ngss crosscutting concepts: scale, proportion, and quantity · 3/19/2013 · the performance...

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March 19, 20136:30 p.m. – 8:00 p.m. Eastern time

NGSS Crosscutting Concepts: Scale, Proportion, and Quantity

Presented by: Amy Taylor and Kelly Riedinger

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Introducing today’s presenters…

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Amy TaylorUniversity of North Carolina Wilmington

Ted WillardNational Science Teachers Association

Kelly RiedingerUniversity of North Carolina Wilmington

Developing the Standards

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Instruction

Curricula

Assessments

Teacher Development


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2011-2013

July 2011


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July 2011

A Framework for K-12 Science Education

Three-Dimensions:

Scientific and Engineering Practices

Crosscutting Concepts

Disciplinary Core Ideas

View free PDF form The National Academies Press at www.nap.edu

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1. Asking questions (for science) and defining problems (for engineering)

2. Developing and using models

3. Planning and carrying out investigations

4. Analyzing and interpreting data

5. Using mathematics and computational thinking

6. Constructing explanations (for science) and designing solutions (for engineering)

7. Engaging in argument from evidence

8. Obtaining, evaluating, and communicating information

Scientific and Engineering Practices

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Crosscutting Concepts1. Patterns

2. Cause and effect: Mechanism and explanation

3. Scale, proportion, and quantity

4. Systems and system models

5. Energy and matter: Flows, cycles, and conservation

6. Structure and function

7. Stability and change

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Life Science Physical ScienceLS1: From Molecules to Organisms:

Structures and Processes

LS2: Ecosystems: Interactions, Energy, and Dynamics

LS3: Heredity: Inheritance and Variation of Traits

LS4: Biological Evolution: Unity and Diversity

PS1: Matter and Its Interactions

PS2: Motion and Stability: Forces and Interactions

PS3: Energy

PS4: Waves and Their Applications in Technologies for Information Transfer

Earth & Space Science Engineering & TechnologyESS1: Earth’s Place in the Universe

ESS2: Earth’s Systems

ESS3: Earth and Human Activity

ETS1: Engineering Design

ETS2: Links Among Engineering, Technology, Science, and Society

Disciplinary Core Ideas

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Life Science Earth & Space Science Physical ScienceEngineering &

TechnologyLS1: From Molecules to Organisms:

Structures and ProcessesLS1.A: Structure and FunctionLS1.B: Growth and Development of

OrganismsLS1.C: Organization for Matter and

Energy Flow in OrganismsLS1.D: Information Processing

LS2: Ecosystems: Interactions, Energy, and Dynamics

LS2.A: Interdependent Relationships in Ecosystems

LS2.B: Cycles of Matter and Energy Transfer in Ecosystems

LS2.C: Ecosystem Dynamics, Functioning, and Resilience

LS2.D: Social Interactions and Group Behavior

LS3: Heredity: Inheritance and Variation of Traits

LS3.A: Inheritance of TraitsLS3.B: Variation of Traits

LS4: Biological Evolution: Unity and Diversity

LS4.A: Evidence of Common Ancestry and Diversity

LS4.B: Natural SelectionLS4.C: AdaptationLS4.D: Biodiversity and Humans

ESS1: Earth’s Place in the UniverseESS1.A: The Universe and Its StarsESS1.B: Earth and the Solar SystemESS1.C: The History of Planet Earth

ESS2: Earth’s SystemsESS2.A: Earth Materials and SystemsESS2.B: Plate Tectonics and Large‐Scale

System InteractionsESS2.C: The Roles of Water in Earth’s

Surface ProcessesESS2.D: Weather and ClimateESS2.E: Biogeology

ESS3: Earth and Human ActivityESS3.A: Natural ResourcesESS3.B: Natural HazardsESS3.C: Human Impacts on Earth

SystemsESS3.D: Global Climate Change

PS1: Matter and Its InteractionsPS1.A:Structure and Properties of

MatterPS1.B: Chemical ReactionsPS1.C: Nuclear Processes

PS2: Motion and Stability: Forces and Interactions

PS2.A:Forces and MotionPS2.B: Types of InteractionsPS2.C: Stability and Instability in

