This document provides resources for a lesson to help students understand how to construct and analyze function tables, including how an equation relates independent and dependent variables. It includes the Common Core standard addressed, vocabulary, a lesson agenda, materials needed, potential misconceptions, and connections to textbook examples. The lesson will use a video and activity on pancake mix to demonstrate how tables can represent relationships between variables and how this relates to equations.
The document provides an overview of effective instructional strategies for teaching the Common Core State Standards for Mathematics, including focusing instruction where the standards focus, thinking across grades and topics to promote coherence, and pursuing conceptual understanding, skill and fluency, and application of mathematical concepts. It discusses the three shifts in instruction required by the CCSS and examples of how to implement tasks, scaffolding, modeling and other strategies to develop students' mathematical understanding and skills.
Daily Lesson Plan-W1-STATistic and probabilityAPHRODITE51
1. The document contains a weekly lesson log for a Grade 11 Statistics and Probability class.
2. The log outlines the objectives, content, procedures, and reflections for lessons on random variables and probability distributions taught from February 1-2, 2024.
3. The objectives are for students to illustrate random variables, distinguish between discrete and continuous variables, find possible values of variables, and illustrate probability distributions of discrete variables.
This unit introduces patterns and sequences to algebra students. It includes 5 investigations exploring patterns in hydrocarbons, integers, arithmetic sequences, geometric sequences, and fractals. Students will represent patterns numerically, graphically, and symbolically. They will write recursive and explicit rules for arithmetic and geometric sequences. The unit aims to help students recognize various representations of patterns and understand sequences and functions. It concludes with a performance task and end-of-unit test assessing students' ability to find patterns and recognize different types of sequences.
The document outlines the learning objectives, assessments, and exam structure for a Year 8 mathematics class taught by Ms. Asiya, including shapes, algebra, numbers, and data topics to be covered in the term, with 3 assessments worth 100 marks each and a 1.5 hour end of term exam. Students are provided with study materials and advice to ensure they understand the topics in preparation for their exams.
The document outlines the learning objectives, assessments, and exam structure for a Year 8 mathematics class taught by Ms. Asiya, including shapes, algebra, numbers, and data topics to be covered in the term, with 3 assessments worth 100 marks each and a 1.5 hour end of term exam. Students are provided with study materials and advice to ensure they understand the topics in preparation for their exams.
This document discusses upcoming changes to education in Wisconsin due to the adoption of Common Core State Standards and new accountability measures. It summarizes that schools will face increased academic rigor, a shift to more informational texts, new standardized assessments aligned to Common Core, and teacher evaluations that incorporate student performance data. This represents major changes requiring adjustments to curriculum, professional development, and student assessment.
Concept: The document discusses teaching algebra concepts to primary school students.
Skill: Students learn algebra through understanding patterns, relationships, and using concrete materials to represent abstract concepts.
Strategy: It is important for students to fully understand underlying concepts before moving to skills and strategies. Teachers should ensure students are confident in concepts through visual and hands-on learning before having them calculate abstract problems.
Students in a 6th grade math class showed improvement in their understanding of relationships between two variables after instruction. Their test scores increased from an average of 42% correct on the pre-test to 88% on the post-test. All learning objectives showed gains, especially identifying independent and dependent quantities which some students initially struggled with. The results indicate the instruction was effective at helping students learn key concepts and improve their math skills.
The document provides an overview of effective instructional strategies for teaching the Common Core State Standards for Mathematics, including focusing instruction where the standards focus, thinking across grades and topics to promote coherence, and pursuing conceptual understanding, skill and fluency, and application of mathematical concepts. It discusses the three shifts in instruction required by the CCSS and examples of how to implement tasks, scaffolding, modeling and other strategies to develop students' mathematical understanding and skills.
Daily Lesson Plan-W1-STATistic and probabilityAPHRODITE51
1. The document contains a weekly lesson log for a Grade 11 Statistics and Probability class.
2. The log outlines the objectives, content, procedures, and reflections for lessons on random variables and probability distributions taught from February 1-2, 2024.
3. The objectives are for students to illustrate random variables, distinguish between discrete and continuous variables, find possible values of variables, and illustrate probability distributions of discrete variables.
This unit introduces patterns and sequences to algebra students. It includes 5 investigations exploring patterns in hydrocarbons, integers, arithmetic sequences, geometric sequences, and fractals. Students will represent patterns numerically, graphically, and symbolically. They will write recursive and explicit rules for arithmetic and geometric sequences. The unit aims to help students recognize various representations of patterns and understand sequences and functions. It concludes with a performance task and end-of-unit test assessing students' ability to find patterns and recognize different types of sequences.
The document outlines the learning objectives, assessments, and exam structure for a Year 8 mathematics class taught by Ms. Asiya, including shapes, algebra, numbers, and data topics to be covered in the term, with 3 assessments worth 100 marks each and a 1.5 hour end of term exam. Students are provided with study materials and advice to ensure they understand the topics in preparation for their exams.
The document outlines the learning objectives, assessments, and exam structure for a Year 8 mathematics class taught by Ms. Asiya, including shapes, algebra, numbers, and data topics to be covered in the term, with 3 assessments worth 100 marks each and a 1.5 hour end of term exam. Students are provided with study materials and advice to ensure they understand the topics in preparation for their exams.
