Teacher Navigation Tool CCSS Math/Oregon Comparison. September, 2011 DRAFT

Transcription

1 Teacher Navigation Tool CCSS Math/Oregon Comparison September, 2011 DRAFT

2 Content: Math Grade: Kindergarten In Kindergarten, Instructional time should focus on two critical areas: (1) Representing and comparing whole numbers, initially with sets of objects; (2) Describing shapes and space. What is similar? Counting and Cardinality Count to 100 by ones and by tens. Count forward by ones beginning with a given number. Write numbers zero to 20. Connect counting to cardinality. When counting objects, pair each object with one and only one number name. Compare the number of objects in one group to another group. Compare two numbers, between one and ten, presented as written numerals. Operations and Algebraic Thinking Model and solve simple joining and separating situations. Counting and Cardinality is separated into three clusters: 1. Know number names and the count sequence. 2. Count to tell the number of objects. 3. Compare numbers. Added to this grade level: a. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement and the order in which they were counted. b. Understand that each successive number name refers to a quantity that is one larger. c. Count to answer how many? ; given a number from 1 20, count out that many objects. Added to this grade level: a. Fluently add and subtract within five. b. Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations. c. Decompose numbers less than or equal to ten, into pairs more than one way (5 = 2 + 3, 5 = 4 + 1). d. For any number from one to nine, find the number that makes ten when added to the given number. Added from 1 st Grade: a Develop and use efficient strategies for adding and subtracting whole numbers. What will I no longer teach? Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 1

3 What is similar? Number and Operations in Base Ten Composing and decomposing numbers into tens and ones (18=10+8). What will I no longer teach? Measurement and Data Describe several measureable attributes, such as length or weight. Directly compare two objects with a measureable attribute in common to see which has more or less of the attribute and describe the difference. Classify objects into given categories and count the number of objects in each category and sort the categories by count. Geometry Describe objects in the environment using names of shapes and relative position of these objects using terms such as, above, below, beside, in front of, behind, and next to. Correctly name shapes regardless of their orientation or size. Identify shapes as two and threedimensional. Analyze and compare two and threedimensional shapes. Model shapes in the world by building shapes from components (ex. craft sticks and marshmallows) and drawing shapes. Compose simple shapes to form larger shapes. Measurement and Data is separated into two clusters: 1. Describe and compare measurable attributes 2. Classify objects and count the number of objects in categories. Geometry is separated into two clusters: 1. Identify and describe shapes. 2. Analyze, compare, create and compose shapes. Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 2

4 Summary Notes: In each grade level these Mathematical Practices are emphasized. These are the Big Ideas of each standard. The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. K.MP.1 Make sense of problems and persevere in solving them. K.MP.2 Reason abstractly and quantitatively. K.MP.3 Construct viable arguments and critique the reasoning of others. K.MP.4 Model with mathematics. K.MP.5 Use appropriate tools strategically. K.MP.6 Attend to precision. K.MP.7 Look for and make use of structure. K.MP.8 Look for and express regularity in repeated reasoning. Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 3

5 Gaps: Changes: Although the content of the CCSS Counting and Cardinality domain, and Number and Operation in Base Ten domain is familiar, the language that describes it is new. Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 4

6 Content: Math Grade: 1 st In grade 1, Instructional time should focus on four critical areas: (1) Developing understanding of addition, subtraction, and strategies for addition and subtraction within 20; (2) Developing understanding of whole number relationships and place value, including grouping in tens and ones; (3) Developing understanding of linear measurement and measuring lengths and iterating length units; and (4) Reasoning about attributes of, and composing and decomposing geometric shapes. What is similar? Operations and Algebraic Thinking Develop and use efficient strategies for adding and subtracting. Use addition and subtraction within 20 to solve word problems with unknowns in all positions. Apply properties of operations as strategies to add and subtract. Relate addition and subtraction as inverse operations. Apply with fluency sums to ten and related subtraction facts. Number and Operations in Base Ten Understand that the two digits of a twodigit number represent the amounts of tens and ones. Compare two digit numbers based on tens and ones. Operations and Algebraic Thinking is separated into four clusters: 1. Represent and solve problems involving addition and subtraction. 2. Understand and apply properties of operations and the relationship between addition and subtraction. 3. Add and subtract within Work with addition and subtraction equations. Added to this grade level: a. Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false. b. Relate counting to addition and subtraction. c. Determine the unknown whole number in an addition or subtraction equation. Number and Operations in Base Ten is separated into three clusters: 1. Extend the counting sequence. 2. Understand place value. 3. Use place value understanding and properties of operations to add and subtract. Added to this grade level: a. Add within 100; relate the strategy to a written method and explain. Understand that in adding two digit numbers, tens are added to tens, ones added to ones; and sometimes it is necessary to compose a ten. b. Given a two digit number, mentally find ten more or ten less than the number, without having to count, and explain the reasoning used. What will I no longer teach? Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 1