Physical Systems

PS3: EnergyPS3.A:Definitions of EnergyPS3.B: Conservation of Energy and

Energy TransferPS3.C: Relationship Between Energy

and ForcesPS3.D:Energy in Chemical Processes

and Everyday Life

PS4: Waves and Their Applications in Technologies for Information Transfer

PS4.A:Wave PropertiesPS4.B: Electromagnetic RadiationPS4.C: Information Technologies

and Instrumentation

ETS1: Engineering DesignETS1.A: Defining and Delimiting an

Engineering ProblemETS1.B: Developing Possible SolutionsETS1.C: Optimizing the Design Solution

ETS2: Links Among Engineering, Technology, Science, and Society

ETS2.A: Interdependence of Science, Engineering, and Technology

ETS2.B: Influence of Engineering, Technology, and Science on Society and the Natural World

Note: In NGSS, the core ideas for Engineering, Technology, and the Application of Science are integrated with the Life Science, Earth & Space Science, and Physical Science core ideas

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Instruction

Curricula

Assessments

Teacher Development


2011-2013

July 2011

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2011-2013

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Closer Look at a Performance ExpectationMS-PS1 Matter and Its Interactions Students who demonstrate understanding can: MS-PS1-d. Develop molecular models of reactants and products to support the explanation that atoms,

and therefore mass, are conserved in a chemical reaction. [Clarification Statement: Models can include physical models and drawings that represent atoms rather than symbols. The focus is on law of conservation of matter.] [Assessment Boundary: The use of atomic masses is not required. Balancing symbolic equations (e.g. N2 + H2 -> NH3) is not required.]

The performance expectations above were developed using the following elements from the NRC document A Framework for K-12 Science Education:Science and Engineering Practices Disciplinary Core Ideas Crosscutting Concepts

Developing and Using Models Modeling in 6–8 builds on K–5 and progresses to developing, using and revising models to support explanations, describe, test, and predict more abstract phenomena and design systems. • Use and/or develop models to predict, describe,

support explanation, and/or collect data to test ideas about phenomena in natural or designed systems, including those representing inputs and outputs, and those at unobservable scales. (MS-PS1-a), (MS-PS1-c), (MS-PS1-d)

---------------------------------------------Connections to Nature of Science

Science Models, Laws, Mechanisms, and Theories Explain Natural Phenomena • Laws are regularities or mathematical descriptions

of natural phenomena. (MS-PS1-d)

PS1.B: Chemical Reactions • Substances react chemically in

characteristic ways. In a chemical process, the atoms that make up the original substances are regrouped into different molecules, and these new substances have different properties from those of the reactants. (MS-PS1-d), ( MS-PS1-e), (MS-PS1-f)

• The total number of each type of atom is conserved, and thus the mass does not change. (MS-PS1-d)

Energy and Matter • Matter is conserved because

atoms are conserved in physical and chemical processes. (MS-PS1-d)

Note: Performance expectations combine practices, core ideas, and crosscutting concepts into a single statement of what is to be assessed. They are not instructional strategies or objectives for a lesson.

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Scale, Proportion, and Quantity:A Crosscutting Concept

Amy Taylor Kelly Riedinger

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Who are we?Amy Taylor• Associate Professor of science education in the Elementary, Middle Level, Literacy

Department at University of North Carolina Wilmington • Prior work includes high school teaching in biology and environmental science,

graduate research with teachers’ and students’ understanding of scale and nanotechnology

• Current work (past 5 years) supporting teachers and students in scientific practices

Kelly Riedinger• Assistant Professor of science education in the Elementary, Middle Level, Literacy

Department at University of North Carolina Wilmington• Prior work includes middle and high school teaching oceanography, physical

science, and earth science as well as teaching in informal science settings (PreK‐8)• Current work (past 2 years) includes learning in informal science education

settings and preservice teacher preparation

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We are not authors of the framework so we have no special insight into the decisions made by the committee.

We can use our expertise having worked with teachers and students to help you think about types of scale and how you can engage your students in scaling, proportions, and quantity.

Caveats

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Why we find scale interesting• Experiences as a former high school science teacher• New emerging technologies have enabled scientists to

observe the extreme scales from the atomic and cosmic sciences

• Scale is common in both science and everyday life and impacts all disciplines of science

• When we asked scientists to indicate how important scale was to their work, responses included: – ‘‘I can’t operate without a sense of scale.’’ – ‘‘Scale is an integral part of what I do.’’ – Scale is ‘‘extremely important.’’ – ‘‘I think it would be impossible for me to practice without the

concept of scale.’’

