1. Common Core Standards in the Classroom
Tom Rye
Ferris High School
Spokane, WA
Visit thomasrye.weebly.com for slides and files

2. Wind Map

3. Since School Started…
Write down:
1 success
1 challenge
1 question

4. Goals Deepen our understanding of mathematics while having some fun!
Examine the relationship between Common Core Standards, current standards, and meaning making / transfer
Continue to explore strategies around teaching for understanding
Finish DCA writing

5. Questions
What is transfer and what does it look like in a mathematics setting?
To what extent do the Common Core Standards call for transfer?
What are the implications of the Standards for Mathematical Practice?
How can we incorporate the Standards for Mathematical Practice into our content standards?
How can we incorporate the Standards for Mathematical Practice into our daily classroom?
How can we assess the Standards for Mathematical Practice?

6. Course Understandings
Transfer of mathematical skills and knowledge is the ultimate goal. Transfer is defined as adaptation and application of skills to new situations or contexts.
In order to transfer skills, students must first make meaning of the importance, relevance and structure of the skills.
Common core standards call for a deep understanding of mathematics, not just mastery of skills.
The standards for mathematical practice emphasize and align with the concepts of UbD and transfer.

7. Agenda Monday, October 29 Status Update Introductory Problem
Examining Student Work
Questioning and Cognitive Demand
Unpacking Standards
Creating Assessment Items
Designing Learning
Sharing

8. Changes to the Agenda

9. By the End of Today
Identified and unpacked standards related to an upcoming DCA
Unpacked into questions sorted by cognitive demand
Created tasks for assessment for upcoming DCA
Develop learning activities for meaning making and transfer
Talk about mathematics all along the way

10. Norms for Math What do you need to be a successful learner?
Time to think
Safe to share
Open to others
Use Study Buddies Guide

11. Opening Problem
Field Trip Student Task

12. Opening Problem What was the mathematical content?
Consider standards
What mathematical practice standards were evident in your work?
How might this problem serve as an activity versus an assessment?

13. Questioning and Cognitive Demand in the Classroom

14. Steps to the Inquiry Process
“Higher-level questions are essential to facilitating conceptual understanding. The inquiry process is facilitated by skillful questioning and provides students with the opportunity to become independent thinkers who master their own learning.”
-Costa
How does this relate to UbD and AMT?

15. COSTA’S LEVELS OF QUESTIONING
Level One:
The answer can be quickly looked up
It is “Google-able”
Very concrete
Information is recalled in the exact manner/form it was heard
Processes that have been repeatedly practiced

16. Sample Questions Level 1:
Gather and Recall Information (Gathering/Input)
Ask Level 1 questions to identify what students know about the problem or question and connect to prior knowledge.
What do you know about the problem?
What does __________mean?
What did you record from your class notes about ____?
What is the formula or mnemonic device (ex. PEMDAS) that will help you identify the steps necessary to solve the problem?

17. COSTA’S LEVELS OF QUESTIONING
Level Two:
The answer requires some inference.
More abstract than a Level One question
Information can be broken down into parts
Involves examining in detail, analyzing motives or causes, making inferences, finding information to support generalizations or decision making
Questions combine information in a new way

18. Sample Questions Level 2:
Make Sense Out of Information Gathered (Processing)
Ask Level 2 questions to begin processing the information gathered, make connections and create relationships.
Can you break down the problem into smaller parts? What would the parts be?
How can you organize the information?
What can you infer from the data?
Can you find a problem/question similar to this to use as an example?

19. COSTA’S LEVELS OF QUESTIONING
Level Three:
The answer goes beyond the text.
Is abstract
Ask that judgments be made from information
Gives opinions about issues, judges the validity of ideas or other products, justifies opinions and ideas

20. Sample Questions Level 3:
Apply and Evaluate Actions/ Solutions (Applying/Output)
Ask Level 3 questions to apply knowledge acquired and connections made to predict, judge, hypothesize or evaluate.
How do you know the solution is correct? How could you check your answer?
Is there more than one way to solve the problem? Could there be other correct answers?
Is there a real life situation where this can be applied or used?
Can you explain it in a new and different way?
Could the method of solving this problem work for other problems?
How would you teach this to a friend?

