Using positive and negative numbers in context mathematical goals
- 1. Using Positive and Negative Numbers in Context Mathematical goals This lesson unit is intended to help you assess how well students are able to understand and use directed numbers in context. It is intended to help identify and aid students who have difficulties in ordering, comparing, adding, and subtracting positive and negative integers. Particular attention is paid to the use of negative numbers on number lines to explore the structures: Starting temperature + Change in temperature = Final temperature Final temperature – Change in temperature = Starting temperature Final temperature – Starting temperature = Change in temperature Introduction The lesson unit is structured in the following way: · Before the lesson students work individually on an assessment task designed to reveal their current understanding. You review their responses and write questions to help them improve their work. · After a whole-class introduction, students work together in small groups on a card-matching task. · In the same small groups, they then create directed number calculations to correspond to temperature changes or city temperatures. To end the lesson there is a whole-class discussion. · In a follow-up lesson, students again work alone on a task similar to the assessment task. Materials required · Each student will need a copy of the assessment task Temperature Changes and Temperature Changes (revisited), a copy of the Temperature Scale, a mini-whiteboard, a pen, and an eraser. · Each small group of students will need a set of cut-up cards from the sheets City Temperatures and Changes in Temperature,
- 2. a glue stick, and a large sheet of paper for making a poster. · You will also need one copy of the cut-up cards Introduction to Negative Numbers. Time needed 15 minutes before the lesson, a 100-minute lesson (or two 55- minute lessons), and 20 minutes in a follow-up lesson. Timings are approximate and will depend on the needs of your class. Lesson Type · CConcept Development Mathematical Practices This lesson involves a range of mathematical practices from the standards, with emphasis on: · MP1:Make sense of problems and persevere in solving them · MP2:Reason abstractly and quantitatively · MP3:Construct viable arguments and critique the reasoning of others · MP4:Model with mathematics · MP6:Attend to precision · MP7:Look for and make use of structure · MP8:Look for and express regularity in repeated reasoning Mathematical Content Standards This lesson asks students to select and apply mathematical content from across the grades, including the content standards: · 7.EE:Use properties of operations to generate equivalent expressions. · 7.EE:Solve real-life and mathematical problems using numerical and algebraic expressions and equations. · 7.NS:Apply and extend previous understandi ngs of operations with fractions to add, subtract, multiply, and divide rational numbers. Compose Your Program and Learning Objectives Scoring Guide CRITERIA NON-PERFORMANCE BASIC PROFICIENT DISTINGUISHED
- 3. Choose the appropriate level of Bloom’s Taxonomy verb for each learning objective or goal. 26% Does not choose a Bloom’s Taxonomy verb for each learning objective or goal. Chooses a verb that does not quite reflect the desired level of Bloom’s Taxonomy verb for one or more learning objectives or goals. Chooses the appropriate level of Bloom’s Taxonomy verb for each learning objective or goal. Chooses the appropriate level of Bloom’s Taxonomy verb for each learning objective or goal. Justifies the choice with sound reasoning. Compose three discrete program objectives or goals, relating each to the intent of the learning experience to be designed. 27% Does not compose program objectives or goals. Composes less than three discrete program objectives or goals; or does not relate each goal to the intent of the learning experience to be designed; or does not adequately describe the relationship between goals and course intent. Composes three discrete program objectives or goals, relating each to the intent of the learning experience to be designed. Composes three discrete program objectives or goals, relating each to the intent of the learning experience to be designed in a clear and concise manner. Compose one to three learning objectives or goals aligned to each of the three program objectives or goals, relating each to the intent of the learning experience to be designed. 27% Does not compose learning objectives or goals. Composes learning objectives or goals but does not align them appropriately to the program objectives or goals or does not relate each to the intent of the learning experience to be designed. Composes one to three learning objectives or goals aligned to
