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Standards for mathematical practice 3-5

Standards for mathematical practice 3-5 . Nicole Standing RISE Educational Services. Mathematical Practices Overview . There are 8 Mathematical Practices that are consistent from kindergarten through 12 th grade.

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Standards for mathematical practice 3-5

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  1. Standards for mathematical practice3-5 Nicole Standing RISE Educational Services

  2. Mathematical Practices Overview • There are 8 Mathematical Practices that are consistent from kindergarten through 12th grade. • The mathematical practices are presented in the beginning of the standards handbook. They are not explicitly stated within the standards. Teachers will have to decide when and how to teach and practice these skills.

  3. When To Teach the Math Practice Standards • “The MP standards must be taught as carefully and practiced as intentionally as the Mathematical Content Standards. Neither should be isolated from the other; effective mathematics instruction occurs when these two halves of the CCSSM come together in a powerful whole.” California’s Common Core Standards for Mathematics http://www.cde.ca.gov/re/cc/

  4. Overview Continued • The Standards for Mathematical Practice describe varieties of expertise students should be taught. These practices are based on important “processes and proficiencies” with longstanding importance in mathematics education. The practices were created from two sources: -http://www.corestandards.org/Math/Practice

  5. Overview Continued Standards for Mathematical Practice • The second source is the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up • The first source is the National Council of Teachers of Mathematics (NCTM) process standards of problem solving, reasoning and proof, communication, representation, and connections. -http://www.corestandards.org/Math/Practice

  6. Standards for Mathematical Practice The Common Core State Standards for Mathematics Kindergarten – Grade 5

  7. Math Practices and Standards Connection Standards for Mathematical Content: Skills and understandings students will learn Identified by grade level or course Standards for Mathematical Practice: Processes and proficiencies that students show when engaged in mathematics Identified for students across all grade levels (K–12) Brokers of Expertise State of California Department of Education: CCSS Mathematics: K-12 Standards for Mathematical Practice. http://myboe.org/portal/default/Content/Viewer/Content?action=2&scId=306591&sciId=11787

  8. Making Math Practices Practical

  9. 1) Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

  10. MP 1: Make Sense of Problems and Persevere in Solving Them • Explain the meaning of a problem and look for entry points • Analyze givens, constraints, relationships, and goals • Plan a solution pathway • Monitor and evaluate progress • Check answer using a different method (asking does this make sense) • Understand the approaches of others and identify correspondences between different approaches

  11. Learning Objectives Math Practice 1 Repeating Topics • Create a coherent representation of the problem (consider units involved, attend to meanings of quantities, know and use different properties of operations and objects). (MP 2) • Evaluate the reasonableness of intermediate results while solving a problem (MP 8) • Interpret results and decide whether the results make sense, improving the model if necessary. (MP 4) • Listen to or read the arguments of others, decide whether they make sense, and ask questions to clarify or improve the argument (MP 3) • Explain the meaning of a problem and look for entry points • Analyze givens, constraints, relationships, and goals • Plan a solution pathway • Monitor and evaluate progress • Check answer using a different method (asking does this make sense) • Understand the approaches of others and identify correspondences between different approaches

  12. Math Practice Learning Objectives 1. Analyze the information in a problem 2. Plan a pathway for solving a problem 3. Represent relationships graphically 4. Analyze relationships mathematically to draw conclusions 5. Identify and explain mathematical patterns 6. Solve problems using skills you know 7. Evaluate the reasonableness of intermediate results 8. Analyze when to use grade level appropriate tools, recognizing insights to be gained and limitations 9. Attend to details while solving a problem 10. Make conjectures about a problem 11. Explain your reasoning 12. Analyze the work/arguments/reasons of others

  13. Lessons + Layered Activities • Content Standards • Math Practices • BBDI lessons with content standards from previously taught lessons • Pacing • BBDI lessons with MPs from previously taught lessons

  14. How Do I Make This Work in My Class? • “In the higher mathematics courses, the levels of sophistication of each MP standard increases as students integrate grade appropriate mathematical practices with the content standards.” www.cde.ca.gov Mathematics Framework: Overview of the Standards Chapter, Pg 24 Teach and practice the MPs at an appropriate level for your grade/students. The application and expectation may differ from grade to grade, but the students should still be held accountable for practicing the MPs in a way that makes sense for their age group.

  15. What does this look like in my classroom?

  16. Sample Year at a Glance

  17. Sample Year at a Glance Con’t

  18. Sample Year at a Glance Con’t

  19. Sample First Week of School Using Previous Year’s Content Day 1: Lesson Math Practice Learning Objective # 1 Learning Objective: Analyze the information in a problem Student Practice: Students do not need to solve; just find goals, information, givens, constraints in word problems Teacher needs: 10-14 problems (2 for model, 4 for guided, 6-8 for independent) Teacher tip: Great place to incorporate communication (speaking and listening) Day 2: Lesson Math Practice Learning Objective # 2 Learning Objective: Plan a solution pathway Student Practice: Students do not need to solve; just plan a solution pathway Teacher needs: use same problems as day 1 Teacher tip: Have students use flow map to lay out solution pathway Day 3: Lesson Math Practice Learning Objective # 7 Learning Objective: Evaluate whether intermediate results are reasonable Student Practice: Students solve; have to stop and check for intermediate results Teacher needs: use same problems as day 1 Teacher tip: Day 4: Lesson Math Practice Learning Objective # 11 Learning Objective: Explain reasoning (process) Student Practice: Student use solved problems from previous day to explain process Teacher needs: use same problems as day 1 Teacher tip: You can intro concept of analyze the work of others during guided practice Day 5: Activity (loop) Math Practice Learning Objectives 1,2,7,11 Description: Students are given 4-6 new problems where they apply all previous days content

  20. Share with a partner what math content you will be teaching in November. Discuss what Math Practice you would want to teach before teaching the content.

