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Common Core State Standards for Mathematics (CCSSM) and Assessments

If you have not downloaded and/or viewed the materials that will be discussed during this webinar, you may access them at the MDE CCSS SharePoint site. Visit https://districtaccess.mde.k12.ms.us/commoncore/ In the left pane, click on Training Materials.

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Common Core State Standards for Mathematics (CCSSM) and Assessments

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  1. If you have not downloaded and/or viewed the materials that will be discussed during this webinar, you may access them at the MDE CCSS SharePoint site. • Visit https://districtaccess.mde.k12.ms.us/commoncore/ • In the left pane, click on Training Materials. • Select the folder “Grades 6-8 Follow-up Webinar”. • Download/print materials as needed.

  2. Common Core State Standards for Mathematics (CCSSM) and Assessments Grades 6 – 8 Follow-up Webinar November 14, 2012 Office of Curriculum and Instruction Marla Davis Office Director for Mathematics

  3. Agenda • Focusing on Planning for Middle Grades • Focusing on a CCSS Sample Lesson for Grade 6 • Focusing on a CCSS Sample Lesson for Grade 7 • Focusing on a CCSS Sample Lesson for Grade 8 • Resources

  4. Focusing on Planning for Middle Grades

  5. CCSSM Progression of Domains Source: Vermont’s Transition to the Common Core State Standards: Mathematics

  6. Key Planning Components for a CCSSM Lesson Plan • PARCC Model Content Frameworks = M • Progression Document = P • Overarching Essential Question • Overarching, Supporting, and Outside CCSSM • Lesson Vocabulary • Previous CCSSM Knowledge

  7. Key Planning Components for a CCSSM Lesson Plan • Lesson Outcomes • Essential Questions • Common Misconceptions • Conceptual Understandings • PARCC Model Frameworks Indicators • Standards for Mathematical Practice • Multiple Representations • Performance Task • ELL Supports

  8. Key Planning Components for a Lesson Plan Each featured lesson plan contains the following instructional guidance: • Materials • Teacher Preparation • Anticipatory Set • Lesson Launch • Student Exploration • Teacher Input • Closure • Homework • Interactive Website(s) • Performance Task

  9. CCSSM Sample Lesson for Grade 6

  10. Critical Areas of Instruction for Grade 6 Students use reasoning about multiplication and division to solve ratio and rate problems about quantities. By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative size of quantities, students connect their understanding of multiplication and division with ratios and rates. Thus students expand the scope of problems for which they can use multiplication and division to solve problems, and they connect ratios and fractions. Students solve a wide variety of problems involving ratios and rates. Refer to CCSSM page 39

  11. CCSSM Grade 6 Sample Lesson Plan Directions: Locate the Sample Lesson Plan “Introduce Me to Your Friends Ratio and Proportion.”

  12. CCSSM Grade 6 Sample Lesson Plan • 6.RP.1: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. • 6.RP.3:Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

  13. CCSSM Grade 6 Sample Lesson Plan Note: There are no MMFR objectives that address ratio, unit rate or rate language until the 7th grade. (7.1.g)

  14. CCSSM Grade 6 Sample Lesson Plan Lesson Vocabulary • fraction • coordinate plane • part-to-part • part-to-whole • proportion • ratio • statistical question • variability • whole number • x-axis • y-axis

  15. CCSSM Grade 6 Sample Lesson Plan Directions: Complete the chart below for the red and green M&Ms as you listen to the following questions.

  16. CCSSM Grade 6 Sample Lesson Plan • How many different colors are in a bag of M&Ms? • Does each bag of M&Ms have the same number of colors in them? • Can you set up a table to display all the possible colors in a bag of M&Ms? • How can I use fractions to represent the colors that are in each bag of M&Ms? • What will the numerator in each fraction represent? • What will the denominator in each fraction represent? • Do the fractions in the last column represent a part-to-part relationship or a part-to-whole relationship? Explain.

  17. CCSSM Grade 6 Sample Lesson Plan Lesson Launch: • TTW demonstrate how to write the ratio for the above diagram in three ways: 4 to 2; 4:2; and . • TTW ask students to interpret what each of the symbolic formats represents to them. • TTW make a clear distinction between the fraction and the ratio expressed as Mathematical Practice 2: Reason abstractly and quantitatively.

  18. CCSSM Grade 6 Sample Lesson Plan Student Exploration: TTW monitor student work as they complete this table and ensure they are using their counters to determine the relationship that exists between the counters. 2:4 4:2 8 6 16 10 ½ n

  19. CCSSM Grade 6 Sample Lesson Plan Directions: At your school site, construct a graph that represents the relationship between the number of red counters to the number of white counters.

  20. CCSSM Grade 6 Sample Lesson Plan

  21. CCSSM Grade 6 Sample Lesson Plan Question: How can you ensure the Standards for Mathematical Practice are incorporated as you teach this skill/concept? Answer: Standards for Mathematical Practice Student Cubes Available online at: https://districtaccess.mde.k12.ms.us/curriculumandInstruction/Mathematics%20Resources/Forms/AllItems.aspx

  22. CCSSM Grade 6 Sample Lesson Plan Directions: Locate Handout #1: Passport Template and create a small booklet.

  23. CCSSM Grade 6 Sample Lesson Plan Directions: • Locate Handout #2: Passport Stickers. • Paste Learning Station 2 on page 2 of your Passport. • As a team, determine which “passport stickers” describe Learning Station 2.

