Learning Map – Stage 1: Word Problems

Teaching writing is not only the job of the ELA teacher – because every teacher is a literacy teacher, and all subject areas must teach writing! In recent years, California has innovated and integrated content standards to support reading, writing, and speaking in subject-specific classrooms. As California’s teachers, we have a responsibility to create meaningful literacy experiences within our subject areas!

This week, you will begin to design learning experiences that focus specifically on literacy skills in your content area that will support student engagement in writing. By the end of the month, your learning map will include strategies for students to access challenging informational text related to your subject area, be assessed on their writing, and have opportunities to engage in discourse with meaningful and relevant text and writing prompts. This week, plant the foundation for your students to make literacy connections to your content area! Keep in mind that in Week 3, you will have an opportunity to implement your content literacy learning map with a group of students!

Instructions

Resources

Review the following resources before you begin your assignment, as they will inform your work.

Read

• Who Owns the Writing Instruction?
• Literacy Shifts in the Content Areas

Directions

Utilize the Learning Map Template to complete Stages 1. You will complete the following sections in Stage 1: CCSS. ELA Standard, CA Content Standard, ELD Standard, Prior Knowledge, Big Questions, Concepts, Skills, Task, Learning Objective Strategy and Performance Verb, Condition, Criterion, Student Learning Target, SEL Strategies, Student Misconceptions.

CCSS.ELA-Literacy

List the CCSS ELA Standard(s)

CCSS.ELA-LITERACY.RI.9-10.1 & CCSS.ELA-LITERACY.RI.11-12.1:

Grades 9-10 & 11-12: Cite strong and thorough textual evidence to support analysis of what the text says explicitly, as well as inferences drawn from the text.

Application: Students will read word problems and cite specific information to support their mathematical reasoning and solutions.

CCSS.ELA-LITERACY.RI.9-10.2 & CCSS.ELA-LITERACY.RI.11-12.2:

Grades 9-10 & 11-12: Determine a text’s central idea and analyze its development over the course of the text, including how it emerges and is shaped and refined by specific details.

Application: Students identify the main idea or the primary question in a word problem, understanding how different pieces

CA Content Standard(s)

List the CA Content Standard(s)

CA.CCSS.Math.Content.HSA-CED.A.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

CA.CCSS.Math.Content.HSA-CED.A.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

ELD Standard

List the English Learning Development Standard(s)

Part I: Interacting in Meaningful Ways

Exchanging Information and Ideas

Engage in conversations about math content, explaining their thinking and the steps taken to solve problems.

Ask and answer questions about word problems and solutions, using complete sentences and specific vocabulary.

Interpreting, Constructing, and Expressing Meaning

Read and understand math texts (word problems), identifying key information and relevant details.

Write out solutions to word problems, clearly explaining the reasoning and steps taken.

Part II: Learning About How English Works

Understanding Text Structure

Recognize and understand the structure of word problems, including the sequence and organization of information.

Expanding and Enriching Ideas

Use a range of general and math-specific vocabulary and language structures to describe mathematical concepts and solutions.

Part III: Using Foundational Literacy Skills

Reading

Apply reading strategies to decode and comprehend word problems, including predicting, making inferences, and summarizing information.

Writing

Write clear and coherent responses to word problems using appropriate grammatical structures and math terminology.

Prior Knowledge

What do students have to know coming into your lesson? Think in terms of content knowledge and literacy skills.

Content Knowledge

• Proficiency in arithmetic (addition, subtraction, multiplication, division) and understanding fractions, decimals, and percentages.
• Familiarity with algebraic expressions, equations, and basic concepts like variables, coefficients, and simple algebraic manipulations.
• Knowledge of basic geometry, including shapes, properties of shapes, and measurement (area, volume, perimeter).
• Understanding key math terms and their meanings is crucial for interpreting and solving word problems.
• Familiarity with relevant mathematical concepts based on word problems, such as basic functions, ratios, and proportions.

Literacy Skills

• Ability to read and understand complex texts. This includes identifying key information, following a sequence of ideas, and making inferences.
• Skills to analyze text, identify relevant and irrelevant information, and understand implicit information or unstated assumptions in a word problem.
• Ability to apply logical reasoning to new situations, which is essential for tackling unfamiliar word problems.
• A good grasp of language used in word problems, which can sometimes be complex or present information less straightforwardly.
• Skills to articulate their mathematical thinking clearly in writing, including the ability to justify their reasoning and explain their solution process. Continuous development of both general and mathematical vocabulary. This includes understanding and using subject-specific terms accurately.

