Context for Lesson ( please describe what students did in lessons before and after this lesson plan)

Before this lesson, students worked on solving single-step algebraic equations using inverse operations. In the following lesson, students will apply their understanding of multi-step equations to solve word problems and real-life scenarios. This lesson serves as a bridge between foundational algebraic concepts and problem-solving applications. By strengthening their ability to manipulate and solve algebraic expressions, students will be better equipped to tackle advanced algebraic concepts such as systems of equations and inequalities.

Common Core and/or PA State Standards

Essential Question(s)

CCSS.MATH.CONTENT.HSA.REI.B.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.CCSS.MATH.CONTENT.HSA.SSE.A.1: Interpret expressions that represent a quantity in terms of its context.

· How can multi-step equations be solved systematically?

· Why is it important to follow a sequence of operations when solving an equation?

· How do algebraic principles apply to real-life problem-solving situations?

· How can identifying patterns in equations improve efficiency in solving them?

· What strategies can be used to check the correctness of a solution?

Overarching Goals/Big Idea (1-2 goals)

Assessment(s)

Students will know that…

Students will develop procedural fluency in solving multi-step equations.

Students will improve their ability to apply algebraic reasoning to solve real-world problems.

Students will demonstrate their understanding of multi-step algebraic equations by completing a teacher-created quiz that includes both mathematical problems and real-world applications, with a goal of achieving at least 80% accuracy. Additionally, they will engage in a class discussion to analyze and explain various solving strategies, fostering a deeper comprehension of problem-solving techniques.

Content/Knowledge Goals (4-5 goals)

Assessment(s)

Students will develop a strong understanding of multi-step equations by applying multiple inverse operations, correctly identifying and combining like terms, and systematically isolating the variable. They will reinforce their learning by checking solutions through substitution and applying these strategies to real-world word problems. To enhance problem-solving skills, students will utilize visual models, step-by-step breakdowns, and guided practice. Additionally, they will explore various equation-solving methods, such as substitution and elimination, to expand their mathematical reasoning and adaptability.

To assess student understanding of multi-step equations, various strategies will be implemented. Exit tickets will require students to solve and explain a multi-step equation, ensuring they can articulate their problem-solving process. A written reflection will prompt students to describe how algebraic principles apply to real-world scenarios, reinforcing the practical significance of equations. A scaffolded worksheet will guide students through problems of increasing complexity, from basic equations to application-based word problems. Additionally, a peer-review activity will allow students to solve a problem, exchange work with a partner, and check for errors, fostering collaboration and critical thinking. Finally, a performance-based assessment will challenge students to create and solve their own word problems, demonstrating their ability to apply multi-step equations in meaningful contexts.

Skill Goals (1-2 goals)

Assessment(s)

Students will develop proficiency in solving multi-step algebraic equations, aiming for at least 80% accuracy on formative assessments. To enhance their problem-solving skills, they will utilize self-monitoring strategies such as graphic organizers and structured checklists, allowing them to track their progress, identify errors, and systematically work through complex equations.

Students will demonstrate procedural fluency in solving multi-step equations by completing a problem set with at least 80% accuracy. To reinforce their understanding and self-monitoring skills, they will also submit self-assessment checklists that outline their problem-solving steps, highlight any errors, and document corrections, fostering a reflective approach to learning.

IEP or ELL Goals (Defer to your instructor’s instructions for this section, not required for all courses)

Assessments

Alex will work toward mastering algebraic equations by correctly completing single-step equations with 70% accuracy within two months and achieving 80% accuracy on multi-step equations by the end of the semester. To enhance his organizational skills, he will implement self-monitoring strategies, aiming to reduce missing assignments by 50% over the semester. Additionally, Alex will demonstrate persistence in problem-solving by actively seeking assistance at least three times per week, ensuring continuous growth and understanding.

Alex will strengthen his problem-solving skills by completing a structured worksheet with guided steps, where assessment will focus on the correct process rather than just the final answer. He will receive targeted teacher feedback on his problem-solving strategies, emphasizing clear organization of steps. Additionally, Alex will participate in small-group discussions, where he will articulate his approach to solving equations, reinforcing his understanding through peer interaction and collaborative learning.

Materials/Resources

To support student learning and problem-solving in algebra, a variety of resources will be utilized. Algebra textbooks will provide foundational knowledge, while interactive whiteboards will facilitate dynamic instruction. Students will use graphic organizers and step-by-step equation-solving templates to structure their work. Scientific calculators and online equation-solving tools will assist with complex calculations, and guided practice worksheets will reinforce concepts. Highlighters will help students identify key parts of equations, enhancing comprehension. Additionally, digital equation-solving software will offer interactive learning experiences, making problem-solving more engaging and accessible.

