Signature Assignment: The Learning Map - PassionateTeachingJourney.com

Introduction

In Weeks One and Two, we developed our ability to unpack a standard and establish criteria for assessing the concepts and skills of our standard. Then, we designed assessments to track learning and instructional strategies to support all students in meeting or exceeding those learning objectives. In Week Three, we focused on the instructional strategies, subject matter organization, and resources needed that are developmentally and academically appropriate for students to learn and progress toward mastery. We will bring the insights we gained from our formative assessments (discussions and assignments), interaction with peers and our instructor, and self-reflection these last three weeks into one cohesive lesson plan, the Signature Assignment Learning Map Template. This will be a fully developed and elaborated lesson plan.

Instructions

Download and save the ITL526 Learning Map Stages One and Two.
Complete all sections. Responses should be clear and concise but thorough enough for another teacher to pick up your learning map and teach your lessons. The learning map must be for a 7th-grade, 8th-grade, or High School lesson.

Stage One

CCSS.ELA-Literacy (be sure to not only cite the standard reference, but to articulate the exact wording from the standard

CCSS.ELA-LITERACY.RST.9-10.1: “Cite specific textual evidence to support analysis of science and technical texts, attending to the precise details of explanations or descriptions.”

This standard can be applied as students read and analyze word problems, citing specific information from the problem to support their understanding and solution.

CCSS.ELA-LITERACY.RST.9-10.2: “Determine the central ideas or conclusions of a text; trace the text’s explanation or depiction of a complex process, phenomenon, or concept; provide an accurate summary of the text.”

Students can use this standard to identify the main question or goal of a word problem and summarize the steps needed to solve it.

CCSS.ELA-LITERACY.RST.9-10.3: “Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks, attending to special cases or exceptions defined in the text.”

This standard is relevant as students follow the steps to translate a word problem into an algebraic equation and solve it, paying attention to any special instructions or conditions in the problem.

CCSS.ELA-LITERACY.WHST.9-10.2: “Write informative/explanatory texts, including the narration of historical events, scientific procedures/experiments, or technical processes.”

Students can apply this standard by writing out their problem-solving process clearly and organized, explaining each step of their solution.

CA Content Standard(s)

List the Standard(s)

Algebra I: 1.0 – “Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the four basic arithmetic operations where applicable.”

This standard can be applied as students work with different types of numbers in their algebraic equations and solutions.

Algebra I: 2.0 – “Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.”

Students can use this standard when solving word problems that involve these operations in their algebraic equations.

Algebra I: 4.0 – “Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x – 5) + 4(x – 2) = 12.”

This standard is relevant as students translate word problems into linear equations and solve them.

Algebra I: 6.0 – “Students graph a linear equation and compute the x- and y-intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4).”

Students can apply this standard when solving word problems that involve graphing linear equations or inequalities.

Algebra I: 9.0 – “Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets.”

This standard is relevant for word problems that involve systems of equations or inequalities.

Algebra I: 14.0 – “Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems.”

Students can use this standard when solving word problems that involve rates, work, or percent mixtures.

ELD Standard

List English Learning Development Standard(s)

Part I: Interacting in Meaningful Ways

B. Interpretive:

9-10th grade: “Determine the meaning of general academic and domain-specific words and phrases in a text relevant to a grade 9–10 topic or subject area.”

This standard can be applied as English learners work to understand the language and vocabulary specific to algebraic word problems.

Part II: Learning About How English Works

A. Structuring Cohesive Texts:

9-10th grade: “Select and connect information and ideas from text with appropriate words, phrases, and clauses using sentence-level connecting words to build cohesion and clarify relationships.”

This standard is relevant as students translate word problems into algebraic equations, requiring them to connect mathematical ideas using appropriate language.

Part III: Using Foundational Literacy Skills

B. Understanding Text Structure:

9-10th grade: “Analyze how authors use text structures to organize information and ideas.”

Students can apply this standard when analyzing the structure of word problems to identify key information and relationships between variables.

Prior Knowledge

What do students have to know coming into your lesson? Think in terms of instructional academic language and vocabulary.

Basic Algebraic Concepts

Variables: Understanding what variables represent in an equation.

Constants: Knowing the difference between constants and variables.

Coefficients: Recognizing coefficients as the numerical factors of variables in terms.

Terms: Identifying terms as the separate components of an expression separated by addition or subtraction.

Expressions: Understanding expressions as combinations of variables, numbers, and operations without an equal sign.

Equations: Knowing that equations are statements that two expressions are equal.

Operations and Properties

Addition, subtraction, multiplication, and division: Basic arithmetic operations.

Distributive property: Understanding how to apply the distributive property to simplify expressions.

Commutative property: Knowing that the order of addition or multiplication does not change the result.

Associative property: Understanding that grouping addition or multiplication does not affect the result.

Equation Solving

Solving linear equations: Techniques for isolating the variable to find its value.

Checking solutions: Substituting the solution back into the original equation to verify its correctness.

Word Problem Strategies

Identifying key information: Recognizing important details and data in the problem.

Setting up an equation: Translating the word problem into an algebraic equation.