21. COSTA’S LEVELS OF QUESTIONING
LEVEL ONE: Define
Describe
Identify
List
Name
Observe
Recite
Scan
LEVEL TWO:
Analyze
Compare
Contrast
Group
Infer
Sequence
Synthesize
LEVEL THREE: Apply
Evaluate
Hypothesize
Imagine
Judge
Predict
Speculate

22. What Level?
Practice Coding with the Geometry Sample Test

23. Unpacking More Standards

24. Unpacking More Standards
Identify the standards to be assessed on an upcoming DCA that needs revision
Select a “high priority” content standard and practice standard to focus on from that set

25. Practice Standard - Problem Solving
Items and tasks require students to construct their own pathway to the solution
Relevant verbs include:
understand, solve, apply, describe, illustrate, interpret, and analyze
Claim 2 focuses on problem solving and requires students to solve a range of complex, well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.
{+}
Evidence for Claim 2 is elicited through selected response, constructed response, extended response, and technology-enhanced items and tasks that focus on problem solving.
Claim 2 items and tasks should require students to construct their own pathway to the solution.
Some relevant verbs that identify content clusters and/or standards for Claim 2 include understand, solve, apply, describe, illustrate, interpret, and analyze.

26. Practice Standard – Communicating Reasoning
Relevant verbs include:
understand, explain, justify, prove, derive, assess, illustrate, and analyze
Claim 3 focuses on communicating reasoning and requires students to clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others. {+} Evidence for Claim 3 is elicited through constructed response, extended response, and technology-enhanced items and tasks that focus on mathematical reasoning. {+}
Relevant verbs that identify content clusters and/or standards for Claim 3 include understand, explain, justify, prove, derive, assess, illustrate, and analyze.

27. Practice Standard – Modeling and Data Analysis
Real world problems
Draw upon knowledge and skills articulated in the progression of standards up to the grade being assessed
Relevant verbs include:
model, construct, compare, investigate, build, interpret, estimate, analyze, summarize, represent, solve, evaluate, extend, and apply
Claim 4 focuses on modeling and data analysis and requires students to analyze complex, real-world scenarios and construct and use mathematical models to interpret and solve problems.
{+}
Evidence for Claim 4 is elicited through performance tasks and collections of extended response items that focus on modeling and data analysis.
Claim 4 tasks are real world problems that are complex and may contain insufficient or superfluous data.
Tasks generating evidence for Claim 4 in a given grade will draw upon knowledge and skills articulated in the progression of standards up to that grade, with strong emphasis on the major work of the grade.
Relevant verbs that identify content clusters and/or standards for Claim 4 include model, construct, compare, investigate, build, interpret, estimate, analyze, summarize, represent, solve, evaluate, extend, and apply.

28. Unpacking More Standards
Write Level 1 questions and tasks for the standard
What questions should the student be able to answer?
What tasks should the student be able to do?
Reference the Costa question starters if you like
Lots of examples at
Be ready to share some Level 1 questions by 11:00 AM

29. 4: Students provides evidence of complete understanding the target and communicates that understanding clearly.
3: Student provides evidence of proficient understanding the target, but may have minor errors unrelated to the target.
2: Student provides evidence of a developing understanding of the target, but have not achieved the target yet.
1: Student shows minimal to no evidence of understanding the target.

30. Unpacking More Standards
Write Level 2 questions and tasks for the standard
What questions should the student be able to answer?
What tasks should the student be able to do?
Reference the Costa question starters if you like

31. Unpacking More Standards
Write a Level 3 question/task or two for the standard
What questions should the student be able to answer?
What tasks should the student be able to do?
Reference the Costa question starters if you like

32. Lunch

33. Unpacking More Standards
Sharing of Questions
Be mindful of students
Will they answer the question at the appropriate level?

34. How fast is Rich Eisen (sports announcer)?
How long did it take to run?
How far?
How long is a stride?
When was he running the fastest? Slowest?
What are those numbers on the field?
How fast did he run?
Why was he wearing a suit?
If he kept running that fast, how long would it take to run the whole field?

35. Times in seconds 5.887 5.9 6.1 5.5 5.7 5.72 5.8 Guesses in mph 4.5 7
5.24 2
7.3

36. Creating Assessment Items

37. Creating Assessment Items
Use your Questions and Tasks to develop actual assessment items for the standards
Write several items for Level 1
Copy and paste is ok!
Basic practice questions live here
Make sure your questions reflect the scope of the standards

38. Creating Assessment Items
Use your Questions and Tasks to develop actual assessment items for the standards
Try to write at least 3 Level 2 items
Don’t forget about the question starters
DCA

39. Creating Assessment Items
Use your Questions and Tasks to develop actual assessment items for the standards
Try to write at least 2 Level 3 items
Start with your own ideas!

40. Task Write 3 Level 2 assessment items Write 2 Level 3 assessment items
These are things you would hand to kids or write on the board for them to do!

