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Math Workshop
January 30, 2014
Introductions and Logistics
• Cell phones
• My Background
• Questions
Agenda
• Common Core Learning Standards Instructional Shifts Standards for Mathematical Practice Content Emphases/Pre and Post Required Grade Level Fluencies
• CCLS Lesson format• NYS Math Modules • Sample PARCC Tasks
Let’s Take a Walk Down Memory Lane
Math Classes– Classroom Environment– Teacher’s Role– Students’ Role– Student Work
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
The Shape of Math in A+ Countries vs US
“Mile Wide, Inch Deep”
CCSS Myths vs Facts
• http://www.corestandards.org/about-the-standards/myths-vs-facts/
• Video
Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the
reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated
reasoning.
Instructional Shifts
1) Focus2) Coherency3) Fluency4) Deep Understanding Rigor5) Application6) Dual Intensity
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
Coherence example: Grade 3The standards make explicit connections at a single
grade
Properties of Operations
Area
Multiplication and Division 3.OA.5
3.MD.7c
3.MD.7a
Rigor From
To
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?”
Video ClipWriting and Speaking About Understanding
•Word Problem
2/5 of the washing machines in a store were sold at a total price of $3840. If 18 washing machines remained in the store. What was the cost of one washing machine?
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?
“Table for 22”A Real World
Geometry Project
Note Evidence of: • Instructional Shifts• Mathematical Practice Standards
Break
Content Standards
• Fewer per grade level• More focused• Progress logically
– Concepts build on prior learning
CCLS Major Content Emphases
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.
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
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
Lesson Overview (P – 5)(Intensity and Balance)
Math Lesson – One Hour
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
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)
Student• Classwork • Problem Set
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
Grade Level FluenciesK – Add/subtract within 51 – Add/subtract within 102 – Add/subtract within 20 *1
Add/subtract within 100 (PP)3 – Multiply/divide within 100 *2
Add/subtract within 1,000 4 – Add/subtract within 1,000,0005 – Multi-digit multiplicationBy end of year, know from memory all sums of two one‐digit numbers *1By end of year, know from memory all products of two one‐digit numbers *2
Facts within 5
+ 0 1 2 3 4 5
0 0 + 0 0 + 1 0 + 2 0 + 3 0 + 4 0 + 5
1 1 + 0 1 + 1 1 + 2 1 + 3 1 + 4
2 2 + 0 2 + 1 2 + 2
3 3 + 0 3 + 1 3 + 2
4 4 + 0 4 + 1
5 5 + 0
Facts within 10
+ 0 1 2 3 4 5 6 7 8 9 10
0 0 1 2 3 4 5 6 7 8 9 10
1 1 2 3 4 5 6 7 8 9 10
2 2 3 4 5 6 7 8 9 10
3 3 4 5 6 7 8 9 10
4 4 5 6 7 8 9 10
5 5 6 7 8 9 10
6 6 7 8 9 10
7 7 8 9 10
8 8 9 10
9 9 10
10 10
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
Sprints
• In action (Bill Davidson)
Let’s try a fluency activity
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!!!
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
Grade 2
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?
Curriculum Overview in A Story of Ratios
Modules are based on Singapore Math Instruction• Uses a concrete to pictorial to
abstract approach to develop understanding and mastery.
Concrete Pictorial ?
Abstract 5 + 3 = ____
Focus on Place Value and Number Sense
500
514 10
4
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.
Focus on mental math strategies(Number Bonds)
6 10
4
Part – part - whole
Mental Math Strategies (Number Bonds)
69 + 22 = ?
Mental Math Strategies (Number Bonds)
69 + 22 = ?
1 21
70 + 21 = ?
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)
Pre and Post Assessment(3 – 8)
• Test Guides for Mathematics
The Coming CCSS Assessments Will Focus Strongly on the Major Work of Each Grade
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
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
PARCC Type 1 Task
Type 1 Task
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
Type 2 “The Field” Part A
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
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 havealtogether?
• 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?
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.
