K-2 Math Task Force
Plan for Day 2
1.
Develop Working Draft of Concepts & Skills to Assess for Spring 2015
Pilot
a.
b.
c.
d.
2.
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
a.
b.
c.
d.
e.
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
3.
Grade levels to share out draft assessment to see the progression
over K-2, including draft assessment protocol
4.
Next Steps
a.
b.
Review things to do between today and Day 3 (March 16th)
Review plans for Day 3
All handouts
from today
are posted
at:
http://www.
shastacoe.o
rg/page.cf
m?p=6225
Part 1
Develop Working Draft of Concepts
& Skills to Assess for Spring 2015 Pilot
Part A: Sharing feedback from
those you represent
Suggested additions
(“Additional” clusters?, etc.)
Suggested deletions
Support for skills/concepts
“as is”
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?
What skills and concepts could
be combined to assess
together?
Begin to consider –
come back to this
question later in
the morning
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
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
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…”
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-
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”
Could we further
narrow our
assessment focus?
PARCC K-2 Model Content
Framework for Mathematics
Kindergarten
K.CC.1
K.CC.3
Fluency
Expectations
-Culminating
Standards
K.CC.5
K.CC.7
K.OA.5
Compare 2
numbers
between 110 presented
as written
numerals.
Fluently add
within 5.
Count to 100
by tens.
Write
numbers
from 0-20.
County to
answer “how
many?”
questions
about as
many as 20
things…
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.
PARCC K-2 Model Content
Framework for Mathematics
Grade 1
1.OA.6
Add within 20.
1.OA.7
1.OA.8
1.NBT.5
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.
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.
Subtract within
20.
Fluently add
within 10.
Fluently subtract
within 10.
Fluency
Expectations
-Culminating
Standards
PARCC K-2 Model Content
Framework for Mathematics
Grade 2
2.OA.2
2.NBT.5
2.NBT.2
Fluency
Expectations
-Culminating
Standards
2.NBT.3
Fluently add
Fluently add
within 20 using
within 100 using
mental strategies. strategies based
on place value…
Count within
1000.
Read numbers to
1000 using base10, number
names,
expanded form.
Fluently subtract
Fluently subtract
within 20 using
within 100 using
mental strategies. strategies based
on place value…
Skip-count by 5s.
Write numbers to
1000 using base10, number
names,
expanded form.
Skip-count by
10s.
Skip-count by
100s.
Know from
memory all sums
of two 1-digit
numbers.
Could we further
narrow our
assessment focus?
Part 1: Final Step
By grade level, come to
agreement on the concepts
and skills we will assess in the
Spring 2015 pilot
Part 2
Develop questions to assess
the concepts & skills
K-12 Standards for
Mathematical Practice (MP)
Represent
the “ways of
doing”
mathematic
s
K-12 Standards for
Mathematical Practice (MP)
Standards for Mathematical
Practice: Video Introduction
LINK: http://mathsolutions.com/common-core-support/
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
Grade 2
Page 3 (Line 72) to
Page 3 (Line 73) to
Page 6 (Line 89)
Page 6 (Line 90)
Standards of Mathematical
Practice (MP)
Reason abst ract ly and quant it at ively .
I can use numbers and words to
help me make sense of problems.
Mathematical Practice 2
!
!
Numbers t o Words
Words t o Numbers
2 + 3 =5
I have 2 yellow flowers and 3 red flowers.
How many flowers altogether?
I have 2 yellow flowers and 3 red flowers.
How many flowers altogether?
2 + 3 =5
22
Clip art licensed from the Clip Art Gallery on DiscoverySchool.com
March 30, 2012
Jordan School District 2012, Grades K-1
M ake sense of problems and persevere in
solving t hem.
When given a problem, I can make
a plan, carry out my plan, and
check my answer.
M at hemat ical Pract ice 1
!!!
!
!
BEFORE...
Think about the
problem.
Ask myself, "Which
strategy will I use?"
Make a plan to
solvethe
problem.
DURING...
Stick to it!
AFTER...
CHECK my work.
Ask myself, "Does
thismakesense?"
Change my plan if it
isn't workingout.
Ask myself,
"Is there another
way to solve
theproblem?"
!!!!!!!!!!!
Clip art licensed from the Clip Art Gallery on DiscoverySchool.com
Watch video and
consider what MP
students were
demonstrating
Jordan School District 2012, Grades 2-3!
LINK:
https://www.teachingchannel.org/
videos/counting-by-ten-lesson
K-12 Standards for
Mathematical Practice (MP)
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.