7 What is similar? Measurement and Data Geometry The content on the CCSS Geometry is the same as the OSS at this grade level. Reason with geometric attributes to determine how they are alike and different. Compose two or three dimensional shapes to create a composite shape. Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters. Understand that more equal shares create smaller c. Subtract multiples of ten from multiples of ten (positive or zero differences), using models or strategies, and relate the strategy to a written method explaining the reasoning used. d. Compare two digit numbers recording the result with the symbols >, <, =. Measurement and Data is separated into three clusters: 4. Measure lengths indirectly and by iterating length units. 5. Tell and write time. 6. Represent and interpret data. Added to this grade level: a. Tell and write time in hours and half hours using analog and digital clocks. b. Organize, represent, and interpret data. c. Order three objects by length; compare the lengths of two objects indirectly by using a third object (ex. 3 < 4 and 4 < 5, therefore 3 < 5). Added from OSS 2 nd Grade: a Express the length of an object as a whole number of length units, by laying a length object end to end. What will I no longer teach? Represent whole numbers on a number line. 2 nd Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 2

8 What is similar? shares. What will I no longer teach? Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 3

9 Summary Notes: In each grade level these Mathematical Practices are emphasized. These are the Big Ideas of each standard. The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. 1.MP.1 Make sense of problems and persevere in solving them. 1.MP.2 Reason abstractly and quantitatively. 1.MP.3 Construct viable arguments and critique the reasoning of others. 1.MP.4 Model with mathematics. 1.MP.5 Use appropriate tools strategically. 1.MP.6 Attend to precision. 1.MP.7 Look for and make use of structure. 1.MP.8 Look for and express regularity in repeated reasoning. Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 4

10 Gaps: Changes: The content in the CCSS Number Operations in Base Ten domain is largely new to this grade level. The content in the CCSS Measurement and Data domain is new to this grade level. Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 5

11 Content: Math Grade: 2 nd In grade 2, Instructional time should focus on four critical areas: (1) Extending understanding of base ten notation; (2) Building fluency with addition and subtraction; (3) Using standard units of measure; and (4) Describing and analyzing shapes. What is similar? Operations and Algebraic Thinking Apply, with fluency, sums to 20 and related subtraction facts. Solve multi digit whole number problems by applying various models of addition and subtraction. Number and Operations in Base Ten Understand and apply base ten numeration and count in multiples of 1, 2, 5, 10, and 100. Understand that the three digits of a three digit number represent amounts of hundreds, tens, and ones (expanded form). Write and compare whole numbers to Fluently add and subtract up to four twodigit numbers. Add and subtract within 1000 using concrete models of drawings. Operations and Algebraic Thinking is separated into three clusters: 1. Represent and solve problems involving addition and subtraction. 2. Add and subtract within Work with equal groups of objects to gain foundations for multiplication. Added to this grade level: a. Determine whether a group of objects has an odd or even number of members and write an equation to express an even number as a sum of two equal addends. b. Add and subtract within 20 using mental strategies. Added from OSS 3 rd grade: a Represent and apply the concept of multiplication as repeated addition. Number and Operations in Base Ten is separated into two clusters: 1. Understand place value. 2. Use place value understanding and properties of operation to add and subtract. Added to this grade level: a. Add up to four two digit numbers using strategies based on place value and properties of operations. b. Explain why addition and subtraction strategies work. c. Mentally add or subtract ten or one hundred from a given number. d. Add and subtract to 1000 and relate the strategy to a written method. What will I no longer teach? Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 1

12 What is similar? What will I no longer teach? Measurement and Data Measure the length of an object by selecting and using appropriate tools. Measure the length of an object twice using different units for the measurements and describe how the two measurements relate to the size of the unit chosen. Estimate lengths using units of inches, feet, centimeters, and meters. Tell and write time from analog and digital clocks to the nearest five minutes. Measurement and Data is separated into four clusters: 1. Measure and estimate lengths in standard units. 2. Relate addition and subtraction to length. 3. Work with time and money. 4. Represent and interpret data. Added to this grade level: a. Measure to determine how much longer one object is to another, expressing the length difference in terms of a standard length unit. b. Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, and equations with a symbol for the unknown number to represent the problem. c. Generate measurement data and show the measurements by making a line plot. d. Draw a picture graph and a bar graph to represent a data set up to four categories. Solve problems using information presented in a bar graph. e. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies using $ and signs. Added from OSS 1 st grade: a Represent whole numbers on a number line. Geometry Added to this grade level: a. Partition a rectangle into rows and columns of same size squares and count to find the total. b. Partition circles and rectangles into two, three, or four equal shares; describe the shares using words. Recognize that equal Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 2

