Nicole Beck & Brandon Graham National Training Network

1. Nicole Beck & Brandon Graham National Training Network

2. Putting the Practices Into Action…

3. Tiling a Patio Patio 1 Patio 2 Patio 3

5. Table Discussion How does the task align to the Common Core State Standards - Standards for Mathematical Practices (SMP’s)? Which SMP’s do you think are most evident in this task?

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

7. Eight Standards for Mathematical Practice

8. Standards for Mathematical Practice 1. Make Sense of Problems and Persevere in Solving Them Common Core State Standards for Mathematics – page 6 Mathematically proficient students start by explaining to themselves the meaning of a problem andlooking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solutionand plan the solution pathway rather than simply jumping into a solution attempt. Theyconsider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight to 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 ordraw 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, andthey continually ask themselves, “Does this make sense?” They can understand approaches of others to solving complex problems and identify correspondences between different approaches.

9. Research:Inside Mathematics: Classroom Observations http://www.insidemathematics.org/index.php/standard-1 “Teachers who are developing students’ capacity to “make sense of problems and persevere in solving them” develop ways of framing mathematical challenges that are clear and explicit, and then check in repeatedly with students to help them clarify their thinking and their process. An early childhood teacher might ask her students to work in pairs to evaluate their approach to a problem, telling a partner to describe their process, saying “what [they] did, and what [they] might do next time.” A middle childhood teacher might post a set of different approaches to a solution, asking students to identify “what this mathematician was thinking or trying out” and evaluating the success of the strategy. An early adolescence teacher might have students articulate a specific way of laying out the terrain of a problem and evaluating different starting points for solving. A teacher of adolescents and young adults might frame the task as a real-world design conundrum, inviting students to engage in a “tinkering” process of working toward mathematical proof, changing course as necessary as they develop their thinking.”

10. Assisting Through Looking At Students

11. ATLAS 2.0

12. Methodology Creating opportunities for students to build conceptual understanding of, and experience success with fundamental skills building connections to higher levels of understanding.

13. Questions to consider during video clip What does this practice look like when students are doing it? How can teachers increase student engagement within the practice?

14. ATLAS 2.0

15. Standard for Mathematical Practice #1Video Clip

16. Connections to ATLAS 2.0 1. Makes sense of problems and perseveres in solving them. • Identify the problem (Step S) • Explain the meaning of the problem (Step S) • Analyze information (Step O) • Line up a plan (Step L) • Use multiple strategies/representations to solve (Step V) • Evaluate and reevaluate progress throughout problem solving situations • Ask, “Does this make sense?” (Step E) • Ask, “Is this accurate? (Step E) • Ask, “Is this reasonable?” (Step E) • Justify reasoning with others

17. Debrief on questions… What does this practice look like when students are doing it? How can teachers increase student engagement within the practice?

18. #1 - Makes sense of problems and perseveres in solving them.

19. Accountable Talk… SOLVE

20. A taste of newfangled word problems New Common Core standards are due to roll out in 46 states by 2014. They're designed to get students ready for college and careers by requiring them to think, write and explain their reasoning. They also de-emphasize multiple-choice test questions in favor of written responses. Here's an example for New York City fifth-graders: Old question: Randa ate 3/8 of a pizza, and Marvin ate 1/8 of the same pizza. What fraction of the pizza did Randa and Marvin eat? a. 5/8 b. 3/8 c. 1/4 d. 1/2 (Answer: d) New question: Tito and Luis are stuffed with pizza! Tito ate one-fourth of a cheese pizza. Tito ate three-eighths of a pepperoni pizza. Tito ate one-half of a mushroom pizza. Luis ate five-eights of a cheese pizza. Luis ate the other half of the mushroom pizza. All the pizzas were the same size. Tito says he ate more pizza than Luis because Luis did not eat any pepperoni pizza. Luis says they each ate the same amount of pizza. Who is correct? Show all your mathematical thinking. (Answer: Luis is right — both ate 1 1/8 of a pizza). Source: New York City Department of Education

21. Problem Solving Framework… Insert Word Problem STUDY THE PROBLEM ORGANIZE THE FACTS LINE UP A PLAN VERIFY YOUR PLAN WITH AN ACTION EXAMINE THE RESULTS

22. Tito and Luis are stuffed with pizza! Tito ate one-fourth of a cheese pizza. Tito ate three-eighths of a pepperoni pizza. Tito ate one-half of a mushroom pizza. Luis ate five-eights of a cheese pizza. Luis ate the other half of the mushroom pizza. All the pizzas were the same size. Tito says he ate more pizza than Luis because Luis did not eat any pepperoni pizza. Luis says they each ate the same amount of pizza. Who is correct? Show all your mathematical thinking. whether Tito or Luis are correct on who ate more pizza addition and comparing add all of the pizza Tito ate to get a total, add all of the pizza Luis ate to get a total, compare the totals to see who is correct Both ate more than 1 whole yes yes Tito Luis yes Luis is correct because they each ate the same; 1 ⅛ of pizza S: Underline the question. The problem is asking me to find: O: Identify the facts Eliminate the unnecessary facts List the necessary facts L: Choose and operation or operations Write in words what your plan of action will be V: Estimate your answer Carry out your plan E: Does your answer make sense? Is your answer reasonable? Is your answer accurate? Write your answer in a complete sentence.

23. You try… Maria’s mother is planning to help her buy a new pair of jeans. They are on sale. The total cost of the jeans, including tax, is $17.00. Her mother gave her $14.50. how much more money does Maria need to purchase the jeans?

24. Break

25. Previous Objective: Solve problems involving perimeter/circumference and area of plane figures You have 44 yards of fencing. You need to make a rectangular runner for your pet dog, Bubba, with a length of 11 yards. What is the width? What is the area of the runner?

26. CCSS Objective: Measurement and Data 4.MD.3Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. You have 44 yards of fencing. You need to make a rectangular runner for your dog, Bubba. Draw some possible runners and find their area. What are the dimensions that will result in the maximum area? What is the maximum area?

29. Taking a question from good to great • Agree or Disagree • Draw a model to justify your answer • Explain your reasoning • How did you know _____? • Justify your answer • Tell how you found your answer

30. Taking a question from good to great

31. Scope and Sequences Meet in grade level teams Take a look at the alignments from your text (Go Math or CMP3) or Engage NY Discuss how these documents are used at your school or what your school is using Share what feedback you received or have about these documents? Share how are you addressing any concerns?

32. Scope and Sequences NYCDOE NYCSED

33. Lesson Planning Let’s take a closer look at the module Brainstorm the different components that you believe are essential to include in a lesson plan How detailed do they need to be? How far in advanced should they be written? How would you want to see differentiation in a lesson plan?

34. Methodology Creating opportunities for students to build conceptual understanding of, and experience success with fundamental skills building connections to higher levels of understanding.

35. Multiplication “__ Groups of __ Items” Connecting Learning

36. Next time… Conduct 3 ATLAS walks and bring copies December 4th Bring (1) example of a math lesson plan from your school Read Chapters 1 - 3