San Jose Unified School District Algebra 1 Pacing Calendar 2009-2010 SJUSD ALGEBRA 1 TIMELINE 2009-2010 Page 1 of 9
SJUSD ALGEBRA 1 PACING GUIDE FOR 2009-2010 The Algebra 1 curriculum has been broken into five logical units of study called Benchmark Periods (BMPs) and four benchmark exams as outlined below. Each of the four benchmark tests is each designed to be completed in two periods. Several days of review have been built into the calendar prior to each assessment, and five days after the assessment to re-teach, review and enrich missed material. Each exam emphasizes all of the state content standards. The first benchmark assessment is to be used as a baseline test. The fourth benchmark assessment is designed to identify areas of focus for the CST review sessions.! There will be 4 district wide benchmark exams over the course of the year. They will be administered over two days (as determined by the school site) during the following testing periods: Benchmark 1: August 24-28 two-period exam Benchmark 2: October 5-9 two-period exam Benchmark : November 0 December 4 two-period exam (Dec. 16, 17, 18 Final exams for high schools) Benchmark 4: February 8-12 two-period exam (June 1, 2, Final exams for high schools)! No calculators of any kind may be used on any of the benchmark exams.! Starred standards make up 70 percent of the CST. Teachers should aim to cover all 25 Algebra 1 standards.! Spiraling will be a major key to success on student achievement and on the CST exams.! The purpose of the pacing calendar and benchmark tests is to promote standards based teaching in preparation for the STAR/CST. SJUSD ALGEBRA 1 TIMELINE 2009-2010 Page 2 of 9
CLARIFICATIONS Calculators and Technology: Calculators are prohibited on all benchmark exams as calculators are not permitted on the CST. Use of graphing calculators throughout the year for exploration and demonstration purposes is highly recommended. Geometer s Sketchpad can be used to develop skills and aid in visualization in the context of the course content. Word Problems: Word problem questions make up between 20% and 25% percent of the CST and should be incorporated into the course and emphasized on a regular basis. Spiraling Curriculum: A spiral approach to developing skills and concepts is suggested since students may not reach mastery in the time allotted. Continuous review will facilitate student retention of concepts. Textbook Alignment: This pacing guideline is designed to be independent of any text. Material is divided and taught in thematic groupings to facilitate student learning. Need to Supplement the Textbook: The Algebra 1 text will need to be supplemented heavily when working on analysis and critical thinking. Most of the texts offer limited experience with problem solving and word problems necessitating the use of additional sources. SJUSD ALGEBRA 1 TIMELINE 2009-2010 Page of 9
VOCABULARY The CST and CAHSEE use a predictable set of vocabulary. Teachers should use appropriate terminology and force their students to do the same. Catchy mnemonics can be useful when introducing a concept, but students need to be fully conversant in mathematical language. The following is not an exhaustive list, but it provides a thorough foundation. VOCABULARY FOR ALGEBRA 1: absolute value acute, right, obtuse angles additive, multiplicative identity additive, multiplicative inverse algebraic proof area and perimeter base, height, altitude, length, width coefficient completing the square consecutive integers coordinate counterexample, justification cross multiplication, proportion degree of monomial, polynomial difference of 2 squares discriminant distributive, associative, commutative domain, range equation, inequality expanded form exponent expressions extraneous solution factor, factoring formulas, literal equation function, relation, function notation greatest common factor graph, axes, origin horizontal, vertical hypotenuse, leg hypothesis, conclusion inductive, deductive reasoning intersection point inverse operations infinite integer, whole number, negative, positive intercepts least common multiple linear combination, elimination method linear, quadratic model with a graph and/or an equation monomial, binomial, trinomial, polynomial motion, uniform motion, vertical motion multi-step equations, inequalities number line ordered pair order of operations, grouping symbols parent function, families of functions parallel, perpendicular perfect square, square root perfect square trinomial pi (!) point-slope form power, exponent, degree, base Pythagorean Theorem Pythagorean triples 0-60-90 & 45-45-90 triangles quadrants Quadratic Formula, equations, expressions quadratic functions, graphs radical, radical expressions, equations rate of change, slope ratio, rational, irrational numbers real numbers reciprocal, negative, opposite root, solution, x-intercept simplify slope-intercept form solution to linear system standard form of a quadratic equation standard form of the equation of a line system of equations, inequalities table of values, T-chart term, coefficient, constant valid, invalid argument vertex form of quadratic equation vertical change, horizontal change x-intercept(s), y-intercept zeros of a function SJUSD ALGEBRA 1 TIMELINE 2009-2010 Page 4 of 9