13 What is similar? shares of identical wholes need not have the same shape. c. Recognize, describe, compare and draw shapes and identify them as triangles, quadrilaterals, pentagons, hexagons, and cubes. What will I no longer teach? Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 3

14 Summary Notes: In each grade level these Mathematical Practices are emphasized. These are the Big Ideas of each standard. The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. 2.MP.1 Make sense of problems and persevere in solving them. 2.MP.2 Reason abstractly and quantitatively. 2.MP.3 Construct viable arguments and critique the reasoning of others. 2.MP.4 Model with mathematics. 2.MP.5 Use appropriate tools strategically. 2.MP.6 Attend to precision. 2.MP.7 Look for and make use of structure. 2.MP.8 Look for and express regularity in repeated reasoning. Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 4

15 Gaps: Changes: This is where number line is introduced. The content in the CCSS Geometry domain is new to this grade level. Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 5

16 Content: Math Grade: 3 rd In grade 3, Instructional time should focus on four critical areas: (1) Developing understanding multiplication and division and strategies for multiplication and division within 100; (2) Developing an understanding of fractions, especially unit fractions (fractions with numerator 1); (3) Developing understanding of the structure of rectangular arrays and of area; and (4) Describing and analyzing two dimensional shapes. What is similar? Operations and Algebraic Thinking Represent and apply the concept of multiplication as repeated addition and division as repeated subtraction. Apply understanding of models of multiplication and division, place value, and properties of operation to solve problems. Apply the inverse relationship between multiplication and division and the relationship between multiples and factors. Number patterns involving multiplication and division. Operations and Algebraic Thinking is separated into four clusters: 1. Represent and solve problems involving multiplication and division. 2. Understand properties of multiplication and the relationship between multiplication and division. 3. Multiply and divide within Solve problems involving the four operations, and identify and explain patterns in arithmetic. Added from OSS 4 th grade: a Apply with fluency multiplication facts and related division facts. b Apply understanding of models for multiplication, place value, and properties of operations. c Select and use appropriate estimation strategies for multiplication to calculate mentally. Added from OSS 5 th grade: a Apply understanding o f models for division and the relationship of division to multiplication to solve problems. What will I no longer teach? Number and Operations in Base Ten Added to this grade level: a. Use place value understanding to round whole numbers to the nearest ten or 100. b. Fluently add and subtract within c. Multiply one digit whole numbers by multiples of ten using strategies based on place value and properties of operations. Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 1

17 What is similar? Number and Operations Fractions Represent common fractions as parts of a whole, parts of a set, or points or distances on a number line. Recognize and demonstrate that sizes of fractional parts are relative to the size of the whole. Use fractions to represent numbers that are equal to, less than, or greater than one. Solve problems that involve comparing and ordering fractions. Identify equivalent fractions using models. Measurement and Data Analyze bar graphs to solve problems using addition and subtraction. Investigate and describe the results of decomposing, and combining, and transforming polygons to make other polygons. Solve real world and mathematical problems involving perimeters of polygons. Added from OSS 4 th grade: a Use models to connect and compare equivalent fractions and decimals. b Compare and order fractions and decimals Measurement and Data is separated into two clusters: 1. Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. 2. Represent and interpret data. Added to this grade level: a. Tell and write time to the nearest minute and solve word problems involving addition and subtraction of time intervals in minutes. b. Measure and estimate liquid volumes and masses of objects using the metric system. c. Solve one step word problems involving masses or volumes given in the same units. d. Relate area to the operations of multiplication and addition. Added from OSS 4 th grade: a Recognize area as an attribute of two dimensional regions. b Determine area by finding the total of same size units of area that cover a shape without gaps or overlaps. c Recognize a square that is one unit on a side as the What will I no longer teach? Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 2

