C285 Task 2 Tyler P
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School
Western Governors University *
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Course
C285
Subject
Mathematics
Date
Apr 3, 2024
Type
docx
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8
Uploaded by AmbassadorUniverseWasp44
Math Direct Instruction Lesson Plan Template
General Information Lesson Title: Graphing functions with Desmos Subject(s): Mathematics- Algebra Grade/Level/Setting: 8
th
Grade
Prerequisite Skills/Prior Knowledge:
The students should have basic understanding of algebraic expressions, linear equations, and how to plot geometrically. Standards and Objectives State/National Academic Standard(s):
Common Core State Standards for Mathematics (CCSS.MATH. CONTENT.8.G. A.1a) (IXL - Common Core Eighth-Grade Math Standards, n.d.).
Learning Objective(s): By the end of the lesson the students should be able to graph functions using Desmos and on paper, while accurately defining the key features such as intercepts, slopes, and transformations. The students will demonstrate this by graphing a set amount of functions and explaining the attributes. Measurable Outcome: Students will be able to successfully graph three different functions on Desmos while describing different features of them for each. Then the students should be able to score over 80%
in the quiz summative assessment. Materials Technology
- Paper -Pencils
-Rulers and Protractors -Desmos Graphing Utility (need laptops)
-Quizzes Technology will be used to enhance the learning of the students through Desmos. It provides them with a dynamic and interactive application to create and compare different shapes with technology. It aligns with the SAMR model because it transcends paper and pencil to a digital tool to redefine their student learning. Language Demands
Specific ways that academic language
(vocabulary, functions, discourse, syntax) is used by students to participate in learning tasks through reading, writing, listening, and/or speaking to demonstrate their understanding. Language Function(s):
1.
Use mathematical vocabulary to describe the features of each function given. 2.
Communicate the mathematical concepts to peers or on paper about the transformations and the function characteristics. Vocabulary:
-Coordinate plane -coordinate -plotting
-graph
-x-axis
-y-axis -function
-translations
-intercepts
-slope
Discourse and/or Syntax:
1. Understand and use appropriate mathematical discourse when explaining the steps to graph functions. Conduct this through peer collaboration during lesson and working time. Using scaffolding as the teacher walks around will promote discourse as they will help the students stay
on track and participate actively with one another. 2. Apply the correct syntax when putting the function within Desmos. This will take effective explanation of how to use Desmos to the students. Planned Language Supports:
Offer additional resources such as a glossary of key vocabulary terms for students to look back on, provide visuals of the process of graphing geometric shapes, and verbal explanations. Then offer a poster for students to write on to express their questions of the lesson that the teacher can address. Instructional Strategies and Learning Tasks
Anticipatory Set:
Activity Description/Teacher
Student Actions
Begin with a brief discussion on the importance and relevance of understanding graphing functions using technology. Then introduce Desmos as an online tool that is very effective to visualize the mathematical concepts of functions. The students then will listen closely and take notes. Ask questions to participate within discussions and then express what they already know with their prior experience in graphing. Presentation Procedures for New Information and/or Modeling:
Activity Description/Teacher
Student Actions
Teacher will demonstrate the functions and basic features of Demos, such as how to enter
in the functions, adjust settings, and how to interpret and understand the graph. (Transformations to the x intercept, y intercept, compression, or elongation, Reflection of x or y axis.) Students will follow along on their laptops, ask questions, and then practice themselves while watching the teacher give examples and how to interpret them. They will also be taking notes in a notebook on key attributes the teacher explains. Guided Practice:
Activity Description/Teacher
Student Actions
Teacher will give the students 3 different functions to graph, then explain 2 attributes about them. They then will practice graphing linear functions and quadratic functions. The teacher will then walk around the classroom and make sure the students know what they are doing. Asking questions such as: What are the transformations to this function as the base is x^2? Are there any concepts where you’re finding trouble? Students will actively participate, ask peers for help, questions, and graph functions on their laptops. They will then ask the teacher if they need additional support and make sure the peers around them are not lost as well. Collaboration is key to understanding. Independent Student Practice:
Activity Description/Teacher
Student Actions
The teacher will assign questions that will reinforce and allow the students to see how they fare with the concepts of graphing functions and explaining the attributes through individual work. They then will Students will work on the assigned problems independently. Graph the functions and writing the key functions of each of them as well through Desmos. They then will note any challenges or additional questions they may have for in-class
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receive 3 different functions and will graph them through Desmos. F(x)=X^2+4x+2
F(x)=2(X^3-5)-2
F(x)=-x^4+3
After graphing, write two descriptions and attributes of each functions including the transformations. discussion. Culminating or Closing Procedure/Activity:
Activity Description/Teacher
Student Actions
Have a class discussion asking about additional questions that the students have. Then review key concepts while asking the students to share their Desmos graphs while explaining the features they had written about each one. Students will actively participate in the discussion, share their graphs and observations. Ask questions and articulate their thinking for graphing functions and explaining translations. Differentiated Instruction Consider how to accommodate for the needs of each type of student. Be sure that you provide content specific accommodations that help to meet a variety of learning needs.