BMP ONE: ALGEBRAIC THINKING & LINEAR EQUATIONS 40 DAYS Weave in standards 24.0 and 25.0 throughout the year as applicable. The unit number is not connected or related to any textbook. It is used to organize the concepts in each benchmark period. Unit 1 ALGEBRAIC THINKING (Standards: 1.0, 2.0,.0, 4.0, and 5.0) Std Days 1.1 Review pre-algebra skills, including roots of perfect squares from 1-100 and roots of perfect cubes from 1-125 1 1.2 Real number properties 1, 2 Simplifying expressions using the distributive property 4 2 1. Properties and operations of exponents 2 Simplifying rational expressions with monomial numerators and 4 2 denominators 1.4 Solve 1-step and 2-step equations and inequalities 4, 5 Simplify expressions within 2-step equations and inequalities 4, 5 Solve multi-step equations, including word problems 4, 5 8 Use T-chart to complete an algebraic proof, using algebraic properties to justify steps in the solution 4, 5 1.5 Simple absolute value equations and inequalities, such as x = 5 and x < 8, including distances Solve absolute value equations and inequalities, such as 2x " = 7 Unit 2 LINEAR EQUATIONS (Standards: 5.0, 6.0, and 7.0) Std Days 2.1 Solve linear equations for the dependent variable 6 Create a table of values for a linear equation 6 Identify the slope of a line from its equation 6 Put a linear equation in slope-intercept form 6 Identify slope as a rate of change 6 6 Graph linear equations and inequalities in slope-intercept form 6 Graph lines using x- and y-intercepts 5, 6 Use standard form to represent and graph a line 5, 6 2.2 Graph linear inequalities 5, 6 2 TOTAL DAYS TEACHING: 26 5 days distributed within the benchmark period for individual teacher review and assessment BMP Recommended Testing (4 days): BMP 1: 2 days between Aug. 24-28 BMP 2: Monday and Tuesday October 5 th and 6 th Post BMP 2 Review, Re-teach, Enrich, and Extend: 5 days BENCHMARK PERIOD ONE TOTAL: 40 DAYS SJUSD ALGEBRA 1 TIMELINE 2009-2010 Page 5 of 9
BMP TWO: LINEAR EQUATIONS, LINEAR SYSTEMS, & QUADRATICS 9.5 DAYS Weave in standards 16, 17, and 18 and connect functions to their graphs throughout the year. Continue to weave in standards 24 and 25. Weave in connection of slope to parallel and perpendicular lines, Standard 8. Unit 2 cont. LINEAR EQUATIONS (Standard: 7.0) Std Days 2. Write and graph the equation of a line given a slope and y-intercept 7 Write and graph the equation of a line given two points 7 Write and graph the equation of a line given a slope and a point 7 9 Solve word problems using linear equations and inequalities 7 Solve linear equations and inequalities 7 Unit LINEAR SYSTEMS (Standards: 9.0 and 15.0) Std Days.1 Solve a system of linear equations by graphing in slope-intercept 9 and standard form 4 Solve systems of linear inequalities by graphing 9.2 Solve a system of linear equations by substitution, when one equation in the system is already in slope-intercept form 9 Solve a system of linear equations by substitution, when both equations in the system are in standard form 9 4. Solve a system of linear equations by linear combination 9 4.4 Solve word problems with systems of linear equations 9 Solve word problems with systems of linear inequalities 9 4 Solve word problems involving rates and mixtures 15 Unit 4 QUADRATICS (Standard: 10.0) Std Days 4.1 Multiply binomials using the distributive property 10 2 TOTAL DAYS TEACHING: 27 5.5 days distributed within the benchmark period for individual teacher review and assessment (.5 day is the Wednesday before Thanksgiving) BMP Recommended Testing (2 days): Thursday and Friday December rd and 4 th Post BMP Review, Re-teach, Enrich, and Extend: 5 days BENCHMARK PERIOD TWO TOTAL: 9.5 DAYS 2 days are reserved for Semester 1 Finals Review (Monday and Tuesday December 14 th and 15 th ) SEMESTER ONE TEACHER-MADE FINALS: Wednesday, Thursday, and Friday December 16 th, 17 th, and 18 th SJUSD ALGEBRA 1 TIMELINE 2009-2010 Page 6 of 9
