COMMON CORE STATE STANDARDS

MATHEMATICAL PRACTICE #6

ATTEND TO PRECISION

Mathematically proficient students try to communicate precisely

to others. They try to use clear definitions in discussion with

others and in their own reasoning. They state the meaning of the

symbols they choose, including using the equal sign consistently

and appropriately. They are careful about specifying units of

measure, and labeling axes to clarify the correspondence with

quantities in a problem.

They calculate accurately and efficiently, express numerical

answers with a degree of precision appropriate for the problem

context. In the elementary grades, students give carefully

formulated explanations to each other. By the time they reach

high school they have learned to examine claims and make

explicit use of definitions.

KEY DATES FOR COMMON CORE TEST

IMPLEMENTATION

DATE ACTIVITY

SPRING

2014

PA STANDARDS AND

PA CORE ALIGNED

PSSA TESTS

GRADES 3 – 8

SPRING

2015

PA CORE ALIGNED

PSSA TESTS

GRADES 3 – 8

VOLUME 1 ISSUE 6

401 N. Whitehall Road

Norristown, PA 19403

610.630.5000 office

www.nasd.k12.pa.us

NORRISTOWN AREA SCHOOL DISTRICT CURRICULUM & INSTRUCTION

JANUARY/FEBRUARY 2014

8 M A T H E M A T I C A L

P R A C T I C E S

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

-Common Core State Standards

WHAT DOES THE TASK LOOK LIKE?

WHAT DOES THE TEACHER DO?

Task

Has precise directions.

Includes assessment criteria for communication of

ideas.

Teacher

Models precision in communication and in

mathematical solutions.

Identifies incomplete responses and asks students

to revise their response.

Encourages students to identify when others are

not addressing the question completely.

ONE HALLMARK OF MATHEMATICAL UNDERSTANDING IS THE ABILITY TO JUSTIFY, IN A WAY

APPROPRIATE TO THE STUDENT’S MATHEMATICAL MATURITY, WHY A PARTICULAR

MATHEMATICAL STATEMENT IS TRUE OR WHERE A MATHEMATICAL RULE COMES FROM. –COMMON CORE STATE STANDARDS

“Somewhere, something incredible is waiting to be known.”

-Carl Sagan

WHAT ARE STUDENTS DOING?

Use and clarify mathematical definitions

in discussions and in their own reasoning

(orally and in writing).

Use, understand and state the meanings

of symbols.

Express numerical answers with a degree

of precision.

VOLUME 1 ISSUE 6

JANUARY/FEBRUARY 2014

Modified from: Institute for Advanced Study/Park City Mathematics Institute

-Hancock (2012)

MATHEMATICAL PRACTICE #6

- Jordan School District (2011)

WHAT ARE TEACHERS DOING?

Facilitates, encourages and expects

precision in communication.

Provides opportunities for students to

explain and/or write their reasoning to

others.

WHAT DOES IT REALLY MEAN?

The title is potentially misleading. While this standard does include “calculate

accurately and efficiently,” its primary focus is precision of communication, in

speech, in written symbols, and in specifying the nature and units of quantities in

numerical answers and in graphs and diagrams.

The mention of definitions can also be misleading. Elementary school children

(and, to a lesser extent, even adults) almost never learn new words effectively from

definitions. Virtually all of their vocabulary is acquired from use in context.

Children build their own “working definitions” based on their initial experiences.

Over time, as they hear and use these words in other contexts, they refine their

working definitions and make them more precise. For example, the toddler’s first

use of “doggie” may refer to all furry things, and only later be applied to a

narrower category. In mathematics, too, children can work with ideas without

having started with a precise definition. With experience, the concepts will become

more precise, and the vocabulary with which we name the concepts will,

accordingly, carry more precise meanings. Formal definitions generally come last.

Communication is hard; precise and clear communication takes years to develop

and often eludes even highly educated adults. With elementary school children, it

is generally less reasonable to expect them to “state the meaning of the symbols

they choose” in any formal way than to expect them to demonstrate their

understanding of appropriate terms through unambiguous and correct use. If the

teacher and curriculum serve as the “native speakers” of clear mathematics, young

students, who are the best language learners around, can learn the language from

them.

OPEN ENDED QUESTIONS

How might you explain the

problem in another way?

What math words have you

learned that might help explain

your thinking?

How would you describe the

problem in your own words?

What words from your

vocabulary journal, anchor

chart, or word wall might be

helpful to help you describe

your thinking?

-Math Made Fun (2013)

Precision Using

Non-Standard Units

https://www.teachingchannel.org/vid

eos/measurement-lesson-ideas

“Somewhere, something incredible is waiting to be known.”

-Carl Sagan

QUESTIONS TO

ASK STUDENTS

How can you use

math vocabulary in

your explanation?

How do you know

those answers are

equivalent?

What does that

mean?