Problem-solving steps: Understanding the steps involved in solving the equation and finding the answer.

Mathematical Vocabulary

Rate, ratio, percent: Understanding these concepts as they apply to real-world situations.

Unknown: Recognizing the unknown quantity as what needs to be solved for in an equation.

Solution: Knowing that the solution is the value or values that make the equation true.

Big Question(s)

Your Learning Target Question(s)

How can we translate a real-world scenario into an algebraic equation?
What strategies can we use to solve different types of algebraic word problems, such as those involving linear equations, systems of equations, and quadratic equations?
How can we verify the correctness of our solutions to algebraic word problems?
In what ways do algebraic word problems relate to real-life situations, and how can solving them help us make informed decisions?

Concepts

The content we want students to learn, evaluate, and apply.

Identifying Key Information: Students should learn how to extract relevant data and variables from word problems, distinguishing between necessary and extraneous information.

Translating Words into Equations: Students should learn to convert verbal descriptions into algebraic expressions and equations using appropriate mathematical symbols and operations.

Solving Linear Equations: Students should learn techniques for solving linear equations, such as the isolation of variables, and apply these methods to find solutions to word problems.

Solving Systems of Equations: Students should learn how to solve systems of linear equations using methods like substitution, elimination, and graphing and apply these techniques to solve problems involving multiple variables.

Solving Quadratic Equations: Students should learn how to solve quadratic equations using factoring, completing the square, or the quadratic formula, and apply these methods to relevant word problems.

Evaluating Solutions: Students should learn to assess the correctness and reasonableness of their solutions by checking their answers in the context of the problem and using estimation or other verification techniques.

Applying Algebraic Concepts to Real-Life Situations: Students should learn to recognize how algebraic problem-solving skills can be applied to various real-world scenarios, such as financial planning, physics problems, and rate calculations.

Critical Thinking and Problem-Solving Skills: Students should develop the ability to approach complex problems systematically, breaking them down into manageable parts and applying appropriate algebraic techniques to find solutions.

Skills

What skills do you want students to master?

Problem Analysis: Ability to read and understand the given information in a word problem, identifying what is known and what needs to be found.

Translation Skills: Translating verbal descriptions into algebraic expressions and equations using appropriate mathematical symbols and operations.

Equation Solving: Proficiency in solving various types of equations, including linear equations, systems of equations, and quadratic equations.

Critical Thinking: Ability to apply logical reasoning to analyze problems, make connections, and develop problem-solving strategies.

Solution Verification: Ability to check the correctness of solutions by substituting them back into the original equations and evaluating their validity in the problem context.

Mathematical Communication: Ability to clearly articulate the problem-solving process, including the steps taken and the rationale behind each decision, both verbally and in written form.

Application of Algebraic Concepts: Ability to apply algebraic techniques to real-life situations and understand the relevance of algebra in various contexts.

Collaboration: Ability to work effectively with peers, share ideas and strategies, and contribute to a collaborative problem-solving process.

Task

List both teacher actions (TA) and student actions (SA) for each skill

Skill: Problem Analysis

TA: Guide students in identifying key information and relevant details in word problems.

SA: Read and comprehend word problems, highlighting or noting important information.

Skill: Translation Skills

TA: Demonstrate how to convert verbal descriptions into algebraic expressions and equations.

SA: Practice translating word problems into mathematical equations using appropriate symbols.

Skill: Equation Solving

TA: Teach various methods for solving equations and provide practice problems for each type.

SA: Apply different techniques to solve linear, quadratic, and system of equations.

Skill: Critical Thinking

TA: Encourage students to think logically and creatively when approaching problems.

SA: Analyze problems, brainstorm possible solutions, and decide on the most effective approach.

Skill: Solution Verification

TA: Show students how to check their solutions and explain the importance of this step.

SA: Substitute their solutions back into the original equations to verify correctness.

Skill: Mathematical Communication

TA: Model clear and concise communication of mathematical ideas and solutions.

SA: Explain their problem-solving process and solutions verbally and in writing.

Skill: Application of Algebraic Concepts

TA: Provide real-life examples and applications of algebraic concepts.

SA: Connect algebraic techniques to real-world scenarios and discuss their relevance.

Skill: Collaboration

TA: Facilitate group activities and discussions, encouraging teamwork and peer learning.

SA: Work together in groups, share ideas, and collaborate on solving problems.

Learning Objective Components: Performance, Condition, Criterion

Strategy

Identify the instructional strategy:

Instructional Strategy: Guided Practice with Collaborative Learning

Direct Instruction:
- The teacher introduces algebraic word problems, explains the translation process, and demonstrates solving various types of equations.
- Students listen, take notes, and ask questions for clarification.
Guided Practice:
- The teacher provides example problems and guides students through the solution process, offering support and feedback.
- Students actively participate in solving problems and seek assistance when needed.
Collaborative Learning:
- The teacher facilitates group work, encouraging students to collaborate and share their problem-solving strategies.
- Students work in small groups to solve word problems, discussing their approaches and learning from each other.
Independent Practice:
- The teacher assigns individual word problems for students to solve independently, catering to different skill levels.
- Students independently apply their skills and strategies to solve the problems, demonstrating their mastery.
Reflection and Assessment:
- The teacher reviews solutions with the class, highlights common mistakes and best practices, and assesses student understanding.
- Students reflect on their learning, identify improvement areas, and demonstrate understanding through assessments.

