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2007 Mississippi Department of Education 2007 Mississippi Mathematics Framework Revised Training (Grades K-5) Day 1

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2007 Mississippi Department of Education Select the number of times per week that you’d like to have chocolate. Multiply this number by 2. Add 5 to the product. Multiply your answer by 50. If you’ve already had your birthday this year, add 1757. If you’re still waiting for your birthday, add 1756. Subtract the four-digit year of your birth. Sweet Thoughts

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2007 Mississippi Department of Education Definition of Problem Solving The process involved to solve a problem or situation for which the individual who confronts it has no procedure that will guarantee a solution

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2007 Mississippi Department of Education Definition of Algorithm A series of steps which, if followed correctly, will lead to a correct answer

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2007 Mississippi Department of Education What level of thinking is required by each task? 1. Temika earns 5 points for every homework assignment that is turned in on time. If she turns in homework on time for 6 days, how many points does she get? a. 20b. 25 c. 30 d. 35 2. Courtney made a pattern with numbers. What is the next number in the pattern? 7, 16, 25, 34, _____ a. 35b. 37c. 43d. 44 3. Find the next three terms in the pattern and determine the rule for the following: 1, 4, 8, 11, 15, 18, 22, 25, 29,... 4. Find the next three terms in the pattern, determine the rule for finding the next number in the pattern, and find a model for the pattern: 1, 1, 2, 3, 5, 8, 13, 21, 34,...

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2007 Mississippi Department of Education Thinking Levels of Tasks What is the cognitive demand of each task? Cognitive demand refers to the level of thinking required by the task or problem. How are the problems alike related to cognitive demand? How are they different?

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2007 Mississippi Department of Education Norman Webb’s Depth of Knowledge Level 1 (Recall) recall information such as a fact, definition, term, or a simple procedure perform a simple algorithm or apply a formula (one- step, well-defined, and straight algorithmic procedure should be included at this lowest level) Key words: identify, recall, recognize, use, and measure

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2007 Mississippi Department of Education Norman Webb’s Depth of Knowledge Level 2 (Skill/Concept) engage in some mental processing beyond a habitual response explain the purpose and use of experimental procedures; carry out experimental procedures; make observations and collect data; classify, organize, and compare data; and organize and display data in tables, graphs, and charts Keywords: classify, organize, estimate, make observations, collect and display data, and compare data (imply more than one step)

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2007 Mississippi Department of Education Norman Webb’s Depth of Knowledge Level 3 (Strategic Thinking) reason, plan, use evidence, and engage in a higher level of thinking than the previous two levels (require students to explain their thinking) require students to make conjectures engage in activities that have more than one possible answer and require students to justify the response they give draw conclusions from observations; cite evidence and develop a logical argument for concepts; explain phenomena in terms of concepts; and use concepts to solve problems

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2007 Mississippi Department of Education Norman Webb’s Depth of Knowledge Level 4 (Extended Thinking) require complex reasoning, planning, developing, and thinking most likely over an extended period of time require high cognitive demands in the task and the work should be very complex require making several connections—relate ideas within the content area or among content areas—and select one approach among many alternatives on how the situation should be solved include designing and conducting experiments; making connections between a finding and related concepts and phenomena; combining and synthesizing ideas into new concepts; and critiquing experimental designs

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2007 Mississippi Department of Education Curriculum materials and DOK Each group has been given a DOK level. Find instances or evidence of the characteristics of that level in your curriculum materials.

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2007 Mississippi Department of Education Number Development Count out 15 tiles. Discuss with your partner: how many different ways can you put the tiles into two groups? Note: disregard color.

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2007 Mississippi Department of Education Number Development What if the number of tiles you had was 20 tiles? How many groups do you think you could make? Discuss with your partner to predict.

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2007 Mississippi Department of Education Part-Whole Diagrams for 15 15 7 8

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2007 Mississippi Department of Education Fact Families 15 = 8 + 7 15 = 7 + 8 15 – 8 = 7 15 – 7 = 8 15 7 8

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2007 Mississippi Department of Education Number Development Model 127 using your Base-ten blocks. Record your solutions in a table like the one below. FlatsLongsUnits

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2007 Mississippi Department of Education Curriculum Framework Using the curriculum framework, look at the objectives in the Number and Operations strand for the grade levels K– 5. At your table, decide which objectives the tasks we completed would address. Are there any terms in the objectives that you’re not clear about? If so, highlight them. Write them on a post-it note and place it on the chart paper.

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2007 Mississippi Department of Education Framework and Textbook Comparison Using your instructional materials, do you find evidence of these objectives? Check to see how these objectives are developed.

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2007 Mississippi Department of Education Contexts for Computations In pairs, you will write– Two word problems or contextual problems that can be solved with addition Three word problems or contextual problems that can be solved with subtraction

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2007 Mississippi Department of Education Review Problem Solutions Were the problems solved in the way you had anticipated? Why or why not?

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2007 Mississippi Department of Education Addition and Subtraction 1.Katie had 16 stickers. She bought 12 more stickers. How many stickers does she have now? 2.There were seven boys playing tag. Two boys went home. How many boys are still playing tag? 3.Tom has 5 brothers. Juan has 3 brothers. How many more brothers does Tom have than Juan? 4.Jesse has 14 golf balls. Teva has 23 golf balls. How many more golf balls does Jesse need to have as many as Teva?

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2007 Mississippi Department of Education Addition and Subtraction 1.Katie had 16 stickers. She bought 12 more stickers. How many stickers does she have now? (Combining) 2.There were seven boys playing tag. Two boys went home. How many boys are still playing tag? (Take-away) 3.Tom has 5 brothers. Juan has 3 brothers. How many more brothers does Tom have than Juan? (Comparison) 4.Jesse has 14 golf balls. Teva has 23 golf balls. How many more golf balls does Jesse need to have as many as Teva? (Missing addend)

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2007 Mississippi Department of Education Addition and Subtraction Actions Consider the actions involved in addition and subtraction. How are they related? How are they different?

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2007 Mississippi Department of Education Curriculum Framework Comparison Look at the Number strand in your grade level. What do you notice about the objectives related to addition and subtraction and their relationship to these models? How does student understanding build from grade to grade?

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2007 Mississippi Department of Education Addition and Subtraction Algorithms Solve in at least three ways: 572 862 + 347 – 295

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2007 Mississippi Department of Education Multiple Algorithms At your tables, discuss: What are the advantages of using different algorithms? What are the disadvantages of using different algorithms?

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2007 Mississippi Department of Education Algorithms in Textbook What algorithms are stressed or developed in your book? How are they alike or similar to the ones we discussed? Were any different algorithms stressed in your text that we did not discuss?

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2007 Mississippi Department of Education Focus Questions How were the topic developments today similar to or different from the way you thought about these ideas? What do you notice about the objectives in the curriculum framework with regard to number and algebraic development? What level of thinking does the topic development of this type promote?

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Learning Outcomes Participants will be able to analyze assessments

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