1. Region 1 (Kindergarten to Grade 4) June 19, 2012
Agenda:
Part 1: Assessing and Developing Key Fluencies Implications for SRBI
Part 2: Break Out Sessions:
K-2 Components of Math
3-4 Unit Planning Process
The goals for today are to create an SRBI plan.
The second goal is different by grade levels.
K-2 is to have a greater understanding of how to use assessments (both formative and summative) to inform planning the three components of the math program.
3 and 4 it is to learn how to plan a unit for the CCSS and begin to do that work using existing resources.
I will make the Power Point as well as the resources I used to create available to you.
Brennan Glasgow
Jill Vannini

2. Common Core State Standards K-12 Mathematics Learning Progressions
Kindergarten 1 2 3 4 5 6 7 8 HS
Counting and Cardinality
Number and Quantity
Number and Operations in Base Ten
The Number System
Number and Operations: Fractions
Ratios and Proportional Relationships (6 and 7)
Operations and Algebraic Thinking
Expressions and Equations
Algebra
Functions
Geometry
Measurement and Data
Statistics and Probability
Statistics
and
Probability
This is a look at the content strands across the grade levels.
Key idea is that it is a mastery curriculum not a spiral curriculum. This has huge implications for SRBI.
Mention Sadra Alberti Video

3. Priorities in Mathematics
Grade
Priorities in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding
K–2
Addition and subtraction, measurement using whole number quantities
3–5
Multiplication and division of whole numbers and fractions 6
Ratios and proportional reasoning; early expressions and equations 7
Ratios and proportional reasoning; arithmetic of rational numbers 8
Linear algebra
Progressions that are available from Arizona website are very informative.
Well worth reading.
Great resources.

4. Key Fluencies K Add/subtract within 5 1 Add/subtract within 10 2
Grade
Required Fluency K
Add/subtract within 5 1
Add/subtract within 10 2
Add/subtract within 20
Add/subtract within 100 (pencil and paper) 3
Multiply/divide within 100
Add/subtract within 1000 4
Add/subtract within 1,000,000 5
Multi-digit multiplication 6
Multi-digit division
Multi-digit decimal operations 7
Solve px + q = r, p(x + q) = r 8
Solve simple 22 systems by inspection
Ramifications for SRBI
If a child is not fluent with multi-digit multiplication in fifth grade, they should be getting extra support in that area, because that is the year they are suppose to have mastered it. This means, it should be introduced in earlier grades.

5. Computational Fluency
What is your definition of computational fluency?
Susan Jo Russell’s article

6. Assessing Fluency – A Few Examples A key point is that we are assessing more than naked number arithmetic. Want to make sure students understand, not just that they are getting the right answer.
Kindergarten Assessment Items –
Unit 1 - Counting and Matching Numerals 0 – 5 with Comparing
Test Mode: Administer one on one 
Rote Count
Teacher: Count out loud starting at 1 and count as high as you can.
Record highest number student accurately counts to.
Ex: Child counts from 1-15 accurately, then skips 16. Stop student
and record last correct number stated.
Stress that K-2 is not part of the formal testing process.
The test involves students in grades 3 to 8 and 11, similar to CMT and CAPT

7. Kindergarten Assessment Items
Unit 2 - Counting and Matching Numerals 6 – 10 with Comparing
Match Numerals Preparation: In advance, teacher puts out groups of objects (ex: counters, unifix cubes or bears) and numeral cards Objects should be arranged in groups of 3, 5, 8 and 10. Teacher: Give students the shuffled set of numeral cards. Count each group. Put the matching numeral card next to each set. Observe and record ( or - ) if student correctly matches all four sets.
This is very similar to a Kathy Richardson Assessment called Changing Numbers.
This is a simple assessment that gives you a lot of information.

8. Kindergarten Assessment Items
Unit 4 - Fluency with Addition and Subtraction within 5
There are 5 apples in a bowl.
Some apples are red. Some apples are green.
How many of each color apple could be in the bowl?
___ red apples ___ green apples
Find a different answer.
___ red apples ___ green apples
When we get to the problem solving, this is one of the problem structures that gives kids the most trouble.
It reminds me of probability – finding all the possible outcomes.
If done systematically, 1 Red, 4 Green -> 2 Red, 3 Green, etc. is not really that difficult, but how many Kindergarten kids think systematically?