Performance (Verb)

List the verbs using Blooms or DOK that will direct student learning

Remembering (DOK Level 1):

Identify: Recognize key information and variables in word problems.
Recall: Remember basic algebraic operations and properties.

Understanding (DOK Level 2):

Explain: Describe the process of translating words into equations.
Interpret: Understand the meaning of algebraic expressions and equations in the context of word problems.

Applying (DOK Level 2):

Apply: Use algebraic methods to solve linear equations, systems of equations, and quadratic equations in word problems.
Calculate: Perform arithmetic operations to find solutions.

Analyzing (DOK Level 3):

Analyze: Break down word problems to identify relationships between variables and relevant information.
Compare: Contrast different methods for solving equations and justify the most appropriate approach.

Evaluating (DOK Level 4):

Evaluate: Assess the reasonableness and correctness of solutions to word problems.
Critique: Analyze the effectiveness of different problem-solving strategies.

Creating (DOK Level 4):

Create: Develop new word problems that involve algebraic concepts.
Formulate: Construct algebraic equations based on given scenarios in word problems.

Condition. (Support with Tools and Resources, Environment)

Describe the circumstances under which the performance takes place: Include: 1. Tools/Resources/Supports (what students will or will not use), 2. Environment (where the performance takes place)

Tools/Resources/Supports:

Whiteboard and Markers: Students will use these for solving problems in class, either individually or in groups.
Calculators: Students are allowed to use calculators for computation, but they are encouraged to understand the underlying algebraic concepts.
Handouts: Students will receive handouts with various algebraic word problems to practice different types of equations.
Textbook and Online Resources: Students can refer to their textbooks and selected online resources for additional practice and clarification of concepts.
Collaboration: Students will work in small groups during certain activities, providing peer support and sharing problem-solving strategies.
Teacher Guidance: The teacher will provide direct instruction, guided practice, and feedback throughout the lesson.

Environment:

Classroom Setting: The performance will primarily occur in the classroom, where students can access the whiteboard, markers, and other instructional materials.
Group Work Areas: For collaborative activities, the classroom will be arranged to facilitate small group discussions and problem-solving.
Individual Workspaces: Students will have individual workspaces for independent practice and assessments.
Technology Integration: If available, a projector or smartboard will be used to display problems and demonstrate solutions, enhancing the visual aspect of instruction.

Criterion: How will you measure student learning?

Describe what the criterion is:

Accuracy of Solutions: Evaluate the correctness of students’ solutions to algebraic word problems. This includes checking if the solution satisfies the equation and if the answer is reasonable within the context of the problem.

Problem-Solving Process: Assess students’ ability to identify key information, translate words into equations, and apply appropriate algebraic methods to solve problems. This can be done through written work, where students show their steps and justify their choices.

Conceptual Understanding: Gauge students’ understanding of algebraic concepts such as variables, coefficients, linear equations, systems of equations, and quadratic equations. This can be measured through short-answer questions or explanations within their problem-solving process.

Application of Strategies: Evaluate students’ ability to apply different strategies for solving word problems, such as graphing, substitution, elimination, or using the quadratic formula. This can be assessed by providing problems that require different approaches and seeing if students choose and implement them effectively.

Communication: Assess students’ ability to communicate their problem-solving process and solutions clearly and accurately. This includes the use of appropriate mathematical language, clear presentation of steps, and logical organization of their work.

Collaboration and Participation: In group activities, observe students’ ability to work collaboratively, share ideas, and contribute to the group’s problem-solving process. Participation in class discussions and willingness to ask questions can also be considered.

Combine to Create a Learning Objective

Write a Learning Objective

Students will in (environment) be able to (verb) by using the strategy of _______________, with the support of (tools/resources) with (speed or accuracy) as measured by (how will you measure student learning).

Students will, in a classroom setting, be able to solve algebraic word problems by using the strategy of translating verbal descriptions into equations, with the support of whiteboards, markers, and calculators, with at least 80% accuracy as measured by a set of 5 graded problems on a quiz.

Student Learning Target (Student-friendly language)

I can statement:

“I can solve word problems in math class by turning the words into math equations and solving them. I will use my math notebook, a calculator, and my teacher’s help. I aim to get at least 4 out of 5 problems right on my next quiz.”

Social and Emotional Learning Strategies

Goal Setting: Encourage students to set personal goals for the lesson, such as understanding a specific concept or improving their problem-solving skills. This helps develop self-management and self-awareness skills.
Collaborative Learning: Use group activities and discussions to foster teamwork and communication. Students can learn from each other, share different perspectives, and develop relationship skills.
Reflection: At the end of the lesson or activity, ask students to reflect on their learning experience, challenges they faced, and how they overcame them. This promotes self-awareness and responsible decision-making.
Growth Mindset: Encourage a growth mindset by praising effort, persistence, and resilience rather than just correct answers. Emphasize that making mistakes is a natural part of learning and an opportunity for growth.
Emotional Regulation: Teach students strategies to manage frustration or anxiety when faced with challenging problems, such as taking deep breaths, breaking the problem into smaller parts, or asking for help. This helps develop self-management skills.
Positive Reinforcement: Provide positive feedback and recognition for students’ efforts and achievements, which can boost their confidence and motivation.
Mindfulness Activities: Incorporate brief mindfulness exercises, such as deep breathing or visualization, to help students relax and focus before starting on complex problems.

