1.  2007 Mississippi Department of Education 2007 Mississippi Mathematics Framework Revised Training (Grades 6-12) Day 2

2.  2007 Mississippi Department of Education Reading Reflections At your table, discuss important ideas you took from the articles you read. How did the ideas relate to our tasks and discussions from yesterday? How did the ideas relate to our exploration of the curriculum framework? Record your ideas on chart paper.

3.  2007 Mississippi Department of Education Understanding by Design: Step 1 1. Define desired results  a. Establish goals: What relevant goals (such as content, competencies or objectives) will this design address?  b. Understandings: What are the big ideas that students will understand? What specific understandings about them are desired? What misunderstandings are predictable?  c. Essential questions: What questions will foster inquiry, understanding, and transfer of learning?  d. What key knowledge and skills will students acquire as a result of this unit or series of lessons? What should they eventually be able to do as a result of such knowledge and skills?

4.  2007 Mississippi Department of Education Understanding by Design: Step 2 2. Assessment Evidence  a. Performance tasks: Through what authentic performance tasks will students demonstrate the desired understandings? By what criteria will performances of understanding be judged?  b. Other evidence: Through what other evidence (such as quizzes, tests, writing prompts) will students demonstrate achievement of the desired results? How will students reflect upon and self-assess their learning?

5.  2007 Mississippi Department of Education Understanding by Design: Step 3 3. Learning Plan  a. Learning activities: What learning experiences and instruction will enable students to achieve the desired results?

6.  2007 Mississippi Department of Education 5 Characteristics of Tasks that Affect Student Learning Introduction of new topics with a problem- solving task Use of communication strategies Connections across topics Development over time Tasks that challenge

7.  2007 Mississippi Department of Education Underlying Learning Theory Problem-solving focus Introduction of topics with problem solving Inclusion of non-routine and application problems Use of higher-order thinking questions

8.  2007 Mississippi Department of Education Underlying Learning Theory Use of communication strategies Reading Writing Speaking Critical listening Multiple representations

9.  2007 Mississippi Department of Education Underlying Learning Theory Connections across topics Links to previous understandings Use of threads or strands through all topics Multiple, linked objectives taught concurrently to eliminate isolated and fragmented teaching

10.  2007 Mississippi Department of Education Underlying Learning Theory Allow time to learn 3–8 days of development for a new topic 8–11 days of repetition Problems change qualitatively over time, not the same type repeated

11.  2007 Mississippi Department of Education Underlying Learning Theory Tasks that challenge Use open-ended questions to allow a wide group of students the opportunity to engage in the question or problem

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13. Curriculum materials Select a chapter in your curriculum materials. Find instances or evidence of the 5 characteristics of learning tasks. Be able to support your examples. Which criteria appear to be missing?

14.  2007 Mississippi Department of Education Solving Equations Solve: 5x – 2 = 10 + 2x

15.  2007 Mississippi Department of Education Solving Equations Solve: 5x – 2 = 10 + 2x A 2 5x = 12 + 2x S 2x 3x = 12 D 3 x = 4 Abbreviations can be used: A  Addition S  Subtraction M  Multiplication D  Division CLT  Combine Like Terms DPMA  Distributive Property of Multiplication over Addition

16.  2007 Mississippi Department of Education Algebra Tile Representations What relationships do you notice among the tiles? Discuss in your group.

17.  2007 Mississippi Department of Education Curriculum Framework Comparison How do these tasks relate to the curriculum framework objectives? How do these tasks relate to the criteria for student learning?

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23. Station 1

24.  2007 Mississippi Department of Education Station 2

25.  2007 Mississippi Department of Education Station 3

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27.  2007 Mississippi Department of Education Station 5

28.  2007 Mississippi Department of Education Comparison to framework and materials How does this exploration in transformational geometry relate to the curriculum framework? How does this exploration relate to your curriculum materials?

29.  2007 Mississippi Department of Education Closing focus questions What are key components of the curriculum framework? Decide at your table what you consider to be critical ideas.