Task 3- Justifications for B-E
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Western Governors University *
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Course
C281
Subject
Mathematics
Date
Apr 3, 2024
Type
docx
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Uploaded by ChiefRain13624
B. Explain how your lesson plan uses the three-phase lesson format to promote teaching through problem solving by doing the following:
1. Justify how the Before phase integrates
one
of the following using a relevant, specific example from your lesson plan:
• activating prior knowledge
• clarifying the problem
• establishing clear expectations
The before phase integrates activating prior knowledge into the lesson by reinforcing the prior knowledge of calculating the area of different quadrilaterals and triangles by reviewing over the formulas and steps to solve five area problems within our 5-a-day warm-up. Students need this prior knowledge in order to successfully explore the composite figure activity. By revisiting the basic concepts of calculating the area of quadrilaterals and triangles, learners refresh their memory and activate their prior knowledge. This primes their minds for more complex tasks involved in decomposing composite figures. It provides a foundation upon which they can build new understanding. Calculating the area of quadrilaterals and triangles is a fundamental skill in geometry. By practicing this skill as a warm-up, learners reinforce their understanding of basic geometric principles. This review ensures that learners have the necessary foundation to tackle more complex tasks later on.
2. Justify how the During phase integrates
one
of the following using a relevant, specific example from your lesson plan:
• observing students’ mathematical thinking
• providing appropriate support
• providing worthwhile extensions
When students are tasked with decomposing composite figures in the during phase, they are required to devise problem-solving strategies. They must analyze the given figure, identify its fundamental shapes, and determine how to break it down into quadrilaterals and triangles. Observing how students approach this task provides insight into their problem-solving strategies, including their ability to apply geometric principles, spatial reasoning, and critical thinking skills. Decomposing composite figures requires flexible thinking, as there can be multiple ways to break down a given shape. Students may encounter different challenges and obstacles along the way, prompting them to adapt their approach and consider alternative strategies. Observing how students navigate these challenges provides valuable insight into their ability to think flexibly and creatively in mathematical contexts. Students must justify their decisions and explain why their chosen decomposition strategy is valid. They need to demonstrate an understanding of geometric properties and relationships to justify why certain shapes can be combined or divided in specific ways. Observing students' explanations and justifications offers valuable information about their ability to apply logical reasoning in mathematical problem-
solving. Exploring composite figures and their decomposition in this activity provides opportunities for students to engage in mathematical communication. They may collaborate with peers, discuss their strategies, and explain their reasoning to others. Observing students' interactions and listening to their explanations allows teachers to assess their ability to communicate mathematical ideas effectively.
3. Justify how the After phase integrates
one
of the following:
• promoting a community of learners
• providing active listening without evaluating
• summarizing the main ideas of the problem and identifying future problems
Encouraging students to share their findings, strategies, and solutions fosters a sense of collaboration and community among learners. It creates an environment where students feel comfortable expressing their ideas, listening to others, and engaging in meaningful discussions. This collaborative atmosphere promotes active learning and allows students to learn from each other's perspectives and approaches.
Discussing different approaches to solving the same polygon encourages students to engage in critical thinking and reflection. They must analyze and compare the various strategies used by
different groups, evaluate their effectiveness, and consider the reasoning behind each approach. This promotes deeper understanding of the problem-solving process and helps students develop their analytical skills.
By highlighting that the total area remains the same regardless of the method of decomposition, students learn to appreciate the importance of multiple perspectives in mathematics. They understand that there can be different valid ways to approach a problem and
that mathematical concepts can be understood from various angles. This promotes a growth mindset and encourages students to be open to exploring different strategies and viewpoints.
C. Justify how the differentiation in your lesson plan from part A helps gifted and talented students experience the benefits of teaching through problem solving while still meeting the stated learning objective. Use a relevant example from the lesson plan to support your justification.
Higher-level composite shapes require gifted and talented students to engage in deeper levels of critical thinking and creativity. They must analyze the unique characteristics of each shape, devise innovative strategies to decompose them effectively, and consider alternative approaches to solve the problem. This cultivates their analytical and creative thinking skills, which are essential for tackling complex mathematical challenges.