Student Misconceptions

Equating Words with Operations: Students might think that certain words always correspond to specific operations (e.g., “more than” always means addition), which can lead to incorrect equation setup.
Ignoring Units: Students may overlook the importance of units in word problems, leading to incorrect interpretations and solutions.
Misinterpreting Variables: Students might confuse the role of variables, treating them as fixed values rather than representing unknown quantities.
Overgeneralizing Linear Equations: Some students may assume that all word problems can be solved with linear equations, ignoring the need for quadratic equations or systems of equations in certain scenarios.
Misapplying Properties: Students might incorrectly apply mathematical properties (e.g., distributive property) when simplifying expressions or solving equations.
Overlooking Key Information: Students may skip essential details in the problem statement, leading to incomplete or incorrect equations.
Mixing Up Solution Methods: Students might confuse the methods for solving different types of equations, such as using elimination when substitution is more appropriate.
Assuming One Solution: Students may assume that every problem has only one solution, not considering the possibility of multiple solutions or no solution.

Stage Two – Instructional Approach: Teaching

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?

Math and Science Skills: Some students have strengths in math and science, which will be beneficial for understanding and solving algebraic word problems.

Writing and Expression: A few students have skills in writing and expression, which can help them articulate their problem-solving process and solutions.

Athletic and Energetic: Some students are athletic and energetic, which indicates they may excel in activities that require active engagement and quick thinking.

Leadership: A few students have leadership skills, which can be leveraged in group activities and collaborative problem-solving.

Public Speaking: Some students are skilled in public speaking, which can be useful for explaining their solutions and reasoning to the class.

Hands-on and Kinetic Learning: A few students prefer hands-on and kinetic learning, which suggests they may benefit from interactive and practical problem-solving activities.

Cultural Pride and Positive Attitude: Some students have traits like cultural pride and a positive attitude, which can contribute to a supportive and inclusive learning environment.

Technology and Medical Interests: A few students have interests in technology and medical fields, which can be connected to real-world applications of algebraic word problems.

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

List students and their CELDT or ELPAC levels:

Micky Han: Fluent English (2nd Generation Korean)
Miguel Feragamo: Moderate English Learner – Level 2 (Basic English / Parents None)
Li Xuan: Tested out in 8th grade (2nd generation Chinese)
Reighley Gomez: Fluent English
Carolina Del Toro: Fluent English
Morgan Shepplor: Fluent English
Angelica Hardgrove: Fluent English
Elias Green: Fluent English
Sacramento Oscoela: Fluent English
Malakai Brown: Fluent English
Jana Beckler: Fluent English
Lana Oscoela: Fluent English
Maya Lopez: Moderate English Learner – Level 3 (Arrived from Mexico G:2)
Kelz O’Keeffe: Fluent English
Davis Brown: Fluent / Dysgraphic (Never tested)
Will Sparks: Fluent English
Elvis Barrlow: Fluent English
Cambria Von Morgan: Fluent English
Hannah Golabiyenka: Mostly Fluent English (Exchange Student: Belarus)
Cari Melendez: Fluent English
Seeley Booth: Fluent English
Brian Hicks: Fluent English
Chan Li Han: Unknown
Aubree Helborn: Fluent English
Juan Santiago: Fluent English
Lance Torres: Moderate English – Level 2 (Basic English / Parents None)
Carlos Montenegro: Tested out in 8th grade (2nd generation Chinese)
Maria Rios: Advanced English Learner – Level 4
Olaf Gunderson: Fluent English
Derrick Haas: Fluent English
Quan Rappaport: Fluent English
Diego Montez: Fluent English
Ricky Hernandez: Fluent English

Cultural and linguistic resources and funds of knowledge (i.e., knowledge and skills derived from cultural experience)

Cultural resources and funds of knowledge:

