DID Model - Slope & y-intercept
Introduction
The Dynamic Instructional Design model was established in 2011 and its purpose is to align lesson planning for a technology rich environment. Each of the components allows for specific feedback and modification of parts to ensure the design remains successful for implementation with all groups of students. Instructors should reflect and make modifications after the design of each of the independent parts that form a cohesive lesson whole. This format is especially helpful when working to develop successful lessons in a district that is one to one.
My students are eighth grade math students and, in general, prefer the use of technology when it has been well organized by the instructor and is easy to use. It is imperative that when selecting technology and implementing it, I have considered the students, their previous knowledge, the intensity of the lesson, the levels of knowledge required by the objectives of the lesson, and the technology being used. The following is one lesson developed for the 8th grade general education math classroom.
Part 1: Getting to Know the Learners
Overall students are 13 to 14 years old. They are general education students in an inclusive classroom where there are multiple levels of learners including some with IEPs, 504s, and ESOL service needs. In order to have an understanding of all learners it will be imperative that I compile the necessary information in an easy accessible format. I have developed a Sheet to summarize the data. This will allow me to have an at a glance overview of student profiles. I will input data as it becomes available to me (rosters are not yet published).
In order to understand the specific learning styles and multiple intelligences of my students I will have students take two surveys at the beginning of the school year, and again during the middle of the year as students experience significant cognitive growth during the 8th grade year and the onset of puberty. To analyze their learning styles, students will take a Learning Styles Inventory; results will be reported in our Google Classroom. Students will also take a Multiple Intelligence Inventory; results will be reported in our Google Classroom.
This information will allow me to form small groups for collaborative learning and small group instruction. I will be able to group learners together with their primary learning style and cater to their individual learning needs to maximize instructional time. This will also give students a more concrete understanding. I will then group students with peers with differing learning styles and ask them to share strategies. This also frees up instructional time to target learners who may need more direct instruction or one on one tutoring. It will also give students a sense of ownership to share with their peers. Making students feel confident in mathematics is a key element in eliminating the fear that is often associated with the content in the upper middle grades.
Part 2: Performance Objectives and Lesson
For this lesson, the standard is 8.F.4b - Determine the slope and the 𝑦-intercept of a linear function given multiple representations, including two points, tables, graphs, equations, and verbal descriptions. The performance objective is as follows: at the completion of this lesson, students will be able to determine the slope and y-intercept of a graph and table with 85% accuracy when given a graph or table with a positive or negative slope using Desmos to answer questions on a digital assessment via Google Classroom. The following learning objects are aligned to Bloom's Revised Taxonomy. The students are required to apply, analyze, and interpret key features of graphs and tables. (Note: this standard has been split in order to teach students another standard that will be required for them to link equations and real-world situations at the end of the two week unit.)
Lesson Plan
This lesson plan format was selected because the lesson is clearly outlined, streamlined, and easy to understand for teachers, curriculum coaches, and administrators. It is easy to complete and modify upon completion of the lesson and reflection. It was selected from the textbook, Teaching and Learning with Technology.
Instructional Standard
8.F.4 - Apply the concepts of linear functions to real-world and mathematical situations.
Instructional Indicator
b - Determine the slope and the 𝑦-intercept of a linear function given multiple representations, including two points, tables, graphs, equations, and verbal descriptions.
Instructional Objectives
Applying: Calculate the slope of a line from a graph.
Applying: Calculate the slope of a line from a table.
Analyzing: Recognize the y-intercept of a line from a graph.
Analyzing: Recognize the y-intercept of a line from a table.
Activities
Tutorial - Using Desmos
Original Video - Interpreting Slope & y-intercept from a Graph
GoFormative - Activity (The GoFormative is private; this is the worksheet that was used to create both A Formative assignments in this lesson.)
ALEKS - digital content requirement
Khan Academy - Writing an Equation from a Graph
Google Form - Summative Assessment
Procedure - Blended Learning Rotation
Group One: Group one will start with the instructor. This will be high level learners who need little direct instruction. They will use Desmos to graph tables and identify slope and y-intercept with the instructor. At their second rotation they will complete two Formative assessments. One assessment will focus on graphs and the other on tables. When they have completed the GoFormative assessments, they will independently move on to completing 15 minutes of ALEKS in the Geometry slice. When they have completed ALEKS they will move on to the Khan Academy lesson for writing an equation from a graph.