This document discusses upcoming changes to education in Wisconsin due to the adoption of Common Core State Standards and new accountability measures. It summarizes that schools will face increased academic rigor, a shift to more informational texts, new standardized assessments aligned to Common Core, and teacher evaluations that incorporate student performance data. This represents major changes requiring adjustments to curriculum, professional development, and student assessment.
Concept: The document discusses teaching algebra concepts to primary school students.
Skill: Students learn algebra through understanding patterns, relationships, and using concrete materials to represent abstract concepts.
Strategy: It is important for students to fully understand underlying concepts before moving to skills and strategies. Teachers should ensure students are confident in concepts through visual and hands-on learning before having them calculate abstract problems.
Students in a 6th grade math class showed improvement in their understanding of relationships between two variables after instruction. Their test scores increased from an average of 42% correct on the pre-test to 88% on the post-test. All learning objectives showed gains, especially identifying independent and dependent quantities which some students initially struggled with. The results indicate the instruction was effective at helping students learn key concepts and improve their math skills.
This unit summary outlines a unit on graphing linear equations that will use technology to help students feel more comfortable with the topic. Recent test results show that almost 100% of students have not mastered graphing linear equations. The unit will teach students to graph linear equations using tables, computer software, and interactive websites. It provides student objectives, content standards, accommodations for different learners, and an assessment plan. Background information defines linear equations and provides an example of graphing a linear equation by plotting points from a table and drawing a line between them.
This document provides an overview of the 6th-8th grade Virginia SOLs and Common Core State Standards for mathematics. It summarizes the key focuses and differences between the two sets of standards, including their approaches to problem solving, use of technology, and emphasis on different mathematical concepts across grades 6-8 such as foundations of algebra, rational numbers, and geometric properties. The document also includes perspectives on the benefits and drawbacks of each set of standards.
Drexel University, College of Engineering2015-2016 Academic Year.docxjacksnathalie
Drexel University, College of Engineering2015-2016 Academic Year
Drexel University
Office of the Dean of the College of Engineering
ENGR 232 – Dynamic Engineering Systems
Week 1 Laboratory Assignment
In this lab we will investigate the use of direction fields to evaluate solutions to first order differential equations.
For this lab, we will study these qualitative analysis tools via the example of population growth using the Gompertz equation as a model. This equation is used to model the growth of tumor cells, and gives an expression of the dependence of tumor size on time.
The differential equation governing the growth is:
Here is the growth rate is a reflection of the carrying capacity of the tumor.
Let ; ; and V range from 0 to 100
1. Plot the graph of vs. . Note you may have to use the vectorization operator “.” to evaluate the function of the differential equation.
2. Determine the equilibrium points (by-hand or MATLAB) and plot them on the same graph as part (1) using red circles. Use a legend to indicate the equilibrium points and the original plot.
3. Using the gradient() function, plot the derivative of versus on the same plot. That is, plot vs. .
4. Determine the stability of each equilibrium point and the region of attraction. Write these answers as comments in your code. Comment on the stability as it related to the graph.
5. From this graph, are we able to tell how long the tumor will take to grow to units if the initial size is units? Why? Write your answers as comments in the code.
We will now use the direction field tool to examine the solution.
6. Download the file from the course website in the MATLAB Resources folder. You may have to right-click and save the file to your computer. IMPORTANT! Make sure it is in the current directory you are working in.
OR
Access the dfield tools at http://math.rice.edu/~dfield/dfpp.html
7. Using the same parameters as above, plot the direction field of this differential equation. Set the time and variable limits appropriately.
8. Compare your results from part (4) to the direction field obtained to check: the stability of each equilibrium point and the region of attraction. Include these as comments in your code.
9. Estimate how long it will take for if. Hint: You can go to: WINDOW DFIELD Keyboard Input to enter the initial conditions.
10. Repeat the direction field plot with and estimate again how long it takes for if . Comment on your results as they compare to part (9).
EH 1020, English Composition II 1
Course Description
Advanced introduction to the basic concepts and requirements of college-level writing. Presents additional skills, methods,
and techniques to improve and polish the student’s completed written documents.
Prerequisites
EH 1010: English Composition I or equivalent
Course Textbook
Aaron, J. E. (2010). The Little, Brown compact handbook with exercises (2nd custom ed.). New York, NY: Longman.
Lester, J. D., Les ...
The lesson plan is for an 8th grade math class reviewing proportional relationships. Students will give examples of proportional and non-proportional real-world situations. They will then work with partners to complete a review covering determining proportionality, slope, y-intercepts, and creating tables and graphs from equations. As an assessment, students will use an app to identify slope and y-intercept and make a table and graph for an equation scenario. The goal is to review what students learned in their recent module and prepare for an upcoming quiz.
This document provides training on backwards design and lesson planning using Florida State Standards. It explains the three stages of backwards design: 1) identifying desired results, 2) determining acceptable evidence, and 3) planning learning experiences. An example is provided walking through backwards design for a 5th grade math standard on graphing points. The goal is for teachers to understand how to design standards-based lessons with clear objectives and assessments. Implementing backwards design is intended to promote student understanding and ownership over their learning.
1. The document is a daily lesson log for a Grade 11 mathematics class taught by Teacher Renante A. Roldan.
2. The lesson objectives were to understand key concepts of functions, relations, and representing real-life situations using functions including piecewise functions.