- 4. each of the three program objectives or goals, relating each to the intent of the learning experience to be designed. Composes one to three learning objectives or goals aligned to each of the three program objectives or goals, relating each to the intent of the learning experience to be designed in a clear and concise manner. Convey clear meaning through appropriate word choice and usage. 10% Does not convey clear meaning through appropriate word choice and usage. Clear meaning is inhibited by a limited vocabulary, vague or ambiguous word choice, or incorrect usage. Convey clear meaning through appropriate word choice and usage. Conveys precise and unequivocal meaning through precise word choice and effective usage. Conveys purpose, in an appropriate tone and style, incorporating supporting evidence and adhering to organizational, professional, and scholarly writing standards. 10% Does not convey purpose, in an appropriate tone and style, incorporating supporting evidence and adhering to organizational, professional, and writing scholarly standards. Conveys purpose, in an appropriate tone or style. Clear, effective communication is inhibited by insufficient supporting evidence and/or minimal adherence to applicable writing standards. Addresses assignment purpose in a well-organized text, incorporating appropriate evidence and tone in grammatically sound sentences. Conveys clear purpose, in a tone and style well-suited to the intended audience. Supports assertions, arguments, and conclusions with relevant, credible, and convincing evidence. Exhibits strict and nearly flawless adherence to organizational, professional, and scholarly writing standards, including APA
- 5. style and formatting. Week 3 Best Practices One of the four conditions essential to motivation, whether in site-based learning environments or the online environment, is maximizing inclusion among adult learners. While there are differences between the two environments, there are even more similarities. This week you engage in both inductive and deductive reasoning to analyze how those similarities and differences are manipulated in a learning environment and how to accommodate those needs in learning experiences. Integrated Design Fink, L. D. (2013). Creating significant learning experiences: An integrated approach to designing college courses (Rev. ed.). San Francisco, CA: Jossey-Bass: · In Chapter 3, “Designing Significant Learning Experiences I: Getting Started,” on pages 67–112, you will explore the beginning steps in using the integrated design. Encouraging Motivation Wlodkowski, R. J., & Ginsberg, M. B. (2017). Enhancing adult motivation to learn: A comprehensive guide for teaching all adults (4th ed.). San Francisco, CA: Jossey-Bass: · In Chapter 5, “Encouraging Motivation in Online Formats,” on pages 107–146, you will learn about the needs of online learners and specific strategies for facilitating motivation in the online environment. · In Chapter 6, “Establishing Inclusion Among Adult Learners,” on pages 147–182 you will focus on specific strategies that promote the core need of inclusion among adult learners, including factors related to culture, neuroscience and onsite versus online environments.
- 6. Professional Learning Module Modeling the enactment of the Formative Assessment: Using Positive and Negative Numbers in Context (Concept Development) This Professional Learning Module describes how a facilitator can implement, with fidelity, the Shell Center’s Formative Assessment Lesson, Using Positive and Negative Numbers in Context, so that participants understand how to enact, in their own classrooms, this lesson that is compatible with the Common Core State Standards (CCSS). Resources for each component of the module are included as page numbers in the Lesson Guide, and as links to additional professional learning tools such as handouts and videos. Shell Center’s Lesson Guide: http://map.mathshell.org/materials/lessons.php?taskid=453&sub page=concept Framing the lesson Teachers frame the lesson so that students know what to expect throughout the entire process, from the pre- to the post-lesson assessment. Participants learn what it means to frame a lesson, why it is important, and what might go wrong if it is neglected. Handout: Framing a Formative Assessment Lesson Temperature Changes: the pre-lesson assessment The pre-lesson assessment is designed to surface the common issues that impede student learning. We have found it important to ask students to complete it individually in class, without help from other students or their teacher. Coaching students to the right answers can keep common issues hidden and hinder student success. The pre-lesson assessment is not graded, but is analyzed to identify student errors. These data are used by
- 7. teachers to develop feedback questions or comments, and to modify instruction. Lesson Guide: page T-2; assessment S-1 & S-2; Facilitator Notes: Administering the Pre-Lesson Assessment Whole-class interactive introduction For successful enactment of the introduction it is important to follow the Lesson Guide’s suggestions exactly. Replacing the whole-class discussion with a mini-lesson will quickly sabotage the entire lesson. Lesson Guide: pages T-4; Temperature Scales S-3, card set S-4; slide Temperature Changes P-1 Introducing the collaborative activity By taking care to introduce the collaborative activity teachers give students the chance to wrap their arms around the activity that they are being asked to do. Students need to be given clear instructions in writing as well as access to these written instructions for the duration of the activity so that they can grapple with the complexities of the activity and maximize their learning. Lesson Guide: page T-5; slide Instructions for Working Together P-2 Engaging in the collaborative activity The collaborative activity is designed as an opportunity for students to learn. This gives students an opportunity to engage in many of the CCSS Standards for Mathematical Practice—for example MP2 (Reason abstractly and quantitatively) and MP3 (Construct viable arguments and critique the reasoning of others). This opportunity to learn is enhanced when teachers give students feedback, allow students to struggle productively in homogeneous pairs, and mini-conference so as to scaffold student learning. Lesson Guide: pages T-5, T-6 & T-7; card sets S-5, S-6 & S-7;