Group Two: Group two will watch the Desmos tutorial followed by the original video, Interpreting Slope & y-intercept from a graph. They will then start the GoFormative for graphs. They will move to the instrutor at some point while working on the GoFormative and any questions will be addressed. While working with the instructor students will use Desmos to graph tables and start the GoFormative assignment addressing tables. They will finish this independently and then move to ALEKS for the remainder of the class period.
Group Three: Group three will work for 15 minutes on ALEKS. When they have completed their 15 minutes on ALEKS they will watch the Desmos tutorial and the original video. They may or may not have time to watch both videos before the teacher moves to this group. This group will work through the graph and table tutorials with the teacher using Desmos. Since this will be my lowest level learners, they will spend the majority of the class with teacher led digital instruction.
Differentiation
Differentiation is described in detail above. Specifically, for higher level learners the added Khan Academy assignment and for lower level learners, the teacher led digital learning experience.
Formative Assessments:
GoFormative: Graphs
GoFormative: Tables
ALEKs report
Small group discussion
Summative Assessment:
Google Form
All assessments are linked in the activities and procedures section of this lesson plan.
Part 3: Teaching and Learning Strategies
The nature of an inclusion classroom brings unique opportunities to teachers and learners. The blended learning model works well because a small group can work directly with one teacher while another teacher monitors and guides the other two groups. For this lesson, the teacher will work with the other two groups on guidance and time management. This allows students to stay focused, maximize learning opportunities, and not be slowed by other learners. The standards require students to use appropriate tools strategically and the implementation of Desmos throughout the lesson gives students access to a learning tool that will be useful throughout their mathematics career. It also gives students experience with digital graphs and manipulation that will translate to other applications. The summative assessment on Google Forms will serve as the evaluation of success for my students’ learning and my teaching strategies. Students will also be surveyed randomly throughout the year, using Google Forms, to gain insight into which strategies students feel most confident learning with.
Small group instruction, independent practice, and collaboration are all part of the strategy of blended learning. Students have access to a teacher at all times but are encouraged to work independently and collaborate with their peers when struggling before reverting to a teacher for clarification. This builds a sense of community and ownership of learning in the classroom and ultimately benefits all learners and teachers.
Part 4: Present and Analyze Technologies Used
Desmos: Desmos is an online graphing tool. Students struggle with finding the slope from a table and this software allows students to graph the table and relate the table as a graph. It is helpful for all levels of learners, but lower level learners, who may struggle with conceptualization of the abstract table gain valuable insight and are able to make strong connections for a deeper learning experience.
YouTube: I created an original video to give learners an opportunity to learn the material from a recognizable instructional voice. This aligns to the personalization principle and gives students a resource to refer to when working on homework or classroom assignments when the teacher is not immediately available. I also created a Desmos tutorial to give students a reference if the technology is confusing.
GoFormative: This site allows me to see student work and to collect work digitally. I generally allow students to work collaboratively, but require individual submissions. Students are only able to answer differently than their group if they can articulate their argument in written form to accompany their submission. The great thing about GoFormative is that I can easily check students work while they are working, even if I am occupied with another group, giving me the unique opportunity to assess students while they are working, without disrupting their working, or leaning over their shoulder.
ALEKs: This is required digital content from the district. I ask students to work in the strand that we are studying to fill in gaps they may have before getting new content.
Khan Academy: In this lesson Khan serves as an extension activity for higher level learners who may finish the assignment early. This is an introduction to future lessons, so it serves a dual purpose. Students enjoy working in Khan and creating their avatar, so early finishers are always excited to be able to work on Khan Academy. This site also collects class data and is a useful tool for forming small groups in future lessons, or in creating lessons that are aligned to student background knowledge.
Google Forms: Google Forms now offers a quiz option that can easily grade multiple choice work for teachers. It offers immediate feedback for those questions if teachers choose and this gives students and teachers immediate opportunities for remediation, or can serve to show that learners are ready to move on.
