Unit 2: Integers Wellspring Learning Community Lina Shakaroun, Lina El Osta, Rana Sabbagh IB MYP Mathematics (Grade 6 Community) A Summary Unit 2: Integers Subject Mathematics Year Grade 6 Community Start date Week 4, September Duration 3 weeks Key and Related Concepts Key Concepts Key Concepts Definition Form is the shape and underlying structure of an entity or piece of work, including its organization, essential nature and external appearance. Form Related Concepts Quantity, Representation Inquiry Global Context & Explorations Global Context & Explorations Explorations to develop Natural and human landscapes and resources Orientation in space and time Statement of Inquiry Being able to represent different forms of quantities has helped humans explore and describe our planet. Inquiry Questions Type Factual Inquiry Questions What is an integer? Wellspring Learning Community Unit 2: Integers Page 1 of 10 Unit 2: Integers Wellspring Learning Community Lina Shakaroun, Lina El Osta, Rana Sabbagh IB MYP Mathematics (Grade 6 Community) A Type Inquiry Questions Conceptual How are different forms of quantities represented? Debatable How do we define where and when? Curriculum Objectives A: Knowing and understanding i. select appropriate mathematics when solving problems in both familiar and unfamiliar situations ii. apply the selected mathematics successfully when solving problems iii. solve problems correctly in a variety of contexts D: Applying mathematics in real-life contexts i. identify relevant elements of authentic real-life situations ii. select appropriate mathematical strategies when solving authentic real-life situations iii. apply the selected mathematical strategies successfully to reach a solution iv. explain the degree of accuracy of a solution v. describe whether a solution makes sense in the context of the authentic real-life situation Content Integers, absolute value, operations on integers, Cartesian plane Skills Defining, comparing and ordering integers Defining and evaluating the absolute value of a number Performing the operations of multiplication, division, addition and subtraction with integers. Applying mathematical strategies to solve problems involving integers. Plotting points on the Cartesian plane. ATL Skills Approaches to Learning Description Learning Experiences: Self-management: In order for students to develop perseverance and persistence in learning and problem solving, students will consider personal Wellspring Learning Community Unit 2: Integers Page 2 of 10 Wellspring Learning Community Unit 2: Integers Lina Shakaroun, Lina El Osta, Rana Sabbagh IB MYP Mathematics (Grade 6 Community) A learning strategies (Self-management: Reflection skills). The strategy students will learn and practice is “check-in”, where students will take stock of how well they are learning unit content and explore what they could do to be a more effective and efficient learner. Thinking: In order for students to be able to appreciate the contribution of mathematics to other areas of knowledge, students will make connections between subject groups and disciplines (Thinking: Transfer skills). Throughout the unit, students will explore how integers are also an integral part of other subjects like physics, chemistry, astronomy and history. These links will be explicit so that students can make easy connections. Self-management - V. Reflection skills (Re-)considering the process of learning; choosing and using ATL skills Consider personal learning strategies Thinking - X. Transfer skills Utilizing skills and knowledge in multiple contexts Make connections between subject groups and disciplines Assessment Summative Assessment Unit Test: (criterion A) In this task, students will answer a wide range of questions, from simple to complex to challenging (in both familiar and unfamiliar situations), all related to representing different forms of quantities. Students will be asked to order integers, graph coordinates and perform mathematical operations with integers. They will also be required to apply their knowledge of integers to solve reallife problems. The test will be completed individually during one class period. Expeditions: (criterion D) In this task, students will analyze a famous expedition that they have not already seen in the unit. They map the journey using our system of latitude and longitude and then create journal entries as if they were the explorer, describing life on the journey. Included in the journal must be authentic examples of using operations with integers as they relate to the expedition (e.g. changes in latitude and longitude). Students will then create their own expedition to a location in outer space. Similar to the first part, they will create a log of the expedition, complete with