18 What is similar? Geometry The content in CCSS Geometry is generally the same as the OSS at this grade level. Identify, describe, compare, analyze, and informally classify triangles and quadrilaterals by their sides and angles. standard unit for measuring area. d Determine the appropriate units, strategies, and tools to solving problems that involve estimating or measuring area. e Connect area measure to the area model used to represent multiplication. f Find the areas of complex shapes that can be subdivided into rectangles. g Solve problems involving perimeters and areas. h Recognize that rectangles with the same area can have different perimeters, and rectangles with the same perimeter can have different areas. What will I no longer teach? Build, draw, and analyze twodimensional shapes to understand attributes and properties Use attributes and properties of two dimensional shapes to solve problems involving parallel and perpendicular lines, congruence, symmetry, and perimeter. 4 th 4 th Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 3

19 Summary Notes: In each grade level these Mathematical Practices are emphasized. These are the Big Ideas of each standard. The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. 3.MP.1 Make sense of problems and persevere in solving them. 3.MP.2 Reason abstractly and quantitatively. 3.MP.3 Construct viable arguments and critique the reasoning of others. 3.MP.4 Model with mathematics. 3.MP.5 Use appropriate tools strategically. 3.MP.6 Attend to precision. 3.MP.7 Look for and make use of structure. 3.MP.8 Look for and express regularity in repeated reasoning. Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 4

20 Gaps: Changes: A large portion of the Measurement and Data domain was moved down from the OSS 4 th grade. The content in the CCSS of Numbers and Operations in Base Ten domain is new to this grade level. Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 5

21 Content: Math Grade: 4 th In grade 4, Instructional time should focus on three critical areas: (1) Developing fluency with multi digit multiplication, and developing understanding of dividing to find quotients involving multi digit dividends; (2) Developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; and (3) Understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry. What is similar? Operations and Algebraic Thinking Number and Operations in Base Ten Apply understanding of models for multiplication, place value, and properties of operations. Develop fluency for multiplying whole numbers and justify. Operations and Algebraic Thinking is separated into three clusters: 1. Use the four operations with whole numbers to solve problems. 2. Gain familiarity with factors and multiples. 3. Generate and analyze patterns. Added to this grade level: a. Interpret a multiplication equation as a comparison and represents a verbal statement. b. Multiply or divide to solve word problems. c. Find all factors pairs in the range d. Generate a number shape pattern that follows a given rule. Added from OSS 5 th grade: a Select and use appropriate estimation strategies for division. b Determine the most appropriate form of the quotient and interpret the remainder. Number and Operations in Base Ten is separated into two clusters: 1. Generalize place value understanding for multi digit whole numbers. 2. Use place value understanding and properties of operations to perform multi digit arithmetic. Added to this grade level: a. Recognize that in a multi digit whole number, a digit in one place represents ten times what it represents in the place to its right. What will I no longer teach? Apply understanding of models for multiplication, place value, and properties of operations. 3 rd Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 1

22 What is similar? Number and Operations Fractions Use models to connect and compare equivalent fractions and decimals. Compare and order fractions and decimals. Extend the base ten system to read, write, and represent decimal numbers. Use models to connect and compare equivalent fractions and decimals. Determine decimal equivalents or approximations of common fractions. b. Read and write whole numbers in expanded form and compare using <, > and =. c. Use place value understanding to round all numbers. d. Fluently add and subtract multi digit whole numbers. Added from OSS 5 th grade: a Apply understanding of models of division and the relationship of division to multiplication to solve problems. b Apply concepts of place value to solve problems involving division. c Develop and use methods to find quotients. d Develop fluency for dividing whole numbers and justify. Number and Operations Fractions is separated into three clusters: 1. Extend understanding of fraction equivalence and ordering. 2. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. 3. Understand decimal notation for fractions and compare decimal fractions. Added to this grade level: a. Understand addition and subtraction of fractions as joining and separating parts of the same whole. b. Decompose a fraction into a sum of fractions with the same denominator and justify. c. Subtract mixed numbers with like denominators. d. Solve word problems involving addition and subtraction of fractions. Added from OSS 3 rd grade: a Add common fractions with like denominators. Added from OSS 6 th grade: a Use and analyze a variety of strategies including models for solving problems with multiplication and division of fractions. What will I no longer teach? Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 2

