 2007 Mississippi Department of Education 2007 Mississippi Mathematics Framework Training Revised (Grades K-5) Day 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.

 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?

 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?

 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?

 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

 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

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

 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

 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

 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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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?

 2007 Mississippi Department of Education Continuous models for fractions Continuous models for fractions: Continuous models could be related to length, area, volume or mass. The quantity represents.

 2007 Mississippi Department of Education Discrete models for fractions Discrete models: Discrete models are typically sets of objects. This represents (ratio of purple to the total).

 2007 Mississippi Department of Education Benchmark Fractions Provide a referent for estimating size of fractions 0 1

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Curriculum materials and fractions Using your curriculum materials, discuss the following: How are fractions introduced or reviewed? Are both continuous and discrete models used? How are the models connected or related for students?

 2007 Mississippi Department of Education Fraction computations: Addition and Subtraction Using the benchmark fractions, estimate the sum and difference of the problems:

 2007 Mississippi Department of Education Using the rulers we created, perform the operations of the problems below. Be able to explain the actions you used on the ruler to get the sum or difference.

 2007 Mississippi Department of Education Perimeter and Area Using the 24-inch long string as the edge, create as many rectangles as you can. Measure the sides and record their dimensions in a table like the one below. DimensionsPerimeterArea

 2007 Mississippi Department of Education Perimeter and Area

 2007 Mississippi Department of Education What patterns do you notice?

 2007 Mississippi Department of Education Perimeter and Area How many rectangles can be made with an area of 36 square units? Use the 36 tiles and find all the rectangles you can.

 2007 Mississippi Department of Education Perimeter and Area Recording Table

 2007 Mississippi Department of Education What patterns do you notice?

 2007 Mississippi Department of Education Perimeter and Area What can you say about the relationships between area and perimeter?

 2007 Mississippi Department of Education Rectangle Area Use base X height rather than length X width.

 2007 Mississippi Department of Education Parallelogram Area

 2007 Mississippi Department of Education Triangle Area

 2007 Mississippi Department of Education Trapezoid Area

 2007 Mississippi Department of Education Measurement Strand What do you notice, as you look across the grades in the measurement strand of the framework, about the progression of the development of measurement formulas?

 2007 Mississippi Department of Education Comparison to Textbooks How does the development of area and perimeter in your textbook compare to the curriculum framework? How is the development we did with area and perimeter similar to your textbook? How is the development we did with area and perimeter different from your textbook?

 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. What questions remain about the framework?