1. Math Workshop
January 30, 2014

2. Introductions and Logistics
Cell phones
My Background
Questions

3. Agenda Common Core Learning Standards CCLS Lesson format
Instructional Shifts
Standards for Mathematical Practice
Content Emphases/Pre and Post
Required Grade Level Fluencies
CCLS Lesson format
NYS Math Modules
Sample PARCC Tasks

4. Let’s Take a Walk Down Memory Lane
Math Classes
Classroom Environment
Teacher’s Role
Students’ Role
Student Work

5. CCSS/CCLS National standards (Math and ELA) States had the option
46 states adopted
Coincided with APPR (Teacher Evals)
Based on student growth and achievement
Lead to an increase in testing

6. The Shape of Math in A+ Countries vs US
“Mile Wide, Inch Deep”

7. CCSS Myths vs Facts
Video

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 strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.

9. Instructional Shifts Focus Coherency Fluency Deep Understanding Rigor
Application
Dual Intensity

10. Common Core Learning Standards
More Focused
Fewer per grade level
Coherent
Progress logically
Concepts build on prior learning
Rigorous so that students
Reach deep conceptual understanding
Attain a high degree of procedural skill and fluency
Have the ability to apply the math they know to solve problems

11. Focus
Kindergarten Lesson
4 minutes

12. Coherence example: Grade 3
The standards make explicit connections at a single grade
Multiplication and Division
Properties of Operations
3.OA.5
Understand properties of multiplication and the relationship between multiplication and division.
CCSS.Math.Content.3.OA.B.5 Apply properties of operations as strategies to multiply and divide.2 Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = = 56. (Distributive property.)
CCSS.Math.Content.3.MD.C.7.a Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
CCSS.Math.Content.3.MD.C.7.c Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.
3.MD.7a
3.MD.7c
Area

13. Rigor From

14. To

15. Rigor - Conceptual Questioning
Goes beyond getting the right answer
Goes beyond Yes/No questions
Encourages recognition of subtleties and exposes current level of student understanding
“Can you think of a case where that would not work?”
“Someone else says the answer is this. Can you prove that they are right/wrong?”
“When we get a like unit for these two fractions, will the like unit be bigger or smaller than the units we have?”
“Can you think of a number between 1/4 and 1/5?”

16. Video Clip Writing and Speaking About Understanding
Word Problem
2/5 of the washing machines in a store were sold at a total price of $ If 18 washing machines remained in the store. What was the cost of one washing machine?
1:35 minute video

17. Turn and Talk Reflections:
How does the speaking about understanding evident in the video compare with what occurs in your school today?
How are the Instructional Shifts evident in your current curriculum?

18. “Table for 22” A Real World Geometry Project
Note Evidence of:
Instructional Shifts
Mathematical Practice Standards

19. Break

20. Content Standards Fewer per grade level More focused
Progress logically
Concepts build on prior learning

21. CCLS Major Content Emphases

22. Key Point
The modules have been written in alignment with the Major Content Emphases. Each grade focuses only on the appropriate math and prioritizes the major work of the grade.
For Grade 3 through Grade 8, the standards identified on the Pre-Post Math Standards as those which should be taught after the state test in April, have been intentionally aligned with the final modules of those grades.

23. NYS Math Modules
A Story of Units (P – 5) A Story of Ratios (6-8) Awarded to Common Core Inc. Started with Standards Modules found on Engage NY

24. Lesson Components Fluency – designed to promote automaticity
Application Problems – directly relte to CD
Multi-step problems
Invite RDW process
Students select and apply math concept to solve real-world problems
CD – major portion of instruction in which new learning is introduces
Debrief – Reflective part of lesson
Students articulate the focus of the lesson
Ongoing assessment
Close with ET

25. Lesson Overview (P – 5) (Intensity and Balance)

26. Math Lesson – One Hour

27. Lesson Organization (6-8)
Header
July 2013
Network Team Institute
TIME ALLOTTED FOR THIS SLIDE:
6 minutes
MATERIALS NEEDED:
1 copy for facilitator of lesson 1 student and teacher
Document projector
Lesson Organization (6-8)
Teacher
Student Outcomes
Lesson Notes (in select lessons)
Classwork
General directions and guidance, including timing guidance
Discussion points with expected student responses
Student classwork with solutions
Scaffolding Boxes
Exit Ticket
Problem Set (with solutions)
6 min
Direct participants to student lesson 1 on pp. x-x and the corresponding teacher lesson on pp. x-x. Demonstrate each feature on the document camera, starting with student materials.
Say: We wanted to show you how the lessons are organized before digging more deeply into the mathematics. This slide shows the features in the student and teacher versions of each lesson.
Paraphrase or say the following-
Opening Exercise: Not all lessons have this feature. If the feature is missing then the first exercise or example builds in the previous day’s work or starts out setting the stage for more in-depth coverage of the lesson content.
Classwork: Depending on the lessons, these could be examples, exercises, exploratory challenges or discussions. Also in the classwork pages you will see key definitions if appropriate and on some lessons a lesson summary box. Students are expected to respond to the classwork on their lesson handout.
Problem Set: Each lesson includes a problem set. Students are expected to work these problems on a separate sheet of paper.
Teacher Materials: In the teacher materials, the lesson type is identified and student outcomes are listed. Then there is commentary and teaching suggestions for the classwork. Scaffolding boxes provide opportunities and suggestions for differentiation of instruction. There are exit tickets for each lesson that assess the student outcomes. Solutions are provided for classwork, exit tickets and assorted problem from the problem set.
Pause to take a look at the closing in the teacher materials (on the doc projector).
Say: The closing is like the pinnacle of your lesson. If you are short on time – this is what you protect at the expense of other parts.
Includes sample dialogue or suggested lists of questions to invite the reflection and active processing of the totality of the lesson experience.
Encourages students to articulate the focus of the lesson and the learning that has occurred.
Promotes mathematical conversation with and among students.
Student
Classwork
Problem Set

