Teaching and learning

Learning Focused Displays

In the classroom

For each unit of study, teachers clearly post “big ideas” and “essential questions” in the classroom. This makes the purpose of the learning clear to students and promotes ongoing conversations around the big ideas.

In the hallways

All bulletin board displays and classroom displays clearly identify the targeted learning that prompted the display. Samples of student work, when displayed, identify the benchmarks, through big ideas or essential questions that are being assessed through the assessment.

Using Data to Improve Learning

Assessment data, both quantitative and qualitative, is used to set goals and target learning improvement for individual students. Grade level teams in the elementary, look at DRA results, running records, and formative assessments based on grade level standards. For Grades 3-9, Measurement of Academic Progress (MAP) data becomes an important data point in addition to common assessment results. In high school, data from Advanced Placement (AP) and International Baccalaureate (IB) in addition to PSAT, SAT results are utilized for goal setting. Common assessment results and formative assessments are equally important as assessments are linked to grade level or course indicators. Data is also used to evaluate programs and refine curriculum. ASD is involved in a collaborative effort with eight other schools for a data dashboard project that utilizes key performance indicators in student achievement as well as human resources, finance, and other areas.

Learning Focused Meetings

There is a distinct difference between a “learning focused” meeting and an “informational” meeting. A learning focused meeting will always focus on either student learning as the focal point of the meeting content, or will have an element of professional learning embedded into the content of the meeting. Beginning a meeting with a professional discussion is always a good starting point and fosters professional learning. Meetings that focus on student work are crucial evidence of being a learning focused school. Our aim at ASD is to have an element of “learning” embedded in every meeting throughout the school.

Standards-Based Curriculum and Understand by Design

The American School of Doha has created a standards-based curriculum that is based on research and best practice. Curriculum is developed using an ongoing curriculum alignment process approach. Each curricular area has a mission statement, a vision statement, and a set of Essential Agreements and Pre-K – 12 standards and benchmarks. Common standards span from Pre-K to Grade 12. Performance Indicators have been developed by grade level for Pre-K though 8, and by course in the high school. We recognize the fact that curriculum alignment and review is an ongoing process and our curriculum is constantly monitored for appropriateness, alignment, and rigor. The Director of Teaching & Learning oversees all curriculum work in conjunction with the leadership team, curricular experts and the ASD faculty.

Please click on the link for Standards-Based Learning.

The American School of Doha uses the AERO (American Education Reaches Out) standards as the basis for curriculum design, and also utilizes the work of national and international benchmarking organizations. ASD is looking at the alignment between our ASD standards and the work that is occurring with the Common Core standards in the US. The ASD curriculum is closely aligned to current best practices in the United States and aligned to the Common Core. At the same time, we also recognize our uniqueness as an international school that embraces a global perspective as we prepare our students to become citizens of the world.

Units of study are developed around the principles of Understanding by Design (Wiggins and McTighe) and include enduring understandings, essential questions and assessments that are aligned to the ASD standards and benchmarks. All courses or grade level subjects are mapped on Atlas Rubicon, and are accessible to all teachers at the ASD Atlas Rubicon site (asdqatar.rubiconatlas.org). By identifying the desired results for a unit of study as the first step in the process of unit design, teachers know that the unit will be completely aligned to the identified standards and benchmarks for the particular course. Enduring Understandings and Essential Questions are created to focus the learning and achieve the desired results. Once the results are identified, an appropriate assessment is created to gather evidence that the targeted learning has been met. Essential Skills and Essential Knowledge are identified. Finally, Learning Activities are crafted to lead students to the Enduring Understandings and the desired results. At ASD we believe that this “backwards” planning model promotes quality instruction, and facilitates quality learning for our students

Please find link to the Atlas Unit Mapping Guide

Assessments Aligned to Standards

Assessment is a key component in a standards-based school that is focused on learning. In the elementary and middle levels, student progress is reported out according to the standard. In the high school, student progress is recorded according to the standard and then reported out with a grade. Toward that end, the faculty collectively made the following agreements relative to assessment practices:

Overarching Assumption: Students are the primary users of assessment.

