Stage 1: Integrate significant concept, area of interaction and unit question, and ensure it can be assessed

Transcription

1 MYP unit planner Unit Title Teacher(s) The Shapes Around Us Martin, Mitchell, Rieder, Roland, Hutson Subject and Grade Level Geometry Level 5 Time frame and Duration First Six Weeks Stage 1: Integrate significant concept, area of interaction and unit question, and ensure it can be assessed Area of Interaction Focus Which AoI will be your focus? Why have you chosen this? Environment Significant Concept(s) What are the big ideas? What do I want my students to retain for years into the future? Building Blocks of geometry, reasoning, transformations MYP Unit Question If you were dropped off anywhere in the Metroplex, could you find your way home? Assessment What task(s) will allow students the opportunity to respond to the unit question? What will constitute acceptable evidence of understanding? How will students show what they have understood? Geometry in the Real World Project (A real-life problem where students are given the opportunity to apply mathematics to a real life context, reflect upon and evaluate their findings.) (Criterion D is strongly recommended as one of the criteria used to assess this task.) Six Weeks Test Which specific MYP objectives will be addressed during this unit? Criterion A: Knowledge and Understanding. _ _A1: Know and demonstrate understanding of the concepts from the 5 branches of mathematics (number, algebra, geometry, statics, and discrete)

2 _ _A2: Use appropriate math concepts and skills to solve problems in familiar and unfamiliar contexts A3: Select and apply general rules to solve problems correctly, including those in a real-life context. Criterion B: Investigating Patterns B1: Select and apply appropriate inquiry and problem solving techniques. _ _B2: Recognize patterns _ _B3: Describe patterns as a relationship or general rule _ _B4: Draw conclusions consistent with findings. B5: Justify or prove mathematical relationships and general rules. Criterion C: Communication in Mathematics _ _C1: Use appropriate math language in both oral and written explanations. _ _C2: Use different forms of mathematical representations (charts, formulae, graphs, diagrams, and models) _ _C3: Communicate and complete and coherent mathematical line of reasoning using different forms of representation when investigating complex problems. Criterion D: Reflection in Mathematics _ _D1: Explain whether results make sense within the context of the problem _ _D2: Explain the importance of findings _ _D3: Justify the degree of accuracy of results where appropriate D4: Suggest improvements to the method when necessary. Which MYP assessment criteria will be used? Criterion C and D Stage 2: Backward planning: from the assessment to the learning activities through inquiry Content What knowledge and/or skills (from my course overview) are going to be used to enable the student to respond to the guiding question? What (if any) state, provincial, district, or local standards/skills are to be addressed? G.1A The student is expected to develop an awareness of the structure of a mathematical system, connecting definitions, postulates, logical reasoning, and theorems. G.2A The student is expected to explore attributes of geometric figures and to make conjectures about geometric relationships. G.2B The student is expected to make conjectures about angles, lines, polygons, circles, and three-dimensional figures and determine the validity of the conjectures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic. G.3A The student is expected to determine the validity of a conditional statement, its converse, inverse, and contrapositive. G.3B The student is expected to construct and justify statements about geometric figures and their properties. G.3C The student is expected to use logical reasoning to prove statements are true and find counter examples to disprove statements that are false. G.3D The student is expected to use inductive reasoning to formulate a conjecture. G.3E The student is expected to use deductive reasoning to prove a statement. G.3C The student is expected to use logical reasoning to prove statements are true and find counter examples to disprove statements that are false. G.4 The student uses a variety of representations to describe geometric relationships and

3 solve problems. The student is expected to select an appropriate representation (concrete, pictorial, graphical, verbal, or symbolic) in order to solve problems. G.5A The student is expected to use numeric and geometric patterns to develop algebraic expressions representing geometric properties. G.7A The student is expected to use one- and two-dimensional coordinate systems to represent points, lines, rays, line segments, and figures. G.7C The student is expected to derive and use formulas involving length, slope, and midpoint. G.8C The student is expected to derive, extend, and use the Pythagorean Theorem. G.9A The student is expected to formulate and test conjectures about the properties of parallel and perpendicular lines based on explorations and [concrete] models Approaches to Learning How will this unit contribute to the overall development of subject-specific and general AtL skills? Clear thinking is emphasized heavily in the beginning of the year, and students have opportunities to show their clear thinking through showing the math processes through both math language and essay writing form. Guided inquiry to open inquiry This teaches students to ask questions as a problem solving tactic. Discovery Learning: Students will use prior knowledge to develop knew knowledge Learning Experiences How will students know what is expected of them? Will they see examples, rubrics, templates, etc.? How will students acquire the knowledge and practise the skills required? How will they practise applying these? Do the students have enough prior knowledge? Teaching Strategies How will we use formative assessment to give students feedback during the unit? What different teaching methodologies will we employ? How are we differentiating teaching and learning for all? Have we considered those learning in a language other than their mother tongue? Have we considered those with special educational needs? The teacher models an example of the desired outcome for students to see. Other student examples can be displayed from past classes. Clear rubrics, including MYP criteria as well as more specific requirements, will be made and communicated. Students will be participating in activities that require them to communicate, both verbally and written, the math process going on in their minds. Clear expectations for homework and activities will be spoken and written for students. Clear expectations, accountable talk, guided practice / daily practice, cooperative learning, peer review, teacher checking for understanding. Resources What resources are available to us? How will our classroom environment, local environment and/or the community be used to facilitate students experiences during the unit? Holt Geometry, Kagan Geometry, Discovering Geometry, patty paper, protractors, tape, construction