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Overview

• What is scale? • Scale, Proportion, and Quantity as a crosscutting concept

• Why scale is important?• Approaches to teaching?

– Vignettes to illustrate and highlight essential features

• Resources• Discussion

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POLL: What do you first think of when you hear the word scale?

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POLL: How comfortable are you with the topic of scale and teaching this concept to K‐12 students?

NoviceI have no understanding

of this concept.

Limited I need to learn more

about scale before I can teach this topic to

students.

Adequate I have some

understanding of scale and I’m ready to try teaching the concept,

but I’d like more information and ideas for learning activities.

ExpertI have an in‐depth

understanding of scale and I’m ready to

implement learning activities with students.

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Scale, Proportion, and Quantity

The word scale has multiple definitions:– Scale can be a device to weigh objects – Can cover a fish or a butterfly– We scale a wall by climbing – Refer to measurement scales such as pH, temperature, or Richter

– In science, when we talk about scale we are referring to the properties of an object that can change as size is increased or decreased, and behavior that changes as a result.

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Scale, Proportion, and Quantity

• Scale is described in terms of range & magnitude.• Three commonly used types of scales in science:

Ordinal Interval Logarithmic Enhanced Fujita Scale Kelvin Richter Saffir‐Simpson scale Celsius pH

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Other Types of ScalesMass Geologic TimeBrightness Decibel scalesNano Light yearsCurrent VoltageParsecs MercaliArchitectural Map scalesMicroscopic Temperature

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Crosscutting Concepts In NGSS

Crosscutting concepts bridge boundaries across the various sub‐disciplines of science and engineering.

The crosscutting concepts provide students with an organizational framework for making sense of and connecting knowledge across the various science disciplines.

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Crosscutting Concept:Scale, Proportion, and Quantity

The concept of scale, proportion, and quantity spans disciplines in science and engineering. It concerns the sizes of things and the mathematical relationships between elements.

Related to this concept, it is important for students to understand what is relevant at different measures and to recognize how changes in scale, proportion, or quantity affect a system’s structure and function.

• Atomic Scale• Energy Transfer at different scales• The structure of matter at the atomic and sub‐atomic scales helps to explain a system’s larger scale structures, properties, and functions

• Radioactive decay, proportions of isotopes• Relationship among different types of quantities can be represented by proportions and ratios (e.g., velocity as a ratio of distance traveled versus time)

• Multiple phenomena (e.g., motion, light, sound, electrical and magnetic fields) occur at the macroscopic scale

Scale, Proportion,

and Quantity

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Examples in Physical Science

• Living things are made of cells that can be observed at different scales

• Surface area and cell transfer• Living organisms vary in size and scale (e.g., cells whales)

• Lifespans vary• Life processes occur at different time scales

Scale, Proportion,

and Quantity

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Examples in Life Science

• The geologic time scale depicts the relative times of events in Earth’s history

• Scale models are used to represent phenomena too large or small to observe (e.g., Earth‐Sun‐Moon models)

• Analyses of rock strata and the fossil record provide only relative dates, not an absolute scale

• Geologists use relative positions to estimate dates • Relative distances of the sun and other stars from one other• Relationship between distance of stars and their apparent brightness

• Topographic maps use scale to represent relief and surface features

Scale, Proportion,

and Quantity

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Examples in Earth Science

Physical Science Earth Science

Elementary School

Relative scales allow objects to be compared and described (e.g., bigger and smaller; hotter and colder; faster and slower). 2‐PS1‐d

Standard units are used to measure and describe physical quantities such as weight, time, temperature, and volume. 5‐PS1‐c

Natural objects and observable phenomena exist from the very small to the immensely large. 5‐ESS1‐a

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Scale, Proportion, and Quantity in the Next Generation Science Standards

Physical Science Life Science Earth Science

Middle School

Proportional relationships (e.g. speed as the ratio of distance traveled to time taken) among different types of quantities provide information about the magnitude of properties and processes. MS‐PS2‐b

Scientific relationships can be represented through the use of algebraic expressions and equations. MS‐PS2‐b

Phenomena that can be observed at one scale may not be observable at another scale. MS‐LS1‐a

Time, space, and energy phenomena can be observed at various scales using models to study systems that are too large or too small. MS‐LS2‐g

Time, space, and energy phenomena can be observed at various scales using models to study systems that are too large or too small. MS‐ESS1‐c, MS‐ESS1‐e, MS‐ESS1‐f, MS‐ESS1‐g

