Common Core Math Grades 3-5

1. Common CoreMathGrades 3-5 Lisa Smith East Point Academy

2. What is common core • The Common Core State Standards Initiative (CCSSI) is an effort designed to improve educational outcomes for students by developing a set of common, voluntary, internationally-benchmarked academic standards in mathematics and English language arts. • South Carolina was the 25th state to adopt the national set of academic benchmarks that detail the math and reading skills students will learn as they move up through public school grades.

3. Mission Statement • The Common Core State Standards provide a consistent, clear understanding of what students are expected to learn, so teachers and parents know what they need to do to help them. The standards are designed to be robust and relevant to the real world, reflecting the knowledge and skills that our young people need for success in college and careers. With American students fully prepared for the future, our communities will be best positioned to compete successfully in the global economy.

4. Common Core State Standards Design Building on the strength of current state standards, the CCSS are designed to be: • Focused, coherent, clear and rigorous • Internationally benchmarked • Anchored in college and career readiness* • Evidence and research based

5. About the Standards • These standards define the knowledge and skills students should have within their K-12 education careers so that they will graduate high school able to succeed in entry-level, credit-bearing academic college courses and in workforce training programs. The standards: • Are aligned with college and work expectations; • Are clear, understandable and consistent; • Include rigorous content and application of knowledge through high-order skills; • Build upon strengths and lessons of current state standards; • Are informed by other top performing countries, so that all students are prepared to succeed in our global economy and society; and • Are evidence-based.

6. Common Core State Standards for Mathematics • Grade-Level Standards • K-8 grade-by-grade standards organized by domain • 9-12 high school standards organized by conceptual categories • Standards for Mathematical Practice • Describe mathematical “habits of mind” • Standards for mathematical proficiency: reasoning, problem solving, modeling, decision making, and engagement • Connect with content standards in each grade

7. Common standards are good for teachers because: • They allow for more focused professional development and promote collaboration. • They can inform the development of a curriculum that promotes deep understanding for all children. • They can give educators more time to focus on depth of understanding and richer units of study rather than focusing on “fitting everything in.”

8. Common standards are good for students because: • They help prepare students with the knowledge and skills they need to succeed in college and careers. • They help make transitions smoother for students moving to different states or districts because the learning goals remain consistent. • Clearer standards help students understand what is expected of them and allow them to engage in more self-directed learning.

9. Common standards are good for parents because: • They help parents understand exactly what students need to know and be able to do at each step in their education. • They help facilitate conversation between parents and teachers about how to help their children reach those education goals. • They assure parents that their children have access to the same high-quality education other students receive in other parts of the country.

10. Standards for Mathematical Practice 1.Make sense of problems and persevere in solving them 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

11. Mathematic Practices Explanations and Examples 1. Make sense of problems and persevere in solving them. Mathematically proficient students know that doing mathematics involves solving problems and discussing how they solved them. Students explain to themselves the meaning of a problem and look for ways to solve it. Students may use concrete objects or pictures to help them conceptualize and solve problems. They may check their thinking by asking themselves, “Does this make sense?” Students listen to other students’ strategies and are able to make connections between various methods for a given problem. 2. Reason abstractly & quantitatively. Mathematically proficient students should recognize that a number represents a specific quantity. They connect the quantity to written symbols and create a logical representation of the problem at hand, considering both the appropriate units involved and the meaning of quantities.

12. Mathematic Practices Explanations and Examples 3. Construct viable arguments and critique the reasoning of others. Mathematically proficient students may construct arguments using concrete referents, such as objects, pictures, and drawings. They refine their mathematical communication skills as they participate in mathematical discussions that the teacher facilitates by asking questions such as “How did you get that?” and “Why is that true?” They explain their thinking to others and respond to others’ thinking. 4. Model with mathematics. Mathematically proficient students experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures, using objects, acting out, making a chart, list, or graph, creating equations, etc. Students require extensive opportunities to generate various mathematical representations and to both equations and story problems, and explain connections between representations as well as between representations and equations. Students should be able to use all of these representations as needed. They should evaluate their results in the context of the situation and reflect on whether the results make sense.

