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The CCSS: Implications for Teachers

The CCSS: Implications for Teachers. Words matter- not a list of topics. Make sense of problems & persevere in solving (MP) decomposing a number leading to a ten (Grade 1); a fraction into unit fractions (Grade 4)

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The CCSS: Implications for Teachers

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  1. The CCSS: Implications for Teachers

  2. Words matter- not a list of topics • Make sense of problems & persevere in solving(MP) • decomposing a number leading to a ten (Grade 1); a fraction into unit fractions (Grade 4) • Explain what a point (x, y) on the graph of a proportional relationship means …the points (0, 0) and (1, r) where r is the unit rate. • Use properties of operations to generate equivalent expressions (Grade 7) • Interpret the structure of an expression • Use polynomial identities to solve problems • Produce an equivalent form of an expression to reveal properties represented by the expression.High School CCSS, 2010

  3. “Understanding” is important • rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. Grade 7 • the connections between proportional relationships, lines, and linear equations.Grade 8 • the concept of a function and use function notation • the relationship between zeros and factors of polynomials • solving equations as a process of reasoning and explain the reasoning High School CCSS, 2010

  4. Emphasis on Visualization • Understand a fraction as a number on the number line; represent fractions on a number line diagram (Grade 3) • Use similar triangles to explain slopeGrade 8 • Experiment with transformations in a plane • Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically • Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k • Estimate areas under the normal curveHigh School CCSS, 2010

  5. The standards are clustered Reasoning with Equations and Inequalities • Understand solving equations as a process of reasoning and explain the reasoning • Solve equations and inequalities in one variable • Solve systems of equations • Represent and solve equations and inequalities graphically High School

  6. Content shifts • Elementary • Focus on number including fraction, • Decrease probability, geometry, statistics • Middle grades • Congruence/similarity through transformations • Linearity through systems of linear equations • Data analysis (grade 6)/probability/samples • High School • Statistics • Build on middle school • Begin with quadratics/exponentials • Formally prove theorems conjectured earlier • CC vs plus standards - no matrices, right triangle trig

  7. How students should work: Mathematical Practices • Make sense of problems 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 CCSS, 2010

  8. Common Core Mathematical Practices: Opportunities for revisiting our own practice

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