9. Mrs. Jones needs 42 cupcakes for the class picnic.
Grade 1 - Assessment Items
Unit 4 - Exploring Addition and Subtraction within 100
Constructed Response
Write a number sentence and solve the problem. Use manipulatives (base-ten blocks, hundreds chart, number lines) or a drawing to show how to solve this problem.
Mrs. Jones needs 42 cupcakes for the class picnic.
She has 32 cupcakes.
How many more cupcakes does she need to buy?
We would pose this type of problem in the problem solving workshop.
This is how Joe found the answer to
= = 60
What did Joe do to solve the problem?

10. The teacher is 70 inches tall. The student is 47 inches tall.
Grade 2 - Assessment Items
Unit 3 - Fluency with Addition and Subtraction within 100
Constructed Response
Solve the problem. 54
- 29
Show or explain how to find the answer two different ways.
Write an equation for this problem. Solve the equation to find the answer.
The teacher is 70 inches tall.
The student is 47 inches tall.
How much taller is the teacher than the student?

11. 823 What is another way to show 729? 700 + 2 + 90 700 + 20 + 9
Grade 2 - Assessment Items
Unit 2 - Place Value to 1,000
Multiple Choice
Circle all the statements that are equal to this number.
823
a) 8 hundreds and 23 tens b) 823 ones
c) 7 hundreds, 12 tens and 3 ones d) 82 tens and 3 ones
e) 8 hundreds and 23 ones f) 7 hundreds and 23 tens
What is another way to show 729?

13. Developing an SRBI Plan
Meet as grade level teams and sketch out a plan for what will be assessed at each grade level as well as how it will be assessed.
How will progress monitoring occur?
What types of interventions are you envisioning? When will they happen?
Hand out Templates to Grade Levels

14. Implications for SRBI Region 10 Plan
What should we intervene for in the fall of each grade level?
Kindergarten = Counting with 1 to 1
First Grade = Fluency to 5
Second Grade = Fluency to 10
Third Grade = Fluency to 20 and Addition and Subtraction to 100
Fourth Grade =Multi-digit Addition and Subtraction Multiplication and Division Fluency (to 100) and Naming Fractions
Big idea: These are the things we are intervening for. In other words, we expect at least 80% of our students to be able to do these things.

15. Resources for Assessing Fluency and Number Sense
Assessing Math Concepts (Kathy Richardson)
Math Solutions (Marilyn Burns)
Xtra Math – Basic Facts
Math Reasoning Inventory –
Whole Numbers
Decimals
Fractions
We usually only use assessments 7, 8, and 9 at these grade levels (3 to 5)
What’s Hidden” assesses fact fluency
Digit Correspondence assesses place value
Computational Fluency (#9) assesses procedural fluency
Xtra Math assess fact fluency and creates reports.
Math Reasoning Inventory Assesses understanding of whole numbers, decimals, and fractions

16. Using Assessment to Inform Planning
Using Progress Monitoring to Choose Number Talks
Show Clip from Sherry Parrish resource
Using Assessment to Choose Stations
Using Assessment to form Ability Based Groups (Guided Math)
K-2 Pulled Groups during Center Time
Grade 3 (Kathy/Dawn) Ability Grouped 2X a week
This slide is intended to wrap up the first session and at the same time set the stage for the second session.
Observation at Stations
Computation Checks – using them to help guide Number Talk Choices and grouping

17. Part 2: Planning
This is different for Early Elementary (K-2) and Upper Elementary (3 and up) for us.

18. Format of Pre-K-8 Standards
Domain
Grade Level
2.NBT (code)
Cluster
Standard
2.NBT.1 (code)
Click to show the headings used to categorize the standards. The broadest header is “Domain” which is the larger groups of related standards. There is a code for each grade level with an abbreviation for the domain (2.NBT)
Clusters are groups of related standards under the domain.
Standards define specifically what students should know and be able to do and are numbers starting with #1.
The coherence of the standards at each grade level is demonstrated through the domains and clusters. The standards are grouped first by domain then by cluster. Each grade has up to 6 domains, and each domain is divided into one or more clusters.
(The next slide will show the progression of domains through grade 8.)

