K-2 Math Task Force

Plan for Day 21. Develop Working Draft of Concepts & Skills to Assess for

Spring 2015 Pilot a. Share feedback from those you represent

b. Tease out the concepts and skills to assess from some standards that have multiple skills/concepts

c. Discuss skills and concepts that could be assessed together

d. Determine if fewer skills and concepts could be assessed

2. Develop questions to assess the concepts and skillsa. Review Standards for Mathematical Practice

b. Reflect on SMP used in the 3rd grade SBAC Performance Task

c. Understand what is available on the market currently

d. 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

e. 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 Stepsa. Review things to do between today and Day 3 (March 16th)

b. Review plans for Day 3

All handouts

from today are posted

at: http://www.shastacoe.org/page.cfm?p=

6225

Part 1Develop 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 skills within a standard do we have agreement to assess?

Which standards have more than one concept or skill that could be assessed?

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 ClusterPages 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-5 Progressions

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 MathematicsKindergarten

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.

Fluency Expectation

s --Culminating Standards

PARCC K-2 Model Content Framework for MathematicsGrade 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.

Fluency Expectation

s --Culminating Standards

PARCC K-2 Model Content Framework for MathematicsGrade 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.

Fluency Expectation

s --Culminating Standards

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 2Develop 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

Kindergarten

Page 3 (Line 70) to

Page 5 (Line 88)

Grade 2

Page 3 (Line 73) to

Page 6 (Line 90)

Read the Standards for Mathematical Practice from the CA Mathematics Framework Grade Level Chapter (Day 1 tab section)

Grade 1

Page 3 (Line 72) to

Page 6 (Line 89)

Standards of Mathematical Practice (MP)

Watch video and consider what MP students were demonstrating

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.

2. How many total cups of lemonade did Jaleen sell in July?

Performance Task: What Standards for Math Practice would be used to successfully answer the question?

Performance Task: What Standards for Math Practice would be used to successfully complete the table?

Complete the table to show how many cups Jaleen sold each week in August.

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.

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

4.

SBAC Constructed ResponseGrade 3: What Standards for Math Practice would be used to successfully answer the question?

Readily Available AssessmentsAIMSweb DIBELS

MathNWEA Renaissan

ce Learning

Track My Progress

Cost

$4/student for math only; $6/student combined

Free in pilot year – undetermined for 2015-16

$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-1 + 2 2-minute whole class2nd: 12 minutes whole class (3 parts)

30 minutes “Assess hundreds of math skills in 32 domains”

30 questions per test

Tech

None None Computer adaptive

Via computer Audio narration, technology enhanced questions

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/makes-good-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 MathematicsKindergarten

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.

Fluency Expectation

s --Culminating Standards

PARCC K-2 Model Content Framework for MathematicsGrade 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.

Fluency Expectation

s --Culminating Standards

PARCC K-2 Model Content Framework for MathematicsGrade 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.

Fluency Expectation

s --Culminating Standards

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/common-core/mathematics/mathematics-assessments/

Silicon Valley Math Initiative

Education Northwest: http://educationnorthwest.org/resources/assessing-mathematical-understanding/assessments

Additional Resourcesavailable online

Balanced Assessment: http://balancedassessment.concord.org/packetprim.html

Georgia: https://www.georgiastandards.org/standards/Pages/NETS-S-Performance-Tasks.aspx

AIMSweb Test of Early Numeracy (K-1): http://www.aimsweb.com/assessments/features/assessments/test-of-early-numeracy/additional-test-of-early-numeracy-resources

Exemplars (some free samples): http://www.exemplars.com/education-materials/free-samples

Illustrative Mathematics: https://www.illustrativemathematics.org/standards/k8

Inside Mathematics (grade 2+ only): http://www.insidemathematics.org/performance-assessment-tasks

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

Question SelectionRoom 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 SessionsGrades K-3

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.

K/1 Math Focus Sessions: 3/9, 3/25, TBD

2/3 Math Focus Sessions: 2/25, 3/12, 4/22