Gifted and Talented:
Give these students more complex functions or even on Desmos if they already mastered this lesson. It will allow them to be more engaged and try to help their classmates when discussion comes along. EL:
Give them a bilingual version depending on what language they speak, offer visual aids and demonstrations to show them what to do. Give them vocabulary sheets to show them the Key terms for them to focus on and to look back onto. Students with Other Special Needs:
Give them additional time to complete these tasks, give them written and verbal instructions as it reinforces their understanding and then allow them to give answers with drawings and diagrams rather than just using written answers. Assessment
Formative
Describe how you will monitor, support, and extend student thinking.
Monitor
: Circulate the classroom, observe the students as they progress through questions on Desmos, offer assistance and ask additional questions to develop their thinking. Ex. I’ve noticed you wrote that it shifts vertically by 3, but what does it mean when there is a negative in front of the variable? (X or Y reflection). Support
: Provide additional guidance for those that struggle more than others, encourage peer collaboration.
Extend
: Challenge those who have mastered the concepts at objective with more complex functions and additional graphing tasks. Summative
(Quizzes, Tests, products) Finish the lesson with a short quiz that will assess the student’s ability to graph functions on Desmos and to write key features. The quiz will include 3 different functions and will be graded base off the accuracy of the graph, then if the 2 key features are also accurate and provide profficient explanation and articulation of the attributes. Quiz will be provided in A3. A3. Supporting Documents Quiz: Q1. Graph and explain 2 features of this function: F(x)= (x-3)^2 -2
Q2. Graph and explain 2 features of this function: F(x)= -x^3+3
Q3. Graph and explain 2 features of this function: F(x)= ½ x^4 -1
Answers that the teacher will have to grade on: Q1.
Two Features: The function is shifting to the right 3 units, then translating down by 2 units. Q2. Two features: The function is reflecting over the y axis, as there is a negative on the -x^3. The function is also vertically translating by 3 units up.
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Q3. Two Features: The function is compressed by ½, and it is a parabola because the exponent on the variable is an even number. The function is also being transitioned vertically down 1 unit. B1. Engagement and interaction: The integration of Desmos technology into the lesson effectively enhances the student learning and understanding because it provides a very dynamic and interactive platform to visualize graphing functions and the translations of it. Desmos allows the students to graph functions in real time and enable them to see their errors in syntax instantly instead of just doing it incorrectly
on paper without knowing. The simple and effective visual representation allows for deeper and easier comprehension of algebraic principles such as x and y intercepts, slopes, transformations, and the students can observe the impact to the graph through adjusting numbers in the equation. This allows the students to go part by part in a function to see things such as vertical translations,
horizontal translations, compression, reflections, all while doing it instantly. By implementing technology, the students not only gain easier and faster understanding of graphing functions and explaining the features, but they also develop understanding of the mathematical concepts and the relationship of the numbers to the graph. B2. Limitations: There are many limitations that might withhold students to their learning and understanding.
Some of them could be technical issues that students could have. This might occur if there are internet issues, laptop malfunctions, students not on the right website or doing something else. This would mess up with the flow of the lesson and some students will not be able to participate with the rest of the class. Another limitation is that some students may have a reliance on technology and not know how to do the foundation of the lesson through paper and pencil. This might limit their understanding of plotting functions and translations on paper. B3. Solution for B2: The teacher could have multiple activities that are created through participation with Desmos while also having some using paper and pencil graphing activities utilizing graph paper. This way the students will have the ability to mirror the concepts from technology and on paper. This would solve the issue with overreliance on technology as it helps them have a balance and a reinforcement of the concepts to really make sure that they understand it and can do it without the use of technology. To fix the problem with technical solutions, the students who do not have the ability to use their own laptop can partner up with a classmate to do the activity together. By implementing this, the teacher can optimize the ability to enhance the student learning and understanding without having to worry about possible challenges. C. Sources Desmos | Geometry
. (n.d.). Www.desmos.com. https://www.desmos.com/geometry
IXL - Common Core eighth-grade math standards
. (2023). Ixl.com. https://www.ixl.com/standards/common-core/math/grade-8