28. Fluency The standards require speed and accuracy in calculation.
Teachers structure class time and/or homework time for students to practice core functions such as single-digit multiplication so that they are more able to understand and manipulate more complex concepts

29. Grade Level Fluencies K – Add/subtract within 5
Add/subtract within 100 (PP)
3 – Multiply/divide within 100 *2
Add/subtract within 1,000
4 – Add/subtract within 1,000,000
5 – Multi-digit multiplication
By end of year, know from memory all sums of two one‐digit numbers *1
By end of year, know from memory all products of two one‐digit numbers *2

30. Facts within 5 + 1 2 3 4 5
0 + 0
0 + 1
0 + 2
0 + 3
0 + 4
0 + 5
1 + 0
1 + 1
1 + 2
1 + 3
1 + 4
2 + 0
2 + 1
2 + 2
3 + 0
3 + 1
3 + 2
4 + 0
4 + 1
5 + 0

31. Facts within 10 + 1 2 3 4 5 6 7 8 9 10

32. Grade Level Fluencies
6 – Multi-digit division Multi-digit decimal operations 7 – Solve px + q = r, p(x+q) = r 8 – Solve simple 2x2 systems by inspection

33. Fluency
A sampling K - 5

34. Sprints
In action (Bill Davidson)

35. Motion Fluency
Video example

36. Let’s try a fluency activity

37. Focus, Coherence, Rigor
At any given grade level 75% of the year should be spent on major areas of work.
The first half of the year should predominantly cover major areas of work.
Use textbook as a resource not your curriculum
Do not teach cover to cover!!!

38. Summary of Major Work in Grades K – 8 (The focus!!!)
K-2 Addition and subtraction – concepts, skills, problem solving and place value
3-5 Multiplication and division of whole numbers and fractions – concepts, skills, and problem solving
6 Ratios and proportional relationships; early expressions and equations
7 Ratios and proportional relationships; arithmetic of rational numbers
8 Linear algebra and linear functions

39. Grade 2
Domains and Clusters

40. Think – Pair - Share Are you familiar with CCLS?
Mathematical Content
Major content emphases
Pre/post standards
Are you familiar with the modules on EngageNY?
If not, is your school’s curriculum aligned with the CCLS?

41. Curriculum Overview in A Story of Units
Math Modules P - 5

42. Curriculum Overview in A Story of Ratios
Lavender – Ratios/Proportions, Peach – Expressions/Equations, Gold – Numbers/Operations, Blue - Geometry , Taupe - Statistics, Green - Functions

43. Modules are based on Singapore Math Instruction
Uses a concrete to pictorial to abstract approach to develop understanding and mastery.
Concrete Pictorial ?
Abstract = ____

44. Focus on Place Value and Number Sense
500 4

45. Problem Solving is at the heart of the curriculum
Real World Problems give students an opportunity to apply their knowledge and approach problems in ways that make sense to them.

46. Focus on mental math strategies (Number Bonds)
Part – part - whole

47. Mental Math Strategies (Number Bonds)
= ?

48. Mental Math Strategies (Number Bonds)
= ?
= ?

49. Guides to the CC Math Test are online
Recommended Instructional Time (Range)
Approximate Number of Test Points (Range)
Cluster Emphasis Page clearly denotes the Post Test Standards
Test Blueprint (Major/Supporting/Additional)

50. Pre and Post Assessment (3 – 8)
Test Guides for Mathematics

51. The Coming CCSS Assessments Will Focus Strongly on the Major Work of Each Grade

52. New Assessments
“ The Grade __ Common Core Mathematics Test is designed to measure students mathematical understanding as defined by the CCLS. As such there will be a noticeable change in rigor and depth in mathematics.”
PARCC challenges

53. PARCC Type 1 Tasks Assess concepts, skills and procedures
Include a balance of conceptual understanding, fluency, and application.
Are machine-scored including innovative, computer-based formats

54. PARCC Type 1 Task

55. Type 1 Task

56. PARCC Type 2 Tasks Assess ability to express mathematical reasoning
Call for written arguments/justifications, critique of reasoning, or precision in mathematical statements
Are hand-scored, or machine-scored with innovative computer-based formats, or a combination

57. Type 2 “The Field” Part A

58. PARCC Type 3 Tasks Assess modeling/applications
Call for modeling/application in a real-world context or scenario
Are hand-scored, machine-scored with innovative computer-based formats, or a combination

59. PARCC Type 3 Task Sample Grade 4 Problem
Jim has three times as much money as Sally. If Jim has $14 more than Sally, how much money do they have
altogether?

60. How do the new PARCC assessments compare with current and previous assessments?
Are the problems in your school’s resources rigorous?
Do the problems in your school’s current resource align with PARCC tasks?

61. Note
The problems woven throughout the modules, as well as the Mid-Module and End-of-Module Assessment Tasks, are aligned with the PARCC problems/tasks.

62. Evaluations Thank you for attending today’s workshop.