23 What is similar? Measurement and Data CCSS has some common content to OSS. Represent money amounts and apply to situations of purchasing and making change. Solve problems involving perimeters and areas of rectangles and squares. Measurement and Data is separated into three clusters: 1. Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. 2. Represent and interpret data. 3. Geometric measurement: understand concepts of angle and measure angles. Added to this grade level: a. Make a line plot to display data in fractions of a unit, and solve problems using addition and subtraction of fractions by using information in line plots. b. Measure angles in whole number degrees using a protractor and sketch. c. Recognize measure angles as additive and solve addition and subtraction problems to find unknown angles. d. Use four operations to solve word problems involving distance, intervals of time, liquid volume, masses of objects, and money. Added from OSS 3 rd grade a Identify right angles and determine if angles are greater or less than a right angle. Added from OSS 6 th grade: a Use the relationship between common decimals and fractions to solve problems. Geometry Added to this grade level: a. Recognize, identify and draw lines of symmetry. Added from OSS 3 rd grade: a Build, draw, and analyze two dimensional shapes to understand attributes and properties. b Use attributes and properties of two dimensional shapes to solve problems involving parallel and perpendicular lines, congruence, symmetry, and perimeter. Added from OSS 5 th grade: a Identify and classify triangles by their angles and sides. What will I no longer teach? Determine area by finding the total of same size units of area that cover a shape without gaps or overlaps Recognize a square that is one unit on a side as the standard unit for measuring area Connect area measure to the area model used to represent multiplication. 3 rd 3 rd 3 rd Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 3

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25 Summary Notes: In each grade level these Mathematical Practices are emphasized. These are the Big Ideas of each standard. The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. 4.MP.1 Make sense of problems and persevere in solving them. 4.MP.2 Reason abstractly and quantitatively. 4.MP.3 Construct viable arguments and critique the reasoning of others. 4.MP.4 Model with mathematics. 4.MP.5 Use appropriate tools strategically. 4.MP.6 Attend to precision. 4.MP.7 Look for and make use of structure. 4.MP.8 Look for and express regularity in repeated reasoning. Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 5

26 Gaps: Changes: New to this grade level is the content in CCSS Operations and Algebraic Thinking And Geometry domains. There have been significant changes to the content in the following CCSS domains: Measurement and Data, and Number and Operation in Base Ten and Number and Operation Fractions. Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 6

27 Content: Math Grade: 5 th In grade 5, Instructional time should focus on three critical areas: (1) Developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions); (2) Extending division to two digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths and developing fluency with whole number and decimal operations; and (3) Developing understanding of volume. What is similar? Operations and Algebraic Thinking Number and Operations in Base Ten Mastering addition and subtraction of decimals. Operations and Algebraic Thinking is separated into two clusters: 1. Write and interpret numerical expressions. 2. Analyze patterns and relationships. Added to this grade level: a. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Added from OSS 6 th grade: a Use order of operations (excluding exponents). b Represent, analyze and determine relationships and patterns. Number and Operations in Base Ten is separated into two clusters: 1. Understand the place value system. 2. Perform operations with multi digit whole numbers and with decimals to hundredths. Added from OSS 4 th grade: a Extend the base ten system to read, write and represent decimal numbers to hundredths. b Compare and order fractions and decimals. c Develop fluency for multiplying multi digit numbers. Added from OSS 6 th grade: a Estimate fraction and decimal products and quotients. b Use and analyze a variety of strategies for solving problems with multiplication and division of decimals. What will I no longer teach? Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 1

28 What is similar? c Develop fluency for multiplying and dividing fractions and decimals. What will I no longer teach? Number and Operations Fractions Content of CCSS generally matches the OSS. Mastering Addition and subtraction of fractions Measurement and Data Content of CCSS closely matches the OSS. Added from OSS 6 th grade: a Use and analyze a variety of strategies including models for solving problems with multiplication and division of fractions. b Develop fluency with multiplication and division of fractions. c Apply the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions and justify why they work. Measurement and Data is separated into three clusters: 1. Convert like measurement units within a given measurement system. 2. Represent and interpret data. 3. Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. Added to this grade level: a. Make a line plot to display a data set of measurements in fractions of a unit (½, ¼, 1/8). b. Use operations on fractions for this grade to solve problems involving information presented in line plots. Added from OSS 6 th grade: a Use the relationship between common decimals and fractions to solve problems involving measurement. Added from OSS 7 th grade: a Convert among different units of measurement to solve problems. Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 2

29 What is similar? Geometry Content of CCSS closely matches the OSS. Identify and classify two dimensional figures using sides and angles. Using formulas to find area. Understand the concept of Volume and find the Volume of three dimensional figures. Geometry is separated into two clusters: 1. Graph points on the coordinate plane to solve real world and mathematical problems. 2. Classify two dimensional figures into categories based on their properties. Added to this grade level: a. Classify two dimensional figures in a hierarchy based on their properties. What will I no longer teach? Identify and classify triangles by their angles and sides. 4 th Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 3