13. Mathematic Practices Explanations and Examples 5. Use appropriate tools strategically. Mathematically proficient students consider the available tools (including estimation) when solving a mathematical problem and decide when certain tools might be helpful. For instance, they may use graph paper to find all the possible rectangles that have a given perimeter. They compile the possibilities into an organized list or a table, and determine whether they have all the possible rectangles. 6. Attend to precision. Mathematically proficient students develop their mathematical communication skills, they try to use clear and precise language in their discussions with others and in their own reasoning. They are careful about specifying units of measure and state the meaning of the symbols they choose. For instance, when figuring out the area of a rectangle they record their answers in square units.

14. Mathematic Practices Explanations and Examples 7. Look for and make use of structure. Mathematically proficient students look closely to discover a pattern or structure. For instance, students use properties of operations as strategies to multiply and divide (commutative and distributive properties). 8. Look for and express regularity in repeated reasoning. Mathematically proficient students should notice repetitive actions in computation and look for more shortcut methods. For example, students may use the distributive property as a strategy for using products they know to solve products that they don’t know. For example, if students are asked to find the product of 7 x 8, they might decompose 7 into 5 and 2 and then multiply 5 x 8 and 2 x 8 to arrive at 40 + 16 or 56.

15. Mathematics: 3 Shifts 1.Focus: Focus strongly where the standards focus. 2.Coherence: Think across grades, and link to major topics. 3.Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application.

16. Key Shift: Focus • Key concepts at different grade levels so that students reach strong foundational knowledge and deep conceptual understanding • Students are able to transfer mathematical skills and understanding across concepts and grades • Focus allows each student to think, practice and integrate each new idea into a growing knowledge structure

17. Key Shift: Coherence • Carefully connect the learning within and across grades so that students can build new understanding onto foundations built in previous years • Begin to count on deep conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning • Provides an opportunity for students to make connections between mathematical ideas • Coherence is necessary because mathematics instruction is not just a checklist of topics to cover, but a set of interrelated and powerful ideas.

18. KEY SHIFT: RIGOR • Teach more than “how to get the answer” and instead support students’ ability to access concepts from a number of perspectives • Students are able to see math as more than a set of mnemonics or discrete procedures • Students demonstrate conceptual understanding of core math concepts by applying them to new situations • Provide opportunities at all grade levels for students to apply math concepts in “real world” situations

19. K – 8 Domains • Counting and Cardinality • Operations and Algebraic Thinking • Numbers and Operations in Base Ten • Numbers and Operations - Fractions • Measurement and Data • Ratios and Proportional Relationships • The Number System • Expressions and Equations • Statistics and Probability • Geometry • Functions

20. How to read the grade level standards • Standards define what students should understand and be able to do. • Clusters are groups of related standards. Note that standards from different clusters may sometimes be closely related, because mathematics is a connected subject. • Domains are larger groups of related standards. Standards from different domains may sometimes be closely related.

21. Grade level overview

22. Explanations of terms used: Explanations of terms used: • Major clusters – areas of intensive focus, where students need fluent understanding and application of the core concepts (approximately 70%). • Supporting clusters – rethinking and linking; areas where some material is being covered, but in a way that applies core understandings (approximately 20%). • Additional Clusters – expose students to other subjects, though at a distinct, level of depth and intensity (approximately 10%).

23. CCSS Critical Areas Grade 3 • In Grade 3, instructional time should focus on four critical areas: (1) developing understanding of multiplication and division and strategies for multiplication and division within 100; (2) developing 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.

24. Grade 3: OVERVIEW Operations and Algebraic Thinking • 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 identify and explain patterns in arithmetic. Number and Operations in Base Ten • Use place value understanding and properties of operations to perform multi-digit arithmetic. Number and Operations—Fractions • Develop understanding of fractions as numbers.

25. Grade 3: overview Measurement and Data • Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. • Represent and interpret data. • Geometric measurement: understand concepts of area and relate area to multiplication and to addition. • Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. Geometry • Reason with shapes and their attributes.

