1. K-2 Math Task Force

2. Plan for Day 2
Develop Working Draft of Concepts & Skills to Assess for Spring Pilot
Share feedback from those you represent
Tease out the concepts and skills to assess from some standards that have multiple skills/concepts
Discuss skills and concepts that could be assessed together
Determine if fewer skills and concepts could be assessed
Develop questions to assess the concepts and skills
Review Standards for Mathematical Practice
Reflect on SMP used in the 3rd grade SBAC Performance Task
Understand what is available on the market currently
Break into small groups to review questions and develop a working draft of an assessment by grade level that includes assessment of math content and practices
In grade level groups, discuss potential questions, including number of questions overall and protocol for giving the assessment
Grade levels to share out draft assessment to see the progression over K-2, including draft assessment protocol
Next Steps
Review things to do between today and Day 3 (March 16th)
Review plans for Day 3
All handouts from today are posted at:

3. Part 1
Develop Working Draft of Concepts & Skills to Assess for Spring 2015 Pilot

4. Part A: Sharing feedback from those you represent
Suggested additions (“Additional” clusters?, etc.)
Suggested deletions
Support for skills/concepts “as is”

5. Part B: Breaking Apart Standards that Assess More Than One Skill
Which standards have more than one concept or skill that could be assessed?
Which skills within a standard do we have agreement to assess?

6. What skills and concepts could be combined to assess together?
Begin to consider – come back to this question later in the morning

7. K-2 Math Content Framework
Purpose:
Guide the development of diagnostic tools and formative instructional tasks that align to the CCSS
Support the implementation of the CCSS
Address areas of emphasis that develop college and career readiness in the early grades
Page 1

8. K-2 Math Content Framework
Components for Each Grade:
Key Advances from the Previous Grade
Fluency Expectations or Culminating Standards
Major Within-Grade Dependencies
Opportunities for Connections
Opportunities for In-Depth Focus
Opportunities for Connecting Math Content & Practices
Content Emphases by Cluster
Pages 9-10

9. Fluency
“In the standards for Kindergarten through grade six there are individual content standards that set expectations for fluency in computation. Such standards are culminations of progressions of learning, often spanning several grades, involving conceptual understanding, thoughtful practice, and extra support where necessary…”

10. Fluency
“…The word ‘fluent’ is used in the standards to mean ‘reasonably fast and accurate’ and the ability to use certain facts and procedures with enough facility that using them does not slow down or derail the problem solver as he or she works on more complex problems. Procedural fluency requires skill in carrying out procedures flexibly, accurately, efficiently, and appropriately. Developing fluency in each grade can involve a mixture of just knowing some answers, knowing some answers from patterns, and knowing some answers from the use of strategies.”
CA Math Framework, Grade 1 Chapter, pages 18-19; Grade 2 Chapter, page 13,
also found in the Counting & Cardinality and Operations & Algebraic Thinking K-5 Progressions

11. K-2 Math Content Framework & Implications for Our Assessment
Kindergarten:
Read pages 12-13
Grade 1:
Read pages 18-19
Grade 2:
Read pages 25-26
Focusing on “Fluency Expectations or Examples of Culminating Standards”
Only culminating

12. Could we further narrow our assessment focus?

13. PARCC K-2 Model Content Framework for Mathematics Kindergarten
Fluency Expectations --Culminating Standards
PARCC K-2 Model Content Framework for Mathematics Kindergarten
K.CC.1
K.CC.3
K.CC.5
K.CC.7
K.OA.5
Count to 100 by tens.
Write numbers from 0-20.
County to answer “how many?” questions about as many as 20 things…
Compare 2 numbers between 1-10 presented as written numerals.
Fluently add within 5.
Count to 100 by ones.
Represent a number of objects with a written numeral.
Given a number from 1-20, count out that many objects.
Fluently subtract within 5.

14. PARCC K-2 Model Content Framework for Mathematics Grade 1
Fluency Expectations --Culminating Standards
PARCC K-2 Model Content Framework for Mathematics Grade 1
1.OA.6
1.OA.7
1.OA.8
1.NBT.5
Add within 20.
Understand the meaning of the equal sign.
Determine the unknown whole number in an addition equation relating 3 whole numbers.
Given a 2-digit number, mentally find 10 more, without having to count; explain the reasoning used.
Subtract within 20.
Fluently add within 10.
Determine if equations involving addition and subtraction are T/F.
Determine the unknown whole number in a subtraction equation relating 3 whole numbers.
Given a 2-digit number, mentally find 10 less, without having to count; explain the reasoning used.
Fluently subtract within 10.

