Practice StandardsTools and Strategies for Grades 3 – 5

Michelle Kilcrease & Tami Bird, Jordan School District

Purpose Share strategies and tools for

mathematics supervisors to help their teachers understand and implement the 8 Standards for Mathematical Practices

Background Utah State Office of Education

recommended CCSS - Math implementation for 6th & 9th Grades in 2011-2012.

As Math Teacher Specialists, we delved into the core to anticipate what PD our teachers would need.

JSD Multi-Tiered PLC Support System

Essential PLC Questions1. What do we want our teachers to know

and be able to do?2. How will we know if they know it and/or

can do it?3. What will we do if they don’t know it

and/or can’t do it?4. What will we do if they do know it

and/or can do it?

What do we want our teachers to know and be able to do? Understand the philosophical and

pedagogical changes of the core. Understand the mathematics of the

Content Standards. Understand and implement the Practice

Standards in mathematics instruction. Access provided resources.

What do we want our teachers to know and be able to do? Understand the philosophical and

pedagogical changes of the core. Understand the mathematics of the

Content Standards. Understand and implement the

Practice Standards in mathematics instruction.

Access resources we had provided.

Differentiation strategies for unpacking and understanding the Practice Standards Working with math leaders (state,

district office, coaches) Working with teachers Working with administrators (district &

building level) Working with community

Strategies: Math Leaders USOE Compare/Contrast: Standards for

Mathematical Practice with NCTM and Utah’s current core ILO’s

USOE Activity #2Bring copies of NCTM’s Principles and Standards for School Mathematics and the Utah 2007 Core. Discuss the following:

Which NCTM Process Standard(s) suggests the same processes and proficiencies as the Common Core Standards for Mathematical Practices?

Activity #3

Drag picture to placeholder or click icon to add

Strategies: Coaches What does it look like? What does it sound like? How can we convey these ideas to

students & teachers?

Connecting to Prior KnowledgeLiteracy

Predict Summarize Main Idea Details Structure Inference ETC….

Math

What would a math poster look like?

SMP #2 Construct viable arguments and critique the reasoning of others.

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize – to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents – and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and such.

SMP #2 Construct viable arguments and critique the reasoning of others.

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize – to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents – and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and such.

Strategies: Teacher LeadersThe next group of people with whom we worked were our teacher writing teams. Each team consisted of 3 – 5 classroom teachers with varying levels of pedagogical content knowledge and with varying levels of mathematics content knowledge.

Changing our view of how to access the practice standards with teachers.

Initial “unpacking” of the Content Standards is a prerequisite for understanding the Practices Standards.

Understanding MathematicsCONCEPTUAL UNDERSTANDING:

What a student needs to KNOW

PROCEDURAL UNDERSTANDING:What a student needs to be able to DO

REPRESENTATIONAL UNDERSTANDING:How a student SHOWS what he/she knows or can do.

Applying CPR to the Common Core

Work in teams to examine the 3rd grade core.

• Highlight and color code phrases in the standards as emphasizing conceptual (KNOW), procedural (DO), or representational (SHOW) understanding.

• Underline the verbs – it will often help you determine what type of understanding is expected.

PLC Activity

Applying CPR to the Common Core – 3.NF 3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

a. Understand two fractions as equivalent (equal) if they are thesame size, or the same point on a number line.

a. Understand two fractions as equivalent (equal) if they are thesame size, or the same point on a number line.

CONCEPTUAL PROCEDURAL REPRESENTATIONAL

Applying CPR to the Common Core – 3.NF

3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

b. Recognize and generate simple equivalent fractions, e.g., 1/2 =2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., byusing a visual fraction model.

b. Recognize and generate simple equivalent fractions, e.g., 1/2 =2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., byusing a visual fraction model.

CONCEPTUAL PROCEDURAL REPRESENTATIONAL

Applying CPR to the Common Core – 3.NF

3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

c. Express whole numbers as fractions, and recognize fractions thatare equivalent to whole numbers. Examples: Express 3 in the form3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same pointof a number line diagram.c. Express whole numbers as fractions, and recognize fractions thatare equivalent to whole numbers. Examples: Express 3 in the form3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same pointof a number line diagram.CONCEPTUAL PROCEDURAL REPRESENTATIONAL

Applying CPR to the Common Core – 3.NF

3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.d. Compare two fractions with the same numerator or the samedenominator by reasoning about their size. Recognize thatcomparisons are valid only when the two fractions refer to thesame whole. Record the results of comparisons with the symbols>, =, or <, and justify the conclusions, e.g., by using a visualfraction model.

d. Compare two fractions with the same numerator or the samedenominator by reasoning about their size. Recognize thatcomparisons are valid only when the two fractions refer to thesame whole. Record the results of comparisons with the symbols>, =, or <, and justify the conclusions, e.g., by using a visualfraction model.

CONCEPTUAL PROCEDURAL REPRESENTATIONAL

A CPR view of a core cluster3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Guiding Question leading to practice standards discussion:What are the implications for teaching and learning based on the CPR review?

• Students and teachers will need a different type of learning experience than they’ve had in the past.

• Content Support • Practices Support

Building practice standard understanding from CPR

K-5 Writing Teacher Teams

• Used CPR activity

• Used 6th grade practice posters to generate discussion for K-5 posters

• Collaboration resulted in K-1st, 2-3rd, 4-5th, and revised 6th grade posters

Upcoming work with K-5 teachers1 - CPR Activity with content standard(s)

2 - Review a practice standard and corresponding posters. Discuss….

• Correlations between the posters and the actual standards

• Evidence of concepts, procedures, and representations • Implementation ideas – classroom use

Other tools in progress to help our audiences find entry points for engaging in the Standards for Mathematical Practices… Conceptual Foundations (teachers) Principal Observation Guides (can be used

by teachers during lesson study, too!) Parent Guides (community, Board

members)

In the end… Strategies for helping other math

leaders and elementary teachers and principals understand the Standards for Mathematical Practices

Contact Informationhttp://www.jordandistrict.org

** access through the curriculum department, elementary mathematics

tami.bird@jordandistrict.orgmichelle.kilcrease@jordandistrict.org