26. Third grade Suggested Pacing guideFirst nine weeks • Use place value understanding to round whole numbers to the nearest 10 or 100 (3.NBT.1) • Use strategies and algorithms to fluently add and subtract within 1000. (3.NBT.2) • Solve two-step word problems using addition and subtraction within 1,000. (3.OA.8) • Use a letter to represent an unknown quantity in equations. (3.OA.8) • Use estimation strategies to assess reasonableness of answers. (3.OA.8) • Identify arithmetic patterns in the addition table and explain them using properties. (3.OA.9) • Explore area as an attribute of plane figures. (3.MD.5) • Measure areas by counting unit squares (𝑐𝑚!,𝑚!, 𝑖𝑛!, 𝑓𝑡!) and nonstandard square units. (3.MD.6) • Find the area of a rectangle by tiling it and showing the relationship to multiplication. (3.MD.7) • Solve real-world and mathematical problems involving area. (3.MD.7) • Decompose rectilinear figures to help find the area. (3.MD.7) • Solve real-world and mathematical problems involving perimeter of polygons (3.MD.8) • Interpret products of whole numbers. (3.OA.1) • Interpret partition models of division. (3.OA.2) • Interpret measurement models of division (repeated subtraction). (3.OA.2) • Use estimation strategies to assess reasonableness of answers. (3.OA.8) • Identify arithmetic patterns in the multiplication table and explain them using properties. (3.OA.9)

27. Third grade Suggested Pacing guideSecond nine weeks • Use multiplication and division within 100 to solve one-step word problems. (3.OA.3) • Determine the unknown whole number in a multiplication or division equation. (3.OA.4) • Apply properties of operations as strategies to multiply and divide. (3.OA.5) • Interpret division as an unknown-factor problem. (3.OA.6) • Use a variety of strategies to fluently multiply and divide within 100. (3.OA.7) • Solve two-step word problems using multiplication and division using single-digit factors and products less than 100. (3.OA.8) • Use estimation strategies to assess reasonableness of answers. (3.OA.8) • Use place value strategies and properties of operations to multiply one-digit whole numbers by multiples of 10 (10-90). (3.NBT.3) • Use a letter to represent an unknown quantity in equations. (3.OA.8) • Identify arithmetic patterns (+ or x) and explain them using properties of operations. (3.OA.9) • Use estimation strategies to assess reasonableness of answers. (3.OA.8) • **Know all products of two one-digit numbers. (3.OA.7) **End-of- Year Goal**

28. Third grade Suggested Pacing guideThird nine weeks • Understand that a fraction (a/b) represents equal parts of a whole. (3.NF.1) • Solve word problems that require fair sharing. (3.NF.1) • Represent fractions on a number line diagram. (3.NF.2) • Recognize two equivalent fractions. (3.NF.3) • Generate and explain two equivalent fractions. (3.NF.3) • Express whole numbers as fractions and fractions as equivalents to whole numbers. (3.NF.3) • Compare two fractions by reasoning about their size (same numerator or same denominator) and justify conclusions (3.NF.3) • Partition shapes into fractional parts of a whole (3.G.2) • Generate measurement data by using rulers to measure objects to the nearest half and fourth on an inch. (3.MD.4) • Construct a line plot using generated data (wholes, halves or quarters). (3.MD.4) • Tell and write time to the nearest minute (3.MD.1) • Measure time intervals (elapsed time) in minutes. (3.MD.1) • Solve word problems (+ & -) involving time intervals (elapsed time) in minutes. (3.MD.1)

29. Third grade Suggested Pacing guideForth nine weeks • Students should pose a question, collect, analyze and interpret data (PCAI) (3.MD.3) • Use data collected to draw a scaled picture graph to represent data with several categories. (3.MD.3) • Use data collected to draw a scaled bar graph to represent data with several categories. (3.MD.3) • Solve one- and two-step problems using information from graphs. (3.MD.3) • Recognize shapes that are and are not quadrilaterals by examining their attributes. (3.G.1) • Classify shapes by attributes and draw shapes that fit specific categories. (3.G.1) • Measure and estimate liquid volumes using milliliters and liters. (3.MD.2) • Measure and estimate masses of objects using grams and kilograms. (3.MD.2) • Solve one-step word problems (+,-,x,÷) involving masses or volumes using the same units. (3.MD.2) • **Know all products of two one-digit numbers. (3.OA.7) **End-of-Year Goal**

30. CCSS Critical Areas Grade 4 • In Grade 4, instructional time should focus on three critical areas: (1) developing understanding and 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; (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.

31. Grade 4: overview Operations and Algebraic Thinking • Use the four operations with whole numbers to solve problems. • Gain familiarity with factors and multiples. • Generate and analyze patterns. Number and Operations in Base Ten • Generalize place value understanding for multi-digit whole numbers. • Use place value understanding and properties of operations to perform multi-digit arithmetic.