Assessments are clearly aligned to ASD’s standards and benchmarks.
ASD uses frequent formative assessment for learning and periodic summative assessment of learning.
Teachers actively involve students in the assessment process through self-reflection, goal-setting, peer collaboration, feedback and conferring.
Feedback is timely, descriptive and objective.
Teachers effectively use a variety of authentic assessments to ensure that student achievement is measured accurately against standards and benchmarks.
Teachers provide clear assessment criteria regarding learning targets, expectations and processes to be shared with students on a regular basis.
Teachers provide models of performance to ensure students understand processes and expectations for their learning.
Teachers share assessment ideas and practices, and in  common courses and grade levels, develop common assessments.

In order to educate all stakeholders in understanding ASD’s assessment practices and policies, support is provided to parents, students, teachers and administrators to understand the elements of accurate and effective assessment practices.

NorthWest Evaluation Association (NWEA) Measures of Academic Progress

ASD uses the NWEA Measures of Academic Progress test as a data-gathering tool to benchmark our students against other students, using US and International performance norms.

The MAP is unique in its structure compared to other standardized tests. Primarily the MAP assessment is aligned to US standards and benchmarks from which we have adapted our ASD standards and benchmarks. This makes MAP much more aligned to our curriculum than other more traditional standardized tests.

The MAP test is given online, and is able to adapt to the appropriate level of each child’s learning. As a result, each student has the same opportunity to succeed and maintain a positive attitude during the testing. The tests are untimed and adjust in level according to the student’s answers. The tests are used to determine the student’s instructional level and to measure academic growth throughout the school year, and from year to year. The students are tested three times a year in the areas of math, reading, and language usage in the elementary and middle school and in math and reading in Grade 9. From the test data, we will be able to see skills and content that the student has mastered, determine the instructional level, and identify areas for future learning. At this point in time, ASD tests all students in Grades 3 through 9.

How do we use the MAP data?

Teachers focus on several data points:

The growth of individual students in their class
Patterns of strengths and weaknesses in their class
Grouping for instruction
Differentiation of instruction based on data

As a school we are looking at the data through the following lenses:

Patterns of strengths and weaknesses
Effectiveness of programs
Data showing student growth individually and across grade levels/subjects

Although we value the information we receive from the MAP testing, we recognize that this type of standardized testing is a “snap-shot” and is not the complete picture of a student’s learning. It serves as one piece of a student’s learning portfolio.

You may like to browse the NWEA site online at http://www.nwea.org/support

Professional and Collaboration Time

Every Tuesday afternoon of a five-day school week, students are dismissed at 12:30pm for teachers to utilize PACT time. We use PACT to collaborate within various changing “Learning Communities” to grow professionally, and to collaborate together to enhance our planning, teaching, and assessment of student learning.

Goals:

To improve student learning
To focus on student work
To enhance instructional practices
To increase professional conversations between ASD faculty members
To effectively implement school improvement initiatives through collaboration

Grade level or department teams organize meetings and structure their time around school, division and team goals. Some common tasks include: looking at student work, analyzing data from a common assessment, evaluating the quality of an assessment task, development of an integrated unit, discussion of professional reading, refining the team’s curriculum map on Atlas Rubicon and professional learning.

Professional Learning

The American School of Doha is committed to the on-going professional learning of all faculty members. The learning of a comprehensive professional learning program serves to further enhance the professionalism and skills of faculty members, and results in both improved levels of student learning and enhanced teaching practice. Professional Learning at ASD is understood as a shared responsibility.

The Professional Learning program within The American School of Doha provides faculty with the opportunity to:

Further develop the skills necessary to more effectively carry out the mission of the school
Further develop the body of knowledge and level of skills necessary to enable the school to successfully become a school of excellence, where students achieve their maximum potential in a culture of continuous improvement

To these ends, the Professional Learning program within the American School of Doha is focused on expanding the repertoire of skills of staff members by:

Meeting the professional needs of the collective staff, enabling each faculty member to move forward within the ASD school improvement plan

Please click on this link for our 2013-2014 strategic overview

Looking for Learning

“Looking for Learning” classroom visits are focused on student learning and not on the teaching. Observers look for student behaviors that demonstrate that sufficient learning is happening. Students converse with the observers about the type of learning in which they are engaged. As outlined in our student learning objectives, looking for learning is an initiative that supports students being able to articulate their own learning.