authentic uses of operations with integers. OCT 8 Grade 6 Summative Assessment Unit 1 and 2. Summative Unit Test Tuesday at 9:00 AM summative review Oct 7, 2019 Wellspring Learning Community Unit 2: Integers Page 3 of 10 Wellspring Learning Community Unit 2: Integers Lina Shakaroun, Lina El Osta, Rana Sabbagh IB MYP Mathematics (Grade 6 Community) A summative review answer key Oct 7, 2019 Please review all your class notes and the slides posted on onenote. The test will be on Integers, absolute value, prime and composite numbers, prime factorization, LCM AND GCF, writing in word, expanded, and standard forms, order of operations, and divisibility rules. https://wellspringlc-my.sharep... OCT 8 Grade 6 Summative Assessment Unit 1 and 2. Summative Unit Test Tuesday at 9:00 AM summative review Oct 7, 2019 summative review answer key Oct 7, 2019 Please review all your class notes and the slides posted on onenote. The test will be on Integers, absolute value, prime and composite numbers, prime factorization, LCM AND GCF, writing in word, expanded, and standard forms, order of operations, and divisibility rules. https://wellspringlc-my.sharep... OCT 8 Grade 6 Summative Assessment Unit 1 and 2. Summative Unit Test Tuesday at 9:00 AM summative review Oct 7, 2019 summative review answer key Oct 7, 2019 Please review all your class notes and the slides posted on onenote. The test will be on Integers, absolute value, prime and composite numbers, prime factorization, LCM AND GCF, writing in word, expanded, and standard forms, order of operations, and divisibility rules. https://wellspringlc-my.sharep... OCT 21 Grade 6 Real Life Task Summative Assessment Unit 2 Criterion D Summative Unit Test Monday at 7:00 AM Requirements for the project: 1) Pick an explorer 2) Pick one of the explorer's voyages 3) Create a chart of the countries/cities that the explorer visited on this specific voyage that you picked.( similar to the real life formative assessment that we did in class). 4) Look for the latitude ( East + , West -) and longitude (North +, South -) of the countries. 5) Write couple paragraphs on what you think life will be on the voyage including: a) the name of the ship and a description and the number of the crew members. Wellspring Learning Community Unit 2: Integers Page 4 of 10 Wellspring Learning Community Unit 2: Integers Lina Shakaroun, Lina El Osta, Rana Sabbagh IB MYP Mathematics (Grade 6 Community) A b) The goal of the journey and what is expected to be found. c) changes in both latitudes and longitudes with each stop, including calculations by finding the sum of all the latitudes, then the sum of all the longitudes Your entry journey (paragraphs) must include your starting longitude and latitude. Please find below the link for the book for the project.It is on page 136-137 or you can refer to the pdf attachment. 6th Grade Real Life Task Project Oct 6, 2019 https://wellspringlc-my.sharep... OCT 21 Grade 6 Real Life Task Summative Assessment Unit 2 Criterion D Summative Unit Test Monday at 7:00 AM Requirements for the project: 1) Pick an explorer 2) Pick one of the explorer's voyages 3) Create a chart of the countries/cities that the explorer visited on this specific voyage that you picked.( similar to the real life formative assessment that we did in class). 4) Look for the latitude ( East + , West -) and longitude (North +, South -) of the countries. 5) Write couple paragraphs on what you think life will be on the voyage including: a) the name of the ship and a description and the number of the crew members. b) The goal of the journey and what is expected to be found. c) changes in both latitudes and longitudes with each stop, including calculations by finding the sum of all the latitudes, then the sum of all the longitudes Your entry journey (paragraphs) must include your starting longitude and latitude. Please find below the link for the book for the project.It is on page 136-137 or you can refer to the pdf attachment. 6th Grade Real Life Task Project Oct 6, 2019 https://wellspringlc-my.sharep... OCT 21 Grade 6 Real Life Task Summative Assessment Unit 2 Criterion D Summative Unit Test Monday at 7:00 AM Requirements for the project: 1) Pick an explorer 2) Pick one of the explorer's voyages 3) Create a chart of the countries/cities that the explorer visited on this specific voyage that you picked.( similar to the real life formative assessment that we did in class). Wellspring Learning Community Unit 2: Integers Page 5 of 10 Unit 2: Integers Wellspring Learning Community Lina Shakaroun, Lina El Osta, Rana Sabbagh IB MYP Mathematics (Grade 6 Community) A 4) Look for the latitude ( East + , West -) and longitude (North +, South -) of the countries. 