VIDEO EXAMPLE

VOLUME 1 ISSUE 6

JANUARY/FEBRUARY 2014

-GO Math! Houghton

Mifflin Harcourt (2012)

MATHEMATICAL PRACTICE #6

-www.curriculuminstitute.org (2012)

-Understanding the Mathematical Practices (2012)

ONE HALLMARK OF MATHEMATICAL UNDERSTANDING IS THE ABILITY TO JUSTIFY, IN A WAY

APPROPRIATE TO THE STUDENT’S MATHEMATICAL MATURITY, WHY A PARTICULAR

MATHEMATICAL STATEMENT IS TRUE OR WHERE A MATHEMATICAL RULE COMES FROM. –COMMON CORE STATE STANDARDS

VOLUME 1 ISSUE 6

JANUARY/FEBRUARY 2014

“Somewhere, something incredible is waiting to be known.”

-Carl Sagan

Write captions for the selected photos.

WHAT ARE STUDENTS DOING?

WHAT IS THE TEACHER DOING?

Students

Use clear definitions and mathematical vocabulary to

communicate reasoning.

Specify labels, units, and answers within the context of the

problem.

Understand and explain the meaning of mathematical

symbols.

Teachers

Modeling and expecting the daily use of mathematical

language and vocabulary.

Modeling specific labels, units, and answers within the

context of the problem.

Providing opportunities for students to explore the

mathematical symbols and their meaning.

-Tompkins Seneca Tioga BOCES (2012)

WHAT DO PROFICIENT

STUDENTS DO?

Attend to Precision

Initial

Communicate their

reasoning and

solution to others.

Intermediate

Incorporate

appropriate symbols

and vocabulary.

Advanced

Use appropriate

symbols, vocabulary,

and labeling to

effectively

communicate and

exchange ideas.

-Hull, Balka, and Harbin Miles (2011)

mathleadership.com

MATHEMATICAL PRACTICE #6

-Lewis, Morgan, Wallen, and Younger (2012)

ONE HALLMARK OF MATHEMATICAL UNDERSTANDING IS THE ABILITY TO JUSTIFY, IN A WAY

APPROPRIATE TO THE STUDENT’S MATHEMATICAL MATURITY, WHY A PARTICULAR

MATHEMATICAL STATEMENT IS TRUE OR WHERE A MATHEMATICAL RULE COMES FROM. –COMMON CORE STATE STANDARDS

VOLUME 1 ISSUE 6

JANUARY/FEBRUARY 2014

“Somewhere, something incredible is waiting to be known.”

-Carl Sagan

Write captions for the selected photos.

References

Curriculum Institute (2013). Standards for Mathematical Practice Posters. Available at

http://www.curriculuminstitute.org/indiana/materials/Standards%20of%20Mathematica

l%20Practice%20Student%20Posters.pdf

GO Math! Houghton Mifflin Harcourt (2012). Supporting Mathematical Practices

Through Questioning. Orlando, FL: Houghton Mifflin Harcourt.

Hancock, Melissa (2011). Practice Standards Walk-Through Document. Available at:

http://katm.org/wp/common-core/

Hull, Balka, and Harbin Miles (2011). Standards of Student Practice in Mathematics

Proficiency Matrix. Available at http://mathleadership.com/ccss.html

Institute for Advanced Study/Park City Mathematics Institute (2011). Rubric-

Implementing Standards for Mathematical Practice. Available at

http://ime.math.arizona.edu/2011-

12/FebProducts/Mathematical%20Practices%20Rubric.pdf

Jordan School District (2011). Mathematical Practices by Standard Posters. Available

at http://elemmath.jordandistrict.org/mathematical-practices-by-standard/

Lewis, S.; Morgan, T.; Wallen, K.; and Younger, J. (2012). Focusing on the

Mathematical Practices of the Common Core Grades K – 8. Available at

http://www.sevier.org/CommonCore/FocusingMathPracticices_CCSS.pdf

Math Made Fun (2013). Classroom Sneak Peak Mathematical Practice #6. Available at

http://michellef.essdack.org/?q=node/165

Precision Using Non-Standarad Units (2014). Available at

https://www.teachingchannel.org/videos/measurement-lesson-ideas

Tompkins Seneca Tioga BOCES (2012). Mathematical Practices and Indicators.

Available at http://tst-math.wikispaces.com/Mathematical+Practices

Understanding the Mathematical Practices (2012). Practice Standard 6: Attend to

Precision. Available at

http://www.cesu.k12.vt.us/modules/groups/homepagefiles/cms/1556877/File/practice%

206.pdf

MATHEMATICAL PRACTICE #6

Norristown Area

School District

401 N. Whitehall Road

Norristown PA 19403

Administration Office:

610.630.5000

www.nasd.k12.pa.us

Are you integrating

the Mathematical

Practices in your

lessons?

Please Share!

Send an email to:

sgardiner@nasd.k12.pa.us

ONE HALLMARK OF MATHEMATICAL UNDERSTANDING IS THE ABILITY TO JUSTIFY, IN A WAY

APPROPRIATE TO THE STUDENT’S MATHEMATICAL MATURITY, WHY A PARTICULAR

MATHEMATICAL STATEMENT IS TRUE OR WHERE A MATHEMATICAL RULE COMES FROM. –COMMON CORE STATE STANDARDS