32. Grade 4: overview • Number and Operations—Fractions • • Extend understanding of fraction equivalence and ordering. • • Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. • • Understand decimal notation for fractions, and compare decimal fractions. • Measurement and Data • • Solve problems involving measurement & conversion of measurements from a larger unit to a smaller unit. • • Represent and interpret data. • • Geometric measurement: understand concepts of angle and measure angles. • Geometry • • Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

33. Forth grade Suggested Pacing guideFirst nine weeks • Use place value to recognize and understand the relationship of multiplying and dividing by muliples of 10. (4.NBT.1) (Numbers ≤ 1,000,000) • Read and write multi-digit whole numbers using various base-ten representations. (4.NBT.2) (Numbers ≤ 1,000,000) • Read and write multi-digit whole numbers using numerals, number names and expanded form. (4.NBT.2) (Numbers ≤ 1,000,000) • Compare two multi-digit whole numbers using >,=,< symbols. (4.NBT.2) (Numbers ≤ 1,000,000) • Use place value understanding to round multi-digit whole numbers to any place. (4.NBT.3) (Numbers ≤ 1,000,000) • Fluently add and subtract multi-digit whole numbers using the standard algorithm. (4.NBT.4) (Numbers ≤ 1,000,000) • Use mental comparison and estimation strategies to assess the reasonableness of the problem. (4.OA.3) • Solve multistep word problems using whole numbers (+,-). (4.OA.3) • Identify equations as multiplicative equations. (4.OA.1) • Write equations for multiplicative comparison. (4.OA.1) • Use drawings to solve word problems (x, ÷) involving multiplicative comparison. (4.OA.2) • Write equations with a symbol for the unknown number to represent the problem. (4.OA.2) • Write equations with a letter to represent problems with an unknown quantity. (4.OA.3) • Distinguish multiplicative comparison from additive comparison. (4.OA.2)

34. Forth grade Suggested Pacing guidesecond nine weeks • Recognize a whole number (1-100) is a multiple of its factors. (4.OA.4) • Find all factor pairs for a whole number in the range of 1-100. (4.OA.4) • Determine if a whole number (range 1-100) is a multiple of a given one digitnumber. (4.OA.4) • Determine whether a given whole number in the range 1-100 is prime or composite. (4.OA.4) • Use strategies based on place value and the properties of operation to multiply up to four-digit by one-digit whole numbers. (4.NBT.5) (Numbers ≤ 1,000,000) • Use strategies based on place value and the properties of operation to multiply two two-digit numbers. (4.NBT.5) (Numbers ≤ 1,000,000) • Use strategies based on place value and properties of operation to divide four-digit dividends and one-digit divisors. (4.NBT.6) • Continue instruction of using the four operations with whole numbers to solve problems (4.OA.1, 4.OA.2) • Use mental comparison and estimation strategies to assess the reasonableness of the problem. (4.OA.3) • Solve multistep word problems using whole numbers (+,-, x, ÷). (4.OA.3) • Represent a solution with a remainder in various contexts. (4.OA.3) • Generate a number or shape pattern that follows a given rule. (4.OA.5) • Identify features of a pattern not given by the rule itself. (4.OA.5) • Use visual fraction models to explain equivalency in fractions. (4.NF.1) • Recognize and generate equivalent fractions. (4.NF.1)

35. Forth grade Suggested Pacing guidethird nine weeks • Compare two fractions with different numerators and different denominators. (4.NF.2) • Compare two fractions using a benchmark fraction. (4.NF.2) • Justify conclusions of comparisons by using visual models. (4.NF.2) • Compose & decompose fractions using the same whole (4.NF.3) • Decompose a fraction and/or mixed number with the same denominators in multiple ways (4.NF.3) • Add and subtract mixed numbers with like denominators. (4.NF.3) • Solve word problems involving addition and subtraction of fractions. (4.NF.3) • Multiply a fraction by a whole number using visual models and strategies. (4.NF.4) • Solve world problems involving multiplication of a fraction by a whole number. (4.NF.4) • Express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100.(4.NF.5) • Add two fractions with respective denominators 10 and 100. (4.NF.5) • Use decimal notation for fractions with denominators 10 or 100. (4.NF.6) • Use understanding of place value (up to hundredths) to express fractions in decimal form (4.NF.5-4.NF.7) • Compare decimals to hundredths. (4.NF.7) • Justify comparison of decimals by using visual models. (4.NF.7)