4 paper, scissors, TAKS formula chart, Promethean Board LEARNING ACTIVITIES THAT INCORPORATE THE MYP Area of Interaction, Learner Profile, Inquiry Based Learning, and International Mindedness blended with FWISD Curriculum Requirements. Explain activities in narrative or bullet point format. Do not list daily plans here; activities can last 30 minutes to 3 days. DAY 1 Begin Building Blocks Vocabulary undefined terms line collinear non-collinear intersection point plane coplanar non-coplanar Class-Building Activity Find person closest to your height, ask what is your favorite animal? Direct Instruction Vocab with Table Discuss Intersections of lines and planes Use sticks and cards for lines and planes Pairs Acivity to draw what it says Kagan p. 6 Guided Practice in pairs or fours DAY 2 Segment and Angle Postulates postulate segment ray endpoint opposite rays protractor coordinate distance length between midpoint congruent segments angle vertex segment bisector interior of an angle straight angle exterior of an angle congruent angles angle bisector degree bisect measure Think-Share: 5K Race Checkpoints Patty Paper Activity to discuss midpoint, segment bisector, angle bisector. Geometry Labs -Protractor Practice p. 4-5 Kagan p.8 DAY 3 Characteristics & Properties of Angle Pairs right angle acute angle obtuse angle nonexample complementary angles adjacent angles linear pair vertical angles supplementary angles Assign Shapes in Life Project Angle Sorting Activity Kagan Develop Angle Pair Definitions

5 DAY 4 Distance, Midpoint, Slope Estimate Shortest Distance on city map. Pythagorean Activities Discover Distance & Midpoint Formulas Assign: Moving Troops Progress Check Product Reflection: How are Pythagorean and Distance Formulas related? DAY 5 Induction, Deduction, Conditional Statements Inductive Reasoning Deductive Reasoning Conjecture Counterexample Identify Mathematical Patterns Activity Develop conjectures based on patterns. Develop Conclusions based on Facts Caught Stealing, You are the Jury scenario DAY 6 Conditional Statements Conditional Statements Hypothesis Conclusion If You Give a Pig a Pancake book review Turning statements into Conditional Statements. Turning facts into ordered events and conclusions. DAY 7 Conditional, Converse, Inverse, Contrapositive Review of various advertisemens: Change them into Conditional Statements Venn Diagram on statements. Foldable indicating statements and If P, then Q. Mind Your P s and Q s Activity DAY 8 Linear and Quadratic Patterns Discuss Why important to know patterns as it relates to laying brick around pools. Examples of Linear Patterns and how to determine equations. Examples of Quadratic Patterns, how to distinguish from Linear and determining equations using Stat/Edit function of calculator. Assign Pool Problem Progress Check Product. DAY 9 Identify Angles formed by 2 lines and a transversal parallel lines parallel planes perpendicular lines skew lines transversal alternate interior angles alternate exterior angles same side interior angles same side exterior angles corresponding angles Engage: AMES Room -- Video: Lead into discussion importance of understanding lines/planes relationships. Activity: Diagram/Label angle pairs formed when two lines are cut by a transversal.

6 DAY 10 Parallel Lines cut by a Transversal Kagan, pp Use of Patty Paper also. Students should work in groups of 3 or 4 to discover properties of angle pairs when the 2 lines are parallel. Guided Practice problems using algebra instead of straight angle measurements. DAY 11 Proving Lines Parallel Engage with review of Conditional Statements Discuss the rules of Parallel Lines cut by a transversal and put them in conditional statement format. Develop the inverse of those conditional statements. Introduce two-column proofs to the Inverses to prove lines parallel. Assign large Angle/Lines combination worksheet. Ongoing reflections and evaluation In keeping an ongoing record, consider the following questions. There are further stimulus questions in the unit planning section of MYP: from principles into practice. Students and Teachers What did we find compelling? Was our disciplinary knowledge/skills challenged in any way? What inquiries arose during the learning? What, if any, extension activities arose? How did we reflect both on the unit and on our own learning? Were there any attributes of the learner profile that were encouraged through this unit? Were there any opportunities for action? Possible connections How successful was the collaboration with other teachers within my subject group and from other subject groups? What interdisciplinary understandings were or could be forged through collaboration with other subjects? Assessment Were students able to demonstrate their learning? Did the assessment tasks allow students to demonstrate the learning objectives identified for this unit? Did I make sure students were invited to achieve at all levels of the criteria descriptors? Are we prepared for the next stage? Data collection How did I decide on the data to collect? Was it useful?