Big Question(s)

What are your Learning Target Question(s)?

• How do I identify and extract key information and variables from a word problem?
• How can I translate a word problem into a mathematical equation or expression?
• How do I apply different mathematical concepts (like algebra, geometry, or basic calculus) to solve word problems?
• How can I check if my solution to a word problem is reasonable and accurate?
• This question is about developing self-checking and validation skills, ensuring students understand how to confirm the correctness of their answers.
• In what ways can solving word problems enhance my critical thinking and problem-solving skills? How can I effectively communicate my solution process and reasoning clearly and organized?

Concepts

What are the subject-specific concepts you want students to learn, evaluate, and apply?

• Students should learn how to read and interpret word problems, identify key information, and discern what the problem is asking them to solve.
• Teaching students to translate word problems into mathematical equations or expressions. This involves identifying variables and constants and understanding how words translate into mathematical operations.
• Applying algebraic concepts to solve word problems, including forming and solving of equations and inequalities.
• Using geometric principles to solve word problems, such as calculating areas and volumes and understanding the properties of shapes.
• Students should be able to perform numerical calculations accurately or make reasonable estimates where exact computation is not feasible.
• Understanding and applying concepts of functions, including linear, quadratic, and exponential functions, and interpreting graphs.
• Developing and applying various strategies for tackling complex problems, such as breaking down a problem into smaller parts, working backward, or using logical reasoning.
• Evaluating the reasonableness of their answers and thinking critically about the methods and strategies used.
• Articulating their thought process and reasoning both orally and in writing includes using proper mathematical vocabulary and notation.
• Understanding how mathematical concepts apply in real-world contexts. Using calculators or other technological tools to assist in solving complex problems.

Skills

What are the literacy skills you want students to become proficient in?

My students must be adept at reading and understanding complex texts, which means deciphering word problems. This skill involves identifying key information, understanding the context, and interpreting the mathematical language embedded within the text. Closely linked to this is the development of critical thinking and analysis skills. Students should be able to analyze the text critically, discern relevant from irrelevant information, and make inferences, which are crucial for understanding and effectively solving word problems.

Another crucial skill is information synthesis, where students learn to integrate information from different parts of a text or multiple sources to construct a complete understanding of a problem. Equally important is their proficiency in mathematical vocabulary and language. Understanding and using mathematical terminology correctly is key to accurately interpreting and solving word problems and communicating solutions effectively.

Moreover, the ability to develop arguments and reasoning is fundamental. Students need to be skilled in logically justifying their solutions, explaining the steps they took, and articulating why they chose a particular method or solution. This leads to the necessity of strong written communication skills, enabling students to articulate their thoughts and solutions clearly and coherently in writing, using proper grammar, punctuation, and mathematical notation.

Additionally, oral communication skills are paramount, especially for class discussions, presentations, and collaborative problem-solving. Being able to verbally express ideas, reasoning, and solutions in an organized manner enhances understanding and fosters a collaborative learning environment. Furthermore, proficiency in note-taking and organization helps students retain and process complex information, a skill that is particularly useful when dealing with multifaceted word problems. Lastly, in an increasingly digital world, technological literacy is important, especially in using tools like graphing calculators or educational software that can aid in understanding and solving mathematical problems.

Learning Tasks

List the (1) learning task, (2) teacher action, and (3) student actions for each skill you are teaching.

Strategy(s) List

What is the instructional strategy(s) that will be used for the learning objective?

• I will begin the lesson by directly teaching the essential concepts and methods for solving word problems. This includes identifying key information and translating text into mathematical expressions.
• I will use the think-aloud method to model the cognitive process involved in solving a word problem, verbalizing my thought process to provide students with a clear example of how to approach these problems.
• I will lead guided practice sessions where I will assist students as they try to solve word problems, providing support and scaffolding to help them understand the process.
• I will organize students into small groups or pairs to work on word problems together. This will encourage them to engage in peer learning, share different problem-solving techniques, and learn from each other.
• I will provide opportunities for students to work on word problems independently, allowing them to apply and practice the skills and strategies they have learned in a self-directed manner.
• I will integrate technology, such as graphing calculators or educational software, into the lesson to assist in solving complex problems and to familiarize students with tools they may encounter in higher education and their future careers.
• I will facilitate class discussions where students can share their solutions and reasoning, and I will encourage them to reflect on the problem-solving process, including what strategies worked well and what areas need improvement. I will differentiate my instruction to meet the diverse needs of my students, providing varying levels of problem complexity and tailored feedback to accommodate different learning styles and levels of proficiency.