15. PARCC K-2 Model Content Framework for Mathematics Grade 2
Fluency Expectations --Culminating Standards
PARCC K-2 Model Content Framework for Mathematics Grade 2
2.OA.2
2.NBT.5
2.NBT.2
2.NBT.3
Fluently add within 20 using mental strategies.
Fluently add within 100 using strategies based on place value…
Count within 1000.
Read numbers to 1000 using base-10, number names, expanded form.
Fluently subtract within 20 using mental strategies.
Fluently subtract within 100 using strategies based on place value…
Skip-count by 5s.
Write numbers to 1000 using base-10, number names, expanded form.
Skip-count by 10s.
Skip-count by 100s.
Know from memory all sums of two 1-digit numbers.

16. Could we further narrow our assessment focus?

17. Part 1: Final Step
By grade level, come to agreement on the concepts and skills we will assess in the Spring 2015 pilot

18. Develop questions to assess the concepts & skills
Part 2
JUDY – Welcome the full group
Develop questions to assess the concepts & skills

19. K-12 Standards for Mathematical Practice (MP)
Represent the “ways of doing” mathematic s
REBECCA

20. K-12 Standards for Mathematical Practice (MP)
REBECCA

21. Standards for Mathematical Practice: Video Introduction
REBECCA
LINK:

22. Explanations & Examples of Standards for Mathematical Practices by Grade Level
Read the Standards for Mathematical Practice from the CA Mathematics Framework Grade Level Chapter (Day 1 tab section)
Kindergarten Page 3 (Line 70) to Page 5 (Line 88)
Grade 1 Page 3 (Line 72) to Page 6 (Line 89)
Grade 2 Page 3 (Line 73) to Page 6 (Line 90)
JUDY

23. Standards of Mathematical Practice (MP)
Watch video and consider what MP students were demonstrating
JUDY
LINK:

24. K-12 Standards for Mathematical Practice (MP)
JUDY

25. Performance Task: What Standards for Math Practice would be used to successfully complete the table?
1. The bar graph shows how many cups of lemonade Jaleen sold in July. Complete the table to show how many cups Jaleen sold each week.
JUDY

26. Performance Task: What Standards for Math Practice would be used to successfully answer the question?
2. How many total cups of lemonade did Jaleen sell in July?
JUDY

27. Performance Task: What Standards for Math Practice would be used to successfully complete the table?
3. Jaleen also sold lemonade for 4 weeks in August. She compares her weekly sales in July to her weekly sales in August.
For week 1, she sold 22 fewer cups in August than in July.
For week 2, she sold 18 more cups in August than in July.
For week 3, she sold 26 more cups in August than in July.
For week 4, she sold 25 fewer cups in August than in July.
Complete the table to show how many cups Jaleen sold each week in August.
JUDY

28. Performance Task: What Standards for Math Practice would be used to successfully complete the problem? 4.
JUDY

29. SBAC Constructed Response Grade 3: What Standards for Math Practice would be used to successfully answer the question?
JUDY

30. Readily Available Assessments
AIMSweb
DIBELS Math
NWEA
Renaissance Learning
Track My Progress
Cost
$4/student for math only; $6/student combined
Free in pilot year – undetermined for
$13.50/student
$1,599 subscription software per school + $2.25/student
$1,500/campus for 250 or less students; $2,500/campus for 500 or less students
Length/Standards
Test of Early Numeracy: 4 1-minute 1 to 1 tests
Concepts & Applications (2nd): 8 minutes + Computation
K: 3 one-minute tests (1-to-1)
1st: 6 minutes 1-to minute whole class
2nd: 12 minutes whole class (3 parts)
30 minutes
“Assess hundreds of math skills in 32 domains”
30 questions per test
Tech
None
Computer adaptive
Via computer
Audio narration, technology enhanced questions
JUDY

31. Assessment Questions
Consider how to embed the Standards of Mathematical Practice within the end-of-year assessment
Consider how the assessment will be administered:
One-on-one
Small group
Whole class
JUDY

32. What makes a good question?
“Students should grapple with language,” said David Wees, who designs Common Core aligned math questions at New Visions for Public Schools. “You have to choose the right level of ambiguity, enough language so that students know what to do without making it obvious what they need to do.”
“A sign of a good math problem, according to Wall, is that kids are able to approach it in many different ways.”
Judy
Jason Zimba, a founding partner of Student Achievement Partners and a member of the Common Core math standards writing team, doesn’t think teachers should throw out age-old math problems like seven plus eight. The standards, for example, still require that students memorize their times tables by third grade.
“If I were managing it in my own classroom,” says Zimba. “I would be sending home fairly traditional-looking problems, not only because that’s what parents are going to be able to work with, but because that’s part of the standards. They’re the end point. That’s the goal.”
LINK:

