North Carolina Department of Public Instruction

Curriculum and Instruction Division

“FOCUS” on CCSS-M

Spring 2012 RESAK-5 Mathematics

Introductions

04/21/23 • page 2

Microsoft

Agenda

• Assessment Overview• Professional Development• Three Mathematical Shifts: Focus

– Major Work of the Grade– Mile Wide and an Inch Deep

• Mathematical Task• Navigating through Navigations

Norms

• Listen as an Ally

• Value Differences

• Maintain Professionalism

• Participate Actively

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Parking Lot

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Technology Session Materials

Breaks

cc: Microsoft.comcc: Microsoft.com

cc: Microsoft.comcc: Microsoft.com

K-2ASSESSMENT

K-2 State Assessment Requirements

• State Statute(115C-174.11):• (a) Assessment Instruments for First and Second Grades. –

The State Board of Education shall adopt and provide to the local school administrative units developmentally appropriate individualized assessment instruments consistent with the Basic Education Program for the first and second grades, rather than standardized tests. Local school administrative units may use these assessment instruments provided to them by the State Board for first and second grade students, and shall not use standardized tests except as required as a condition of receiving federal grants.

K-2 State Assessment Requirements

• The State Board of Education requires that schools and school districts implement assessments at grades K, 1, and 2 that include documented, on-going individualized assessments throughout the year and a summative evaluation at the end of the year. These assessments monitor achievement of benchmarks in the North Carolina Standard Course of Study. They may take the form of the state-developed materials, adaptations of them, or unique assessments adopted by the local school board.

K-2 State Board RequirementsIntended purposes of these assessments:

• to provide information about the progress of each student for instructional planning and early interventions; document growth over time

• to inform parents about the status of their children relative to grade-level standards

• to provide next-year teachers with information about the status of each of their incoming students

• to provide the school and school district information about the achievement status and progress of groups of students in K, 1, and 2

K-2 Assessment

• 2012 K-2 Assessment Committee– Identify Assessment Critical Components.– Write K-2 Assessment Items.– Re-design the K-2 Observation Profile.– Create a “How To” resource for assessment

implementation.

• Completion & Distribution: June 15*

*Final date subject to change

K-2 Assessment• On-Going Assessment

– Bank of Items• 1-3 items per cluster/standard

– Mostly consists of Performance Tasks

• Summative Assessment– Focuses on the Critical Areas– Mostly consists of Performance Tasks– Is in similar format to current summative assessment– Distributed only to each LEA K-2 Math Administrator

3-5ASSESSMENT

Year Standards To Be TaughtStandards To Be

Assessed

2011 – 2012 2003 NCSCOS 2003 NCSCOS

2012 – 2013 CCSS CCSS (NC)

2013 – 2014 CCSS CCSS (NC)

2014 – 2015 CCSS CCSS (SBAC)

Common Core State Standards Adopted June, 2010

Technology and Testing

Content of the North Carolina assessments is aligned to the CCSS-M; however, the technology will not be as sophisticated as in assessments created by the Smarter Balanced Assessment Consortium (SBAC).

Let’s look at a familiar

problem…

Which of the following represents ?

a.

b.

c.

d.

Same problem- a new twist…

For numbers 1a – 1d, state whether or not each figure has of its whole shaded.

1a.

1b.

1c.

1d.

ο Yes ο No

ο Yes ο No

ο Yes ο No

ο Yes ο No

Turn and Talk• This item is worth 0 – 2

points (depending on the responses). – What series of Yes and

No responses would a student earn• 2 points?

• 1 point?

• 0 points?

For numbers 1a – 1d, state whether or not each figure has of its whole shaded.

1a.

1b.

1c.

1d.

ο Yes ο No

ο Yes ο No

ο Yes ο No

ο Yes ο No

2 points: YNYN 1 point: YNNN, YYNN, YYYN

0 point: YYYY, YNNY, NNNN, NNYY, NYYN, NYNN NYYY, NYNY, NNYN, NNNY, YYNY, YNYY

Or numbers 1a - 1d, state whether or not each figure has of its whole shaded.

Let’s Do Some Math!

Sample Open-Response Question

In the barnyard is an assortment of chickens and pigs. Counting heads I get 13; counting legs I get 46. How many pigs and chickens are there?

- Bill McCallum, 2012

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.

Standards for Mathematical Practices

http://www.k12.wa.us/smarter/

Shifting Gears….

How did you become an effective teacher?