The Looking for Learning Protocol supports teachers and leaders as they look for learning in classrooms by questioning students about their learning. Follow up conversations between observers and a teacher about the type of learning that is taking place is critical in creating a mind shift from teaching to learning.

English / Language Arts Vision, Mission & Essential Agreements

Reading Literature - RL

Students read a wide range of literature from many periods in many genres to build an understanding of the many dimensions (e.g., philosophical, ethical, aesthetic) of human experience.

RL.1 Read closely to determine what the text says explicitly and to make logical inferences from it; cite specific textual evidence when writing or speaking to support conclusions drawn from the text.

RL.2 Determine central ideas or themes of a text and analyze their development; summarize the key supporting details and ideas.

RL.3 Analyze how and why individuals, events, and ideas develop and interact over the course of a text.

RL.4 Interpret words and phrases as they are used in a text, including determining technical, connotative, and figurative meanings, and analyze how specific word choices shape meaning or tone.

RL.5 Analyze the structure of texts, including how specific sentences, paragraphs, and larger portions of the text (e.g., a section, chapter, scene, or stanza) relate to each other and the whole.

RL.6 Assess how point of view or purpose shapes the content and style of a text.

RL.7 Integrate and evaluate content presented in diverse formats and media, including print and digital resources.

RL.8 Delineate and evaluate the argument and specific claims in a text, including the validity of the reasoning as well as the relevance and sufficiency of the evidence.

RL.9 Analyze how two or more texts address similar themes or topics in order to build knowledge or to compare the approaches the authors take.

RL.10 Read and comprehend complex literary and informational texts independently and proficiently.

Reading Informational Text - RI

Students read a wide range of print and non-print texts to build an understanding of texts, of themselves, and of the cultures of the United States and the world; to acquire new information; to respond to the needs and demands of society and the workplace; and for personal fulfillment. Among these texts are fiction and nonfiction, classic and contemporary works.

RI.1 Read closely to determine what the text says explicitly and to make logical inferences from it; cite specific textual evidence when writing or speaking to support conclusions drawn from the text.

RI.2 Determine central ideas or themes of a text and analyze their development; summarize the key supporting details and ideas.

RI.3 Analyze how and why individuals, events, and ideas develop and interact over the course of a text.

RI.4 Interpret words and phrases as they are used in a text, including determining technical, connotative, and figurative meanings, and analyze how specific word choices shape meaning or tone.

RI.5 Analyze the structure of texts, including how specific sentences, paragraphs, and larger portions of the text (e.g., a section, chapter, scene, or stanza) relate to each other and the whole.

RI.6 Assess how point of view or purpose shapes the content and style of a text.

RI.7 Integrate and evaluate content presented in diverse formats and media, including print and digital resources.

RI.8 Delineate and evaluate the argument and specific claims in a text, including the validity of the reasoning as well as the relevance and sufficiency of the evidence.

RI.9 Analyze how two or more texts address similar themes or topics in order to build knowledge or to compare the approaches the authors take.

RI.10 Read and comprehend complex literary and informational texts independently and proficiently.

Reading Foundational Skills

Students apply a wide range of strategies to comprehend, interpret, evaluate, and appreciate texts. They draw on their prior experience, their interactions with other readers and writers, their knowledge of word meaning and of other texts, their word identification strategies, and their understanding of textual features (e.g., sound-letter correspondence, sentence structure, context, graphics).

RF.1 Demonstrate understanding of the organization and basic features of print.

RF.2 Demonstrate understanding of spoken words, syllables, and sounds (phonemes).

RF.3 Know and apply grade-level phonics and word analysis skills in decoding words.

RF.4 Read with sufficient accuracy and fluency to support comprehension.

Writing - W

Students employ a wide range of strategies as they write and use different writing process elements appropriately to communicate with different audiences for a variety of purposes.

W.1 Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence.

W.2 Write informative/explanatory texts to examine and convey complex ideas and information clearly and accurately through the effective selection, organization, and analysis of content.

W.3 Write narratives to develop real or imagined experiences or events using effective technique, well-chosen details, and well-structured event sequences.

W.4 Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.

W.5 Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach.

W.6 Use technology, including the Internet, to produce and publish writing and to interact and collaborate with others.