  21. Use of Sentence Stems and Frames www.cde.ca.gov: Mathematics Framework: Overview of the Standards Chapter, Page 14 of 27

  22. Last year, I read 18 books over 6 months. I wanted to figure out how many books that was each month, so I multiplied 18 x 6 and got 108 books.

  23. Objective Evaluate the reasonableness of results

  24. Review Some of the problems today may be word problems, so we need to remember: R – Read the problem U – Underline the givens (facts/information) L – Locate the goal (question) E – Express the problem (determine the operation) S – Solve

  25. Review Estimation: Rounding to the nearest whole number so we can easily do the calculation in our head. Ex: 62.8 ÷ 7.1 would be 63 ÷ 7, which means the answer should be close to 9 Alternate Method: We’ve learned several strategies for certain problems: Ex. Draw a model to multiply fractions, or just multiply the fractions – ½ x ¾

  26. An answer is considered reasonable if it makes sense in the context of the problem. Good mathematicians check the reasonableness of their answers to make sure they solved the problem correctly. They ask themselves, “Does my answer make sense?” If it doesn’t, they go back and decide if a mistake was made doing the work, with the operation they chose, or with what they thought the problem was asking them to do.

  27. The type of problem we are given will help us to decide what strategy to use to determine if an answer is reasonable. There are two common strategies that will work: Estimation Using an Alternate Method to Solve If we think an answer is not reasonable, we must be able to explain why we think so, and it helps to figure out what error was made.

  28. Kaitlyn’s teacher asked her to multiply 32.5 by 6.2. She got an answer of 2,025.0 and her work is shown below: I can use estimation to round 32.5 to 30 and 6.2 to 6. When I multiply 30 x 6, I get 180. That’s not close to 2,025 at all! Kaitlyn must have made a mistake. The results are not reasonable because when I estimated an answer, I got 180. 180 and 2,025 are not close enough for Kaitlyn’s results to make sense. She incorrectly placed the decimal point.

  29. Steps: • Read/look at the problem. • Determine if the results are reasonable by using one of the following strategies: • Estimate an answer • Use an alternate method to solve • Justify your reasoning using one of the following sentence frames: • The results are reasonable because ________________ ________________________________________. • The results are not reasonable because ______________ ________________________________________. • If possible, explain the error that was made.

  30. Aaron drew a model to demonstrate I can use an alternate strategy to solve this, by multiplying the fractions The results are not reasonable because I used an alternate method and got a different answer. Aaron’s model only shows 1/3 x 1/3, not 1/3 x 2/3.

  31. Danielle added 5.6 and 13.85 and got 19.45 as her answer. Her work is shown below: Decide which strategy you can use to check the reasonableness of Danielle’s results: Estimation or Alternative Method The results are ______________ because ____________ _______________________________________________.

  32. Delaney drew a model for 0.23 x 4and got an answer of 0.69. Her work is shown below: Decide which strategy you can use to check the reasonableness of Delaney’s results: Estimation or Alternative Method The results are ______________ because ____________ _______________________________________________.

  33. Eric solved the following problem: James worked for 7 hours on Monday and made a total of $73.50 for the day. How much did James make per hour? Eric’s work: Decide which strategy you can use to check the reasonableness of Eric’s results: Estimation or Alternative Method The results are ___________ because _________________ _______________________________________________.

  34. Kayla divided 42.72 by 6 and got an answer of 71.2. Her work is shown below: Decide which strategy you can use to check the reasonableness of Kayla’s results: Estimation or Alternative Method The results are ______________ because ____________ _______________________________________________.

  35. What was our objective?

  36. Objective Evaluate the reasonableness of results

  37. What was our objective? • What makes an answer reasonable?

  38. An answer is considered reasonable if it makes sense in the context of the problem. Good mathematicians check the reasonableness of their answers to make sure they solved the problem correctly. They ask themselves, “Does my answer make sense?” If it doesn’t, they go back and decide if a mistake was made doing the work, with the operation they chose, or with what they thought the problem was asking them to do.

  39. What was our objective? • What makes an answer reasonable? • Why do good mathematicians check the reasonableness of their results?

  40. An answer is considered reasonable if it makes sense in the context of the problem. Good mathematicians check the reasonableness of their answers to make sure they solved the problem correctly. They ask themselves, “Does my answer make sense?” If it doesn’t, they go back and decide if a mistake was made doing the work, with the operation they chose, or with what they thought the problem was asking them to do.

  41. What was our objective? • What makes an answer reasonable? • Why do good mathematicians check the reasonableness of their results? • How can we determine if an answer is reasonable?

  42. Steps: • Read/look at the problem. • Determine if the results are reasonable by using one of the following strategies: • Estimate an answer • Use an alternate method to solve • Justify your reasoning using one of the following sentence frames: • The results are reasonable because ________________ ________________________________________. • The results are not reasonable because ______________ ________________________________________. • If possible, explain the error that was made.

  43. Which would you teach first?What would the MP look like at your grade level? Third Grade: OA 8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Fourth Grade: OA 3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computations and estimation strategies including rounding. Fifth Grade: NF 2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. • Math Practice: Look for entry points and plan a solution pathway

  44. Math Practice Video

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