30 Summary Notes: In each grade level these Mathematical Practices are emphasized. These are the Big Ideas of each standard. The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. 5.MP.1 Make sense of problems and persevere in solving them. 5.MP.2 Reason abstractly and quantitatively. 5.MP.3 Construct viable arguments and critique the reasoning of others. 5.MP.4 Model with mathematics. 5.MP.5 Use appropriate tools strategically. 5.MP.6 Attend to precision. 5.MP.7 Look for and make use of structure. 5.MP.8 Look for and express regularity in repeated reasoning. Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 4

31 Gaps: Changes: Operations and Algebraic Thinking are new at this grade level. Number and Operations is divided into two domains Base Ten and Fractions. Multiplication and division is now a 5 th grade standard. Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 5

32 Content: Math Grade: 6 th In grade 6, Instructional time should focus on four critical areas: (1) Connecting ratio and rate to whole number multiplication and division using concepts of ratio and rate to solve problems; (2) Completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) Writing, interpreting, and using expressions and equation; and, (4) Developing understanding of statistical thinking. What is similar? What will I no longer teach? Ratio & Proportional Relationships CCSS emphasizes proportional thinking; rather than CCSS does not include Content in CCSS generally match the OSS. decimal, percents, etc. probability. Develop, analyze and apply the meaning of CCSS incorporates problem solving using ratio and rate, ratio and percent to solve problems. proportions. Determine decimal and percent equivalents CCSS does not separately teach pi; instead it is for common fractions. incorporated as a ratio. Added from OSS 7 th grade 7.2.5: a. Convert among different units of measurement to solve problems, including rates. Number Systems Content in CCSS generally match the OSS, and the language is more general (rational number vs. fraction). Develop fluency for multiplying and dividing fractions and decimals. Apply the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions and justify why they work. Number systems is separated into three clusters: 1. Multiplication & Division of Fractions 2. Factors & Multiples 3. Apply Rational Numbers to Real World Mathematical Problems CCSS includes general concepts rather than specific algorithms. Added from OSS 5 th grade: a Develop and use accurate, efficient, and generizable methods to find quotients for multi digit division problems. b Develop fluency with whole numbers. c Develop fluency with adding/subtracting fractions. Added from OSS 9 12 th grades: a A.1 Compare, order, and locate real Estimate fraction and decimal products and quotients Use and analyze a variety of strategies for solving problems with multiplication and division of fractions Use and analyze a variety of strategies for solving problems with multiplication and division of decimals Use the relationship between common decimals and fractions to solve problems involving measurement. Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 1 5 th 5 th 5 th 5 th

33 What is similar? What will I no longer teach? numbers on a number line. Expressions & Equations CCSS match closely to the OSS. Use order of operations. Represent, analyze, and determine relationships and patterns. Develop meanings and uses of variables Apply the properties of operations to simplify calculations. Write, evaluate, and use expressions and formulas to solve problems. Solve one step equations. Geometry CCSS is mostly new content for 6 th grade, or drawn from other grade levels. Expressions & Equations is separated into three clusters: 1. Algebraic Expressions. 2. Solve one variable equations and inequalities. 3. Represent and analyze relationships between related variables. Added from OSS 7 th grade: a write and solve linear equations with one variable. Added from OSS 8 th grade: a Using linear functions and equations. Added from OSS 9 12 th grades: a A.4 Equivalent algebraic expressions. b A.4 Convert among different representations of a linear relationship. c A.5 Analyze relationship between dependent and independent variables. Geometry, although included in the OSS 6 th grade, has been expanded in the CCSS to include area, volume, and coordinate systems. Added to this grade level: a. Determining missing dimensions. b. using nets in 3 dimension Develop the concept of pi. Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 2 7 th

34 What is similar? What will I no longer teach? Statistics & Probability Represent, analyze, and determine relationships and patterns. Added from OSS 5 th grade: a formulas for the areas of triangles and parallelograms b use surface area and volume to solve problems Added from OSS 7 th grade: a use models to explain formulas for surface area and volume b find area, volume of complex and irregular shapes Although probability is included in the OSS 6 th grade, it has been eliminated in the CCSS which now includes statistics. Statistics and Probability is separated into two clusters: 1. Understanding statistics. 2. Summarize and describe distributions. Added to this grade level: displaying numerical data on a number line (dot plots). Added from OSS 8 th grade: a Organize and display data. b Use measures of center. c Interpret and analyze displays. d Describe strengths and limitations of particular statistical measures Understand the meaning of probability Determine experimental and theoretical probabilities. 7 th 7 th Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 3