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Life Science Earth Science

HighSchool

The significance of a phenomenon is dependent on the scale, proportion, and quantity at which it occurs. HS‐LS2‐a

Using the concept of orders of magnitude allows one to understand how a model at one scale relates to a model at another scale. HS‐LS2‐b

Algebraic thinking is used to examine scientific data and predict the effect of a change in one variable on another (e.g., linear growth vs. exponential growth). HS‐LS3‐d

Patterns observable at one scale may not be observable or exist at other scales. HS‐ESS1‐a, HS‐ESS1‐I

Algebraic thinking is used to examine scientific data and predict the effect of a change in one variable on another (e.g. linear growth vs. exponential growth). HS‐ESS1‐g

The significance of a phenomenon is dependent on the scale, proportion, and quantity at which it occurs. HS‐ESS2‐a

Using the concept of orders of magnitude allows one to understand how a model at one scale relates to a model at another scale. HS‐ESS2‐f36


K‐2: Measurement; Counting, compare quantities, order quantities; Use of scale models, diagrams, and maps

3‐5: Measurement with standard units; Understanding that with natural objects scales range from very small to immensely large; Construct and interpret data models and graphs

MS: Estimation; Powers of 10 scales; Use algebraic thinking and equations; Recognize the function of a system may change with scale and that phenomena observable at one scale may not be observable at another scale

HS: Move back and forth between models at various scales; Understand that the significance of a phenomenon is dependent on the scale at which it occurs; Use more complex algebraic thinking and statistical relationships

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Scale, Proportion, and Quantity: Progression

The Next Generation Science Standards and Scale

The Framework Identifies 8 Science & Engineering Practices

Asking questions and defining problems

Using mathematics and computational thinking

Developing and using models Developing explanations and designing solutions

Planning and carrying out investigations

Engaging in argument from evidence

Analyzing and interpreting data

Obtaining, evaluating, and communicating information

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Quick Write Prompts

• What are some examples of ways you have used scale, proportion, and quantity in your classroom?

[Type your responses in the Chat.]

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Time to Chat

• Any other questions?

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Science Teaching Examples: Measurement

• Tools of measurement – Physical properties (e.g., meter stick, graduated cylinder, balance, electronic scale)

– Weather data tools (e.g., barometer, thermometer, rain gauge, wind vane)

– Oceanography tools (e.g., current cross, secchi disk, salinometer, pH water test kit)

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Science Teaching Examples: Scale

• Types of scales (e.g., Geologic time scale, Fujita tornado scale, pH scale)

• Relative scales (e.g., bigger vs. smaller, colder vs. warmer)

• Scaled maps, models, diagrams– Topographic maps– Earth‐Sun‐Moon models– Dinosaur models– Ocean floor topography

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• Counting quantities (e.g., bacteria, leaves on a branch, number of flowering buds)

• Comparisons of counting • Ordering quantities• Creating, analyzing and interpreting graphs

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Science Teaching Examples: Quantity

POLLWhich item would be in the “middle” if you were to arrange them from smallest to largest?

A. Width of football field

C. Thickness of a penny

B. School bus

D. Diameter of a human hair

E. Length of an adult’s shoe

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POLL

A. Distance from Earth to International Space Station

C. Distance you could walk in 10 minutes

B. Diameter of Earth

D. Distance from Earth to Sun

E. Distance from Earth to Moon

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Which item would be in the “middle” if you were to arrange them from smallest to largest?

POLL

1. Diameter of DNA strand

3. Size of a hydrogen atom

2. Diameter of a proton

4. Diameter of typical cell

5. Size of a typical small molecule

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Which item would be in the “middle” if you were to arrange them from smallest to largest?

POLLCan you assign the actual size to the item?

Size of a typical small molecule:

A. 10 ‐12

C. 10 ‐15

D. 10 ‐10

B. 10 ‐5

E. 10 ‐9

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Why is it important?

• Fascination with the size and scale of things• What research says…

– How people understand scale in terms of:• Learning of scale• Powers of Ten• Measurement and estimation• Use of scale in work/school

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Students’ Thinking…

A little girl was riding in an airplane and while the plane was taking off she turned around to her parents and said:

“When do we get small?”

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As teachers…do we care if students are off by a factor of…

–10?–100?–1000?–1,000,000?