PHI DELTA KAPPA International

Research Bulletin“If we spend more money on traditional form of professional development, such as workshops, conferences, presentations, and courses remotely related to the daily challenges of teaching, we can expect little return on our investments.” http://www.pdkintl.org/research/rbulletins/resbul27.htm

Key Points Professional development should

involve teachers in the identification of what they need to learn and, when possible, in the development of the learning opportunity and/or process.

Phi Delta Kappan, 2005

Professional development should be primarily school based and integral to the school operations.

Key Points

Phi Delta Kappan, 2005

Professional development should provide opportunities to engage in developing a theoretical understanding of the knowledge and skills to be learned.

Phi Delta Kappan, 2005

Key Points

“Despite virtually unanimous criticism of most traditional forms of professional development, these ineffective practices persist.”

Phi Delta Kappan, 2005

Horizon Research

• After a one year study on the traditional model of Professional Development, the study found…–Impact on teachers’ use of

instructional practices to elicit student thinking

“But NO Impact on….”

• Teacher content knowledge • Teachers’ use of representations in

instruction• Teachers’ focus on mathematics

reasoning in instruction• Student achievement

Garet et al., 2010

What Works?

Effective Teacher Development–Collaboration

» PLCs–Coaching

Steve Leinwand, 2012

Turn and Talk

• Take a moment to:– Reflect on the

information about effective teacher development.

– Share strategies for supporting teacher development.

39

Three Mathematical Shifts

FocusCoherence

Rigor

Coleman & Zimba (2012) www.achievethecore.org

PLC for Today

• Norm –Keep a focus on the students

• Goal–Know and articulate the major

work of your grade level or course.

A focus on “FOCUS”

• In your PLC:–Discuss the three topics

provided for each grade level.–Decide which of the three should

not receive intense focus at the indicated grade.

Table of Contents

Time to Reflect

04/21/23 • page 47

Major Work

48

In Your Grade Level Groups

• Identify clusters/standards as:– major work of the

grade level– supporting work of

the grade level– additional work of

the grade level

• Major Work of the Grade– Greater emphasis;

Intense focus:• The depth of the

ideas/learning• The time that they take

to master• Their importance to

future mathematics

First Grade Example

54

Let’s Get Started!• Identify

clusters/standards as:– major work of the

grade level– supporting work of

the grade level– additional work of

the grade level

• Please sit with the grade level groups of 3-5 people.

www.ncdpi.wikispaces.net

LUNCH

Let’s Get Started!• Identify

clusters/standards as:– major work of the

grade level– supporting work of

the grade level– additional work of

the grade level

• Please sit with the grade level of your choice.

www.ncdpi.wikispaces.net

Time to Reflect

Digging Deeper

Turn and Talk

• How are the handouts different from one another?

Mile Wide, Inch Deep?Make true equations. Write one number in every space. Draw a picture if it helps.

63

First Grade2003 NC Standard Course of Study

Common Core State Standards

Build understanding of place value (ones, tens).

Understand place value.2. Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: 10 can be thought of as a bundle of ten ones — called a “ten.” The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). 3. Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

Use place value understanding and properties of operations to add and subtract.4. Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. 5. Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. 6. Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Second Grade2003 NC Standard Course of Study

Common Core State Standards

Use a variety of models to build understanding of place value (ones, tens, hundreds)..

Understand place value.1. Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: 100 can be thought of as a bundle of ten tens — called a “hundred.” The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). 2. Count within 1000; skip-count by 5s, 10s, and 100s. 3. Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. 4. Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

Use place value understanding and properties of operations to add and subtract.5. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. 6. Add up to four two-digit numbers using strategies based on place value and properties of operations. 7. Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. 8. Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. 9. Explain why addition and subtraction strategies work, using place value and the properties of operations.1

Time to Reflect

What can be more fundamental in mathematics than numbers and operations, yet numbers and arithmetic are so familiar to most of us that we run the risk of underestimating the deep, rich knowledge and proficiency that these standards encompass?

Chapin & Johnson, 2006

Let’s Do Some Math!

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.

Standards for Mathematical Practices

Overarching habits of mind of a productive Mathematical Thinker

Spin to Win

72

• What strategies did you use to create the largest number?

• What strategies did you use to create the smallest number?

Record Your Thoughts

• What content standards & Mathematical Practices did this task address?

• How could this task be altered to meet the needs of different learners?

74

Let’s Do Some More!

1. Tell Me – Show Me/ Compare– Number Name, Place Value, & Expanded Form

2. Human Number Line3. Race for a Square4. Make a Square Disappear5. Close to 100!

Your Turn

• In your small group:– Read & explore your

task.– Discuss and write your

thoughts on the Record Your Thoughts handout

– Be prepared to teach the rest of your table your task.

76

Teach Your Table• At your table:

– Teach your task.• After all tasks have been

taught, discuss:– What content standards &

Mathematical Practices did this task address?

