Common Core State Standards Mathematical Practices

1. Common Core State Standards Mathematical Practices Jeremy Centeno

2. You would never hear someone say: I am not very good at reading. I can’t read.

3. You do hear people say: I am not good at math. I can’t do math. When I was a kid math was my worst subject

4. What is the difference? The difference between the USA and other higher performing nations is that a culture of learning math is established from the beginning of a students career in school. Students are informed and taught everyone can do math.

5. What are the following? • Cryptanalyst $137,780/yr • Computational Biologist $150,000/yr • Mathematical Physicist $166,400/yr • Actuary $160,000/yr

6. The way we taught students in the past simply does not prepare them for the higher demands of college and careers today and in the future. Your school and schools throughout the country are working to improve teaching and learning to ensure that all children will graduate high school with the skills they need to be successful. In mathematics, this means three major changes. • Teachers will concentrate on teaching a more focused set of major math concepts and skills. This will allow students time to master key math concepts and skills in a more organized way throughout the year and from one grade to the next. It will also call for teachers to use rich and challenging math content and to engage students in solving real-world problems in order to inspire greater interest in mathematics.

7. Class Building/Corners • Look at the posters in the room • Pick which is your favorite math concept to teach: • Operations: Addition/Subtraction/Multiplication/Division • Place Value: Skip counting/Base Ten/ Greater Than/ Less Than/ Equal To • Measurement • Geometry Think about the following Question: • Why is this concept your favorite concept to teach? Timed Rally Robin

8. Corners Continued • Pick your corner by least favorite concept to teach Think about the following Question: Why do you feel this concept is your least favorite concept to teach? Timed Rally Robin:

9. Team Building/4 Corners Name Tag • Take a Piece of notebook paper and fold it so that it stands on its own • Write Your Name in the Center • In the Upper Left hand corner draw a shape that represents you • In the Upper Right hand corner pick an operation that represents you • In the Lower Left Corner pick your favorite temperature • In the Lower Right Hand corner write your favorite number

10. Team Interview • Person Number 1 will ask person number 2 to answer upper left hand corner out loud for the group • Person Number 2 will be standing and Answer Question • Person Number 3 will make a connection • Person Number 4 will praise • Person 1 turns Mat and Person Number 2 becomes person number 1 and repeats the same process (Continue until I say stop)

11. Reflection/Talking Chips • Think about the activities for class building and team building • How would you use these activities with students in a math class? Why is it necessary to team build and class build in order to have engaging activities in your classroom? • When the signal word is given anyone can speak but they must put a chip in as they talk. • All chips must be down on the table if there is time pick up chips and continue conversation

12. Mathematical Practice #1Problems and Perseverance 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. … —CCSS

13. CCSS Mathematical Practice #1 • I can try many times to understand and solve a math problem.

14. Key Points • Life Happens (Not just a Chapter in a Book) • Puzzler’s Disposition (A good puzzle creates a drive to succeed) • Toolkit (Need to solve) • Hard problems broken into simpler problems

15. CCSS Practice #1

16. My Number Bond Name Tag Jeremy Centeno 6 7 3 3 7 3 10 3 + 10 = 3 + 10 = 13

17. Choose Three Ways • Each person will get a math problem • On your graphic organizer you will chose three ways to solve your problem and show how you solved it • You will work on your own first • When you hear the signal word begin

18. Numbered Head Together • Person number one reads their problem • Everyone Answers their problem without looking at each others board • As each person gets done stand up • When all people are standing discuss how each of you solved the problem • Agree and praise/ Or Coach and Praise • Repeat with person number 2

19. Video • https://www.teachingchannel.org/videos/problem-solving-math?fd=1

20. http://www.insidemathematics.org/index.php/classroom-video-visits/public-lessons-word-problem-clues/438-word-problem-clues-lesson-5http://www.insidemathematics.org/index.php/classroom-video-visits/public-lessons-word-problem-clues/438-word-problem-clues-lesson-5

21. Mathematical Practice #2Reason Abstractly and Quantitatively Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. —CCSS

22. CCSS Mathematical Practice #2 • I can think about the math problem in my head first

23. CCSS Practice #2

24. Math StringsMental Math • The number of fingers on two human hands • Subtract the number of toes on one human foot • Multiply it by the number doughnuts in a half dozen • Divide by the number of eyes on a human face • Add to it the number of hearts in a human body • The answer is? 16