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?
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.
Performance Task: What Standards for
Math Practice would be used to
successfully complete the problem?
4.
SBAC Constructed Response
Grade 3: What Standards for
Math Practice would be used to
successfully answer the question?
Length/Standards
Cost
Readily Available Assessments
AIMSweb
DIBELS
Math
NWEA
$4/student for math only;
$6/student combined
Free in pilot
year –
undetermined
for 2015-16
$13.50/stude
nt
$1,599
subscription
software per
school +
$2.25/student
$1,500/campu
s for 250 or less
students;
$2,500/campu
s for 500 or less
students
Test of Early Numeracy: 4
1-minute 1 to 1 tests
K: 3 oneminute tests (1to-1)
1st: 6 minutes 1to-1 + 2 2minute whole
class
2nd: 12 minutes
whole class (3
parts)
30 minutes
“Assess
hundreds of
math skills in 32
domains”
30 questions
per test
None
Computer
adaptive
Via computer
Audio
narration,
technology
enhanced
questions
Concepts & Applications
(2nd): 8 minutes +
Computation
Tech
None
Renaissance
Learning
Track My
Progress
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
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.”
LINK:
http://hechingerreport.org/content/makesgood-common-core-math-question_17841/
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
Post these on the
4 walls by
standard #,
grouped by
assessed skill
PARCC K-2 Model Content
Framework for Mathematics
Kindergarten
K.CC.1
K.CC.3
Fluency
Expectations
-Culminating
Standards
K.CC.5
K.CC.7
K.OA.5
Compare 2
numbers
between 110 presented
as written
numerals.
Fluently add
within 5.
Count to 100
by tens.
Write
numbers
from 0-20.
County to
answer “how
many?”
questions
about as
many as 20
things…
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.
PARCC K-2 Model Content
Framework for Mathematics
Grade 1
1.OA.6
Add within 20.
1.OA.7
1.OA.8
1.NBT.5
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.
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.
Subtract within
20.
Fluently add
within 10.
Fluently subtract
within 10.
Fluency
Expectations
-Culminating
Standards
PARCC K-2 Model Content
Framework for Mathematics
Grade 2
2.OA.2
2.NBT.5
2.NBT.2
Fluency
Expectations
-Culminating
Standards
2.NBT.3
Fluently add
Fluently add
within 20 using
within 100 using
mental strategies. strategies based
on place value…
Count within
1000.
Read numbers to
1000 using base10, number
names,
expanded form.
Fluently subtract
Fluently subtract
within 20 using
within 100 using
mental strategies. strategies based
on place value…
Skip-count by 5s.
Write numbers to
1000 using base10, number
names,
expanded form.
Skip-count by
10s.
Skip-count by
100s.
Know from
memory all sums
of two 1-digit
numbers.
Assessment Resources
Copied
Copies for Each Teacher:
 Bridges: http://bridges1.mathlearningcenter.org/resources/materials/ccss
 Federal Way Public Schools Assessments & Problem Solving:
http://www.fwps.org/tfl/math-ccss/
 North Carolina: http://maccss.ncdpi.wikispaces.net/Elementary
2 Sets Available in Room:
 Hawaii: http://standardstoolkit.k12.hi.us/commoncore/mathematics/mathematics-assessments/
 Silicon Valley Math Initiative
 Education Northwest: http://educationnorthwest.org/resources/assessingmathematical-understanding/assessments
Additional Resources
available online
 Balanced Assessment: http://balancedassessment.concord.org/packetprim.html
 Georgia: https://www.georgiastandards.org/standards/Pages/NETS-SPerformance-Tasks.aspx
 AIMSweb Test of Early Numeracy (K-1):
http://www.aimsweb.com/assessments/features/assessments/test-of-earlynumeracy/additional-test-of-early-numeracy-resources
 Exemplars (some free samples): http://www.exemplars.com/educationmaterials/free-samples
 Illustrative Mathematics: https://www.illustrativemathematics.org/standards/k8
 Inside Mathematics (grade 2+ only):
http://www.insidemathematics.org/performance-assessment-tasks
Completing Part 2
Come to agreement on Draft
Questions for Math
Assessment
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?
Grade Level Sharing
Draft Assessments &
Assessment Protocol
Where are we headed
on Day 3?
•Review draft assessments & protocol
•Ongoing assessment
•Discuss instructional implications &
strategies for teaching toward mastery
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 www.shastacoe.org Professional Development
Calendar.