Micky Han: Interested in K-Pop.
Miguel Feragamo: Speaks Spanish.
Li Xuan: Aspires to be a doctor, family pride.
Reighley Gomez: Part of JV Cheer squad.
Carolina Del Toro: Attended Stanford Law Summer Camp, wants to be a lawyer.
Morgan Shepplor: Artistic, youngest of 5 children.
Angelica Hardgrove: Social butterfly.
Elias Green: Class clown.
Sacramento Oscoela: Barrona Indian, cultural pride.
Malakai Brown: Athletic.
Jana Beckler: Involved in soccer and softball, team player.
Lana Oscoela: Hopes to be a nurse.
Maya Lopez: Wants to be a Tik-Tok fashion influencer.
“Kelz” O’Keeffe: Flamboyant personality, highly social.
Davis Brown: All-league in golf and tennis.
Will Sparks: Interested in technology and cars.
Elvis Barrlow: Opens up when talking about technology.
Cambria Von Morgan: Exceptional online gamer.
Hannah Golabiyenka: Foreign exchange student from Belarus.
Cari Melendez: Peacemaker, involved in church activities.
Seeley Booth: Olympic hopeful in target shooting.
Brian Hicks: Plays guitar in class.
Chan Li Han: Absent since the first 3 days of school.
Aubree Helborn: In 3rd foster home, ditches classes.
Juan Santiago: Sophomore class president, social chameleon.
Lance Torres: Interested in Marvel Cinematic Universe.
Carlos Montenegro: Logical.
Maria Rios: Interested in cooking/baking.
Olaf Gunderson: Addicted to surfing, vibrant, free-spirited.
Ricky Hernandez: Works at uncle’s tire shop, streetwise.
Diego Montez: Balances dating multiple girls, public speaker.
Quan Rappaport: Aspires to be a doctor.

Linguistic resources and funds of knowledge:

Micky Han: Fluent English, 2nd generation Korean.
Miguel Feragamo: Moderate English learner (Level 2), speaks Spanish, basic English proficiency.
Li Xuan: Tested out of ELL in 8th grade, 2nd generation Chinese, parents do not speak much English.
Reighley Gomez: Fluent in English.
Carolina Del Toro: Fluent in English.
Morgan Shepplor: Fluent in English.
Angelica Hardgrove: Fluent in English.
Elias Green: Fluent in English.
Sacramento Oscoela: Fluent in English.
Malakai Brown: Fluent in English.
Jana Beckler: Fluent in English.
Lana Oscoela: Fluent in English.
Maya Lopez: Moderate English learner (Level 3), arrived from Mexico in 2nd grade, fluent in conversational English.
“Kelz” O’Keeffe: Fluent in English, social-emotional support.
Davis Brown: Fluent in English, dysgraphic.
Will Sparks: Fluent in English, ADHD, dysgraphia.
Elvis Barrlow: Fluent in English, transitioned out of Asperger’s Syndrome support in 8th grade.
Cambria Von Morgan: Fluent in English.
Hannah Golabiyenka: Mostly fluent in English, exchange student from Belarus.
Cari Melendez: Fluent in English.
Seeley Booth: Fluent in English.
Brian Hicks: Fluent in English.
Chan Li Han: English proficiency unknown.
Aubree Helborn: Fluent in English.
Juan Santiago: Fluent in English.
Lance Torres: Moderate English learner (Level 2), basic English proficiency.
Carlos Montenegro: Tested out of ELL in 8th grade, 2nd generation Chinese.
Maria Rios: Advanced English learner (Level 4).
Olaf Gunderson: Fluent in English.
Ricky Hernandez: Fluent in English.
Diego Montez: Fluent in English.
Quan Rappaport: Fluent in English.

Prior experiences and interests related to the content

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

Micky Han: Use K-Pop-related word problems that involve calculations related to music sales, concert attendance, or merchandise production.
Miguel Feragamo: Create word problems that involve scenarios relevant to Spanish-speaking countries or communities, allowing him to leverage his bilingual skills.
Li Xuan: Develop word problems related to healthcare or medicine, aligning with her aspiration to become a doctor and her role as a translator for her parents.
Reighley Gomez: Integrate cheerleading-related word problems, such as calculating the number of possible routines or the distance traveled for competitions.
Carolina Del Toro: Use legal-themed word problems, such as calculating the division of assets in a settlement or the time required for legal processes.
Morgan Shepplor: Incorporate art-related word problems, such as calculating the area of a canvas or the ratio of colors needed for a painting.
Angelica Hardgrove: Create word problems that involve social scenarios or event planning, leveraging her expressive and friendly nature.
Elias Green: Design word problems that involve stage setups or audience calculations, catering to his interest in being “on stage.”
Sacramento Oscoela: Develop word problems related to tribal practices or economic benefits, such as calculating the distribution of tribal gambling revenue.
Malakai Brown: Use sports-related word problems, such as calculating the average points per game or the distance traveled for away games.
Jana Beckler: Create word problems related to team sports, such as calculating the total score of a soccer team or the percentage of wins in a softball season.
Lana Oscoela: Develop word problems related to nursing or healthcare, such as calculating medication dosages or the number of patients a nurse can see in a day.
Maya Lopez: Integrate fashion-related word problems, such as calculating the cost of materials for a clothing line or the profit from social media endorsements.
“Kelz” O’Keeffe: Use word problems related to social media analytics, such as calculating the growth rate of followers or the engagement rate of posts.
Davis Brown: Incorporate sports-related word problems, such as calculating golf course distances or the probability of winning a tennis match.
Will Sparks: Develop word problems related to automotive technology, such as calculating the fuel efficiency of a car or the cost of car modifications.
Elvis Barrlow: Create technology-related word problems, such as calculating the processing speed of a computer or the number of components needed for a robot.
Cambria Von Morgan: Integrate gaming-related word problems, such as calculating the probability of winning a game or the time required to reach a certain level.
Hannah Golabiyenka: Use word problems related to language translation or cultural differences, leveraging her experience as a foreign exchange student.
Cari Melendez: Develop word problems related to conflict resolution or community service, such as calculating the time required to mediate a dispute or the number of people needed for a volunteer event.
Seeley Booth: Incorporate word problems related to sports statistics or national competitions, such as calculating the accuracy of target shooting or the travel expenses for competitions.
Brian Hicks: Create music-related word problems, such as calculating the frequency of guitar strings or the revenue from music sales.
Chan Li Han: Develop word problems related to truancy or community resources, considering his absence from school and the challenges in reaching his parents.
Aubree Helborn: Integrate word problems related to foster care or emotional well-being, such as calculating the number of foster homes in a region or the cost of mental health services.
Juan Santiago: Use leadership-related word problems, such as calculating the budget for a class project or the number of votes needed to win an election.
Lance Torres: Develop word problems related to the Marvel Cinematic Universe, such as calculating the box office earnings of a movie or the number of characters in a series.
Carlos Montenegro: Integrate word problems related to logic or technology, considering his interest in logical reasoning and his Chinese heritage.
Maria Rios: Create word problems related to cooking or baking, such as calculating the ingredients needed for a recipe or the profit from selling baked goods.
Olaf Gunderson: Develop word problems related to surfing or environmental conservation, such as calculating the speed of a wave or the impact of pollution on marine life.
Ricky Hernandez: Incorporate word problems related to automotive mechanics or entrepreneurship, considering his work at his uncle’s tire shop and his streetwise nature.
Diego Montez: Use word problems related to social dynamics or public speaking, such as calculating the number of possible date combinations or the duration of a speech.
Quan Rappaport: Develop word problems related to healthcare or volunteering, aligning with her aspiration to be a doctor and her volunteering experience in the E.R.