5) Write couple paragraphs on what you think life will be on the voyage including: a) the name of the ship and a description and the number of the crew members. b) The goal of the journey and what is expected to be found. c) changes in both latitudes and longitudes with each stop, including calculations by finding the sum of all the latitudes, then the sum of all the longitudes Your entry journey (paragraphs) must include your starting longitude and latitude. Please find below the link for the book for the project.It is on page 136-137 or you can refer to the pdf attachment. 6th Grade Real Life Task Project Oct 6, 2019 https://wellspringlc-my.sharep... MYP Assessment Criteria 6/8 A: Knowing and understanding N/A B: Investigating patterns N/A C: Communicating 6/8 D: Applying mathematics in real-life contexts Description The Unit Test will allow students to apply the content they have learned to a wide range of questions and verify that they can represent different forms of quantities and perform mathematical calculations with them. Many of the questions will include applications involving human explorations. In the Expeditions task, students will represent different forms of numbers in order to recreate a famous historical expedition and create their own journey into outer space. They will keep a journal of the journey, including information about what the expedition is like and calculations important to the expedition. They will see how being able to describe and calculate changes using different forms of numbers would have helped explorers to navigate and complete their journeys. Learning Experiences Learning Experiences and Teaching Strategies Learning experiences: Unit 2 Week 4: 1) Introducing real numbers: Sets and subsets. Matching the definitions of integers, whole, natural, rational, and irrational numbers activity.https://drive.google.com/open?... 2) Introducing unit 2 Key concept, global context, related concepts, statement of inquiry, ATL skills by showing the students a picture on page 92 from the 7th grade book.(https://drive.google.com/drive/u/0/folders/1cj1byvCpNCBQ31S2zxW6AYdXegSYsG4) Wellspring Learning Community Unit 2: Integers Page 6 of 10 Wellspring Learning Community Unit 2: Integers Lina Shakaroun, Lina El Osta, Rana Sabbagh IB MYP Mathematics (Grade 6 Community) A 3) Absolute Value: Investigation 1 Absolute Value on page 98. Reflect and discuss on page 98 Did you know on page 99 Practice 2 on page 99 3) Integers: Introducing integers by doing ATL 1 activity: finding the opposites on page 93 Reflect and discuss on page 94 Practice 1 on pages 95-96 Homework: Integers Worksheet Integer Worksheet Sep 30, 2019 4) Absolute Value: Investigation 1 Absolute Value on page 98. Reflect and discuss on page 98 Did you know on page 99 Practice 2 on page 99 Homework: Absolute value Worksheet Absolute Value worksheet Sep 30, 2019 Week 5: 5) Integers' Operations: Adding Integers: Dart Activity, loss/profit, number line, adding integers song on youtube (https://www.youtube.com/ watch?v=hz_ndxvJzws), examples, and desmos activity (https://teacher.desmos.com/dashboard/ 5d89e3ef132d824b465ef860#summary). Subtracting Integers: Adding the opposites by applying keep change change (KCC), examples, and desmos activity ( https://teacher.desmos.com/activitybuilder/custom/59e8b1797188fa18debdca96) Adding/Subtracting Integers worksheet: # 2 THROUGH 40 EVENS only Adding/Subtracting Integers Worksheet Sep 30, 2019 Multiplying Integers: Introducing Multiplication Rules and practice 2. Investigation on Multiplying Integers on Desmos: https://teacher.desmos.com/das... Homework: Evens numbers only Multiplying Integer Worksheet Oct 1, 2019 Dividing Integers Wellspring Learning Community Unit 2: Integers Page 7 of 10 Wellspring Learning Community Unit 2: Integers Lina Shakaroun, Lina El Osta, Rana Sabbagh IB MYP Mathematics (Grade 6 Community) A Introducing division Rules https://teacher.desmos.com/activitybuilder/custom/580e2f88612b5fdb051c0ae7 Homework: Evens numbers only Dividing Integers Worksheet Oct 1, 2019 Quiz on Integers's operations and Absolute Value Week 6: Unit Review Summative assessment : Criterion A and C on Unit 1 and Unit 2 The coordinate grid Did you know on page 101 (7th grade book) Investigation 2: Plotting coordinate points on pages 102-103 (7th grade book) Practice 3 on page 104 Homework: Coordinate plane worksheet Coordinate_Plane_Homework_Sheet.pdf Oct 8, 2019 Formative assessment 2 Criterion D as a classwork on pages 124-125 (7th grade book) Summative Assessment Criterion D as a project on page 136 Differentiation Different approaches have been used to explain the same concept: • Profit/Loss method: Through the dart game, students were able to add integers intuitively. This skill was then transferred into abstract algebraic problems. • Counters: Hands-on activity