3. Various tasks and activities were provided to help students practice applying concepts of functions to real-life examples and solve problems representing functional relationships.
Math Resources! Problems, tasks, strategies, and pedagogy. An hour of my 90-min session on math task design at Cal Poly Pomona for a group of teachers (mainly elementary school).
1. The document provides an overview of a new developmental math course called Mathematical Literacy for College Students (MLCS).
2. MLCS aims to provide an alternative pathway to college-level math for non-STEM majors by integrating numeracy, proportional reasoning, algebraic reasoning, and functions.
3. The course is designed to develop students' mathematical maturity through problem solving, critical thinking, writing, and communication while covering topics over four units in a semester.
The document discusses designing a systemic K-12 Common Core State Standards mathematics curriculum. It outlines a multi-phase process for task forces to collaboratively design units that vertically and horizontally align standards across grades. Specifically, it describes designing unit names, enduring understandings, essential questions, standards for mathematical practice, and vocabulary before integrating these elements into units of study. The document provides examples of how other states have structured their CCSS math course design and unit mapping.
The assessment was designed to evaluate 8th grade students' understanding of pre-algebra concepts from Chapter 1, administered to 12 students. It consisted of multiple choice, short answer, essay, and other question types focusing on order of operations, integers, and real-world math applications. Most students struggled with level 2 and 3 questions, the essay question, and a question requiring inductive reasoning. Recommendations included clarifying language in questions about overdrawn bank accounts, down payments, par-3 golf courses, and changing "give a counterexample" to "explain why incorrect".
Building Pre-algebra Skills through Project Based Learningccpc
Khanh Bui
Associate for Curriculum Development
ConnectEd: The California Center for College and Career
Berkeley, CA
Pier Sun Ho
Senior Associate for Curriculum Development
ConnectEd: The California Center for College and Career
Berkeley, CA
This highly interactive session introduces participants to a set of engineering- and technology-related, project-based pre-algebra units. They are suitable for a summer school program, after-school supplementary instruction, or a middle-school pre-algebra class. Participants complete a modified activity that illustrates actual classroom instruction.
This document is a daily lesson log for an 8th grade mathematics class. It outlines the objectives, content, learning procedures, and evaluation for a lesson on linear equations in two variables. The objectives are for students to identify and solve linear equations with two variables and present solutions accurately. The content covers the standard form of these equations and how to find ordered pairs and graph the linear equations. The learning procedures take students through a review, examples of linear equations with two variables, how to solve and graph them, practice problems, and an evaluation.
These slides are from a webinar on why reading mathematics is challenging for many students and what teachers can do. We will examine how mathematics symbols, vocabulary, and content presentation can create roadblocks to students’ mathematics understanding. Learn how to address students’ difficulties by approaching mathematics as a language and to use specific strategies to improve mathematics learning.
This document discusses the importance of teaching reading skills in mathematics. It defines reading mathematics as making sense of mathematical texts, symbols, and representations. Several strategies are presented to help students read and understand mathematics, including teaching vocabulary, using literacy strategies before, during and after reading, and having students communicate about mathematics. Problem solving approaches like KNW, KWC, and SQRQCQ are also described to help students comprehend and solve mathematical problems.
1) The document provides a mathematics curriculum guide for first grade addition, subtraction, and number systems. It outlines big ideas, essential questions, unit vocabulary, and Arizona state standards to be covered.
2) Key concepts include counting quantities, comparing numbers, and composing and decomposing numbers. Students will learn strategies for addition and subtraction word problems involving combining, separating, and comparing quantities.
3) The guide provides examples and explanations for how students can use objects, drawings, and equations to represent addition and subtraction word problems involving unknown values in different positions. It emphasizes developing fluency with addition and subtraction facts to 10.
Technology Lesson Plan Assignment: Quadratice Functionsdart11746
This technology-infused lesson plan teaches 9th grade students about quadratic functions through a week-long unit. Students will learn to solve and graph quadratic equations and functions algebraically and graphically using tools like graphing calculators, online graphing calculators, and SMART Notebook software. Formative and summative assessments include group presentations and a unit test on quadratic functions. The lesson incorporates student-centered learning and supports various learning styles.
This document provides a rubric and outline for a Strategy Instruction Resource Project Notebook. The rubric evaluates the notebook on its organization, number and appropriateness of instructional strategies included, inclusion of research to support the strategies, and quality of research summaries. It is worth a total of 150 points. The outline specifies that the notebook should have three sections for reading, writing/spelling, and math strategies. Each section should include strategy lists, 10 strategies, a research article, and summary of the article supporting the strategies. The document provides general mathematics teaching strategies and parallel activities to help struggling students, ways to modify math assignments, and student aids. It concludes with additional strategies like mnemonic devices and emphasizes the importance of conceptual understanding
The document discusses curriculum planning at Roxbury Preparatory Charter School in Roxbury, MA. The school serves a population that is 100% African American or Latino. Teachers spend 3 weeks each summer developing curriculum and analyzing student assessment data. Throughout the year, teachers create detailed curriculum maps and assessments to ensure standards-based instruction. The school uses rigorous planning and data analysis to prepare students for college.