- 8. slides More Temperature Changes P-3 & P-4; Videos: A Teacher Listens, The Importance of Homogeneous Grouping & Mini-Conference Temperature Changes (revisited): the post-lesson assessment & sharing prepared feedback Students are given back their pre-lesson assessments and their teachers’ feedback questions and comments before being asked to complete the post-lesson assessment. The post-lesson assessment gives students the chance to demonstrate growth across the pre- and post-lesson assessments. We have found it important to ask students to complete it individually in class, without help from other students or their teacher. Lesson Guide: page T-8; assessment S-8 & S-9; Facilitator Notes: Administering the Post-Lesson Assessment Whole-class discussion This is the most difficult part of almost any lesson. Teachers who have enacted the Shell Center’s Formative Assessment Lessons tell us that this is the part of the lesson where they feel the most vulnerable, and the part where they find the Lesson Guide’s specific advice on what they might say to their students most useful. Lesson Guide: page T-7 & T-8; Video: Whole-class discussion Ann Shannon & Associates, LLC Professional Learning Module Following up on the enactment of the Formative Assessment Lesson: Using Positive and Negative Numbers in Context (Concept Development)
- 9. This Professional Learning Module describes how to follow up on the enactment of the lesson Using Positive and Negative Numbers in Context, and how to facilitate the professional learning opportunities that are afforded by Formative Assessment Lessons. Shell Center’s Lesson Guide: http://map.mathshell.org/materials/lessons.php?taskid=453&sub page=concept Resource: Facilitator Notes The mathematics of Using Positive and Negative Numbers in Context Participants reflect on the lesson to determine its mathematics. They consider its alignment to the CCSS and reflect upon how the lesson presents students with an opportunity to learn. Lesson Guide: page T-1; Handout: The Mathematics of Using Positive and Negative Numbers in Context Analyze student responses to the pre-lesson assessment Participants analyze a small set of student responses to the pre - lesson assessment to identify and name the 3 to 5 most important common issues evident in the student work. Participants record these data in a copy of the Growth Analysis Spreadsheet. Lesson Guide: pages T-3, & T-8; Student work: Temperature Changes; Spreadsheet: Growth Analysis Spreadsheet; Handout: How to use the Student Analysis Growth Spreadsheet Write feedback questions and comments that will move the learner forward Using the Criteria for Feedback handout, participants practice developing 3 to 5 feedback questions that are designed to encourage students to think more deeply about the common issues and move their learning
- 10. forward. This written feedback is shared with students at the beginning of the lesson to help them re-engage with the problem. Handout: Criteria for Feedback Analyze student responses to the post-lesson assessment Participants analyze a small set of student responses to the post- lesson assessment and add these data to their copy of the Growth Analysis Spreadsheet in order to illustrate student growth across the pre- and post- lesson assessments. Lesson Guide: page T-9; Student work: Temperature Changes (Again) Modifying subsequent instruction Assessment is not formative until it is used to modify subsequent instruction. The formative assessment lessons are designed to reveal evidence about student learning. Here participants use all of the evidence —the evidence revealed during the lesson and that collected from the assessments—to modify subsequent instruction so that it better promotes student learning and is compatible with the CCSS. Link the structure of the lessons to the theory of formative assessment The Big Idea and the Five Strategies studied earlier convey the interpretation of formative assessment that underpins the Shell Center’s lessons. Participants consider how the structure of the lessons maps on to the theory. Handout: Big Idea of Formative Assessment; Handout: Five Strategies of Formative Assessment When to enact this lesson in your classroom Deciding when to enact a Formative Assessment Lesson can be a challenge. Many lessons fit well about two-
- 11. thirds of the way through a compatible unit of instruction, but would also work well as part of a review. The Course Outline provides a suggestion for when to enact this lesson. Resource: A Course Outline for Grade 7 Ann Shannon & Associates, LLC