For example, the following problem below would require these students to draw upon their understanding of properties of special quadrilaterals, principles of measurement, and techniques for calculating area to successfully decompose the composite shapes and find the total area. This reinforces their mastery of these concepts and enhances their ability to apply them flexibly in different situations. As you can see, there are several ways that students may choose to decompose the shape and within those smaller shapes, students would have to successfully calculate the individual measurements.
D. Justify how the differentiation in your lesson plan from part A helps English learner students experience the benefits of teaching through problem solving while still meeting the stated learning objective. Use a relevant example from the lesson plan to support your justification.
Assigning peer partners who can help translate unknown vocabulary provides EL students with immediate support in understanding the instructions and mathematical concepts. This collaborative approach not only assists EL students in overcoming language barriers but also fosters a sense of belonging and community within the classroom. It allows EL students to participate more actively in the problem-solving process by ensuring they have access to the necessary linguistic support.
Providing EL students with access to their student notebooks, which include academic vocabulary and visual aids, offers additional support in comprehending mathematical concepts. These resources serve as valuable reference materials that EL students can consult as needed to clarify unfamiliar terms or reinforce their understanding of key concepts. Access to visual aids
helps EL students make connections between words and their corresponding mathematical representations, facilitating comprehension and retention.
Allowing EL students to use coloring to differentiate between the different shapes that make up the given polygon enhances their understanding of geometric decomposition. Color-coding helps EL students visually distinguish between the various components of the composite figure, making it easier for them to identify and analyze each shape individually. This visual scaffolding promotes comprehension and encourages active engagement in the problem-solving process.
Presenting EL students with simpler polygons that can be decomposed into a smaller number of quadrilaterals or triangles, with most or all measurements provided, reduces cognitive overload and allows them to focus on mastering the core concepts of geometric decomposition. By simplifying the task, EL students can build confidence and develop foundational skills in problem-solving and geometry. Given measurements provide additional support by removing the need for extensive language processing and allowing EL students to focus on applying mathematical procedures.
In the problem below, there is only one valid decomposition strategy, which is to split the shape into a rectangle and triangle. These students would be able to highlight the two shapes, consult their student notebooks if needed, and then apply their previous knowledge of area calculations to conclude the problem-solving process. Most all of the measurements are given, so these students would not be hindered by the additional concepts allowing them to find success in their learning. E. Justify how the differentiation in your lesson plan from part A helps students with other special needs different from those in part C and part D experience the benefits of teaching through problem solving while still meeting the stated learning objective. Use a relevant example from the lesson plan to support your justification.
Providing students with special needs access to their student notebooks, which include academic vocabulary and visual aids, offers additional support in comprehending mathematical
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concepts. These resources serve as valuable reference materials that students can consult as needed to clarify unfamiliar terms or reinforce their understanding of key concepts. Access to visual aids helps students with special needs make connections between words and their corresponding mathematical representations, facilitating comprehension and retention.
Allowing students with special needs to use coloring to differentiate between the different shapes that make up the given polygon enhances their understanding of geometric decomposition. Color-coding helps these students visually distinguish between the various components of the composite figure, making it easier for them to identify and analyze each shape individually. This visual scaffolding promotes comprehension and encourages active engagement in the problem-solving process, which can be particularly beneficial for students who may struggle with abstract concepts.
Presenting students with special needs with simpler polygons that can be decomposed into a smaller number of quadrilaterals or triangles, with most or all measurements provided, reduces cognitive overload and allows them to focus on mastering the core concepts of geometric decomposition. By simplifying the task, these students can build confidence and develop foundational skills in problem-solving and geometry. Given measurements provide additional support by removing the need for extensive processing and allowing students to focus on applying mathematical procedures, which can be particularly helpful for students with special needs who may struggle with processing information.
As with English language learners, in the problem below, there is only one valid decomposition strategy, which is to split the shape into a trapezoid and a square. These students would be able to highlight the two shapes, consult their student notebooks if needed, and then apply their previous knowledge of area calculations to conclude the problem-solving process. All of the measurements are given, so these students would not be hindered by the additional concepts allowing them to find success in their learning. By using these strategies, I am able address individual learning needs, provide additional scaffolding, promote active participation, and facilitate comprehension, ultimately supporting students with special needs in their mathematical learning and development.