W.7 Conduct short as well as more sustained research projects based on focused questions, demonstrating understanding of the subject under investigation.

W.8 Gather relevant information from multiple print and digital sources, assess the credibility and accuracy of each source, and integrate the information while avoiding plagiarism.

W.9 Draw evidence from literary or informational texts to support analysis, reflection, and research.

W.10 Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of tasks, purposes, and audiences.

Listening and Speaking - LS

Students use speaking, listening, and information literacy to accomplish their own purposes (e.g., for learning, enjoyment, persuasion, and the exchange of information).

LS.1 Prepare for and participate effectively in a range of conversations and collaborations with diverse partners, building on others’ ideas and expressing their own clearly and persuasively.

LS.2 Integrate and evaluate information presented in diverse media and formats, including visually, quantitatively, and orally.

LS.3 Evaluate a speaker’s point of view, reasoning, and use of evidence and rhetoric.

LS.4 Present information, findings, and supporting evidence such that listeners can follow the line of reasoning and the organization, development, and style are appropriate to task, purpose, and audience.

LS.5 Make strategic use of digital media and visual displays of data to express information and enhance understanding of presentations.

LS.6 Adapt speech to a variety of contexts and communicative tasks, demonstrating command of formal English when indicated or appropriate.

Language Foundation - L

Students apply knowledge of language structure, language conventions (e.g., spelling and punctuation), media techniques, figurative language, and genre to create, critique, and discuss print and non-print texts.

L.1 Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.

L.2 Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.

L.3 Apply knowledge of language to understand how language functions in different contexts, to make effective choices for meaning or style, and to comprehend more fully when reading or listening.

L.4 Determine or clarify the meaning of unknown and multiple-meaning words and phrases by using context clues, analyzing meaningful word parts, and consulting general and specialized reference materials, as appropriate.

L.5 Demonstrate understanding of word relationships and nuances in word meanings.

L.6 Acquire and use accurately a range of general academic and domain-specific words and phrases sufficient for reading, writing, speaking, and listening at the college and career readiness level; demonstrate independence in gathering vocabulary knowledge when considering a word or phrase important to comprehension or expression.

English Language Arts K-12 Standards and Performance Indicators

Mathematics Mission, Vision & Essential Agreements

Math Practice Standards

Mathematics' Standards

Counting and Cardinality

K.CC.A Know number names and the count sequence
K.CC.B Count to tell the number of objects
K.CC.C Compare Numbers.

Operations and Algebraic Thinking

K.OA.A Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from
1.OA.A Represent and solve problems involving addition and subtraction
1.OA.B Understand and apply properties of operations and the relationship between addition and subtraction
1.OA.C. Add and subtract within 20.
1.OA.D. Work with addition and subtraction equations
2.OA.A. Represent and solve problems involving addition and subtraction
2.OA.B. Add and subtract within 20
2.OA.C. Work with equal groups of objects to gain foundations for multiplication
3.OA.A. Represent and solve problems involving multiplication and division
3.OA.B. Understand properties of multiplication and the relationship between multiplication and division
3.OA.C. Multiply and divide within 100
3.OA.D. Solve problems involving the four operations, and identify and explain patterns in arithmetic
4.OA.A. Use the four operations with whole numbers to solve problems.
4.OA.B. Gain familiarity with factors and multiples
4.OA.C. Generate and analyze patterns
5.OA.A. Write and interpret numerical expressions
5.OA.B. Analyze patterns and relationships

Numbers & Operations in Base Ten

K.NBT.A. Work with numbers 11-19 to gain foundations for place value
1.NBT.A. Extend the counting sequence
1.NBT.B. Understand place value
1.NBT.C. Use place value understanding and properties of operations to add and subtract
2.NBT.A. Understand place value
2.NBT.B. Use place value understanding and properties of operations to add and subtract
3.NBT.A. Use place value understanding and properties of operations to perform multi-digit arithmetic
4.NBT.A. Generalize place value understanding for multi-digit whole numbers
4.NBT.B. Use place value understanding and properties of operations to perform multi-digit arithmetic
5.NBT.A. Understand the place value system
5.NBT.B. Perform operations with multi-digit whole numbers and with decimals to hundredths

