Depth of Knowledge - Math
- 1. DEPTH OF KNOWLEDGE ASSESSMENT THROUGH CONSTRUCTED RESPONSES - MATH
- 3. WHY THE SHIFT TOWARDS DEEPER INQUIRY? Level 3 and 4 Questioning Strategic Reasoning – • complex thinking • rationalizing, • more than one possible answer 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 circumstances
- 4. WHY THE SHIFT TOWARDS DEEPER INQUIRY? Level 3 and 4 Questioning Strategic Reasoning – • complex thinking • rationalizing, • more than one possible answer CST 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 circumstances CST has only assessed students on their ability to think at levels 1 and 2.
- 5. WHY THE SHIFT TOWARDS DEEPER INQUIRY? 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 circumstances SBAC will be assessing students both in level 1 and 2, as well as in their ability to think at higher levels.
- 6. 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)10 This is a grade 8 item that is coded to depth of knowledge level one. This item requires students to recall the rules for exponents to evaluate each expression and select the expression or expressions with a value between zero and one.
- 7. 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 use the formula for the volume of a cylinder, as well as a basic understanding of rate, to calculate the number of minutes Jane will take to fill the water tank.
- 8. 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 to perform calculations in order to respond to each part. In addition, students are required to provide an explanation for each answer.
- 9. LEVEL 4 EXAMPLE: GRADE 8 During the task, the student assumes the role of an architect who is responsible for designing the best plan for a park with area and financial restraints. The student completes tasks in which he/she compares the costs of different bids, determines what facilities should be given priority in the park, and then develops a scale drawing of the best design for the park and an explanation of the choices made. This investigation is done in class using a calculator, an applet 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 level four. This item requires students to use concepts of geometry, numbers and operations, and statistics to determine the best solution to a problem where all constraints cannot be satisfied at the 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 120 minutes.
- 10. Skills developed in the various Depth of Knowledge levels. Classroom application of these skills
Editor's Notes
- #7: This is a grade 8 item that is coded to depth of knowledge level one. This item requires students to recall the rules for exponents to evaluate each expression and select the expression or expressions with a value between zero and one.
- #8: This is a grade 8 item that is coded to depth of knowledge level two. This item requires students to use the formula for the volume of a cylinder, as well as a basic understanding of rate, to calculate the number of minutes Jane will take to fill the water tank.
- #9: This is a grade 8 item that is coded to depth of knowledge level three. This item requires students to perform calculations in order to respond to each part. In addition, students are required to provide an explanation for each answer.
- #10: This is a description for a grade 8 performance task that is coded to depth of knowledge level four. This item requires students to use concepts of geometry, numbers and operations, and statistics to determine the best solution to a problem where all constraints cannot be satisfied at the 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 120 minutes.