This document provides resources and guidance for teaching a unit on chemical formulas to 8th grade science students. It includes:
- A pacing guide outlining when chemical formulas and reactions will be taught over 6 weeks
- Details on relevant TEKS and expectations for students to understand chemical formulas and balanced equations
- Links to videos and textbooks to support teacher content knowledge on balancing equations and relating it to the law of conservation of mass
This document provides guidance for teachers on getting started with teaching the Common Core State Standards. It discusses aligning pacing guides to the CCSS, understanding the structure and components of the CCSS document, using standards and crosswalks to identify what content is staying the same and what is changing, the emphasis on mathematical practices, examples of performance tasks and sample test items, and strategies for teaching like proof drawings and math talks. It also addresses assessment design and ensuring lessons and pacing allow sufficient time for students to master the depth and rigor of the new standards.
This unit summary outlines a unit on graphing linear equations that will use technology to help students feel more comfortable with the topic. Recent test results show that almost 100% of students have not mastered graphing linear equations. The unit will teach students to graph linear equations using tables, computer software, and interactive websites. It provides student objectives, content standards, accommodations for different learners, and an assessment plan. Background information defines linear equations and provides an example of graphing a linear equation by plotting points from a table and drawing a line between them.
This document provides an overview of the 6th-8th grade Virginia SOLs and Common Core State Standards for mathematics. It summarizes the key focuses and differences between the two sets of standards, including their approaches to problem solving, use of technology, and emphasis on different mathematical concepts across grades 6-8 such as foundations of algebra, rational numbers, and geometric properties. The document also includes perspectives on the benefits and drawbacks of each set of standards.
Drexel University, College of Engineering2015-2016 Academic Year.docxjacksnathalie
Drexel University, College of Engineering2015-2016 Academic Year
Drexel University
Office of the Dean of the College of Engineering
ENGR 232 – Dynamic Engineering Systems
Week 1 Laboratory Assignment
In this lab we will investigate the use of direction fields to evaluate solutions to first order differential equations.
For this lab, we will study these qualitative analysis tools via the example of population growth using the Gompertz equation as a model. This equation is used to model the growth of tumor cells, and gives an expression of the dependence of tumor size on time.
The differential equation governing the growth is:
Here is the growth rate is a reflection of the carrying capacity of the tumor.
Let ; ; and V range from 0 to 100
1. Plot the graph of vs. . Note you may have to use the vectorization operator “.” to evaluate the function of the differential equation.
2. Determine the equilibrium points (by-hand or MATLAB) and plot them on the same graph as part (1) using red circles. Use a legend to indicate the equilibrium points and the original plot.
3. Using the gradient() function, plot the derivative of versus on the same plot. That is, plot vs. .
4. Determine the stability of each equilibrium point and the region of attraction. Write these answers as comments in your code. Comment on the stability as it related to the graph.
5. From this graph, are we able to tell how long the tumor will take to grow to units if the initial size is units? Why? Write your answers as comments in the code.
We will now use the direction field tool to examine the solution.
6. Download the file from the course website in the MATLAB Resources folder. You may have to right-click and save the file to your computer. IMPORTANT! Make sure it is in the current directory you are working in.
OR
Access the dfield tools at http://math.rice.edu/~dfield/dfpp.html
7. Using the same parameters as above, plot the direction field of this differential equation. Set the time and variable limits appropriately.
8. Compare your results from part (4) to the direction field obtained to check: the stability of each equilibrium point and the region of attraction. Include these as comments in your code.
9. Estimate how long it will take for if. Hint: You can go to: WINDOW DFIELD Keyboard Input to enter the initial conditions.
10. Repeat the direction field plot with and estimate again how long it takes for if . Comment on your results as they compare to part (9).
EH 1020, English Composition II 1
Course Description
Advanced introduction to the basic concepts and requirements of college-level writing. Presents additional skills, methods,
and techniques to improve and polish the student’s completed written documents.
Prerequisites
EH 1010: English Composition I or equivalent
Course Textbook
Aaron, J. E. (2010). The Little, Brown compact handbook with exercises (2nd custom ed.). New York, NY: Longman.
Lester, J. D., Les ...
The lesson plan is for an 8th grade math class reviewing proportional relationships. Students will give examples of proportional and non-proportional real-world situations. They will then work with partners to complete a review covering determining proportionality, slope, y-intercepts, and creating tables and graphs from equations. As an assessment, students will use an app to identify slope and y-intercept and make a table and graph for an equation scenario. The goal is to review what students learned in their recent module and prepare for an upcoming quiz.
This document provides training on backwards design and lesson planning using Florida State Standards. It explains the three stages of backwards design: 1) identifying desired results, 2) determining acceptable evidence, and 3) planning learning experiences. An example is provided walking through backwards design for a 5th grade math standard on graphing points. The goal is for teachers to understand how to design standards-based lessons with clear objectives and assessments. Implementing backwards design is intended to promote student understanding and ownership over their learning.
1. The document is a daily lesson log for a Grade 11 mathematics class taught by Teacher Renante A. Roldan.
2. The lesson objectives were to understand key concepts of functions, relations, and representing real-life situations using functions including piecewise functions.
3. Various tasks and activities were provided to help students practice applying concepts of functions to real-life examples and solve problems representing functional relationships.
Math Resources! Problems, tasks, strategies, and pedagogy. An hour of my 90-min session on math task design at Cal Poly Pomona for a group of teachers (mainly elementary school).
1. The document provides an overview of a new developmental math course called Mathematical Literacy for College Students (MLCS).