BMP THREE: QUADRATICS & QUADRATIC APPLICATIONS 1 DAYS Weave in standards 16, 17, and 18 and connect functions to their graphs throughout the year. Emphasize the connections between the equation, the table, and the graph. Continue to weave in standards 24 and 25. Unit 4 QUADRATICS (Standards: 11.0, 14.0 and 21.0) Std Days 4.2 Graph quadratics using the vertex, a table of values, and the axis of symmetry, identifying, and if necessary estimate, the x-intercepts of the graph 21 4 4. Factor a quadratic with a leading coefficient of 1, include taking out a common factor 11 Factor quadratics using special factoring patterns, such as the difference of perfect squares 11 4 Recognize the square of a binomial 11, 14 Factor quadratics with a leading coefficients other than 1 11, 14 4.4 Solve all types of quadratics by factoring to find x-intercepts Connect the roots of a quadratic equation to its x-intercepts and 11, 14 zeros Graph a quadratic using factors to find x-intercepts 11, 14 4 Identify the x-intercepts of a graph as the solutions of an equation 21 Use the Zero Product Property to find the zeros of a quadratic equation 14 4.5 Use quadratics to find the maximum areas of rectangles 11, 14 1 Unit 5 QUAD. APPLICATIONS (Standards 11.0, 14.0, 19.0, and 20.0) Std Days 5.1 Graph and solve quadratic equations in the form ax 2 + c = 0 11, 14 1 5.2 Solve quadratic equations using completing the square 14 Derive the quadratic formula by completing the square 19 5. Solve quadratic equations with the quadratic formula 19, 20 TOTAL DAYS TEACHING: 20 4 days distributed within the benchmark period for individual teacher review and assessment BMP 4 Recommended Testing (2 days): Tuesday and Wednesday February 9 th and 10 th Post BMP 4 Review, Reteach, Enrichment, and Extension: 5 days BENCHMARK PERIOD THREE TOTAL: 1 DAYS SJUSD ALGEBRA 1 TIMELINE 2009-2010 Page 7 of 9
BMP FOUR: QUADRATIC APPLICATIONS & RATIONAL EXPRESSIONS 4 DAYS Spiral as many key standards as possible. Continue to weave in standards 24.0 and 25.0 throughout the year as applicable. Unit 5 QUAD. APPLICATIONS (Standards: 14.0, 19.0, 22.0, and 2.0) Std Days 5.4 Choose the best method for solving a quadratic 14, 19 Solve word problems with quadratics 2 5 Solve word problems involving falling objects, acceleration due to 2 gravity, and velocity 5.5 Solve a quadratic equation and determine if it has 0, 1, or 2 roots 22 1 Unit 6 RATIONAL EXPRESSIONS (10.0, 12.0, 1.0, and 15.0) Std Days 6.1 Add and subtract polynomials, including combining like terms 10 Multiply and divide polynomials using the distributive property 10 4 Solve word problems with polynomials 10 6.2 Simplify rational expressions by canceling simple and complex factors 12 2 6. Multiply rational expressions with linear numerators and denominators 1 Multiply rational expressions with polynomial numerators and denominators, particularly by first factoring and canceling common factors 1 2 6.4 Divide rational expressions 1 2 6.5 Add/subtract and reduce rational expressions with common denominators 1 Add/subtract rational expressions with unlike denominators 1 4 Solve word problems with rational equations, particularly applications involving rates, work, and mixtures 15 TOTAL DAYS TEACHING: 20 4 days distributed within the benchmark period for individual teacher review and assessment CAHSEE Testing Days: 2 additional days in mid-march CST Review: 5 days (before Spring Break) CST Testing: days reserved BENCHMARK PERIOD FOUR TOTAL: 4 DAYS SJUSD ALGEBRA 1 TIMELINE 2009-2010 Page 8 of 9
BMP FIVE: AFTER THE CST - PREPARING FOR GEOMETRY 26 DAYS This unit is designed to front-load geometry concepts to give students a head start on next year s concepts. This early accessibility to geometry should give next year s geometry teachers more time to cover proofs and other new geometry concepts in depth. Unit 7 Preparing for Geometry Std Days 7.1 Radical Expressions: Simplifying, Add, Subtract, Multiply, and Divide 2 7.2 Pythagorean Theorem and its converse 7. Distance and Midpoint Formulas 7.4 Review writing equations of lines given the slope and a point or given two points Identify lines as parallel or perpendicular. Find equation of a line perpendicular/parallel to another line and passing through a point 7.5 Solving Proportions: Connect it to scale drawings and similarity 2 7.6 Basic Coordinate Geometry: Including graphing a circle given center and radius, finding the area, perimeter of figures on a coordinate plane (circle, rectangles, triangles. parallelograms), using distance formula on figures in the coordinate plane. 7.7 Geometric reasoning and logic 2 TOTAL DAYS TEACHING: 18 days distributed within the benchmark period for individual teacher review and assessment 2 days are reserved for Semester 2 Finals Review (Thursday and Friday May 27 th and 28 th ) SEMESTER TWO TEACHER-MADE FINALS: Tuesday, Wednesday, and Thursday June 1 st, 2 nd, and rd BENCHMARK PERIOD FIVE TOTAL: 26 DAYS SJUSD ALGEBRA 1 TIMELINE 2009-2010 Page 9 of 9