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

2007 Mississippi Department of Education Sweet Thoughts 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. 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 2007 Mississippi Department of Education

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

What level of thinking is required by each task? 1. Solve for x: 2x – 5 = 17 a. 6 b. 11 c. 17 d. 22 2. Write an equation whose solution is 3. 3. Find two fractions with unlike denominators in simplest form whose difference is . 4. Draw the 5th term. Describe the pattern in words and symbols. Without drawing, describe what the 7th and 8th terms would look like. 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? 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 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) 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 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 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. 2007 Mississippi Department of Education

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

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

2007 Mississippi Department of Education Which benchmark is each fraction closest to: 0, , or 1? 2007 Mississippi Department of Education

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

2007 Mississippi Department of Education Benchmark fractions Using your ideas from the benchmarking task, estimate the sum, difference, product and quotient of the following problems. How does use of the benchmarks impact student learning? 2007 Mississippi Department of Education

Rational number development Using the curriculum framework, look at the number strand. What do you notice about rational number development? 2007 Mississippi Department of Education

Curriculum framework discussion (Bingo problem) What objective(s) in the framework link to tasks of this type? How is this task related to non-routine problem solving? What mathematics can be developed from this task? 2007 Mississippi Department of Education

Toothpick Lab and Bingo Problem How are these tasks alike? How are they different? 2007 Mississippi Department of Education

Curriculum framework comparison How would the Toothpick lab be used in the classroom? What mathematics does it promote as related to the curriculum framework? 2007 Mississippi Department of Education

Comparison to curriculum framework: Knotty Problem Where does the Knotty problem fit with regard to the curriculum framework? What type of thinking is required for this type of task? What DOK level might describe it? 2007 Mississippi Department of Education

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? 2007 Mississippi Department of Education