2. MLCS aims to provide an alternative pathway to college-level math for non-STEM majors by integrating numeracy, proportional reasoning, algebraic reasoning, and functions.
3. The course is designed to develop students' mathematical maturity through problem solving, critical thinking, writing, and communication while covering topics over four units in a semester.
The document discusses designing a systemic K-12 Common Core State Standards mathematics curriculum. It outlines a multi-phase process for task forces to collaboratively design units that vertically and horizontally align standards across grades. Specifically, it describes designing unit names, enduring understandings, essential questions, standards for mathematical practice, and vocabulary before integrating these elements into units of study. The document provides examples of how other states have structured their CCSS math course design and unit mapping.
The assessment was designed to evaluate 8th grade students' understanding of pre-algebra concepts from Chapter 1, administered to 12 students. It consisted of multiple choice, short answer, essay, and other question types focusing on order of operations, integers, and real-world math applications. Most students struggled with level 2 and 3 questions, the essay question, and a question requiring inductive reasoning. Recommendations included clarifying language in questions about overdrawn bank accounts, down payments, par-3 golf courses, and changing "give a counterexample" to "explain why incorrect".
Building Pre-algebra Skills through Project Based Learningccpc
Khanh Bui
Associate for Curriculum Development
ConnectEd: The California Center for College and Career
Berkeley, CA
Pier Sun Ho
Senior Associate for Curriculum Development
ConnectEd: The California Center for College and Career
Berkeley, CA
This highly interactive session introduces participants to a set of engineering- and technology-related, project-based pre-algebra units. They are suitable for a summer school program, after-school supplementary instruction, or a middle-school pre-algebra class. Participants complete a modified activity that illustrates actual classroom instruction.
This document is a daily lesson log for an 8th grade mathematics class. It outlines the objectives, content, learning procedures, and evaluation for a lesson on linear equations in two variables. The objectives are for students to identify and solve linear equations with two variables and present solutions accurately. The content covers the standard form of these equations and how to find ordered pairs and graph the linear equations. The learning procedures take students through a review, examples of linear equations with two variables, how to solve and graph them, practice problems, and an evaluation.
These slides are from a webinar on why reading mathematics is challenging for many students and what teachers can do. We will examine how mathematics symbols, vocabulary, and content presentation can create roadblocks to students’ mathematics understanding. Learn how to address students’ difficulties by approaching mathematics as a language and to use specific strategies to improve mathematics learning.
This document discusses the importance of teaching reading skills in mathematics. It defines reading mathematics as making sense of mathematical texts, symbols, and representations. Several strategies are presented to help students read and understand mathematics, including teaching vocabulary, using literacy strategies before, during and after reading, and having students communicate about mathematics. Problem solving approaches like KNW, KWC, and SQRQCQ are also described to help students comprehend and solve mathematical problems.
1) The document provides a mathematics curriculum guide for first grade addition, subtraction, and number systems. It outlines big ideas, essential questions, unit vocabulary, and Arizona state standards to be covered.
2) Key concepts include counting quantities, comparing numbers, and composing and decomposing numbers. Students will learn strategies for addition and subtraction word problems involving combining, separating, and comparing quantities.
3) The guide provides examples and explanations for how students can use objects, drawings, and equations to represent addition and subtraction word problems involving unknown values in different positions. It emphasizes developing fluency with addition and subtraction facts to 10.
Technology Lesson Plan Assignment: Quadratice Functionsdart11746
This technology-infused lesson plan teaches 9th grade students about quadratic functions through a week-long unit. Students will learn to solve and graph quadratic equations and functions algebraically and graphically using tools like graphing calculators, online graphing calculators, and SMART Notebook software. Formative and summative assessments include group presentations and a unit test on quadratic functions. The lesson incorporates student-centered learning and supports various learning styles.
This document provides a rubric and outline for a Strategy Instruction Resource Project Notebook. The rubric evaluates the notebook on its organization, number and appropriateness of instructional strategies included, inclusion of research to support the strategies, and quality of research summaries. It is worth a total of 150 points. The outline specifies that the notebook should have three sections for reading, writing/spelling, and math strategies. Each section should include strategy lists, 10 strategies, a research article, and summary of the article supporting the strategies. The document provides general mathematics teaching strategies and parallel activities to help struggling students, ways to modify math assignments, and student aids. It concludes with additional strategies like mnemonic devices and emphasizes the importance of conceptual understanding
The document discusses curriculum planning at Roxbury Preparatory Charter School in Roxbury, MA. The school serves a population that is 100% African American or Latino. Teachers spend 3 weeks each summer developing curriculum and analyzing student assessment data. Throughout the year, teachers create detailed curriculum maps and assessments to ensure standards-based instruction. The school uses rigorous planning and data analysis to prepare students for college.
This document provides resources and guidance for teaching a unit on chemical formulas to 8th grade science students. It includes:
- A pacing guide outlining when chemical formulas and reactions will be taught over 6 weeks
- Details on relevant TEKS and expectations for students to understand chemical formulas and balanced equations
- Links to videos and textbooks to support teacher content knowledge on balancing equations and relating it to the law of conservation of mass
This document provides guidance for teachers on getting started with teaching the Common Core State Standards. It discusses aligning pacing guides to the CCSS, understanding the structure and components of the CCSS document, using standards and crosswalks to identify what content is staying the same and what is changing, the emphasis on mathematical practices, examples of performance tasks and sample test items, and strategies for teaching like proof drawings and math talks. It also addresses assessment design and ensuring lessons and pacing allow sufficient time for students to master the depth and rigor of the new standards.