35 Summary Notes: In each grade level these Mathematical Practices are emphasized. These are the Big Ideas of each standard. The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. 6.MP.1 Make sense of problems and persevere in solving them. 6.MP.2 Reason abstractly and quantitatively. 6.MP.3 Construct viable arguments and critique the reasoning of others. 6.MP.4 Model with mathematics. 6.MP.5 Use appropriate tools strategically. 6.MP.6 Attend to precision. 6.MP.7 Look for and make use of structure. 6.MP.8 Look for and express regularity in repeated reasoning. Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 4

36 Gaps: Changes: Most of the standards in this grade level are new. Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 5

37 Content: Math Grade: 7th In grade 7, Instructional time should focus on four critical areas: (1) Developing understanding of and applying proportional relationships; (2) Developing understanding of operations with rational numbers and working with expressions and linear equations; (3) Solving problems involving scale drawings and informal geometric constructions, and working with two and three dimensional shapes to solve problems involving area, surface area, and volume; and, (4) Drawing inferences about populations based on samples. What is similar? Ratio & Proportional Relationships Content in CCSS generally matches the OSS. Convert, represent and use proportional relationships. CCSS emphasizes proportional thinking; rather than only ratio and slope CCSS incorporates proportional relationships to write equations Added in this grade: Graphs of proportional relationships and the meaning of a point on such a graph Added from OSS 8 th grade: a Determine the slope of a line b Identify and interpret linear relationships What will I no longer teach? The Number System Content in CCSS generally match the OSS, and the language is more general (rational number vs. fraction). Develop, analyze and apply models using negative numbers. Problem solving using integers and rational numbers. Added at this grade level: a. Situations in which opposite quantities make zero (zero pairs). b. Rewriting subtraction as to add the inverse. c. The rules of multiplying signed numbers. d. Extending division of fractions to negative numbers. Added from OSS 6 th grade: a Use strategies to simplify calculations b Determine decimal and percent equivalents of common fractions Northwest Regional ESD Instruction & School Improvement September 2011 DRAFTPage 1

38 What is similar? Expressions & Equations Very little matches the OSS. Apply properties of rational numbers and algebra to write and solve linear equations. Expressions & Equations is separated into two clusters: 1. Use properties of operations to generate equivalent expressions 2. Solve real life and mathematical problems using numerical and algebraic expressions and equations. Added to this grade level: a. Apply properties to rewrite linear expressions. b. Understanding that rewriting an expression in different forms can shed light on a problem. c. Solve multi step real life mathematical problems. d. Use variables to construct simple equations and inequalities. e. Solve word problems with equations and inequalities. What will I no longer teach? Geometry Content in CCSS closely matches the OSS. Use proportions to solve problems. Use models to explain formulas for surface area and volume. Find area, volume of complex and irregular shapes. Geometry is separated into two clusters: 1. Draw, construct and describe geometrical figures and describe the relationships between them. 2. Solve real life and mathematical problems involving angle measure, area, surface area, and volume. Added to this grade level: a. Slicing a plane through 3 dimensional figures. Added from OSS 6 th grade: a Develop the concept of pi. Added from OSS 9 12 th grades: a G.5 Determine missing dimensions or angles. b G.6 Determine if three lengths form a triangle and classify Convert among different units of measurement to solve problems. 5 th Northwest Regional ESD Instruction & School Improvement September 2011 DRAFTPage 2

39 What is similar? Statistics & Probability Probability models are introduced at this grade level. Statistics and Probability is separated into three clusters: 1. Use random sampling to draw inferences about a population. 2. Draw informal comparative inferences about two populations. 3. Investigate chance processes and develop, use, and evaluate probability models. Added to this grade level: a. Develop a probability model and use it to find probability of events. b. Find probability of compound events using organized lists, tables, tree diagrams, and simulations. c. Design and use a simulation to generate frequencies for compound events. Added from OSS 6 th grade: a Understand the meaning of probability b Determine experimental and theoretical probabilities. Added from OSS 8 th grade: a Use measures of center. b Describe the strength and limits of a statistical measure. c Use data to estimate the likelihood of future events. Added from OSS 9 12 th grades: a S.1 Use theoretical probability to calculate the probability of simple events. b S.3 Compute and interpret probabilities for independent, dependent, complimentary and compound events. What will I no longer teach? Northwest Regional ESD Instruction & School Improvement September 2011 DRAFTPage 3