Performance (Verb)

What are the verbs being used? (Cite Bloom’s Taxonomy or Depth of Knowledge)

• Provide: This verb is used to introduce basic knowledge and facts to students, which aligns with Bloom’s “Remembering” level and DOK Level 1 (Recall & Reproduction).
• Demonstrate: This verb is used to illustrate a concept or process to students, and it fits into Bloom’s “Understanding” and “Applying” levels and DOK Level 2 (Skill/Concept).
• Verbalize: This verb is used to explain concepts or processes clearly and corresponds to Bloom’s “Understanding” level and DOK Level 2.
• Offer: This verb is used to provide targeted assistance or resources to support learning, and it is tied to Bloom’s “Applying” level and DOK Level 2.
• Organize: This verb is used to arrange and structure activities for effective learning through collaborative learning/group work, and it relates to Bloom’s “Applying” level and DOK Level 2.
• Encourage: This verb is used to motivate students to engage deeper with content, analyze it, and make judgments, and it falls under Bloom’s “Analyzing” and “Evaluating” levels and DOK Level 3 (Strategic Thinking).
• Promote: This verb is used to facilitate the application and analysis of knowledge through independent practice, and it corresponds to Bloom’s “Applying” and “Analyzing” levels and DOK Level 3.
• Integrate: This verb is used to apply technology as a tool in learning, and it aligns with Bloom’s “Applying” level and DOK Level 2.
• Facilitate: This verb is used to guide students in evaluating their learning and understanding through class discussion and reflection, and it ties into Bloom’s “Evaluating” level and DOK Level 3.
• Reflect: This verb is used to critically review and make judgments about one’s own learning through class discussion and reflection, and it corresponds to Bloom’s “Evaluating” level and DOK Level 3.
• Employ: This verb is used to indicate the application of various teaching strategies to meet diverse learning needs, and it aligns with Bloom’s “Applying” level and DOK Level 2 through differentiated instruction.

Conditions

What are the circumstances under which the performance takes place?

Tools, Resources, and Supports:

Students will be able to use calculators, especially for complex calculations and functions. Graphing calculators may also be used to help visualize functions and understand geometric problems.

Educational software and online resources will be utilized whenever available, particularly for interactive problem-solving and accessing a wider range of problems.

Whiteboards and projectors will be used for demonstrations and explanations. Handouts with word problems and step-by-step solution guides will be provided.

For group work, resources like shared documents (e.g., Google Docs) or collaborative platforms (in case the lesson is conducted online) will be used to facilitate group discussions and problem-solving.

Reference materials such as textbooks, notes, and formula sheets will be available to students. Translated materials or vocabulary lists may be provided for English Language Learners and students who require additional support.

Students may be restricted from using calculators for certain problems where manual calculation is feasible and educational to encourage problem-solving skills and understanding.

Environment:

The lesson will primarily take place in a traditional classroom environment suitable for individual and group work. The classroom will be arranged to facilitate easy movement for group activities and discussions.

In the case of remote or hybrid learning situations, the lesson will be conducted via an online platform, ensuring interactive engagement through digital tools and breakout rooms for group activities.

Safe and Inclusive Space: The environment will be structured to be safe and inclusive, where every student feels comfortable participating, sharing ideas, and asking questions.

Resource Accessibility: All necessary resources and materials will be made accessible to all students, ensuring that everyone has what they need to participate fully in the lesson.

Criterion: How will you measure student learning?

What is the learning criterion for this objective?

Criterion for Learning:

• Students should accurately solve at least 80% of the word problems provided to demonstrate proficiency. This includes correct calculation, proper use of formulas, and the application of appropriate mathematical concepts.
• Students must clearly understand the problem-solving process. This involves identifying key information in word problems, translating them into mathematical equations, and applying relevant math concepts to find solutions.
• Students must be able to communicate their solutions effectively. This includes providing clear, logical, and coherent written explanations of their problem-solving process and verbal communication during class discussions or presentations.
• Students must exhibit evidence of critical thinking and analytical skills in approaching and solving word problems. This includes breaking down complex problems, exploring different problem-solving strategies, and justifying their methods and answers.