  24. CCSSM Grade 6 Sample Lesson Plan Proportion of black is 60% Ratio of white to black is 2:3 Mathematical Practice 3: Construct viable arguments and critique the reasoning of others.

  25. CCSSM Grade 6 Sample Lesson Plan Closure: Mathematical Practice 7: Look for and make use of structure.

  26. CCSSM Grade 6 Sample Lesson Plan Homework: Option A (reinforcement/remediation)

  27. CCSSM Grade 6 Sample Lesson Plan Homework: Option B (Scavenger Hunt with the Family)

  28. Think-Pair-Share As a team, identify one way you can incorporate Chemistry or Science into this introductory lesson on ratios and proportions.

  29. MCT2 Sample Item Taken from Mississippi MCT2 7th and 8th grade Practice Tests 2. Available online at: http://www.mde.k12.ms.us/student-assessment

  30. PARCC Sample Item and Task Prototypes for Math Presenter will discuss PARCC Sample Assessment Item for Grade 6 and Grade 7 .

  31. The Progression of Ratios and Proportions Grades K - 12

  32. CCSSM Sample Lesson for Grade 7

  33. Critical Areas of Instruction for Grade 7 Adding, subtracting, multiplying, and dividing rational numbers is the culmination of numerical work with the four basic operations. The number system will continue to develop in grade 8, expanding to become the real numbers by the introduction of irrational numbers, and will develop further in high school, expanding to become the complex numbers with the introduction of imaginary numbers. Because there are no specific standards for rational number arithmetic in later grades and because so much other work in grade 7 depends on rational number arithmetic, fluency with rational number arithmetic should be the goal in grade 7. Refer to PARCC Model Content Frameworks for Mathematics page 31

  34. CCSS Grade 7 Sample Lesson Plan Directions: Locate the Sample Lesson Plan “Change is the Name of the Game”.

  35. CCSS Grade 7 Sample Lesson Plan • 7.NS.2:Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. • 7.NS.3: Solve real-world and mathematical problems involving the four operations with rational numbers.

  36. CCSS Grade 7 Sample Lesson Plan Note: • The MMFR includes all operations, while the CCSSM focuses on addition and subtraction of rational numbers. • CCSSM 7.NS.2 focuses on multiplication and division of rational numbers. • The CCSSM focuses on the possible outcomes when you convert a rational number to a decimal. (7.1.c)

  37. CCSS Grade 7 Sample Lesson Plan Lesson Vocabulary • fraction • decimal • decimal multiplier • fraction multiplier • percent • percent increase/decrease • proportion • ratio

  38. CCSS Grade 7 Sample Lesson Plan Note: The approved PARCC Calculator Policy indicates that calculators will be available for Grades 6-8. A four-function calculator with a square root will be available for Grades 6 and 7.

  39. CCSS Grade 7 Sample Lesson Plan Anticipatory Set: “The Reaction Wheel” “Kyle is at the mall with some of his friends shopping for a new shirt to wear to the Mississippi State Fair tomorrow. While in Abercrombie and Fitch he notices a $50 shirt on the 35% off rack. The problem is, the calculator on his new cell phone does not have a percent key. How can Kyle use his cell phone calculator to determine the discounted sale price ?”

  40. CCSS Grade 7 Sample Lesson Plan TTW place a check mark (), an (X), or a question mark (?) beside student responses as the students work sample problems without technology. () = this response is true and has been confirmed (X) = this response is false and has been invalidated (?) = this response was not proven true or false and further investigation (or examples) is needed.

  41. CCSS Grade 7 Sample Lesson Plan Lesson Launch: • How do we convert percentages to decimals? • What is the relationship between a fraction, a decimal and a percentage? • Is there always an inverse relationship between a percentage increase and decrease? • What are the essential steps for using a four-function calculator when working with percentages? • When dealing with percentages, how can you verify the results of your calculations with/without a calculator? Mathematical Practice 1: Make sense of problems and persevere in solving them. Mathematical Practice 5: Use the appropriate tools strategically.

  42. CCSS Grade 7 Sample Lesson Plan Directions: • Locate Handout #1: “Percentage Increase and Decrease Activity Cards”. • Locate Card Sets B – E.

  43. CCSS Grade 7 Sample Lesson Plan Directions: • Arrange Card Set E on the table as illustrated below: • Use Card Sets B, C, and D to model two relationships. `

  44. CCSS Grade 7 Sample Lesson Plan x ¾ Up by 60% x 0.5 Up 6.25% Down by 20%

  45. CCSS Grade 7 Sample Lesson Plan Directions: Record the relationship between the Money Cards on the Percent, Decimal and Fraction (2) template.

  46. CCSSM Grade 7 Sample Lesson Plan Question: How can literacy or writing be incorporated to assess student understanding of this skill/concept? Answer: Standards for Mathematical Practice Puzzle Organizer Available online at: https://districtaccess.mde.k12.ms.us/curriculumandInstruction/Mathematics%20Resources/Forms/AllItems.aspx

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