40 Summary Notes: In each grade level these Mathematical Practices are emphasized. These are the Big Ideas of each standard. The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. 7.MP.1 Make sense of problems and persevere in solving them. 7.MP.2 Reason abstractly and quantitatively. 7.MP.3 Construct viable arguments and critique the reasoning of others. 7.MP.4 Model with mathematics. 7.MP.5 Use appropriate tools strategically. 7.MP.6 Attend to precision. 7.MP.7 Look for and make use of structure. 7.MP.8 Look for and express regularity in repeated reasoning. Northwest Regional ESD Instruction & School Improvement September 2011 DRAFTPage 4

41 Gaps: Changes: Most of the additions to this grade level were in the domains of Expressions and Equations and Statistics and Probability. This grade level is where probability is introduced and first applied. Statistical models and simulations are also introduced at this grade level. Northwest Regional ESD Instruction & School Improvement September 2011 DRAFTPage 5

42 Content: Math Grade: 8th In grade 8, Instructional time should focus on three critical areas: (1) Formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations; (2) Grasping the concept of a function and using functions to describe quantitative relationships; (3) Analyzing two and three dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem. What is similar? The Number System Content in CCSS closely matches OSS. Added at this grade level: a. Irrational numbers b. Convert terminating and repeating decimals to rational numbers. Added from OSS 9 12 th grades a. 1A.1 Compare, order and locate real numbers on a number line b. 1A.3 Square roots as decimals What will I no longer teach? Expressions & Equations Identify and determine the properties of linear relationships. Expressions & Equations is separated into three clusters: 1. Work with radicals and integer exponents. 2. Understand the connections between proportional relationships, lines, and linear equations. 3. Analyze and solve linear equations and pairs of simultaneous linear equations. Added from OSS 9 12 th grades: a. 1A.2 Evaluate and compute numeric and algebraic expressions in scientific notation, square roots. b. 2A.4 Fluently convert among forms of a line (tables, equations in different forms). c. 2A.7 Write, use and solve linear equations and inequalities using graphical and symbolic methods. d. 2A.8 Solve systems of two linear equations graphically and algebraically, and solve systems of two linear inequalities graphically. Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 1

43 What is similar? Functions There is very little in the CCSS that matches the OSS. Use linear functions to make predictions and inferences. Geometry Content in CCSS closely matches the OSS Use properties of angle relationships to determine parallel, perpendicular, similarity and congruence. Apply the Pythagorean Theorem. Functions is separated into two clusters: 1. Define, evaluate and compare functions. 2. Use functions to model relationships between quantities. Added at this grade level: a. Classify y=mx+b as a linear function. b. Understand that a function is a rule that assigns each input exactly one output. c. Compare properties of two functions represented in different ways. d. Construct a function to model a linear relationship. Added from OSS 9 12 th grades : a. 2A.1 Identify functional relationships. b. 2A.2 Identify the slope of a line from an equation, determine the x and y intercepts. Geometry is separated into three clusters: 1. Understand congruence and similarity using physical models, transparencies or geometry software. 2. Understand and apply the Pythagorean Theorem. 3. Solve real world and mathematical problems involving volume of cylinders, cones, and spheres. Added to this grade level : a. Using rotations, reflections and translations understand that two 2 dimensional figures are congruent. b. Know the formulas for volume of cones, cylinders and spheres. Added from OSS 7 th grade a Use proportions to solve problems. b Use models to explain formulas for surface area and volume. Added from OSS 9 12 th grades a. 1G.1 Use angle relationships among two lines and a transversal to determine parallel, perpendicular lines. b. 1G.3 Apply theorems of corresponding parts of congruent and similar figures to determine missing sides and angles of polygons. What will I no longer teach? Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 2

44 What is similar? Statistics & Probability Organize and display data. Added to this grade level : a. Construct and interpret tables of bivariate data. Added from OSS 9 12 th grades: a. 1S.4 Use or construct scatter plots and determine if there are positive or negative correlations, and determine if there is a linear, quadratic, exponential, or no trend. What will I no longer teach? Use measures of center Interpret and analyze displays Describe strengths and limitations of particular statistical measures. 6 th 6 th 6 th Use data to estimate the likelihood of future events. 7 th Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 3

45 Summary Notes: In each grade level these Mathematical Practices are emphasized. These are the Big Ideas of each standard. The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. 8.MP.1 Make sense of problems and persevere in solving them. 8.MP.2 Reason abstractly and quantitatively. 8.MP.3 Construct viable arguments and critique the reasoning of others. 8.MP.4 Model with mathematics. 8.MP.5 Use appropriate tools strategically. 8.MP.6 Attend to precision. 8.MP.7 Look for and make use of structure. 8.MP.8 Look for and express regularity in repeated reasoning. Northwest Regional ESD Instruction & School Improvement September 2011 DRAFT Page 4