Number & Operations

3.NF.A. Develop understanding of fractions as numbers
4.NF.A. Extend understanding of fraction equivalence and ordering
4.NF.B. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers
4.NF.C. Understand decimal notation for fractions, and compare decimal fractions
5.NF.A. Use equivalent fractions as a strategy to add and subtract fractions
5.NF.B. Apply and extend previous understandings of multiplication and division to multiply and divide fractions

Measurement & Data

K.MD.A. Describe and compare measurable attributes
K.MD.B. Classify objects and count the number of objects in each category
1.MD.A. Measure lengths indirectly and by iterating length units
1.MD.B. Tell and write time
1.MD.C. Represent and interpret data
2.MD.A. Measure and estimate lengths in standard units
2.MD.B. Relate addition and subtraction to length
2.MD.C. Work with time and money
2.MD.D. Represent and interpret data
3.MD.A. Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects
3.MD.B. Represent and interpret data
3.MD.C. Geometric measurement: understand concepts of area and relate area to multiplication and to addition
3.MD.D. Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures
4.MD.A. Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit
4.MD.B. Represent and interpret data
4.MD.C. Geometric measurement: understand concepts of angle and measure angles
5.MD.A. Convert like measurement units within a given measurement system
5.MD.B. Represent and interpret data
5.MD.C. Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition

Ratios & Proportional Relationships

6.RP.A. Understand ratio concepts and use ratio reasoning to solve problems.
7.RP.A. Analyze proportional relationships and use them to solve real-world and mathematical problems.
7.RP.A.1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

The Number System

6.NS.A. Apply and extend previous understandings of multiplication and division to divide fractions by fractions
6.NS.B. Compute fluently with multi-digit numbers and find common factors and multiples
6.NS.C. Apply and extend previous understandings of numbers to the system of rational numbers
7.NS.A. Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers
8.NS.A. Know that there are numbers that are not rational, and approximate them by rational numbers

Expressions & Equations

6.EE.A. Apply and extend previous understandings of arithmetic to algebraic expressions
6.EE.B. Reason about and solve one-variable equations and inequalities
6.EE.C. Represent and analyze quantitative relationships between dependent and independent variables
7.EE.A. Use properties of operations to generate equivalent expressions.
7.EE.B. Solve real-life and mathematical problems using numerical and algebraic expressions and equations
8.EE.A. Work with radicals and integer exponents.
8.EE.B. Understand the connections between proportional relationships, lines, and linear equations
8.EE.C. Analyze and solve linear equations and pairs of simultaneous linear equations

Functions

8.F.A. Define, evaluate, and compare functions
8.F.B. Use functions to model relationships between quantities.

Geometry

K.G.A. Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres)
K.G.B. Analyze, compare, create, and compose shapes
1.G.A. Reason with shapes and their attributes
2.G.A. Reason with shapes and their attributes
3.G.A. Reason with shapes and their attributes
4.G.A. Draw and identify lines and angles, and classify shapes by properties of their lines and angles
5.G.A. Graph points on the coordinate plane to solve real-world and mathematical problems
6.G.A. Solve real-world and mathematical problems involving area, surface area, and volume
7.G.A. Draw construct, and describe geometrical figures and describe the relationships between them
7.G.B. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume
8.G.A. Understand congruence and similarity using physical models, transparencies, or geometry software

Statistics & Probability

6.SP.A. Develop understanding of statistical variability
6.SP.B. Summarize and describe distributions
7.SP.A. Use random sampling to draw inferences about a population
7.SP.B. Draw informal comparative inferences about two populations
7.SP.C. Investigate chance processes and develop, use, and evaluate probability models
8.SP.A. Investigate patterns of association in bivariate data

The Real Number System

HSN-RN.A. Extend the properties of exponents to rational exponents
HSN-RN.B. Use properties of rational and irrational numbers

Quantities

HSN-Q.A. Reason quantitatively and use units to solve problems

The Complex Number System

HSN-CN.A. Perform arithmetic operations with complex numbers
HSN-CN.B. Represent complex numbers and their operations on the complex plane
HSN-CN.C. Use complex numbers in polynomial identities and equations

Vector & Matrix Quantities

HSN-VM.A. Represent and model with vector quantities
HSN-VM.B. Perform operations on vectors
HSN-VM.C. Perform operations on matrices and use matrices in applications