36. Forth grade Suggested Pacing guideforth nine weeks • Measure a set of objects to the nearest unit. (4.MD.4) o Display the data set of measurements in a line plot. (4.MD.4) o Solve fractional addition and subtraction problems by using information presented in line plots. (4.MD.4) • Know the following units of measure: km, m, cm; kg, g; lb, oz; l, ml; hr, min, sec. (4.MD.1) • Convert measurements from larger units to smaller units within the same system. (4.MD.1) • Solve multi-step word problems related to measurement. (4.MD.2) • Represent measurement quantities using diagrams that feature a measurement scale. (4.MD.2) • Apply the area and perimeter formulas for rectangles in real world and mathematical problems. (4.MD.3) • Generate a number or shape pattern that follows a given rule. (4.OA.5) • Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint. (4.MD.5) • Recognize angle measurement as a series of 1 degree turns in a circle. (4.MD.5) • Measure angles in whole-number degrees using a protractor. (4.MD.6) • Sketch angles of specified measurements. (4.MD.6) • Decompose an angle into smaller parts.(4.MD.7) • Solve addition and subtraction problems to find unknown angle measurements. (4.MD.7) • Write an equation with a symbol for the unknown angle measurement. (4.MD.7) • Identify points, lines, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines in two-dimensional figures. (4.G.1) • Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines). (4.G.1) • Classify two-dimensional figures using parallel or perpendicular lines or by angle measurement. (4.G.2) • Recognize and identify right triangles. (4.G.2) • Recognize a line of symmetry for two-dimensional figures. (4.G.3) • Identify line-symmetric figures and draw lines of symmetry. (4.G.3)

37. CCSS Critical AreaSGrade 5 • 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 2-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.

38. Grade 5: overview Operations and Algebraic Thinking • Write and interpret numerical expressions. • Analyze patterns and relationships. Number and Operations in Base Ten • Understand the place value system. • Perform operations with multi-digit whole numbers and with decimals to hundredths. Number and Operations—Fractions • Use equivalent fractions as a strategy to add and subtract fractions. • Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

39. Grade 5: overview Measurement and Data • Convert like measurement units within a given measurement system. • Represent and interpret data. • Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. Geometry • Graph points on the coordinate plane to solve real-world and mathematical problems. • Classify two-dimensional figures into categories based on their properties.

40. Fifth grade Suggested Pacing guideFirst nine weeks • Recognize that in a multi-digit number, a digit in the one’s place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. (5.NBT.1) • Multiply multi-digit whole numbers (not to exceed a three-digit factor by a two-digit factor). (5.NBT.5) • Divide multi-digit whole numbers (not to exceed a four-digit by two-digit divisor). (5.NBT.6) • Use place value to recognize and understand the relationship of multiplying and dividing by multiples of 10 including decimal placement. (5.NBT.2) • Read and write decimals to thousandths using base-ten numerals, number names, and expanded form. (5.NBT.3) • Use place value understanding to round decimals to any place. (5.NBT.4) • Use symbols to compare two decimals to the thousandths. (5.NBT.3) • Use whole-number exponents to denote powers of 10. (5.NBT.2) • Use multiple strategies to add, subtract, multiply, and divide decimals to hundredths and explain the reasoning used. (5.NBT.7)

41. Fifth grade Suggested Pacing guidesecond nine weeks • Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers. (5.NF.3) • Interpret a fraction as division of the numerator by the denominator. (5.NF.3) • Add and subtract fractions (including mixed numbers) with unlike denominators. (5.NF.1) • Solve word problems involving addition and subtraction of fractions by using fraction models or equations. (5.NF.2) • Use benchmark fractions to estimate and assess reasonable answers. (5.NF.2) • Explain why multiplying a given number by a fraction greater than one results in a product greater than the given number. (5.NF.5) • Multiply a fraction or a whole number by a fraction using visual fraction models and create a story context. (5.NF.4) • Explain why multiplying a given number by a fraction less than one results in a product less than the given number. (5.NF.5) • Solve real world problems involving multiplying fractions/mixed numbers. (5.NF.6) • Divide unit fractions by whole numbers and by unit fractions within context. (5.NF.7)