33. Post these on the 4 walls by standard #, grouped by assessed skill
How might we assess each concept and skill to address the Standards of Math Practice?
Break into partners and identify which set of partners will research which skill(s) or concept(s)
Using samples from states, projects, etc., identify options.
Share options with grade level
Recommend if more than one question should be used for each skill/concept
Consider balance of assessment: whole group problem solving and one-on-one interviews
Write in such a way that the information is clear without further explanation needed
JUDY

34. PARCC K-2 Model Content Framework for Mathematics Kindergarten
Fluency Expectations --Culminating Standards
PARCC K-2 Model Content Framework for Mathematics Kindergarten
K.CC.1
K.CC.3
K.CC.5
K.CC.7
K.OA.5
Count to 100 by tens.
Write numbers from 0-20.
County to answer “how many?” questions about as many as 20 things…
Compare 2 numbers between 1-10 presented as written numerals.
Fluently add within 5.
Count to 100 by ones.
Represent a number of objects with a written numeral.
Given a number from 1-20, count out that many objects.
Fluently subtract within 5.

35. PARCC K-2 Model Content Framework for Mathematics Grade 1
Fluency Expectations --Culminating Standards
PARCC K-2 Model Content Framework for Mathematics Grade 1
1.OA.6
1.OA.7
1.OA.8
1.NBT.5
Add within 20.
Understand the meaning of the equal sign.
Determine the unknown whole number in an addition equation relating 3 whole numbers.
Given a 2-digit number, mentally find 10 more, without having to count; explain the reasoning used.
Subtract within 20.
Fluently add within 10.
Determine if equations involving addition and subtraction are T/F.
Determine the unknown whole number in a subtraction equation relating 3 whole numbers.
Given a 2-digit number, mentally find 10 less, without having to count; explain the reasoning used.
Fluently subtract within 10.

36. PARCC K-2 Model Content Framework for Mathematics Grade 2
Fluency Expectations --Culminating Standards
PARCC K-2 Model Content Framework for Mathematics Grade 2
2.OA.2
2.NBT.5
2.NBT.2
2.NBT.3
Fluently add within 20 using mental strategies.
Fluently add within 100 using strategies based on place value…
Count within 1000.
Read numbers to 1000 using base-10, number names, expanded form.
Fluently subtract within 20 using mental strategies.
Fluently subtract within 100 using strategies based on place value…
Skip-count by 5s.
Write numbers to 1000 using base-10, number names, expanded form.
Skip-count by 10s.
Skip-count by 100s.
Know from memory all sums of two 1-digit numbers.

37. Assessment Resources Copied
Copies for Each Teacher:
Bridges:
Federal Way Public Schools Assessments & Problem Solving:
North Carolina:
2 Sets Available in Room:
Hawaii: core/mathematics/mathematics-assessments/
Silicon Valley Math Initiative
Education Northwest: mathematical-understanding/assessments

38. Additional Resources available online
Balanced Assessment:
Georgia: Performance-Tasks.aspx
AIMSweb Test of Early Numeracy (K-1): numeracy/additional-test-of-early-numeracy-resources
Exemplars (some free samples): materials/free-samples
Illustrative Mathematics:
Inside Mathematics (grade 2+ only):

39. Come to agreement on Draft Questions for Math Assessment
Completing Part 2
Come to agreement on Draft Questions for Math Assessment

40. Question Selection
Room Walk: Read every question option. Stay with one wall until signal is given to switch.
Grade Level Discussion: Is there a need of more than one question for any of the skills?
Voting: Place one sticky dot per skill, unless group agrees to more than one question for a skill.
Protocol Language: Based on the questions selected for the working draft, what protocol is needed for consistency in administration and scoring?

41. Draft Assessments & Assessment Protocol
Grade Level Sharing
Draft Assessments & Assessment Protocol

42. Where are we headed on Day 3
Where are we headed on Day 3? •Review draft assessments & protocol •Ongoing assessment •Discuss instructional implications & strategies for teaching toward mastery
Get feedback from those you represent on questions and protocol
Take the assessment yourself
Give to at least one student (average)
Afterschool connection

43. Math Focus Sessions Grades K-3
K/1 Math Focus Sessions: 3/9, 3/25, TBD
2/3 Math Focus Sessions: 2/25, 3/12, 4/22
This 3-day series will focus on the new content addressed within the Common Core State Standards. Teachers will take a close look at the California Math Framework for their grade level and consider new strategies for teaching the content. An emphasis will be placed on balancing conceptual development, problem solving and fluency. This series will be different than the series offered in the past. All sessions start at 3:30 pm and end at 5:30 pm.
The cost for this 3-day series is $120 per person and you can register at Professional Development Calendar.