Student Activities (Highlight all that apply for activities throughout lesson):

Building Background:

Links to Experience

Links to Prior Learning

Key Vocabulary

Explicit Instruction

Scaffolding:

Modeling

Guided

Independent (IEP)

Explicit Instruction

Grouping:

Whole Class

Small Group

Partners

Independent

Processes:

Reading

Writing

Listening

Speaking

Strategies:

Hands-on

Meaningful

Linked to Objectives

Assessment:

Individual

Group

Written

Oral

Instructional steps

include the amount of time allocated for each step, add as many parts as you need – be aware of transition time

Lesson Hook: Warm-up/Motivation/Pre-Assessment (5-10 mins)

· Activity: Students will begin with a quick warm-up exercise, solving a simple one-step equation on their whiteboards. The teacher will then present an equation with multiple steps and ask, "What is different about this equation compared to the warm-up?" This will encourage students to recognize the complexity of multi-step equations and engage their prior knowledge.

· Visualization: The teacher will display an equation-solving flowchart on the interactive whiteboard, showing the sequence of solving multi-step equations. Students will discuss patterns they notice in equation-solving processes.

Main Activity:

Part 1 – Modeling and direct instruction (_15_ minutes)

· The teacher will explicitly demonstrate the step-by-step process of solving a multi-step equation. Key vocabulary such as inverse operations, combining like terms, and isolating the variable will be reinforced.

· Graphical Support: A structured graphic organizer will be used to break down each step, with visual cues highlighting key operations. Alex and other students who require scaffolding will use a pre-filled template to guide them through the process.

· Student Interaction: The teacher will pause after each step, prompting students to explain why each operation is necessary.

Part 2 – Guidance with student as a whole class or in partners (_15_ minutes)

· Students will work on example problems in pairs, applying the demonstrated strategies.

· Scaffolding: Alex will be paired with a peer tutor for additional support. Prompts, such as hint cards, will be provided for those who need them.

· Think-Pair-Share: Students will discuss their solutions with partners before presenting to the class. The teacher will circulate to offer feedback and ensure students follow the correct steps.

Part 3 – Students work independently (_15__minutes)

· Students will solve five problems independently, applying the strategies learned.

· Additional Support: Alex and other students needing accommodations will have access to a reference sheet summarizing the steps.

· Extension: Advanced learners will attempt a word problem requiring real-world application, such as balancing a budget or analyzing a physics equation.

Lesson Closure:

· Students will solve one multi-step equation and explain their reasoning in a short written response.

· Review: The teacher will address common misconceptions and summarize key takeaways from the lesson.

Universal Design for Learning <= click on this link. Please include a minimum of one way to apply UDL pedagogy to your lesson for each of the three criteria listed below. Considerations must be specific to your lesson.

Engagement: The lesson includes interactive components such as collaborative problem-solving, the use of whiteboards, and real-world problem scenarios to maintain student interest.

Representation: Concepts will be presented using multiple modalities, including verbal instruction, visual aids, and hands-on activities like using equation-solving templates.

Action and Expression: Students will demonstrate their understanding through oral discussions, written responses, and structured step-by-step solutions.

Differentiation Strategies:

ELL: Key vocabulary will be explicitly taught and reinforced using visuals, sentence stems, and real-life examples. Peer support and translated notes will be provided when necessary.

LCLP (low content, low process): Students will receive extra guided practice and a step-by-step breakdown of problem-solving processes, using structured checklists and additional worked examples.

HCHP (high content, high process): Advanced learners will work on real-world problem-solving applications that require deeper algebraic reasoning, including multi-variable equations and algebra-based logic puzzles.

IEP/504 Accommodations ( EDUC 201/501/402/406/407/408 only): Alex will receive extended time, graphic organizers, preferential seating, step-by-step scaffolding, self-monitoring tools, and structured feedback from the teacher.

Classroom arrangement

Students will be seated in pairs to encourage peer learning, with flexible seating options for those who need reduced distractions.

Possible Problems with solutions – must be specific to your lesson plan

What do you do if you run out of time?

Assign independent practice problems as homework and review them in the next lesson.

What do you do if your lesson ends early?

Provide enrichment problems that require deeper critical thinking, such as real-world applications of algebraic concepts.

What do you do if your resources fail?

Utilize printed worksheets and have students work through problems collaboratively using whiteboards.

What behavioral challenges and solutions do you anticipate?

If students become disengaged, incorporate movement-based activities such as solving problems on the board. If a student struggles with frustration, allow short breaks and use self-regulation strategies.

After teaching this lesson, I will assess student performance based on formative assessments and adjust pacing as needed. If students struggle with multi-step problem-solving, additional scaffolding strategies will be implemented in future lessons. If students grasp the material quickly, they will have enrichment opportunities involving algebraic word problems that require deeper critical thinking.