Similar to Math 6 Pocket PD - Express - Equations.pptx (20)
Top 10 AI Trends to Watch in 2024 with Intelisyncnehapardhi711
As we advance further into the digital age, artificial intelligence (AI) continues to evolve, shaping various industries and aspects of our daily lives. The advancements in AI for 2024 promise significant transformations across multiple sectors. From agentic AI and open-source AI to AI-powered cybersecurity and sustainability, these trends highlight the growing influence of AI on our world. By staying informed and embracing these trends, businesses and individuals can harness the power of AI to innovate and thrive.
This article explores the top 10 AI trends to watch in 2024, providing an overview, impact, and examples of each trend.
Top 10 AI Trends to Watch in 2024
Trend 1: Agentic AI
Overview of Agentic AI
Agentic AI represents a fundamental shift in artificial intelligence. These AI systems are designed to comprehend complex workflows and pursue difficult objectives autonomously, with minimal human assistance. Essentially, agentic AI functions similarly to human employees, understanding intricate contexts and instructions in normal language, defining goals, deducing subtasks, and adapting actions to changing circumstances.
Impact of Agentic AI
Agentic AI has the potential to drastically alter organizational roles, procedures, and relationships. AI assistants with advanced thinking and planning capabilities can perform tasks previously managed by humans. This shift enhances productivity by fully automating complex processes, freeing workers from repetitive tasks to focus on more critical activities. The ability to adapt quickly to changing circumstances ensures continuous operational improvements.
Examples and Use Cases of Agentic AI
Autonomous Vehicles: Self-driving cars use agentic AI to navigate roads, interpret traffic signals, and make real-time decisions to ensure passenger safety.
Smart Home Devices: AI-powered home assistants, like smart thermostats and security systems, operate autonomously to optimize energy usage and enhance security.
Customer Service Bots: Advanced chatbots handle complex customer queries, provide solutions, and escalate issues to human agents when necessary.
Trend 2: Open Source AI
Overview of Open Source AI
Open-source AI involves freely available source code, encouraging developers to collaborate, use, adapt, and share AI technology. This openness fosters innovation and speeds up the development of practical AI solutions across various sectors, including healthcare, finance, and education.
Impact of Open Source AI
The collaborative nature of open-source AI promotes transparency and facilitates continuous improvement, leading to feature-rich, reliable, and modular solutions. These platforms enable the creation of applications such as real-time fraud detection, medical image analysis, personalized recommendations, and customized learning experiences.
Examples and Use Cases of Open Source AI
TensorFlow: An open-source machine learning framework by Google, widely used for building and deploying AI models.
HEM Webinar - Navigating the Future - Social Media Trends for 2024 in Educati...Higher Education Marketing
Explore our comprehensive slides on the 2024 social media landscape, tailored for educators and marketing professionals in the field of education. With more than 5 billion social media users worldwide and an average individual engagement across as many as seven platforms monthly, understanding these dynamics is crucial for effective educational outreach. Our slides delve into the pivotal trends and strategic adaptations necessary for thriving in this digital arena. Don't miss this opportunity to enhance your strategies with our expert insights.
Importance of Customer Service in Fashion IndustryShantilal Hajeri
Fashion Industry is a highly specialised and personalised field. Customer Service is more important in fashion indsutry since the taste, choice and expectations of each customer are different.
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E-learning and traditional learning are two distinct approaches to education, each offering unique advantages and facing specific challenges. E-learning provides flexibility and convenience, allowing students to access materials and complete assignments at their own pace and schedule. Traditional learning fosters direct, face-to-face interaction between students and instructors, which can enhance communication, immediate feedback, and a sense of community.
Facebook Marketing Strategy with SNJ Global Services.pptxsarfrazkhanm47
Explore the potential of Facebook marketing with SNJ Global Services. We specialize in targeted ad campaigns and engaging content strategies to enhance your brand's visibility and drive conversions. Discover more about our solutions at SNJ Global Services:
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Advanced Storytelling Concepts for MarketersEd Shimp
Every marketer knows you’re supposed to tell a story, but do you know how to tell a story? Do you know why you’re supposed to tell a story? Do you even truly know what a story is? While many marketing presentations emphasize the value of mythic storytelling, the nuts and bolts of actually constructing a story are never explored.
The goal of marketing may be to achieve specific KPIs that drive sales, which is very objective, but the top of the marketing funnel requires a softer approach. In our data-driven results-oriented fast-paced world, marketers must quantify results, but those results will never be achieved unless prospects are first approached with humanity.
There is a common misunderstanding that the so-called “soft skills” of marketing such as language and art are unmeasurable and subjective, but while the objective measures of market research are merely 100 years old, the rules of aesthetics have been perfected over the last 2,500 years.
Great story construction is a skill that requires significant knowledge and practice. This presentation will be a review of the ancient art of story construction.
