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# Depth of Knowledge - Math

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### Depth of Knowledge - Math

1. 1. DEPTH OFKNOWLEDGEASSESSMENT THROUGH CONSTRUCTEDRESPONSES - ELA
2. 2. WHY THE SHIFT TOWARDS DEEPERINQUIRY? Level 3 and 4 Questioning Strategic Reasoning – • complex thinking • rationalizing, • more than one possible answer Extended Reasoning- • Multiple Steps • Across Content AreasLevel 1 and 2 Questioning • Applied to real world andRecall – novel circumstances• Facts and basic knowledgeSkills / Concepts –• Application in predicable circumstances
3. 3. WHY THE SHIFT TOWARDS DEEPERINQUIRY? Level 3 and 4 Questioning Strategic Reasoning – • complex thinking • rationalizing, • more than one possible answerCST Extended Reasoning- • Multiple Steps • Across Content AreasLevel 1 and 2 Questioning • Applied to real world andRecall – novel circumstances• Facts and basic knowledgeSkills / Concepts –• Application in predicable circumstances CST has only assessed students on their ability to think at levels 1 and 2.
4. 4. WHY THE SHIFT TOWARDS DEEPERINQUIRY? Level 3 and 4 Questioning Strategic Reasoning – • complex thinking • rationalizing, • more than one possible answer SBAC Extended Reasoning- • Multiple Steps • Across Content Areas Level 1 and 2 Questioning • Applied to real world and Recall – novel circumstances • Facts and basic knowledge Skills / Concepts – • Application in predicable circumstancesSBAC will be assessing students both in level 1 and 2, as well as in their ability to think at higher levels.
5. 5. LEVEL 1 EXAMPLE: GRADE 8 Select all of the expressions that have a value between 0 and 1. 87 –12 8 74 7–3 2 9 1 1 3 3 (–5)6 (–5)10This is a grade 8 item that is coded to depth of knowledge level one. This itemrequires students to recall the rules for exponents to evaluate each expression andselect the expression or expressions with a value between zero and one.
6. 6. LEVEL 2 EXAMPLE: GRADE 8 A cylindrical tank has a height of 10 feet and a radius of 4 feet. Jane fills this tank with water at a rate of 8 cubic feet per minute. How many minutes will it take Jane to completely fill the tank without overflowing at this rate? Round your answer to the nearest minute.This is a grade 8 item that is coded to depth of knowledge level two. This item requires students to usethe formula for the volume of a cylinder, as well as a basic understanding of rate, to calculate thenumber of minutes Jane will take to fill the water tank.
7. 7. LEVEL 3 EXAMPLE: GRADE 8 The total cost for an order of shirts from a company consists of the cost for each shirt plus a one-time design fee. The cost for each shirt is the same no matter how many shirts are ordered. The company provides the following examples to customers to help them estimate the total cost for an order of shirts. • 50 shirts cost \$349.50 • 500 shirts cost \$2370 Part A: Using the examples provided, what is the cost for each shirt, not including the one-time design fee? Explain how you found your answer. Part B: What is the cost of the one-time design fee? Explain how you found your answer.This is a grade 8 item that is coded to depth of knowledge level three. This item requires students toperform calculations in order to respond to each part. In addition, students are required to provide anexplanation for each answer.
8. 8. LEVEL 4 EXAMPLE: GRADE 8During the task, the student assumes the role of an architectwho is responsible for designing the best plan for a park witharea and financial restraints. The student completes tasks inwhich he/she compares the costs of differentbids, determines what facilities should be given priority inthe park, and then develops a scale drawing of the bestdesign for the park and an explanation of the choices made.This investigation is done in class using a calculator, anapplet to construct the scale drawing, and a spreadsheet.This is a description for a grade 8 performance task that is coded to depth of knowledge levelfour. This item requires students to use concepts of geometry, numbers and operations, andstatistics to determine the best solution to a problem where all constraints cannot be satisfied atthe same time. Additionally, the student must provide justifications to support reasoning.Students are expected to engage with the task for an extended period of time, up to 120minutes.
9. 9. Skills developedin the variousDepth ofKnowledgelevels. Classroom application of these skills