Common Core Trajectory

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  • 1. + Operations and Algebraic Thinking Stephenie Cannon
  • 2. + Kindergarten Standards  CCSS.Math.Content.K.OA.A.1 Represent addition and subtraction with objects, fingers, mental images, drawings, sounds , acting out situations, verbal explanations, expressions, or equations.  CCSS.Math.Content.K.OA.A.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.  CCSS.Math.Content.K.OA.A.3 Group numbers less than or equal to 10 into pairs in more than one way. Can be done by using objects or drawings, and record each decomposition by a drawing or equation.  CCSS.Math.Content.K.OA.A.4 For any number from 1 to 9, find the number that makes 10 when added to the given number by using objects or drawings, and record the answer with a drawing or equation.  CCSS.Math.Content.K.OA.A.5 Add and subtract within 5. Summary  Students will be able to represent numbers 1 through 10 using visual aids. They will be able to add, subtract, and group these numbers by using objects or drawings. They will also be able to solve addition and subtraction word problems.
  • 3. + Kindergarten  Understand addition and understand subtraction
  • 4. + First Grade Standards  CCSS.Math.Content.1.OA.A.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.  CCSS.Math.Content.1.OA.A.2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.  CCSS.Math.Content.1.OA.B.3 Apply properties of operations as strategies to add and subtract.  CCSS.Math.Content.1.OA.B.4 Understand subtraction as an unknown-addend problem.  CCSS.Math.Content.1.OA.C.5 Relate counting to addition and subtraction.  CCSS.Math.Content.1.OA.C.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten, decomposing a number leading to a ten, using the relationship between addition and subtraction, and creating equivalent but easier or known sums.  CCSS.Math.Content.1.OA.D.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.  CCSS.Math.Content.1.OA.D.8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. Summary  Students will continue to use addition and subtraction to solve word problems and equations. They will expand their range from 1 to 20. They will also learn to apply properties of operations. Students will also use a number of strategies to add and subtract problems.
  • 5. + First Grade  Represent and solve problems involving addition and subtraction.  Understand and apply properties of operations and the relationship between addition and subtraction.  Add and subtract with 20.  Work with addition and subtraction equations.
  • 6. + Second Grade Standards  CCSS.Math.Content.2.OA.A.1 Use addition and subtraction within 100 to solve one- and two-step word problems by using drawings and equations with a symbol for the unknown number to represent the problem.  CCSS.Math.Content.2.OA.B.2 Add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.  CCSS.Math.Content.2.OA.C.3 Determine whether a group of objects (up to 20) has an odd or even number of members; write an equation to express an even number as a sum of two equal addends.  CCSS.Math.Content.2.OA.C.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. Summary  Students will continue solving word problems with more complex numbers (within 100). Students will also focus on using mental strategies to add and subtract within 20. Students will identify odd and even numbers and additional structured in arrays. Students will also practice writing equations to demonstrate their understanding. Students will be introduced to multiplication.
  • 7. + Second Grade  Represent and solve problems involving addition and subtraction.  Add and subtract within 20.  Work with equal groups of objects to gain foundations for multiplication.
  • 8. + Third Grade Standards  CCSS.Math.Content.3.OA.A.1 Interpret products of whole numbers, e.g., interpret 5 7 as the total number of objects in 5 groups of 7 objects each.  CCSS.Math.Content.3.OA.A.2 Interpret wholenumber quotients of whole numbers, e.g., interpret 56 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each.  CCSS.Math.Content.3.OA.A.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1  CCSS.Math.Content.3.OA.A.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. Summary  Third grade focuses on multiplication and division of whole numbers. Students will use multiplication and division to solve problems involving equal groups, arrays, and measurement quantities, etc.
  • 9. + Third Grade  Represent and solve problems involving multiplication and division.  Understand properties of multiplication and the relationship between multiplication and division.  Multiply and divide within 100.  Solve problems involving the four operations and ifentify and explain patterns in arithmetic.
  • 10. + Fourth Grade Standards  CCSS.Math.Content.4.OA.A.1 Interpret a multiplication equation as a comparison. Represent verbal statements of multiplicative comparisons as multiplication equations.  CCSS.Math.Content.4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.  CCSS.Math.Content.4.OA.A.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding Summary  Students will continue to work with multiplication and division. Students will be introduced to the x variable and be required to complete whole number problems in which all operations are used and contain an unknown quantity. Students begin to move away from drawings and representations to written equations with variables for unknown numbers. Students begin too generate and analyze patterns.
  • 11. + Fourth Grade  Use the four operations with whole numbers to solve problems.  Gain familiarity with factors and multiples.  Generate and analyze patterns.
  • 12. + Fifth Grade Standards  CCSS.Math.Content.5.OA.A.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.  CCSS.Math.Content.5.OA.A.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.  CCSS.Math.Content.5.OA.B.3 Generate two numerical patterns using two given rules. Identify relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the patterns, and graph the ordered pairs on a grid. Summary  Students will learn the importance of parentheses, brackets, and braces and learn how to accurately solve equations that have them. Students will write simple equations without evaluating them. In addition, students will learn to solve problems based on set “rules” (patterns). Students will continue to graph the ordered pairs on a grid.
  • 13. + Fifth Grade  Write and interpret numerical expressions.  Analyze patterns and relationships.
  • 14. + Sixth Grade Standards  CCSS.Math.Content.6.RP.A.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.  CCSS.Math.Content.6.RP.A.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.  CCSS.Math.Content.6.RP.A.3 Use ratio and rate reasoning to solve real-world and mathematical problems.  CCSS.Math.Content.6.RP.A.3a Make tables of equivalent ratios relating quantities with wholenumber measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  CCSS.Math.Content.6.RP.A.3b Solve unit rate problems including those involving unit pricing and constant speed.  CCSS.Math.Content.6.RP.A.3c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  CCSS.Math.Content.6.RP.A.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Summary  Content shifts from Operations and Algebraic Thinking to Ratios and Proportional Relationships. Students will learn about ratios, ratio terminology, and how ratios are used in mathematical problems and every day life. Students will be able to solve different math problems using ratios such as problems involving unit pricing, constant speed, percent, etc. Students will also know how to manipulate ratios.
  • 15. + Sixth Grade  Understand ratio concepts and use ratio reasoning to solve problems
  • 16. + Middle School and High School Continuum 5th grade, the standards for operations and algebraic thinking get more specific per grade. Grade 6 and 7 focus on ratios and proportional relationships. All of the middle school grades focus on non-rational numbers and how to analyze, approximate, and rationalize them. The high school grades focus primarily on extending the properties of exponents to rational exponents and using properties of rational and irrational numbers.  After