The Dynamic Instructional Design model was established in 2011 and its purpose is to align lesson planning for a technology rich environment. Each of the components allows for specific feedback and modification of parts to ensure the design remains successful for implementation with all groups of students. Instructors should reflect and make modifications after the design of each of the independent parts that form a cohesive lesson whole. This format is especially helpful when working to develop successful lessons in a district that is one to one.
My students are eighth grade math students and, in general, prefer the use of technology when it has been well organized by the instructor and is easy to use. It is imperative that when selecting technology and implementing it, I have considered the students, their previous knowledge, the intensity of the lesson, the levels of knowledge required by the objectives of the lesson, and the technology being used. The following is one lesson developed for the 8th grade general education math classroom.
Part 1: Getting to Know the Learners
Overall students are 13 to 14 years old. They are general education students in an inclusive classroom where there are multiple levels of learners including some with IEPs, 504s, and ESOL service needs. In order to have an understanding of all learners it will be imperative that I compile the necessary information in an easy accessible format. I have developed a Sheet to summarize the data. This will allow me to have an at a glance overview of student profiles. I will input data as it becomes available to me (rosters are not yet published).
In order to understand the specific learning styles and multiple intelligences of my students I will have students take two surveys at the beginning of the school year, and again during the middle of the year as students experience significant cognitive growth during the 8th grade year and the onset of puberty. To analyze their learning styles, students will take a Learning Styles Inventory; results will be reported in our Google Classroom. Students will also take a Multiple Intelligence Inventory; results will be reported in our Google Classroom.
This information will allow me to form small groups for collaborative learning and small group instruction. I will be able to group learners together with their primary learning style and cater to their individual learning needs to maximize instructional time. This will also give students a more concrete understanding. I will then group students with peers with differing learning styles and ask them to share strategies. This also frees up instructional time to target learners who may need more direct instruction or one on one tutoring. It will also give students a sense of ownership to share with their peers. Making students feel confident in mathematics is a key element in eliminating the fear that is often associated with the content in the upper middle grades.
Part 2: Performance Objectives and Lesson
For this lesson, the standard is 8.F.4b - Determine the slope and the 𝑦-intercept of a linear function given multiple representations, including two points, tables, graphs, equations, and verbal descriptions. The performance objective is as follows: at the completion of this lesson, students will be able to determine the slope and y-intercept of a graph and table with 85% accuracy when given a graph or table with a positive or negative slope using Desmos to answer questions on a digital assessment via Google Classroom. The following learning objects are aligned to Bloom's Revised Taxonomy. The students are required to apply, analyze, and interpret key features of graphs and tables. (Note: this standard has been split in order to teach students another standard that will be required for them to link equations and real-world situations at the end of the two week unit.)
- Applying: Calculate the slope of a line from a graph.
- Applying: Calculate the slope of a line from a table.
- Analyzing: Recognize the y-intercept of a line from a graph.
- Analyzing: Recognize the y-intercept of a line from a table.
Lesson Plan
This lesson plan format was selected because the lesson is clearly outlined, streamlined, and easy to understand for teachers, curriculum coaches, and administrators. It is easy to complete and modify upon completion of the lesson and reflection. It was selected from the textbook, Teaching and Learning with Technology.
Instructional Standard
8.F.4 - Apply the concepts of linear functions to real-world and mathematical situations.
Instructional Indicator
b - Determine the slope and the 𝑦-intercept of a linear function given multiple representations, including two points, tables, graphs, equations, and verbal descriptions.
Instructional Objectives
Applying: Calculate the slope of a line from a graph.
Applying: Calculate the slope of a line from a table.
Analyzing: Recognize the y-intercept of a line from a graph.
Analyzing: Recognize the y-intercept of a line from a table.
Activities
Tutorial - Using Desmos
Original Video - Interpreting Slope & y-intercept from a Graph
GoFormative - Activity (The GoFormative is private; this is the worksheet that was used to create both A Formative assignments in this lesson.)
ALEKS - digital content requirement
Khan Academy - Writing an Equation from a Graph
Google Form - Summative Assessment
Procedure - Blended Learning Rotation
Group One: Group one will start with the instructor. This will be high level learners who need little direct instruction. They will use Desmos to graph tables and identify slope and y-intercept with the instructor. At their second rotation they will complete two Formative assessments. One assessment will focus on graphs and the other on tables. When they have completed the GoFormative assessments, they will independently move on to completing 15 minutes of ALEKS in the Geometry slice. When they have completed ALEKS they will move on to the Khan Academy lesson for writing an equation from a graph.