We will discuss:
• Rhetoric – The art of effective communication
• The Socratic Method – You cannot teach, but you can persuade people to learn
• Plato’s Cave – You sell products, but you market ideas
• Aristotle’s Six Dramatic Elements – The secret recipe for marketing stories
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2. Purpose
Standards
Expressions and
Equations
Learning
Progression
Lesson Agenda
Getting Ready
for the Lesson
(Resources and
Tips)
Vocabulary
Activities
Lesson
(Presentation
and Video)
Textbook
Connections
Additional
Resources
Provided is a lesson for teachers to use to help students
understand how to construct and analyze function tables. Included
are the following resources:
3. Common Core Standards
6.EE.9 Use variables to represent two
quantities in a real-world problem that change
in relationship to one another; write an
equation to express one quantity, thought of as
the dependent variable, in terms of the other
quantity, thought of as the independent
variable. Analyze the relationship between the
dependent and independent variables using
graphs and tables, and relate these to the
equation.
(Understand, 3) (Apply, 3) (Analyze, 3)
4.
5. Math Practices
MP1
• Make sense of problems and
persevere in solving them.
MP8
• Look for and express regularity
in repeated reasoning.
6. Expressions & Equat
Prerequisite Skills: CC Math 6
https://commoncoretools.files.wordpress.com/2011/04/ccss_progression_ee_2011_04_25.pdf
7. Progressions in Grade Level
Standards
Grades K –
5
Connectin
g
standards
Writing
numerical
expressions
Interpreting
numerical
expressions
without
evaluating
them.
Source:
https://commoncoretools.files.wordpress.com/2011/04/ccss_progression_ee_2011_04_25.pdf-
6th
Grade
Applying and
extending
previous
understanding
s of arithmetic
to algebraic
expressions.
Reason about
and solve
one-variable
equations and
inequalities.
Represent and
analyze
quantitative
relationships
between
dependent
and
independent
variables.
7th
Grade
Use properties of
operations to
generate
equivalent
expressions.
Solve multi-step
and real-life
mathematical
problems posed
with positive and
negative rational
numbers in any
form.
Solve real-life
and
mathematical
problems using
numerical and
algebraic
expressions and
8th
Grade
**New Course
Work with
radicals and
integer
exponents.
Understand
the
connections
between
proportiona
l
relationship
s, lines, and
linear
equations.
Analyze and
solve linear
equations
and pairs of
simultaneou
8. Learning Progression: Road to HS Algebra
http://commoncoretools.me/wp-content/uploads/2012/12/ccss_progression_algebra_2012_12_04.pdf
11. Getting Ready
O Pre-assessment- used to determine understanding of
prerequisite skills
O Prerequisite skills include
O 6 EE.1
O Write and evaluate numerical expressions involving whole number
exponents.
O 6 EE.2A
O Write expressions that record operations with numbers and letters
standing for numbers.
O 6 EE.6
O Use variables to represent numbers and write expressions when
solving a real-world or mathematical problem; understand that a
variable can represent an unknown number, or, depending on the
purpose at hand, any number in a specified set.
Source: http://curtismapper.pic.ucla.edu/MapApp/app/#/map
12. Misconceptions and Anticipated
Issues
Common Issues
a. Plotting points (y,x)
instead of (x,y).
b. Viewing the relationship
shown in an equation
backwards. For
example, y = 6x,
students may think this
means that x is 6 times
larger than y.
c. Not being able to
identify the independent
and dependent variables
Suggested
Strategies/Resources
a. Use a whole-class
discussion to review
order of plotting points.
b. Use a whole-class
discussion to analyze
and interpret the
relationship shown
within several sample
equations.
c. Teacher models how to
identify independent
and dependent variables
using think-aloud
strategy during whole-
class discussion.
13. Required Resources
Materials Required
Special Materials:
O Graph paper for each student
Handouts:
O LearnZillion presentation handouts
O LearnZillion additional worksheets
O https://learnzillion.com/lesson_plans/681-recognize-how-an-
equation-relates-independent-and-dependent-variables
15. Learnzillion
For this lesson you need to create an
account to access the handouts from
Learnzillion.
This is a free account and you will have
access to many more lessons.
16. Understand and solve unit rate problems by
using graphs of equivalent ratios
https://learnzillion.com/lesson_plans/681-recognize-how-an-
equation-relates-independent-and-dependent-variables
17. Planning and Time
Activities Time Notes
Preparation 2 hours Includes creating a pre-
assessment, making
copies, obtaining materials
Pre-lessons 2 hours Review of 6th grade EE
standards
Vocabulary 1 hour Defining equation,
dependent and
independent variables
Pancake Task-Lesson 2 hours Explanation and
completion of work
Practice and Additional
Tasks
3 hours Additional worksheets from
LearnZillion, Textbook
practice, Illustrative
Mathematics Tasks
Total Time 10 hours
18. Textbook Connection:
California Math
O Textbook Course 1 Section 8.1
O Problem-Solving Investigation: Making a Table, Pages
611-612
O Classwork: Page 582-584, problems 1 – 7
O Homework: Page 584, problems 8-13
O Extra Practice: Course 1 Resources by Chapter Section
8.1
O Lesson 8.1 HW Practice
O Lesson 8.1 Extra Practice: Completing Function Tables
O Student Re-teaching Section 8.1
O Re-teaching: Function Tale
O Assessment Book Course 1 Section 8.1
O Self-Check Quick 8.1
19. Additional Resources
O Illustrative Mathematics -
www.illustrativemathematics.com
O Chocolate Bar Sales
O https://www.illustrativemathematics.org/content-
standards/tasks/806
O Khan Academy - www.khanacademy.org
O Inside Mathematics
O Gym Task
O http://www.insidemathematics.org/assets/common-
core-math-tasks/gym.pdf
O Mathematics Assessment Project
O Modeling: Car Skid Marks
O http://map.mathshell.org/lessons.php?collection=8&uni
t=6210#task588
20. Textbook Connection:
Go Math
O Lesson 12.2: Independent and Dependent Variables
in Tables and Graphs
O Classwork Page 344, Problems 1 – 5
O Homework Page 345-346, Problems 6-10
O Lesson 12.3: Writing Equations From Tables
O Classwork Page 350, Problems 1 – 6
O Homework Page 351-352, Problems 7-15
O Lesson 12.4: Representing Algebraic Relationships
in Tables and Graphs
O Classwork Page 356, Problems 1 – 4
O Homework Page 357-358, Problems 5-14
21. Textbook Connection
CPM
O 8.1.2 What is Typical Value?