for students to better understand addition and division of integers. • Number line: A visual approach also hands on to see the operations on the number line. • Song: A song to remember the rules particularly for the auditory students. Different technologies have been employed to engage as many students possible: • • • • Desmos Activities Kahoot for formative assessment Quizlet for formative assessment Mathletics for extra practice and monitoring students' progress In class support was provided as we understand this integers and operations on integers are normally introduced in grade 7. We Wellspring Learning Community Unit 2: Integers Page 8 of 10 Wellspring Learning Community Unit 2: Integers Lina Shakaroun, Lina El Osta, Rana Sabbagh IB MYP Mathematics (Grade 6 Community) A expected that students would understand the concepts at different paces so we had extra help in class to cater for everybody's needs. Reflections General Reflections Prior to studying the unit Lina Shakaroun Dec 14, 2019 at 11:23 PM We already expect that this unit will be a challenge for 6th graders particularly operations on integers. Normally this topic is introduced in 7th grade, but because we have to cater for the Lebanese Program, we are covering it in 6th grade. In-class learning support is needed for this unit, it is highly recommended to ask the Math support teacher to assist 6th graders during this chapter. Introducing operations on integers with the dart activity, makes this concept attainable for students. Experience tells us that starting with an intuitive approach to introduce addition and subtraction of integers secures student engagement and boosts their confidence in this new topic. After the loss/profit apporach, we move to the number line, counters, and hacks. During the unit Lina Shakaroun Dec 14, 2019 at 11:23 PM The different approaches to addition and subtraction of integers catered for the different types of learners in class: The dart activity was engaging and helped students understand profit loss.The song also helped students memorize the processes (auditory learners) The number line was the least favorite among students, but we insisted on practicing this method and convinced students of its importance. Some students mastered the concepts in this unit faster than others. This is expected for this unit, and despite all differentiation techniques adopted, some students were still struggling with operations and order of operations. While extra support sessions were given to the low achieving students, we expect to continue practicing operations on integers all this year in spiral review and Mad Minute Math. After the unit Lina Shakaroun Dec 14, 2019 at 11:23 PM Some students sought help from their parents at home and learned different methods than the one done in class. Next year we'll communicate this concern to parents and anticipate the problem. Sometimes the strategies taught by parents at home, focus on the process and rarely tackle the conceptual understanding like we planned it. This will only cause confusion to students.Counters are proven to be very effective for teaching operations on integers. Kinesthetic learners could benefit greatly from counters to better understand subtraction of integers. These are not available in school, we should place an order for next year. Wellspring Learning Community Unit 2: Integers Page 9 of 10 Wellspring Learning Community Unit 2: Integers Lina Shakaroun, Lina El Osta, Rana Sabbagh IB MYP Mathematics (Grade 6 Community) A Stream & Resources Resources Rana Sabbagh Posted 1 file on Dec 14, 2019 at 10:40 PM Multiplication and Division of Integers This PowerPoint show highlights the conceptual understanding of multiplying and dividing integers. Through investigations, students deduced the rules related to multiplying and dividing integers. Multiplication_and_division_of_integers.ppsx 600 KB File Rana Sabbagh Posted 1 file on Dec 14, 2019 at 10:39 PM Addition and Subtraction of Integers This resource details the different conceptual approaches to add and subtract integers. We first introduce the number line then the profit loss approach. Students are then asked to practice adding and subtracting integers using each method. Addition_and_Subtraction_of_Integers.pdf 600 KB PDF Document Lina El Osta Posted 1 file on Sep 30, 2019 at 5:57 PM Main Resource - Oxford MYP Mathematics This is the main resource used for this unit. Oxford MYP Mathematics Year 2. Negative integers and operations on integers are introduced in grade 6 to map for the Lebanese Baccalaureate. They are not a requirement in MYP at this grade level. Integers_Oxford_3__3_.pdf 3 MB PDF Document Wellspring Learning Community Unit 2: Integers Page 10 of 10
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