Group Two: Group two will watch the Desmos tutorial followed by the original video, Interpreting Slope & y-intercept from a graph. They will then start the GoFormative for graphs. They will move to the instrutor at some point while working on the GoFormative and any questions will be addressed. While working with the instructor students will use Desmos to graph tables and start the GoFormative assignment addressing tables. They will finish this independently and then move to ALEKS for the remainder of the class period.
Group Three: Group three will work for 15 minutes on ALEKS. When they have completed their 15 minutes on ALEKS they will watch the Desmos tutorial and the original video. They may or may not have time to watch both videos before the teacher moves to this group. This group will work through the graph and table tutorials with the teacher using Desmos. Since this will be my lowest level learners, they will spend the majority of the class with teacher led digital instruction.
Differentiation
Differentiation is described in detail above. Specifically, for higher level learners the added Khan Academy assignment and for lower level learners, the teacher led digital learning experience.
Formative Assessments:
GoFormative: Graphs
GoFormative: Tables
ALEKs report
Small group discussion
Summative Assessment:
Google Form
All assessments are linked in the activities and procedures section of this lesson plan.
Part 3: Teaching and Learning Strategies
The nature of an inclusion classroom brings unique opportunities to teachers and learners. The blended learning model works well because a small group can work directly with one teacher while another teacher monitors and guides the other two groups. For this lesson, the teacher will work with the other two groups on guidance and time management. This allows students to stay focused, maximize learning opportunities, and not be slowed by other learners. The standards require students to use appropriate tools strategically and the implementation of Desmos throughout the lesson gives students access to a learning tool that will be useful throughout their mathematics career. It also gives students experience with digital graphs and manipulation that will translate to other applications. The summative assessment on Google Forms will serve as the evaluation of success for my students’ learning and my teaching strategies. Students will also be surveyed randomly throughout the year, using Google Forms, to gain insight into which strategies students feel most confident learning with.
Small group instruction, independent practice, and collaboration are all part of the strategy of blended learning. Students have access to a teacher at all times but are encouraged to work independently and collaborate with their peers when struggling before reverting to a teacher for clarification. This builds a sense of community and ownership of learning in the classroom and ultimately benefits all learners and teachers.
Part 4: Present and Analyze Technologies Used
Desmos: Desmos is an online graphing tool. Students struggle with finding the slope from a table and this software allows students to graph the table and relate the table as a graph. It is helpful for all levels of learners, but lower level learners, who may struggle with conceptualization of the abstract table gain valuable insight and are able to make strong connections for a deeper learning experience.
YouTube: I created an original video to give learners an opportunity to learn the material from a recognizable instructional voice. This aligns to the personalization principle and gives students a resource to refer to when working on homework or classroom assignments when the teacher is not immediately available. I also created a Desmos tutorial to give students a reference if the technology is confusing.
GoFormative: This site allows me to see student work and to collect work digitally. I generally allow students to work collaboratively, but require individual submissions. Students are only able to answer differently than their group if they can articulate their argument in written form to accompany their submission. The great thing about GoFormative is that I can easily check students work while they are working, even if I am occupied with another group, giving me the unique opportunity to assess students while they are working, without disrupting their working, or leaning over their shoulder.
ALEKs: This is required digital content from the district. I ask students to work in the strand that we are studying to fill in gaps they may have before getting new content.
Khan Academy: In this lesson Khan serves as an extension activity for higher level learners who may finish the assignment early. This is an introduction to future lessons, so it serves a dual purpose. Students enjoy working in Khan and creating their avatar, so early finishers are always excited to be able to work on Khan Academy. This site also collects class data and is a useful tool for forming small groups in future lessons, or in creating lessons that are aligned to student background knowledge.
Google Forms: Google Forms now offers a quiz option that can easily grade multiple choice work for teachers. It offers immediate feedback for those questions if teachers choose and this gives students and teachers immediate opportunities for remediation, or can serve to show that learners are ready to move on.