A Sense of Scale

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Understanding Scale

Teachers• Most accurate in their

knowledge of human scale • Being able to directly

experience objects and distances influenced by concepts of size and scale

• Teachers hold more accurate concepts of large scale than small scale

Students• More difficulty with sizes

outside the human scale• Found small scales more

difficult to conceptualize than large scales

• Aware of very small and large objects but lacked accurate knowledge of the exact sizes, as well as their relative sizes

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Body Rulers

• Study examined the impact of teaching students to use their bodies as rough measurement tools

• Results showed that teaching students to use body rulers for estimation had a significant influence on their estimation accuracy

• Proportional reasoning was significantly correlated with students’ measurements

• Hopefully giving them a lifelong tool that they could use to make linear measurements and estimations

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Powers of Ten

• Study that examined the impact of the film Powers of Ten on middle school students’ understanding of ‘‘size and scale’’

• Students’ proportional reasoning ability was found to be positively correlated with their accuracy of ordering objects and assigning them with correct size labels

(Eames Office, 2009)58

(Eames Office, 2009)59

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Over 50 Scientists & Community Professionals

Used scale to…– Design buildings– Discover ancient cultures– Track hurricanes– Design equipment– Create sculpture– Build a home– Survey a stream

• Repeatedly these individuals said, ‘scale is my job’, ‘scale is in everything I do’, ‘it is essential to my job’, and ‘scale is critical.’

• Across disciplines, understanding the sizes of things and scale is essential to understanding phenomena and processes.

• To be effective in their job, they needed to be able to move from small‐scale to large‐scale flexibly.

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Time to Chat

• What questions do you have?• How has the content presented so far influenced your thinking about teaching scale to students?

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Implications For Teaching

Examples of lessons using scale

Grade Life Science Earth Science Physical Science

3‐5 Cartesian Diver Lab

6‐8 Topographic Maps Sea Floor Mapping

9‐12 Cell Size Sea Floor Mapping

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Sample Activity: Elementary School

Cartesian Diver

• Demonstrate ratios of density and pressure

• How it works:– Squeezing the bottle increases

the pressure and compresses the air in the diver (represented through dropper, ketchup packet, etc.).

– This increases the density of the diver, thus changing the buoyancy and causing it to sink.

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Creating Topographic Maps

• Use Play‐doh® to create a landscape.• Measure and mark off 2cm sections from

the base of the landscape to the top.• Use fishing line to cut a layer for each of

the marked sections. Place each section on paper and trace around. Repeat with remaining marks.

• Have students note and compare the landforms to their created maps. Help them to make connections between this activity and topographic maps.

• As an extension, use real topographic maps and have students create the landforms using their Play‐doh®.

USGS Activity

http://vulcan.wr.usgs.gov/Outreach/Publications/GIP19/chapter_three_play‐dough_topo.pdf

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Sample Activity: Middle School

Mapping the Ocean Floor

NOAA Activity

http://csc.noaa.gov/psc/seamedia/Lessons/G5U4L3%20Seafloor%20Profiling.pdf

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Sample Activity: Middle/High School

Similar technique of “determining topography” at the nanoscale!

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Atomic Force Microscope

Cell Size and Surface Area

• Obtain three agar/potato cubes:– 1 cm3, 2 cm3, 3 cm3

• Place the cubes in the beaker and pour in enough diffusion medium to cover them and soak for 20 minutes.

• Cut the cubes in half and examine and compare their inside appearance.

• Measure the depth of the colored zones for each cube in mm and record data.Extreme Science Activity

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Sample Activity: High School

Parameters Case I Case III Case V Case VII Case IX

Length 1 3 5 7 9

Face area 1 9 25 49 81

Surface area 6 54 150 294 486

Volume 1 27 125 343 729

Area/Volume ratio 6 2 1.2 0.86 0.67

Volume: Length x Width x HeightSurface Area: Length x Width x 6 (# of faces of cube)

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Effects of Scale

Examples of the impact of increasing surface area include:

• Why we chew food before swallowing (more surface area leads to faster digestion in the stomach)

• Villi in intestines and alveoli lungs• Why elephant ears are so large (more surface area

leads to faster cooling rates)• Decreasing surface area helps an animal retain

body heat, such as when a dog curls up outside on a cold day

• Volume of single‐celled organisms is restricted by the need for metabolites to reach interior of the cell solely by diffusion

As scales change, surface area to volume relationships have significant influences on physical, chemical, geological, and biological processes and phenomena.