– How could this task be altered to meet the needs of different learners?

77

Tell Me, Show Me

& Be Sure to

CompareNumber Name, Place Value Name, and Expanded Form

79

80

Human Number Line

82

Race for a Square

Make a SquareDisappear

Close to 100!

Place Value• How would you define place value?• What is the distinguishing characteristic of the base-ten number system?• Why do you think we use a base-ten number system rather than different

base?

86

What Do Students Think?

• At your tables,• Review the student work example.• Answer the following questions together:

• What does this student understand about place value?

• What questions would you ask to gain a better understanding of student place value knowledge and/or to reflect on his/her thinking?

• What questions/task would you provide next?

• Be prepared to share your table’s thoughts with the whole group.

88

1

89

2

90

3

91

4

92

5

93

6

Turn and Talk

• Discuss at your table:– Why would it be

important for students to have a firm foundation of place value before introducing decimals?

• Before considering decimal numerals with students, it is advisable to review some ideas of whole number place value. One of the most basic of these ideas is the 10 to 1 relationship between the value of 2 adjacent positions.

95

Chapin & Johnson, 2006

Exploration Stations: Decimals

• Spin to Win/Compare• Tell Me – Show Me• Number Line• Make a Square & Race for a Square• Make a Square Disappear

Exploration Stations• With your partner, visit each of

the different stations. Explore each task.

• Record ideas, extensions and additional explanations you want to remember.

• Be prepared to share your thoughts & experiences at the end of the session.

http://www.online-stopwatch.com/eggtimer-countdown/

Exploration Stations: Reflection

99

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.

Standards for Mathematical Practices

101

102

103

104

Turn and Talk

• Discuss at your table:– What are your

thoughts about introducing decimals through place value?

106

Glasgow, et al. (2000). The Decimal Dilemma, NCTM.

107

Glasgow, et al. (2000). The Decimal Dilemma, NCTM.

108

Glasgow, et al. (2000). The Decimal Dilemma, NCTM.

Time to Reflect

CCSS for Reading Standards• Ask and answer questions to demonstrate

understanding of a text, referring explicitly to the text as the basis for the answers.

• Describe characters in a story (e.g., their traits, motivations, or feelings) and explain how their actions contribute to the sequence of events.

• Determine the meaning of words and phrases as they are used in a text, distinguishing literal from nonliteral language.

111

Finding Rich Tasks- It’s a Process

113

Navigate through Navigations• Decide on a grade band: K-2

or 3-5• Form groups of 3-4 people

within your grade band– Select a Navigations book– Choose 3-5 lessons– Use the template located on the

wiki to record the CCSS alignment:

114

www.ncdpi.wikispaces.net

Navigation Alignment

What are Features of a Good Task?

• It begins where the students are; accessible to wide range of learners.

• It is seen as something to make sense of.• It requires justifications and explanations for

answers and methods.• The focus is on making sense of the

mathematics involved and thereby increasing understanding.

Van de Walle, 2004

What are Features of a Good Task?

• It challenges the learners to think for themselves.

• It offers different levels of challenge.

• It encourages collaboration and discussion.

• It has the potential for revealing patterns or leading to generalizations.

• It invites children to make decisions.

nrich.maths.org

Altering the Lesson:Place Value in Whole Numbers & Decimals

• Changed the sequence of tasks• Omitted some tasks• Added an additional task• Extended some tasks• Used small group & stations rather than whole

group instruction• Altered the recording sheets

Alter Your Lesson• In your small group:

– Choose 1 lesson– Discuss how this lesson may

be altered• To align with the CCSS and

Mathematical Practices.• To meet the needs of different

learners.• To exhibit features of a “Good

Task”.

– Be Prepared to share your ideas with the whole group

119

Food for Thought

• NCTM’s Navigation Series

Until we meet again

• Performance metrics

Time to Reflect

www.ncdpi.wikispaces.net

04/21/23 123

DPI Contact Information

Kitty RutherfordElementary Mathematics Consultant919-807-3934kitty.rutherford@dpi.nc.gov

Amy ScrinziElementary Mathematics Consultant919-807-3839amy.scrinzi@dpi.nc.gov

Robin BarbourMiddle Grades Mathematics Consultant919-807-3841robin.barbour@dpi.nc.gov

Johannah MaynorSecondary Mathematics Consultant919-807-3842johannah.maynor@dpi.nc.gov

Barbara BissellK – 12 Mathematics Section Chief919-807-3838barbara.bissell@dpi.nc.gov

Susan HartProgram Assistant919-807-3846susan.hart@dpi.nc.gov