common core state standards math – standards of ... 8 the task ... common core state standards...
TRANSCRIPT
© 2012 Noyce Foundation
Performance Assessment Task Picking Apples
Grade 8 The task challenges a student to demonstrate understanding of the concepts representing and analyzing mathematical situations and structures using algebra. A student must understand and be able to represent a break‐even point in cost analysis. A student must be able to use symbolic algebra, a table, a graph, or a verbal explanation to represent and explain mathematical relationships. A student must be able to judge the meaning, utility, and reasonableness of results of one or more of these representations. A student must make sense of this mathematics in a real world context of picking apples in two different orchards.
Common Core State Standards Math ‐ Content Standards Expressions and Equations Analyze and solve linear equations and pairs of simultaneous linear equations.. 8.EE.8 Analyze and solve pairs of simultaneous linear equations.
b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.
c. Solve real‐world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.
Common Core State Standards Math – Standards of Mathematical Practice MP.1 Make sense of problems and persevere in solving them.Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. MP.5 Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.
© 2012 Noyce Foundation
Assessment Results
This task was developed by the Mathematics Assessment Resource Service and administered as part of a national, normed math assessment. For comparison purposes, teachers may be interested in the results of the national assessment, including the total points possible for the task, the number of core points, and the percent of students that scored at standard on the task. Related materials, including the scoring rubric, student work, and discussions of student understandings and misconceptions on the task, are included in the task packet. Grade Level Year Total Points Core Points % At Standard
8 2005 10 5 45%
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Picking Apples Rubric The core elements of performance required by this task are: • work out costs from given rules Based on these, credit for specific aspects of performance should be assigned as follows
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(c) Noyce Foundation 2005
Grade 8 – 2005 pg. !"
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(c) Noyce Foundation 2005
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(c) Noyce Foundation 2005