O Classwork, Pages 382-383
O Homework, Pages 384-388
O 8.1.3 How else can I describe the data ?
O Classwork, Pages 389-392
O Homework, Page 393
Facilitator notes
Time: 2-3 minutes
Handouts/participant activity: n/a
Focus points:
Identifying the standards for lesson and unwrapping them.
Facilitator notes
Time: 2-3 minutes
Handouts/participant activity: n/a
Focus points:
Yellow, Red, & Green circles indicate the appropriate levels of DOK as required by the standards
The Blue circles fill in the instructional paths needed to assist students in reaching those DOK levels.
Facilitator notes
Time: 1-2 minutes
Handouts/participant activity: n/a
Focus points:
Review the math practices associated with the lesson being presented.
Facilitator notes
Time: 2-3 minutes
Handouts/participant activity: n/a
Focus points:
Review the prerequisite skills the students completed prior to 6th grade and connect to what they will study during the CC Math 6 course.
Facilitator notes
Time: 2-3 minutes
Handouts/participant activity: n/a
Focus points:
There are major changes at each grade level with the domain of statistics and probability that have caused a shift in standards from CST time to Common Core Standards
Major points- Statistics and probability are no longer in Grades K – 5. Standards have switched between the 6th and 7th grade. There is also a completely new course for 8th grade students, which is CC Math 8. Therefore, the are now standards that were shifted from CST courses and into this new Common Core Course.
Facilitator notes
Time: 2-3 minutes
Handouts/participant activity: n/a
Focus points:
Let’s take closer look at the California Department of Education’s description of the CC Math 8 course.
Read the highlighted portion
The state framework shows the importance of the Grade 8 Math Course and how it has became the new gateway course for higher level math, as well as how Algebra 1 had shifted to high school.
Facilitator notes
Time: 2-3 minutes
Handouts/participant activity: n/a
Focus points:
Review the lesson agenda prior to implementation
Facilitator notes
Time: 1 minute
Handouts/participant activity: n/a
Focus points:
Title Page for lesson
Facilitator notes
Time: 2-3 minutes
Handouts/participant activity: n/a
Focus points:
Review what standards should be covered in a pre-assessment activity. This shows what students should have already learned prior to your course. Using a pre-assessment activity will assist students in frontloading prior knowledge before beginning new
Facilitator notes
Time: 2-3 minutes
Handouts/participant activity: n/a
Focus points:
These are guided questions to improve our students’ learning when misconceptions may occur.
These are guided questions to improve our students’ learning.
Facilitator notes
Time: 2-3 minutes
Handouts/participant activity: n/a
Focus points:
Review the list of resources needed for the lesson and where to find materials online.
Facilitator notes
Time: 4-5 minutes
Handouts/participant activity: n/a
Focus points:
This shows a list of required academic language vocabulary that is needed for the lesson. In addition, a strategy, “Layered Book” is shown with the suggestion that there are alternative strategies that can be used as well.
Facilitator notes
Time: 4-5 minutes
Handouts/participant activity: n/a
Focus points:
This is an introduction to the Learnzillion.com website where today’s lesson was pulled from. Teachers can sign up for a free account and have full access.
Facilitator notes
Time: 15 - 20 minutes
Handouts/participant activity: n/a
Focus points:
Click on the hyper link to take you to the lesson. Lesson includes: PowerPoint, Video, and handouts. As a department, we will explore this resources together
Facilitator notes
Time: 1 - 2 minutes
Handouts/participant activity: n/a
Focus points:
Suggested pacing for this lesson
Facilitator notes
Time: 1-2 minutes
Handouts/participant activity: n/a
Focus points:
Connections to the California Math textbook for this specific standard / concept. As a department we may want to review this as well to compare to the Learnzillion lesson.
Facilitator notes
Time: 3 - 4 minutes
Handouts/participant activity: n/a
Focus points:
This is a list of additional resources surrounding the standards that may be used. If time permits, as a department, explore these sites.
Facilitator notes
Time: 1-2 minutes
Handouts/participant activity: n/a
Focus points:
Connections to the Go Math textbook for this specific standard / concept. As a department we may want to review this as well to compare to the Learnzillion lesson.
Facilitator notes
Time: 1-2 minutes
Handouts/participant activity: n/a
Focus points:
Connections to the CPM textbook for this specific standard / concept. As a department we may want to review this as well to compare to the Learnzillion lesson.