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Los Angeles Unified School District Algebra 1A1/1A2 Sample Assessment Items The purpose of these sample assessment items is to provide teachers with examples of questions that address the assessed standards. Although the assessment items will not be identical to these samples, the test format, level of rigor, and type of questions will be similar. Not all assessed standards are represented. The intent is not to create a pretest or to layer an additional assessment MULTIPLE CHOICE QUESTIONS Sample Item #1 Algebra I 1.0 Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the four basic arithmetic operations where applicable. Strand: *Standard: Four arithmetic statements are shown in the box below. 5+2=7 5−2 =3 5 × 2 = 10 5÷2=2 1 2 These four statements show that closure for integers applies to all operations except A addition. B division. C subtraction. D multiplication. Answer: B *assessed standard key standard Los Angeles Unified School District Algebra 1A1/1A2 Sample Assessment Items Sample Item #2 Strand: Algebra I 4.0 Students simplify expressions before solving linear equations and inequalities in one variable, such as 3 ( 2 x + 5) + 4 ( x − 2 ) = 12 . *Standard: Which of the following equations is equivalent to x− 1 1 (2 − x) = ( x+2)? 2 2 1 x +1 2 A −1= B 1 1 1 x −1= x +1 2 2 C 2x − 1 = 1 x +1 2 D 2x + 1 = 1 x +1 2 Answer: B Sample Item #3 Strand: *Standard: Algebra I 5.0 Students solve multi-step problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step. Daria has a grocery budget of $50 per week. She spent $63.92 on groceries this week, but plans to spend less for the next 3 weeks to stay within her budget. What is the average amount that Daria should spend on groceries per week for the next three weeks to meet this goal? A B C D $34.02 $36.08 $45.36 $46.52 *assessed standard key standard Los Angeles Unified School District Algebra 1A1/1A2 Sample Assessment Items Sample Item #4 Strand: *Standard: Algebra I 6.0 Students graph a linear equation, and compute the x- and y-intercepts. If a line has a slope of 3 and an x–intercept of − 2, what is the y–intercept? A −6 B −2 C 1 D 6 Answer: D Sample Item #5 Strand: Standard: Algebra 1 5.0 Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step. A prize of $25,000 is to be divided among Fernando, Kathy, and Joel. Fernando is to receive $5,000 more than Kathy, and Kathy is to receive twice as much as Joel. How much should Joel receive? A B C D $4,000 $6,700 $8,000 $13,000 Answer: A *assessed standard key standard Los Angeles Unified School District Algebra 1A1/1A2 Sample Assessment Items Sample Item #6 Strand: *Standard: Algebra I 9.0 Students solve a system of two linear equations in two variables algebraically, and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables, and to sketch the solution sets. Which of the following systems of linear inequalities is shown in the graph below? A B C D y < 3 and y > x + 1 y > 3 and y < x + 1 y > 3 and y > x + 1 y < 3 and y < x + 1 Answer: B Sample Item #7 Strand: *Standard: Algebra I 5.0 Students solve multi-step problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step. If 2 x + 6 = 20, what is the value of − 3 x + 5? A −54 B −36 C −34 D −16 Answer: D *assessed standard key standard Los Angeles Unified School District Algebra 1A1/1A2 Sample Assessment Items Sample Item #8 Strand: *Standard: Algebra I 6.0 Students graph a linear equation, and compute the x- and yintercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4). Which is the graph of y < 3 x + 2 ? Answer: B CONSTRUCTED RESPONSE Strand: Algebra I *Standard: 2.0 For the equation y = 1 − • • Students understand and use such operations as taking the opposite, finding the reciprocal. 1 , write the following: x the opposite of y the reciprocal of y For both the opposite and the reciprocal, show each step of the operation that proves your answers are correct. *assessed standard key standard Los Angeles Unified School District Algebra 1A1/1A2 Sample Assessment Items Rubric: 4-point response: The student indicates an advanced proficiency of taking the opposite and finding the reciprocal. 1 • The student correctly writes the opposite of y as −1. x x . • The student correctly writes the reciprocal of y as x −1 • The student proves that the answer is the opposite by showing the sum of the two is zero. 1 1 1 1 y + (− y )= 1 − + − 1 = 1 − 1 + − = 0 x x x x • The student proves that the second answer is the reciprocal by showing the product of the two is one. 1 1 x x x − 1 x ( x − 1) = i y = 1 − i = =1 y x x − 1 x − 1 x ( x − 1) x 3-point response: The student indicates proficiency of taking the opposite and finding the reciprocal. • The student correctly finds the opposite and reciprocal of y and attempts to prove both are true but makes a mistake on one of the proofs. 2-point response: The student indicates partial proficiency of taking the opposite and finding the reciprocal. • The student correctly finds the opposite and reciprocal of y and attempts to prove both are true but is unable to do so. OR • The student does not find either or both the opposite and reciprocal correctly but does show some good work strategies and attempts the proofs. 1-point response: The student indicates little or no proficiency of taking the opposite and finding the reciprocal. • • The student attempts the problem but does no part correctly. OR The student does not attempt the problem. *assessed standard key standard LOS ANGELES UNIFIED SCHOOL DISTRICT Instructional Support Services District Mathematics Program Algebra 1A1/1A2 BLUEPRINT: 2004-05 Quarter 1 Multiple Choice STANDARD 1.0 Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the four basic operations where applicable. 6 2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents. 12 4.0 Students simplify expressions before solving linear equations and inequalities in one variable. 12 TOTAL 30 Key standard Constructed Response 1 1 LOS ANGELES UNIFIED SCHOOL DISTRICT Instructional Support Services District Mathematics Program Algebra 1A1/1A2 BLUEPRINT: 2004-05 Quarter 2 STANDARD Multiple Choice Constructed Response 1 5.0 Students solve multi-step problems, including word problems, involving linear equations in one variable and provide justification for each step. 9 6.0 Students graph a linear equation and compute the x- and yintercepts (e.g., graph 2x+y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4) 10 7.0 Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations using the point-slope formula. 9 Key standard Linking Items from Quarter 1 2 TOTAL 30 1 LOS ANGELES UNIFIED SCHOOL DISTRICT Instructional Support Services District Mathematics Program Algebra 1A1/1A2 BLUEPRINT: 2004-05 Quarter 3 Multiple Choice STANDARD 3.0 Students solve equations and inequalities involving absolute values. 3 5.0 Students solve multi-step problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step. 7 6.0 Students graph a linear equation and compute the x- and yintercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., sketch the region defined by 2x + 6y < 4). 5 7.0 Students verify that a point lies on a line, given the equation of the line. Students are able to derive the equation of a line by using the point-slope formula. 6 9.0 Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets. 7 Linking Items from Quarter 2 2 TOTAL 30 Key standard Constructed Response 1 1 LOS ANGELES UNIFIED SCHOOL DISTRICT Instructional Support Services District Mathematics Program Algebra 1A1 (End-of-Course) BLUEPRINT: 2004-05 Quarter 4 STANDARD Multiple Choice 4 Constructed Response 2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents. 3.0 Students solve equations and inequalities involving absolute values. 4 4.0 Students simplify expressions prior to solving linear equations and inequalities in one variable, such as 3(2x-5)+4(x-2)=12 4 5.0 Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step. 10 6.0 Students graph a linear equation and compute the x- and yintercepts (e.g., graph 2x+y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4) 10 7.0 Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations using the point-slope formula. 10 8.0 Students understand the concept of parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point. 4 9.0 Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets. 10 15.0 Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems. 4 1 TOTAL 60 1 Key standard