41. 101 Questions

42. Designing Learning

43. Designing Learning
Angry Birds -

44. Designing Learning What must students be told?
What can students discover for themselves?

45. Designing Learning What is the role of the teacher day by day?
What is the role of the student?

46. Designing Learning Video of classrooms
While watching the video, please take notes around the following questions:
What is the role of the teacher and student – who is doing what?
What (you must listen very closely) does the teacher actually say to the students?

47. Designing Learning Bill buys eight bottles of cola for $4.00.
What is the cost of each bottle?
It takes 40 minutes to bake 8 potatoes.
How long does it take to bake one potato?
If you buy ten bottles you get a 5% discount.
Is buying six bottles a week a good idea?

48. Designing Learning Asking questions that may not have “answers”
How many chips have you eaten in your life?
How many seconds have you been alive?
How many hours did it rain last year?
What is the surface area of a banana?
How many leaves in an Oak tree?

49. Designing Learning Asking open ended questions
What set of data has a mean of 5 and a median of 6?
What shape has an area of 60 square inches?
What equation has the solution x = 5?
What can you tell me about a rectangle?

50. Good Morning

51. Designing Learning
Ask students to justify – provide examples and counter examples
Is it Never true, Sometimes true, or Always true?
Doubling each number in a set of data doubles the mean
Multiplying by an odd number gives an odd number
When you subtract you always get a smaller answer
Squaring a number always makes it bigger
A triangle has three acute angles
A triangle has two obtuse angles
A quadrilateral has three right angles

52. Designing Learning
Ask students to justify – provide examples and counter examples
Is it Never true, Sometimes true, or Always true?
Doubling each number in a set of data doubles the mean
Multiplying by an odd number gives an odd number
When you subtract you always get a smaller answer
Squaring a number always makes it bigger
A triangle has three acute angles
A triangle has two obtuse angles
A quadrilateral has three right angles

53. Opening Problem
Crickets Student Task

54. Opening Problem What was the mathematical content?
Consider standards
What mathematical practice standards were evident in your work?
How might this problem serve as an activity versus an assessment?

55. Designing Learning
Now develop explorations and experiences that will help students achieve the standards and be successful on the tasks
Some Examples
Focus on meaning making and transfer!
Remember our questions:
What must students be told?
What can students discover for themselves?

56. Sharing

57. Sharing By the End of Today
Identified and unpacked standards related to an upcoming DCA
Unpacked into questions sorted by cognitive demand
Created tasks for assessment for upcoming DCA
Develop learning activities for meaning making and transfer

58. Sharing Find another team to work with: Advanced Math and Algebra II
Algebra II and Geometry
Geometry and Algebra
Algebra and 8th Grade
8th Grade and 7th Grade
7th Grade and 6th Grade
And so on…

59. Sharing Each team give a 2 minute summary of their work
Exchange Assessment Items and Learning Experiences
Provide feedback on Post-it notes

60. Sharing “I wonder…” or “I notice…” Post-it note considerations
To what extent do the assessment items reflect all 3 levels of questions?
To what extent do the assessment items span the breadth of the standard?
How much are the students being told?
To what extent do the learning experiences scaffold things for students?
To what extent are students constructing meaning?
To what extent are students transferring?

61. Cool Math Art

62. Performance Tasks, Transfer Tasks, and Rubrics Oh my!

63. Examining Student Work

64. Examining Student Work (select a note-taker)
First, recall and re-familiarize the standards assessed
Content standard
Practice Standard
Second, sort student work into 2 piles
Meeting standard
Not meeting standard
Third, sort again
Meeting standard into Exemplary vs. Just made it
Not meeting standard into: Just missed it vs. A long way to go

65. Examining Student Work
The note-taker
Be sure to write down all the criteria referenced during each sorting process
Note how often a criteria is used

66. Examining Student Work
Use the sorting and the notes to formalize a rubric for the standard(s)

67. Rubric Examples
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68. Rubric Resources Marzano Research

69. Rubrics for DCA Tasks
Rubrics are not about points, they represent levels of understanding (the extent to which they meet standard)
Can a student look at the rubric and know what they need to know to move to the next level?

70. Revising and Writing DCAs

71. Reading
ways-to-apply-algebra-with-the-new-york-times/

72. Questions
What is transfer and what does it look like in a mathematics setting?
To what extent do the Common Core Standards call for transfer?
What are the implications of the Standards for Mathematical Practice?
How can we incorporate the Standards for Mathematical Practice into our content standards?
How can we incorporate the Standards for Mathematical Practice into our daily classroom?
How can we assess the Standards for Mathematical Practice?