specific roles within each group, such as facilitator, recorder, or presenter. This ensures that all students are actively engaged and contributing to the group work. This strategy supports action and expression by offering options for physical action and optimizing access to tools and assistive technologies (e.g., allowing a student who excels in technology to handle digital tools).
• Clear Instructions and Expectations (Multiple Means of Representation): Providing clear, concise instructions both verbally and in written form for group activities. This helps ensure that all students understand the task and what is expected of them. This strategy offers multiple means of representation by clarifying vocabulary and symbols and providing options for comprehending instructions.
• Regular Monitoring and Feedback (Multiple Means of Engagement): I will circulate among the groups, offering guidance, answering questions, and providing feedback. This helps keep groups on task and address any misunderstandings promptly, encouraging on-the-spot assistance and scaffolding and aligns with the principle of offering appropriate feedback and support.
• Use of Collaborative Tools (Multiple Means of Action & Expression): Incorporating collaborative tools such as shared digital documents or interactive whiteboards for group problem-solving. This can enhance communication and organization within groups. This strategy supports action and expression by offering varied ways for students to interact and express their understanding.
• Reflection and Self-Assessment (Multiple Means of Engagement): After group activities, I will encourage students to reflect on their group dynamics, their individual contributions, and what they learned from the experience. This activity promotes self-assessment and reflection, helping students to develop self-regulation and awareness of their learning process.
• Rotating Group Members (Multiple Means of Engagement): Periodically rotating group members so students can work with a variety of peers, promoting broader social interactions and diverse learning experiences. This will enhance engagement by exposing students to a range of perspectives and collaboration styles.

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). 

Instructional Strategies and UDL Principles

Multimodal Instruction (Multiple Means of Representation): I will use a combination of verbal explanations, written notes, visual aids (like diagrams and charts), and hands-on activities to cater to various learning styles. This aligns with offering options for perception and options for comprehension, ensuring content is accessible in different formats.

Interactive Technology Use (Multiple Means of Representation and Engagement): Integrating technology such as interactive whiteboards, educational software, and graphing calculators to demonstrate concepts and solve problems supports representation through digital media and engagement through interactive learning tools.

Gradual Release Model

I Do (Modeling): I will model the process of solving a word problem, explaining each step aloud (think-aloud strategy). I will demonstrate how to identify key information, translate the problem into a mathematical equation, and apply relevant mathematical concepts to find the solution. This demonstrates the UDL principle of offering ways of customizing the display of information and providing options for comprehension.

We Do (Guided Practice): I will present a new word problem and guide the class through solving it together. During this process, I’ll ask targeted questions to gauge understanding and encourage students to contribute their ideas on how to approach the problem. This immediate feedback allows me to assess and address any misconceptions. Engaging students in guided practice aligns with the UDL guidelines of offering options for collaboration and community and providing options for executive functions by guiding them in organizing and planning their problem-solving approach.

You Do (Independent Practice): Students will then be given a set of word problems to solve independently, applying the strategies and methods we’ve practiced together. This independent work allows students to consolidate their learning and demonstrate their understanding. This step supports the UDL principle of offering options for self-regulation by allowing students to apply their learning in a more autonomous context.

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

• Whiteboard and Markers: For demonstrating problem-solving processes and strategies. The whiteboard is essential for visual representation and allows for dynamic, interactive teaching.
• Handouts with Word Problems: These will include a variety of word problems of different levels of difficulty and covering different mathematical concepts like algebra, geometry, and basic calculus. Handouts allow students to have a tangible resource to refer to during and after the lesson.
• Graph Paper and Rulers: For geometry-related problems, these tools will help students draw accurate diagrams and aid in visualizing and solving problems that involve shapes and measurements.
• Calculators: To assist in computations, especially for more complex calculations. This helps students focus more on problem-solving rather than getting bogged down with lengthy arithmetic.
• Projector or Smartboard: A projector or smartboard can display problems, demonstrate solutions, and engage the whole class in interactive problem-solving activities.
• Educational Software or Apps: Software that allows for the simulation of mathematical problems or interactive problem-solving can be highly beneficial, especially for visual and kinesthetic learners. This includes graphing tools, geometry software, or apps for practice problems.
• Online Collaborative Tools: Tools like Google Docs or educational platforms that allow for collaborative work can be used for group activities. This is particularly useful for facilitating group work in a remote or hybrid learning setting.
• Digital Note-taking Tools: For students who prefer or need digital methods of note-taking, tools like tablets or laptops can be incorporated, possibly with styluses, for ease of writing/drawing.Learning Management System (LMS): An LMS (like Canvas or Google Classroom) can be used for distributing materials, collecting assignments, and facilitating discussions outside of class time.

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

• Simplified Language and Visual Aids: For students like ER who have limited English proficiency, simplifying the language used in word problems and providing visual aids can enhance comprehension.
• Bilingual Resources: Offering bilingual resources, such as word problems or instructions in both English and Spanish, will support bilingual students like ER and A.S.
• Alternative Formats for Material: Providing materials in alternative formats, such as large print or audio recordings, can support students with visual impairments or reading difficulties.
• Extended Time: Allowing extended time for completing tasks and tests can support students who may need more time to process and respond, such as JB.
• Preferential Seating: Positioning students who might need more direct interaction with the teacher, like JB, closer to the front of the class to facilitate easier communication and support.
• Text-to-Speech and Speech-to-Text Software: This can support students who struggle with reading or writing, such as ER and A.S., by converting text to audio and vice versa.
• Graphing Calculator Software: For students like JB, who might benefit from visual representations of mathematical concepts, graphing calculator software can be a helpful tool.
• Screen Readers and Magnification Software: These tools can assist students with visual impairments in accessing digital text and images.
• Digital Note-taking Tools: Providing access to laptops or tablets for digital note-taking can help students who may have difficulties with handwriting or organizing their notes, like JB and A.S.
• Educational Apps for Skill Reinforcement: Apps that offer practice problems and tutorials can be beneficial for reinforcing skills outside of class time, particularly for students who need additional practice.