Measuring Learning:

• Written quizzes or tests with a variety of word problems, in-class assignments, and homework that includes a mix of word problems.
• Observing students during problem-solving activities, particularly guided and independent practice sessions and group work.
• Encouraging students to reflect on their problem-solving process and self-assess their understanding and strategies.
• Incorporating peer review sessions where students assess each other’s approach and solutions to word problems, providing constructive feedback.
• Having students present their problem-solving process and solutions to the class can be a part of the assessment. Collecting and reviewing students’ work over the course of the unit to assess their progress and understanding.

Write a Learning Objective

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

Students in a high school mathematics classroom will be able to accurately solve and effectively communicate solutions to word problems by using the strategies of direct instruction, guided practice, collaborative group work, and independent problem-solving, with the support of tools such as calculators, educational software, whiteboards, and handouts. With mastery of learning being measured by least 80% accuracy in problem-solving and clarity in communication as measured by written assessments, oral presentations, and teacher observations of class activities.

Student Learning Target

Write an “I can” statement written from the student’s perspective.

I can accurately solve word problems in mathematics and clearly communicate my solutions by applying different problem-solving strategies and using tools like calculators and educational software. I will demonstrate my understanding and skills by achieving at least 80% accuracy in my solutions and effectively presenting my thought process.

Social Emotional Learning Strategies

What are some of the strategies you will use to support social and emotional learning in your content area classroom?

• I will cultivate a safe and respectful learning environment where every student feels valued. I will use positive reinforcement and celebrate diverse perspectives to build a community of respect and inclusion.
• I will encourage a growth mindset by praising students for their effort, strategies, and progress. I will emphasize the importance of persistence and learning from mistakes rather than just intelligence or grades.
• I will organize group work and peer learning activities to enhance mathematical understanding and teach important interpersonal skills like teamwork and effective communication.
• I will start classes with short emotional check-ins to understand how my students are feeling. This will help build empathy and alert me to any issues affecting their learning.
• I will encourage students to reflect on their learning experiences and challenges. This may be done through journaling or class discussions to foster self-awareness and resilience.
• I will introduce brief mindfulness exercises or stress-management techniques, especially before assessments, to help students manage anxiety and stay focused.
• I will provide students with strategies for managing emotions and maintaining focus, such as time management tips and methods to handle frustration.
• I will integrate real-life scenarios into my teaching to make mathematics more relevant and engaging. This will help students to connect math with their everyday experiences.
• I will give students some control over their learning, such as allowing them to choose specific problems or projects. This will increase their engagement and sense of ownership. I will be attentive to students needing additional support and provide guidance or direct them to appropriate school counseling or support services.

Student Misconceptions

Where do you foresee there being student misconceptions during this lesson?

• Students may struggle to understand the problem statement, especially if it is written in a complex or unfamiliar manner. This can lead to incorrect assumptions about the calculations or variables involved.
• One of the most challenging aspects of solving word problems is converting the text description into a mathematical equation or expression. Students may misinterpret certain words or phrases, resulting in incorrect equations.
• Problems that involve units (such as meters, liters, or grams) can be confusing. Students may mix units without proper conversion or fail to comprehend the significance of different dimensions in a problem.
• Misunderstanding specific mathematical terms can lead to errors. For example, confusing ‘sum’ with ‘product’ or misinterpreting terms like ‘less than’ or ‘per’.
• Students may apply the wrong mathematical principle or formula to a problem. This may occur if they do not fully understand the underlying concepts or if they jump to conclusions without thoroughly analyzing the problem.
• In some instances, students may follow incorrect lines of reasoning or logical fallacies. This can lead to valid processes but incorrect conclusions.
• Some students may oversimplify complex problems, overlooking key details, while others may overcomplicate them by adding unnecessary steps or information.
• Simple numerical errors in calculation, often due to haste or lack of attention to detail, can lead to incorrect answers even if the mathematical process is correct.
• Students may struggle to differentiate between relevant and irrelevant information in a word problem, leading to confusion and incorrect solutions. Math anxiety or a lack of confidence in their problem-solving abilities can lead students to second-guess themselves or give up too quickly rather than persisting to find a solution.