Lesson management structure

What behavioral expectations will you model and expect?

Respect and Inclusion: Encourage a respectful and inclusive environment where all students feel valued and are comfortable sharing their thoughts and ideas.

Active Participation: Expect students to actively participate in discussions, group activities, and problem-solving sessions, contributing their unique perspectives and skills.

Collaboration: Foster a collaborative atmosphere where students work together, support each other, and learn from one another’s experiences and cultural backgrounds.

Responsibility: Encourage students to take responsibility for their learning by completing assignments on time, staying organized, and seeking help when needed.

Focus and Engagement: Model and expect students to stay focused and engaged during the lesson, minimizing distractions such as phone use and off-topic conversations.

Critical Thinking: Encourage students to think critically about word problems, ask questions, analyze information, and develop strategies for solving them.

Persistence: Model and expect persistence in problem-solving, encouraging students to persevere through challenging problems and learn from their mistakes.

Respect for Different Learning Styles: Acknowledge and respect the diverse learning styles and linguistic backgrounds in the classroom, adapting instruction to meet the needs of all students.

Positive Attitude: Encourage a positive attitude towards learning and problem-solving, celebrating successes and viewing challenges as opportunities for growth.

Self-Regulation: Expect students to practice self-regulation by managing their emotions, staying on task, and maintaining a positive and productive learning environment.

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?

I expect students to deeply understand the following:

Identification of Key Information: Students should be able to identify and extract relevant information from word problems to form algebraic equations.

Translation of Words into Equations: Students should understand how to translate word problems into algebraic equations, recognizing the relationship between the language used in the problem and the mathematical operations required.

Problem-Solving Strategies: Students should grasp different strategies for solving algebraic word problems, such as using diagrams, tables, or graphs to visualize the problem.

Application of Algebraic Concepts: Students should understand how to apply concepts such as linear equations, systems of equations, and quadratic equations to solve real-world problems.

Critical Thinking: Students should develop critical thinking skills to analyze word problems, determine the best solution, and justify solutions.

Collaboration and Communication: Students should understand the importance of collaborating with peers, sharing ideas, and effectively communicating their thought processes and solutions.

After the lesson, I expect students to retain:

Problem-Solving Skills: The ability to confidently approach and solve algebraic word problems using appropriate strategies and techniques.

Algebraic Understanding: A deeper understanding of algebraic concepts and how they apply to real-world situations.

Critical Thinking and Analysis: Enhanced critical thinking and analytical skills to tackle complex problems and make informed decisions.

Collaboration and Communication: Improved collaboration and communication skills, enabling them to work effectively in group settings and articulate their ideas clearly.

Adaptability: The ability to adapt their approach to different types of word problems and apply their knowledge to future learning in mathematics and other disciplines.

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

Students might have the following misunderstandings or misconceptions:

Equating Words with Operations: Students may think that certain words always correspond to specific mathematical operations (e.g., “more than” always means addition), leading to incorrect equation setups.

Ignoring Units: Students might overlook the importance of units in word problems, leading to incorrect interpretations and solutions.

Confusing Variables: Students may confuse the role of variables, treating them as fixed values rather than representing unknown quantities.

Overgeneralizing Linear Equations: Some students might assume that all word problems can be solved with linear equations, ignoring the need for quadratic equations or systems of equations in certain scenarios.

Misapplying Mathematical Properties: Students could incorrectly apply mathematical properties (e.g., distributive property) when simplifying expressions or solving equations.

