Reflect on whether these two lessons worked, what was good, and what wasn't good.

Jacob is currently enrolled as a fourth-grade student. He has been attending thesame school since kindergarten, thereby fostering a stable learning environment and facilitating the development of consistent relationships with peers and staff. According to his academic records, Jacob started receiving special education services under an Individualized Education Program (IEP) in second grade, following identification of a specific learning disability in mathematics. His educators observed initial difficulties with number sense and fundamental operations, which led to a formal evaluation and the implementation of appropriate support measures.

Currently, Jacob demonstrates moderate proficiency in basic math operations, such as addition and subtraction. However, he still requires regular reminders and visual aids to help him solve multi-step problems. When observed in class, Jacob actively participates in group activities but appears hesitant to work independently, especially when tasks involve multiplication or division. According to his current teacher, Jacob greatly benefits from structured routines and explicit instruction; however, he occasionally becomes frustrated when introduced to new math concepts. Overall, his performance highlights both his strengths in teamwork and his ongoing need for targeted support in foundational and complex math skills.

Throughout the assessment, the student remained focused and showed enthusiasm for answering each question. Occasionally, he shared his thought process, mentioning things like "I don't recall this" or "Maybe like this." The student often relied on scratch paper for calculations, suggesting a method for tackling multi-step problems. Overall, the student appeared slightly anxious at the beginning but became more at ease as the test progressed.

Most errors committed by the student were procedural in nature; for instance, he frequently established addition problems correctly but made errors in the process of carrying out the calculations. Certain conceptual misunderstandings were apparent in word problems, where the student mistakenly conflated addition and subtraction depending on the context of the problem. Factual inaccuracies, such as basic multiplication facts, were infrequent. The pattern indicates that the student comprehends overall concepts but encounters difficulties with multi-step procedures and translating word problems into mathematical expressions.

To address procedural errors, I recommend implementing step-by-step guided practice complemented by visual aids, such as place value blocks, during addition and subtraction lessons. For enhanced conceptual understanding, integrating word problem templates and utilizing graphic organizers can help students parse problem statements more effectively. Regular math fact drills, such as flashcards or timed games, will help

reinforce fundamental facts and improve speed. Furthermore, periodic reflection requiring students to articulate their reasoning aloudcan facilitate the identification and self-correction of errors in real-time.

Word Problem 1:

Problem: Emily has 24 apples. She decides to give away some to her friends and keep the rest. If she gives eight apples to 2 friends equally, how many apples does she have left?

Task Analysis:

Mathematical Concepts:

Addition and subtraction

Division (distributing evenly)

Multi-step problem-solving

Understanding remainders and final quantities

Lesson Plan for Problem 1:

Objectives:

The student will be able to perform basic addition and subtraction.

The student will understand how to divide equally among a group.

Materials:

24 manipulatives (e.g., counters or blocks to represent apples)

Whiteboard and markers

Worksheets for practice

Procedure/Agenda:

Advanced Organizer: Begin with a discussion about apples: Where do they come from? What can we do with them?

Instruction:

Explain the problem using manipulatives for visual learning.

Direct Instruction: Model how to subtract the number of apples given away and how to divide the apples equally among friends.

Ask questions: "How many apples does Emily have after giving them away?" and "How many does each friend get?"

Guided Practice: Have the student use manipulatives to solve a similar problem in pairs.

Strategies, Modifications, and Accommodations:

If the student needs extra help, provide number lines or counting charts to support their learning.

Allow extended time for tasks.

Provide verbal prompts during guided practice.

Word Problem 2:

Problem: A toy shop has 150 toys. If they sold 45 toys on Monday and 35 toys on Tuesday, how many toys do they have left?

Task Analysis:

Mathematical Concepts:

Addition and subtraction

Multi-step calculation

Understanding total reduction

Place value comprehension

Lesson Plan for Problem 2:

Objectives:

The student will apply subtraction strategies to determine remaining quantities.

Students will learn to tackle multi-step problems.

Materials:

Visual aids (pictures of toys)

Subtraction worksheets

Whiteboard and markers

Procedure/Agenda:

Advanced Organizer: Use toys to engage students: Discuss different kinds of toys.

Instruction:

Present the problem and use visual aids to illustrate the number of toys sold.

Direct Instruction: Walk the student through the first subtraction, and then the second one.

Use prompting questions: "How do we find out how many are left?"

Guided Practice: Allow the student to work out another toy-related problem.

Strategies, Modifications, and Accommodations:

Use visual models for those struggling with abstract concepts.

Provide written instructions along with verbal explanations.

Word Problem 3:

Problem: At a fundraiser, each cupcake costs $3. If Sarah buys five cupcakes and Maria buys 4, how much do they spend in total?

Task Analysis:

Mathematical Concepts:

Multiplication

Addition

Multi-step operations

Understanding the concept of total cost

Lesson Plan for Problem 3:

Objectives:

The student will learn multiplication as a form of repeated addition.

Students will apply addition to find total expenditures.

Materials:

Cupcake counters or images

Worksheets with similar problems

Whiteboard

Procedure/Agenda:

Advanced Organizer: Discuss the purpose of a fundraiser and what fundraising entails.

Instruction:

Introduce the problem using counters to visualize the cupcakes being purchased.

Direct Instruction: Show how to multiply the cost of cupcakes by the quantity purchased and then add the results.

Prompt with questions: "What is the cost of Sarah's cupcakes?" and "What about Maria's?"

Guided Practice: Have students calculate the cost of cupcakes for different quantities.

Strategies, Modifications, and Accommodations:

If the student needs extra assistance, pair him with a buddy for support.

Ensure clear and straightforward instructions are provided in writing.

Use colored markers to highlight necessary steps in calculations