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POLL: How comfortable are you with the topic of scale and teaching this concept to K‐12 students?

NoviceI have no understanding

of this concept.

Limited I need to learn more

about scale before I can teach this topic to

students.

Adequate I have some

understanding of scale and I’m ready to try teaching the concept,

but I’d like more information and ideas for learning activities.

ExpertI have an in‐depth

understanding of scale and I’m ready to

implement learning activities with students.

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Suggestions for Teaching Scale

• Take time to emphasize sizes and scales• Verbalize reasoning across scales• Teach students to estimate (body rulers and pacing)• Teach measurement and various units• The Powers of Ten video works!• Teach them benchmark sizes and how to reason with benchmarks

• Encourage curiosity and scale thinking across disciplines

• Awareness of emerging field of nanotechnology

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Other Scale Resources

Eames Office Website. Powers of Ten Film at http://www.powersof10.com/film

Jones, M.G., Taylor A., & Falvo, M. (2009). Extreme Science. Arlington VA: NSTA Press, 356 pages.

Jones, M.G., Falvo, M., Taylor, A., & Broadwell, B. (2007). Nanoscale Science. Arlington VA: NSTA Press, 155 pages.

Nanoscale Science Education: http://www.ncsu.edu/project/scienceEd/

Taylor, A., Jones, M.G., & Pearl, T.P. (2008). Bumpy, sticky, and shaky: Nanoscale science and the curriculum. Science Scope, 31(7), 28‐35.

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ACKNOWLEDGEMENT

This material is based upon work supported by the NSF under Grants No. 0411656, and 0507151

All research based on collaboration with M. Gail Jones, Professor of Science Education from North Carolina State University

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Contact Information

Amy [email protected]

Kelly [email protected]

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NSTA Resources on NGSSwww.nsta.org

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NSTA Resources on NGSSwww.nsta.org/ngss

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Community Forums

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NSTA Print Resources

NSTA Reader’s Guide to the Framework

NSTA Journal Articles about the Framework and the Standards

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NSTA National Conference

San Antonio, TexasApril 11-14

The place to be to learn about

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Web Seminars on Crosscutting Concepts

Feb. 19: PatternsMarch 5: Cause and effect: Mechanism and explanationMarch 19: Scale, proportion, and quantityApril 16: Systems and system modelsApril 30: Energy and matter: Flows, cycles, and conservationMay 14: Structure and functionMay 28: Stability and change

All sessions will take place from 6:30-8:00 p.m. Eastern time on Tuesdays

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Web Seminars on NGSS

Archives of past programs

Fall 2012Scientific and Engineering Practices (series of 8)

Winter/Spring 2013Second Draft of NGSSEngineering in NGSSNGSS in the Elementary GradesConnecting NGSS with Common Core Math and ELACrosscutting Concepts series

http://learningcenter.nsta.org/products/symposia_seminars/NGSS/webseminar.aspx

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on NGSS

Moving Toward NGSS: Using Formative Assessment to Link Instruction and LearningMembers: $179; Non-members $199Live web seminars on April 18, 25, May 2Presenter: Page Keeley

Moving Toward NGSS: Visualizing K-8 Engineering Education Members: $179; Non-members $199Live web seminars on May 16, 23, 30Presenters: Christine Cunningham and Martha Davis

Register at: learningcenter.nsta.org/ngss94

Thanks to today’s presenters!

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Amy TaylorUniversity of North Carolina Wilmington

Ted WillardNational Science Teachers Association

Kelly RiedingerUniversity of North Carolina Wilmington

Thank you to the sponsor of today’s web seminar:

This web seminar contains information about programs, products, and services offered by third parties, as well as links to third-party websites. The presence of a listing or such information does not constitute an endorsement by NSTA of a

particular company or organization, or its programs, products, or services.96

National Science Teachers AssociationDavid Evans, Ph.D., Executive Director

Zipporah Miller, Associate Executive Director, Conferences and Programs

NSTA Web Seminar TeamAl Byers, Ph.D., Assistant Executive Director,

e-Learning and Government PartnershipsBrynn Slate, Manager, Web Seminars, Online

Short Courses, and SymposiaJeff Layman, Technical Coordinator, Web

Seminars, SciGuides, and Help Desk97

ngss crosscutting concepts: scale, proportion, and quantity · 3/19/2013 · the performance...

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