Overlooking Key Information: Students may skip essential details in the problem statement, leading to incomplete or incorrect equations.

Mixing Up Solution Methods: Students might confuse the methods for solving different types of equations, such as using elimination when substitution is more appropriate.

Assuming One Solution: Students may assume that every problem has only one solution, not considering the possibility of multiple solutions or no solution.

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

After the lesson, students are expected to have the following knowledge and skills:

Understanding of Key Concepts: Students should have a solid understanding of the key algebraic concepts involved in solving word problems, such as linear equations, systems of equations, and quadratic equations.

Problem-Solving Skills: Students should be able to apply problem-solving strategies effectively to break down word problems, identify relevant information, and set up appropriate algebraic equations.

Translation Skills: Students should be proficient in translating word problems into mathematical equations and understanding how to convert verbal descriptions into algebraic expressions.

Critical Thinking: Students should be able to critically analyze word problems, determine the best approach for solving them, and justify their solutions logically.

Collaboration and Communication: Students should have enhanced collaboration and communication skills, enabling them to work effectively in groups, share ideas, and explain their thought processes and solutions clearly.

Application of Knowledge: Students should be able to apply the knowledge and skills gained from the lesson to solve real-world problems and in future learning, particularly in other areas of mathematics and science.

Confidence in Mathematics: Students should feel more confident in their ability to tackle algebraic word problems and feel empowered to approach mathematical challenges positively.

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:

Can you identify the key information needed to set up an equation from the word problem?
Are you able to translate the verbal descriptions into algebraic expressions?
What challenges are you facing in understanding or solving the word problems?

Meeting the Learning Goals:

How do you decide which algebraic method to use when solving a word problem?
Can you explain the steps you took to solve the word problem and how you arrived at your solution?
How do you check if your solution to the word problem is reasonable and correct?

Exceeding the Learning Goals:

Can you create your own word problem that involves a similar algebraic concept and solve it?
How can you apply the skills you learned in this lesson to solve more complex or real-world problems?
Are you able to explain multiple approaches to solving a word problem and compare their effectiveness?

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

To demonstrate achievement of content during the lesson, students will:

Engage in guided practice problems where they identify key information, set up equations, and solve them with the teacher’s support.
Collaborate in small groups to solve a set of word problems, applying different algebraic concepts and strategies.
Solve individual word problems independently, demonstrating their ability to apply the skills learned during the lesson.
Present their solutions to the class, explaining their steps and reasoning behind their methods.
Write a brief reflection on what they learned during the lesson, including any challenges they faced and how they overcame them.

The following Universal Design for Learning (UDL) Principle Guidelines are incorporated:

Multiple Means of Representation: Providing word problems in various formats (e.g., written, visual, auditory) and using different representations (e.g., graphs, tables) to convey the information.
Multiple Means of Action and Expression: Allowing students to demonstrate their understanding through various means, such as solving problems on paper, using manipulatives, or presenting solutions orally.
Multiple Means of Engagement: Offering choices in how students approach the problems, fostering collaboration through group work, and connecting the content to students’ interests and real-life scenarios.

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

To determine if students understand the content of the lesson, the following evidence will be collected:

Completed Practice Problems: I will review students’ work on guided practice and independent practice problems to assess their ability to set up and solve algebraic word problems correctly.
Group Work Observations: I will observe students during group activities to assess their collaboration, problem-solving strategies, and understanding of the content.
Solution Explanations: I will evaluate students’ explanations of their solutions during presentations or discussions, focusing on their ability to articulate the steps and reasoning behind their methods.
Written Reflections: I will collect and review students’ written reflections on what they learned, their challenges, and how they overcame them to gauge their understanding and self-awareness.
Assessment Results: I will use results from quizzes or assessments that include word problems to evaluate students’ mastery of the content.

The following Universal Design for Learning (UDL) Principle Guidelines are incorporated:

Multiple Means of Representation: I will provide content in various formats and use different representations to ensure all students can access and understand the material.
Multiple Means of Action and Expression: I will allow students to demonstrate their understanding through various means, such as written work, oral explanations, or visual representations.
Multiple Means of Engagement: I will offer choices in how students engage with the content and express their understanding to maintain interest and motivation.

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 Principal Guidelines incorporated.

During the lesson, students will be involved in the following activities to support their achievement of the learning goals:

Warm-Up Activity: Students will briefly review basic algebraic operations and equations to activate prior knowledge and prepare for the lesson.
Guided Practice: Students will work through example word problems as a class, while I demonstrate the process of identifying key information, setting up equations, and solving them.
Group Work: Students will collaborate in small groups to solve a set of word problems, applying different algebraic concepts and strategies. This activity encourages peer learning and discussion.
Independent Practice: Students will complete a set of word problems individually, allowing them to apply the skills and concepts learned during the lesson on their own.
Solution Presentations: Students will present solutions to selected word problems to the class, explaining the steps taken and the reasoning behind the methods used.
Reflection and Discussion: Students will reflect on the learning experience, discussing any challenges and strategies to overcome them. This activity promotes metacognition and self-assessment.