19. The State has created a scope and sequence for each grade level (K-8)
It is not a required scope and sequence, but you may want to review it as you make transition plans.
I think it is as interesting for what is not included as much as for what is included.
While local districts can create their own scope and sequence, the State has created a suggested one.
Over the next few years, the units will be developed so we are ready to implement.
Our district has agreed to use the unit plan framework the state is using. It is similar to UBD, but is based on the work of Larry Ainsworth.

20. Early Elementary (K-2)
We have decided not to include all the units the state is suggesting in our math time. We have also decided to try and see these grade bands as fluid. A child could be in Kindergarten and working on fluency within 20, if based on assessment that is deemed appropriate. We want to be as student-centered as possible in these early grades because numeracy is just emerging and that process happens at different times for different children.
Handouts by grade level – Should include a listing of the units and the displaced concepts (take these from the transition guide)

21. Components of the K-2 Program
Morning Meeting Routines
Calendar
Graph of the Week
Number Talks
Problem of the Day
Station or Center Work

22. Early Elementary (K-2)
Components of the Region 10 program and how they address CCSS
Handouts by grade level – Should include a listing of the units and the displaced concepts (take these from the transition guide)

23. The clearing house is suppose to be a collection of lessons and resources teachers can access to enhance instruction. We are going to use our existing resources for grades 3 to 5 and just try to imbed some tasks based on what we currently know about the Smarter Balanced Assessments - Problem Based Tasks

24. Practice Standards Teaching through Problems (Tasks)
This is an area that we can get started on across all the grade levels right now. Problem solving is not limited to any specific content, so you can teach problem solving no matter what units you decide to teach during the transition from the CMT to the CCSS.
Share K-2 Problem Structures for addition and subtraction (handout)
Also share the fact that there is a similar chart for multiplication and division

25. Mathematically Proficient Students Will…
Persistence is the most important quality to me.
Adapted from Inside Mathematics

26. Standards for Mathematical Practice
November 19-21, 2008
Standards for Mathematical Practice
2. Reason abstractly and quantitatively
3. Construct viable arguments
and critique the reasoning of
others
Make sense of problems and persevere in solving them
6. Attend to precision
Overarching habits of mind of a productive
mathematical thinker.
7. Look for and make use of
structure.
8. Look for and express regularity
in repeated reasoning
4. Model with mathematics
5. Use appropriate tools
strategically
Reasoning and explaining
Modeling and using tools
Seeing structure and generalizing
©TERC, 2007 Please Do Not Duplicate

27. Connecting the Practices to the Content
Math content standards describe what students should understand and be able to do.
Math practices describe ways in which students should interact with mathematics.
Curricula, assessment and professional development should be focused on connecting the mathematical practices and the content standards.
(CCSS p. 8)
To often we take a show and tell approach to math rather than a problem based approach.
Show and tell teaching is usually very superficial and does not transfer to other situations.
Problem based teaching on the other hand is often internalizes and students recognize other situations when that type of thinking or strategy will work.
PD should be focused on learning how to teach the content through problems.

28. Breakout Sessions K-2 Tasks Number Talks
Writing Problems (CCSS Problem Structures)
Stations or Centers for Assessed Skills
Counting
Early Number Relationships
Fact Fluency
Multi-digit Fluency
Jill will work with K-2 to work on using assessments to choose Number Talks and Stations
I will work with them later on the problem solving writing.
Handout Problem solving matrix at this time if I have not done so before.

29. Breakout Sessions 3-4 Tasks Unit Planning
Identify Concepts and Skills by Unit
Plan a problem based task per unit
Possible resources: Math Forum, Exemplars, etc
I will work with teams in terms of how to fill out template for planning.
Since they have different programs may not be able to work whole group.

30. Smarter Balanced Test Specifications
You can get a better sense of what the CCSS test is going to look like if you visit the web site and view the test specifications.
Share the multiple choice test item from Showcase 3

31. Resources:
Common Core State Standards Home Page:
Inside Math: This site has videos of teachers using problem based lessons.
Illustrative Math Project – Another way to look at the Standards. Is more compact so some people like this organization better.
CT State Department of Education:
Sandra Alberti, Common Core Video