25. Math Task Cards/Word Problem Activities • Taking a look at Task Cards • Taking a Look at Activities

26. Decontextualizing/Recontextualizing • How many buses are needed for 99 children if each bus fits 44 students? • Find the Answer • How did I come about my answer? (recontexualize)

27. Video • https://www.teachingchannel.org/videos/third-grade-mental-math

28. http://insidemathematics.org/index.php/classroom-video-visits/public-lessons-proportions-a-ratios/199-proportions-a-ratios-problem-1http://insidemathematics.org/index.php/classroom-video-visits/public-lessons-proportions-a-ratios/199-proportions-a-ratios-problem-1

29. Mathematical Practice #3Construct Arguments and Critique Reasoning Mathematically proficient students … justify their conclusions, communicate them to others, and respond to the arguments of others. They … distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. … Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. … Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. —CCSS

30. CCSS Mathematical Practice #3 • I can make a plan, called a strategy, to solve the problem and discuss other students’ strategies to make sense.

31. Key Points • Children like to talk but explanation is difficult • Focus on “Shared Context” • Interest Based • Student should not critique from desk • Key is to “Show as well as tell” • Give Depth not one process problems • Challenging problems worked on together creates a natural pull to reason

32. CCSS Practice #3

33. Find the Fiction • My number is 100. • I can be broken into 4 parts equally • I represent a millennium • My quantity in pennies is equal to a dollar

34. Find the Fiction • On your board write the number of the statement that is fiction and write the word fiction next to that number (DO NOT SHOW ANYONE) • Example: 4 Fiction • When you hear the signal word discuss with your group one at a time your answer. Come to a consensus • Answer: 2 is the Fiction • Praise: Expert Thinking

35. Page 6.32 Partners take turns, One solving a problem while the other coaches. Teacher Coach 0 % Engagement 100% Engagement!

36. How Many Ways Task • How many ways can I make 28 cents? • How many ways can I make 28 cents without quarters? • How many ways can I make a 5 inch tower with 1 inch cubes using 1 white cube and 4 blue cubes? • Now try with 3 white and 2 blue cubes.

37. Consideration • Young students should not developmentally be held accountable for critiquing another students argument.

38. http://insidemathematics.org/index.php/classroom-video-visits/public-lessons-proportions-a-ratios/204-proportions-a-ratios-problem-3-part-chttp://insidemathematics.org/index.php/classroom-video-visits/public-lessons-proportions-a-ratios/204-proportions-a-ratios-problem-3-part-c

39. Mathematical Practice #4Model Mathematics • Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life…. In early grades, this might be as simple as writing an addition equation to describe a situation.… Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation…. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs…. They…reflect on whether the results make sense…. —CCSS

40. CCSS Mathematical Practice #4 • I can use math symbols and numbers to solve the problem.

41. CCSS Practice #4

42. Children are Curious about the World • Use of real life interest • Play: Experiment, Tinker, and Push Buttons to see what happens • Curiosity: Size, Shape, Fit, Quantity, and Number • To catch a ball what does one need to figure? • Math is not a collection of skills that are demonstrated

43. What does this Array tell us?

44. Why Arrays?

45. Peter Penguins Clues • As a team use your mats to see who is person 1,2,3, or 4 • Person 1: Pass out clue cards • Person 2: Colors in Answer Sheet when done • Person 3: Checks all Answers • Person 4: Praises if correct • Turn board for next game

46. http://www.insidemathematics.org/index.php/classroom-video-visits/public-lessons-proportions-a-ratios/202-proportions-a-ratios-problem-3-part-ahttp://www.insidemathematics.org/index.php/classroom-video-visits/public-lessons-proportions-a-ratios/202-proportions-a-ratios-problem-3-part-a

47. Mathematical Practice #5Use Tools Appropriately • Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet…. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. —CCSS

48. CCSS Mathematical Practice #5 • I can use math tools, pictures, drawings, and objects to solve problems

49. CCSS Practice #5

50. Key Notes • Make a list of standard tools in classrooms • Pencil and Paper • Area Model of Multiplication • Many Choice Options for Students • Student made decisions on tools • Different problems to create choice of tools • Proscribed or Prescribed tool activities