The following Universal Design for Learning (UDL) Principle Guidelines are incorporated:

Multiple Means of Representation: Word problems are provided in various formats (e.g., written, visual, auditory) and using different representations (e.g., graphs, tables) to convey information.
Multiple Means of Action and Expression: Students can demonstrate their understanding through various means, such as solving problems on paper, using manipulatives, or presenting solutions orally.
Multiple Means of Engagement: Students are offered choices in how they approach the problems, fostering collaboration through group work, and connecting the content to their interests and real-life scenarios.

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

To group students and manage group work effectively in support of student learning during the lesson, the following strategies can be employed:

Heterogeneous Grouping: I can form students into groups with various abilities, backgrounds, and interests to encourage diverse perspectives and peer learning. This can help students learn from each other and provide support to their peers.
Clear Roles and Responsibilities: I can assign specific roles (e.g., facilitator, recorder, presenter) within each group to ensure all students are actively involved and contributing to the group work.
Guided Instructions: I can provide clear instructions and guidelines for group work, including the tasks to be completed, the expected outcomes, and the time allocated for each activity.
Monitoring and Support: I can circulate among the groups to monitor progress, provide guidance, and address any questions or challenges that arise.
Reflection and Feedback: After group work, I can have students reflect on their experience and provide feedback to each other. This can help them improve their collaboration skills and learn from the process.
Flexible Grouping: I can adjust groups based on student needs and dynamics. This can involve regrouping students for different activities or based on their progress and understanding.

The following Universal Design for Learning (UDL) Principle Guidelines are incorporated:

Multiple Means of Engagement: Group work encourages collaboration and social interaction, which can increase engagement and motivation for learning.
Multiple Means of Representation: By working in groups, students can share and discuss different content representations, enhancing their understanding through multiple perspectives.
Multiple Means of Action and Expression: Group work allows students to express their understanding in various ways, whether through discussion, problem-solving, or presentation.

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).

To support student learning through multiple modalities and use gradual release in the lesson, the following instructional strategies can be employed:

I Do (Modeling)

Strategy: Explicitly model the process of solving algebraic word problems, including identifying key information, translating words into equations, and solving the equations.

UDL Incorporation: Use multiple means of representation by verbally and visually modeling the problem-solving process (e.g., writing on the board, using diagrams).

Specific Action: Demonstrate solving a word problem step-by-step while thinking aloud to show my thought process and decision-making.

We Do (Guided Practice)

Strategy: Engage students in guided practice with similar word problems, providing support and scaffolding as needed.

UDL Incorporation: Use multiple means of engagement by encouraging students to work in pairs or small groups to discuss and solve problems together.

Specific Action: Pose a word problem to the class, ask students to work with a partner to set up the equation, and then solve it together as a class, encouraging students to share their thinking and provide immediate feedback.

You Do (Independent Practice)

Strategy: Assign independent practice problems for students to solve independently, allowing them to apply their understanding and skills.

UDL Incorporation: Use multiple means of action and expression by providing a variety of problem types and allowing students to choose the problems they want to work on or the method they want to use to solve them.

Specific Action: Provide a set of word problems for students to solve independently, with varying difficulty levels to cater to different skill levels. Check their work and provide feedback to reinforce learning and address any misconceptions.

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

Whiteboard and Markers: To demonstrate solving methods and illustrate key concepts during the lesson.

Projector or Smartboard: To display word problems and visual aids and to facilitate interactive sessions where students can solve problems in front of the class.

Handouts: Containing various algebraic word problems, these will be used for both group activities and individual practice. They should cover linear equations, systems of equations, and quadratic equations.

Calculators: To assist students in performing calculations and checking their answers.Algebra Textbook: As a reference for students to review concepts and practice additional problems.

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

To support individual student learning needs beyond the Universal Design for Learning (UDL) supports built into the lesson, the following adaptations and accommodations, including assistive technologies, can be implemented:

Language Support for ELL Students: Provide glossaries or dictionaries for English Language Learners (ELL) to assist with mathematical vocabulary. Use visual aids and simplified language when explaining concepts.

Text-to-Speech Software: For students with reading difficulties or visual impairments, text-to-speech software can be used to read word problems aloud, helping them to understand the problem better.

Large Print Materials: Provide handouts and materials in large print for students with visual impairments.

Graphic Organizers: Use graphic organizers or templates to help students organize information from word problems and set up equations, especially helpful for students with executive functioning challenges.

Speech-to-Text Software: Allow students with writing difficulties or physical impairments to input their solutions and explanations using speech-to-text software.

Extended Time: Provide additional time for students who require more time to process information and solve problems.

Alternative Seating: Arrange alternative seating options for students who need to be closer to the board or require a quieter space to focus.

Breaks: Allow for short breaks during the lesson for students who may become easily fatigued or overwhelmed.

Peer Support: Pair students with peers for support during group activities, ensuring that each student’s strengths are utilized.

Differentiated Instruction: Provide alternative problems or tasks more aligned with individual students’ skill levels and learning styles.

Check for Understanding: Regularly check for understanding with individual students, especially those with learning disabilities, to ensure they are following along and grasping the concepts.