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COMMON CORE MATH STANDARDS Grade 7 & 8 Math Curriculum Compacted Vs. Standard Objective To provide a standards-based math program to meet the needs of all learners in order that: All students will build a strong foundation in mathematics at a pace which develops each student’s mathematical understanding and ability to apply concepts to problems; All students will demonstrate at least grade level proficiency on Common Core Assessments. Key Changes New standards provide focus and coherence New framework highlights the Standards for Mathematical Practices New content standards rely on mastery of prior content to ‘Push Down’ curriculum 2000-2011 MA State Frameworks 5 Strands carried throughout each year Number Sense and Operations Patterns, Relations and Algebra Geometry Measurement Data Analysis, Statistics and Probability Common Core Standards PK-8 Common Core Standards 9-12 The high school standards are listed in conceptual categories: Number and Quantity (N) Algebra (A) Functions (F) Modeling () Geometry (G) Statistics and Probability (S) Standards for Mathematical Practices Make sense of problem solving and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and express regularity in repeated reasoning New content standards rely on mastery of prior content to ‘Push Down’ curriculum What is ‘Push Down’ Introduction of new material higher level thinking skills Movement from concrete to abstract thinking Mathematical Modeling Examples of ‘Push Down’ New to Grade 7: Use proportional relationships to solve multi-step ratio and percent problems. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Examples of ‘Push Down’ New to Grade 8 Solve linear equations with rational number coefficients, including expanding expressions using the distributive property and collecting like terms. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Use informal arguments to establish facts about geometric properties Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots…informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. Examples of ‘Push Down’ New to Algebra 1 Extend the properties of exponents to rational exponents. Use properties of rational and irrational numbers. Interpret the structure of expressions including linear, quadratic and exponential expressions Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Distinguish between situations that can be modeled with linear functions and with exponential functions. Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Compute (using technology) and interpret the correlation coefficient of a linear fit. Challenge: Pacing ‘Pushing Down’ curriculum impacts instructional pacing Student readiness Importance of strong foundation Grade 7 and 8 Presently 7th grade 8th grade 9th grade Grade 7 Math Algebra 1 Geometry Grade 7 Math Grade 8 Math Algebra 1 Grade 7 Presently Grade 7 Curriculum presently assumes all students are ready for High School Level Math in Grade 8 Grade 7 & 8 Standards are Compacted 5 Strands 39 Standards Grade 8 Presently Grade 8 (based on gr. 7 performance) has two course offerings: Algebra 1 (approx. 80% of students) 5 Strands 19 Standards Grade 8 Math 5 Strands 9 Standards Review of Grade 8 Grade 7 and 8 Moving Forward 7th grade Compacted Grade 7 Math Standard Grade 7 Math 8th grade 9th grade Algebra 1 Geometry Standard Grade 8 Math Algebra 1 Grade 7 Standard Curriculum 25 Content Standards Unit 1: Rational Numbers Unit 2: Proportionality and Linear Relationships Unit 3: Introduction to Sampling and Inference Unit 4: Creating, Comparing, and Analyzing Geometric Figures Compacted Curriculum 40 Content Standards Unit 1: Rational Numbers and Exponents (6 additional standards) Unit 2: Proportionality and Linear Relationships (3 additional standards) Unit 3: Introduction to Sampling and Inference (no additional standards) Unit 4: Creating, Comparing, and Analyzing Geometric Figures (6 additional standards) Grade 8 Standard Curriculum 28 Content Standards (grade 8) Unit 1: Formulating, Reasoning and Modeling with Linear Equations Unit 2: Linear Functions Unit 3: Patterns of Association with Bivariate Data Unit 4: Creating, Comparing, and Analyzing Geometric Figures Unit 5: Expressions and Equations Compacted Curriculum 63 Content Standards (13 grade 8 and 50 Alg 1) Unit 1: Relationships between Quantities and Reasoning with Equations Unit 2: Linear and Exponential Functions Unit 3: Descriptive Statistics Unit 4: Expressions and Equations Unit 5: Quadratic Functions and Modeling Grade 9 • Algebra 1 • 50 Content Standards • Geometry • 44 Content Standards • Unit 1: Relationships between • Unit 1: Congruence, Proof, and • • • • Quantities and Reasoning with Equations Unit 2: Linear and Exponential Functions Unit 3: Descriptive Statistics Unit 4: Expressions and Equations Unit 5: Quadratic Functions and Modeling • • • • • Constructions Unit 2: Similarity, Proof, and Trigonometry Unit 3: Extending to Three Dimensions Unit 4: Connecting Algebra and Geometry Through Coordinates Unit 5: Circles With and Without Coordinates Unit 6: Applications of Probability Placement Process Inform Parents/Guardians Course Descriptions Placement Process-3 Parts Teacher Recommendation Preliminary Math MCAS Score Grade Level Cumulative Exam Score Placement Recommendations Late June via letter to Parents Parent choice to Opt out of Recommendation Students are evenly distributed among grade level teams Math placement does not effect any other subject area Let’s Revisit the Objective To provide a standards-based math program to meet the needs of all learners in order that: All students will build a strong foundation in mathematics at a pace which develops each student’s mathematical understanding and ability to apply concepts to problems; All students will demonstrate at least grade level proficiency on Common Core Assessments. What Does Placement in the Standard Course Mean Long Term? Gr 7 Standard Course & Gr 8 Standard Course High School Algebra 1, Geometry, Algebra 2, PreCalculus Or Summer Program between grade 7 & 8 for students who have demonstrated ability to master content quickly Taking HS Geometry and Algebra 2 simultaneously in Gr 10, gr 11 PreCalculus, gr 12 Calculus Adaptations as needed- Overall: Strong Foundation, Content Mastery, Confidence, Success What Does Placement in the Compacted Course Mean Long Term? Gr 7 Compacted Course & Gr 8 Compacted Algebra 1 Course High School Geometry, Algebra 2, PreCalculus, Calculus Adaptations as needed- Overall: Strong Foundation, Content Mastery, Confidence, Success