42. Fifth grade Suggested Pacing guidethird nine weeks • Convert among different-sized standard measurement units within a given measurement system. (5.MD.1) • Solve multi-step real world problems using conversions with a given measurement system. (5.MD.1) • Make a line plot to display a data set of measurements in fractions of a unit and solve related problems. (5.MD.2) • Reason about attributes of two-dimensional shapes and how they are categorized by these attributes. (5.G.3) • Classify two-dimensional figures in a hierarchy based upon attributes. (5.G.4) • Use visual models to find the area of a rectangle with fractional side lengths. (5.NF.4) • Recognize volume as an attribute of solid figures. (5.MD.3) • Investigate and build an understanding of volume measurement using non-standard units (unit cubes). (5.MD.3) • Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. (5.MD.4) • Solve real world problems involving volume using multiplication and addition using visual models. (5.MD.5)

43. Fifth grade Suggested Pacing guidefourth nine weeks • Use and evaluate numerical expressions using parentheses, brackets, or braces. (5.OA.1) • Write and interpret simple numerical expressions. (5.OA.2) • Recognize the attributes of the coordinate plane within the first quadrant (axes, origin, ordered pairs, coordinates). (5.G.1) • Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane. (5.G.2) • Interpret coordinate values of points in relationship between them. (5.OA.3) • Generate two numerical patterns (independent/dependent variables) using two given rules • Demonstrate the relationship between two numerical patterns by graphing on the coordinate plane. (5.OA.3)

44. Major Work/Major Concerns Operations and Algebraic Thinking • Concrete use of the basic operations (word problems) • Mathematical meaning and formal properties of the basic operations • Prepare students to work with expressions and equations in middle school Number and Operations—Base Ten • Place value understanding • Develop base-ten algorithms using place value and properties of operations • Computation competencies (fluency, estimation) Number and Operations—Fractions • Enlarge concept of number beyond whole numbers, to include fractions • Use understanding of basic operations to extend arithmetic to fractions • Lay groundwork for solving equations in middle school

45. Major Work/Major Concerns Measurement and Data • Emphasize the common nature of all measurement as iterating by a unit • Build understanding of linear spacing of numbers and support learning of the number line • Develop geometric measures • Work with data to prepare for Statistics and Probability in middle school Geometry • Ascend through progressively higher levels of logical reasoning about shapes • Reason spatially with shapes, leading to logical reasoning about transformations • Connect geometry to number, operations, and measurement via notion of partitioning

46. Key Points In Mathematics • The K-5 standards provide students with a solid foundation in whole numbers, addition, subtraction, multiplication, division, fractions and decimals—which help young students build the foundation to successfully apply more demanding math concepts and procedures, and move into applications. • The K-5 standards build on the best state standards to provide detailed guidance to teachers on how to navigate their way through knotty topics such as fractions, negative numbers, and geometry, and do so by maintaining a continuous progression from grade to grade.

47. Key Points In Mathematics • The standards stress not only procedural skill but also conceptual understanding, to make sure students are learning and absorbing the critical information they need to succeed at higher levels - rather than the current practices by which many students learn enough to get by on the next test, but forget it shortly thereafter, only to review again the following year.

48. Myths About Content and Quality: Math • Myth: The Standards do not prepare or require students to learn Algebra in the 8th grade, as many states’ current standards do. • Fact: The Standards do accommodate and prepare students for Algebra 1 in 8th grade, by including the prerequisites for this course in grades K‐7. Students who master the K‐7 material will be able to take Algebra 1 in 8th grade. At the same time, grade 8 standards are also included; these include rigorous algebra and will transition students effectively into a full Algebra 1 course. • Myth: Key math topics are missing or appear in the wrong grade. • Fact: The mathematical progressions presented in the common core are coherent and based on evidence.

49. video • Support Videos for the Common Core State Standards in Mathematics http://secc.sedl.org/common_core_videos • Visit the Videos by Grade to view support videos for the Common Core State Standards by grade level

50. Common Core State Standards for Math VIDEO https://www.teachingchannel.org/videos/common-core-state-standards-for-math?fd=1 Learn about the key features and differences of the new standards