Seeing Structure in Expressions

HSA-SSE.A. Interpret the structure of expressions
HSA-SSE.B. Write expressions in equivalent forms to solve problems

Arithmetic with Polynomials & Rational Functions

HSA-APR.A. Perform arithmetic operations on polynomials
HSA-APR.B. Understand the relationship between zeros and factors of polynomials
HSA-APR.C. Use polynomial identities to solve problems
HSA-APR.D. Rewrite rational expressions

Creating Equations

HSA-CED.A. Create equations that describe numbers or relationships

Reasoning with Equations & Inequalities

HSA-REI.A. Understand solving equations as a process of reasoning and explain the reasoning
HSA-REI.B. Solve equations and inequalities in one variable
HSA-REI.C. Solve systems of equations
HSA-REI.D. Represent and solve equations and inequalities graphically

Interpreting Functions

HSF-IF.A. Understand the concept of a function and use function notation
HSF-IF.B. Interpret functions that arise in applications in terms of the context
HSF-IF.C. Analyze functions using different representations

Building Functions

HSF-BF.A. Build a function that models a relationship between two quantities
HSF-BF.B. Build new functions from existing functions

Linear, Quadratic, and Exponential Models

HSF-LE.A. Construct and compare linear and exponential models and solve problems
HSF-LE.B. Interpret expressions for functions in terms of the situation they model

Trigonometric Functions

HSF-TF.A. Extend the domain of trigonometric functions using the unit circle
HSF-TF.B. Model periodic phenomena with trigonometric functions
HSF-TF.C. Prove and apply trigonometric identities

Congruence

HSG-CO.A. Experiment with transformations in the plane
HSG-CO.B. Understand congruence in terms of rigid motions
HSG-CO.C. Prove geometric theorems
HSG-CO.D. Make geometric constructions

Similarity, Right Triangles, & Trigonometry

HSG-SRT.A. Understand similarity in terms of similarity transformations
HSG-SRT.B. Prove theorems involving similarity
HSG-SRT.C. Define trigonometric ratios and solve problems involving right triangles
HSG-SRT.D. Apply trigonometry to general triangles

Circles

HSG-C.A. Understand and apply theorems about circles
HSG-C.B. Find arc lengths and areas of sectors of circles

Expressing Geometric Properties with Equations

HSG-GPE.A. Translate between the geometric description and the equation for a conic section
HSG-GPE.B. Use coordinates to prove simple geometric theorems algebraically

Geometric Measurement & Dimension

HSG-GMD.A. Explain volume formulas and use them to solve problems

Modeling with Geometry

HSG-MG.A. Apply geometric concepts in modeling situations

Interpreting Categorical & Quantitative Data

HSS-ID.A. Summarize, represent, and interpret data on a single count or measurement variable
HSS-ID.B. Summarize, represent, and interpret data on two categorical and quantitative variables
HSS-ID.C. Interpret linear models

Making Inferences & Justifying Conclusions

HSS-IC.A. Understand and evaluate random processes underlying statistical experiments
HSS-IC.B. Make inferences and justify conclusions from sample surveys, experiments and observational studies

Conditional Probability & the Rules of Probability

HSS-CP.A. Understand independence and conditional probability and use them to interpret data
HSS-CP.B. Use the rules of probability to compute probabilities of compound events in a uniform probability model

Using Probability to Make Decisions

HSS-MD.A. Calculate expected values and use them to solve problems
HSS-MD.B. Use probability to evaluate outcomes of decisions

Common Core State Standards for Mathematics

science mission, vision & essential agreements

Science and Engineering Practices in the NGSS

Practice 1: Asking Questions and Defining Problems

Students at any grade level should be able to ask questions of each other about the texts they read, the features of the phenomena they observe, and the conclusions they draw from their models or scientific investigations. For engineering, they should ask questions to define the problem to be solved and to elicit ideas that lead to the constraints and specifications for its solution.

Practice 2: Developing and Using Models

Modeling can begin in the earliest grades, with students’ models progressing from concrete “pictures” and/or physical scale models (e.g., a toy car) to more abstract representations of relevant relationships in later grades, such as a diagram representing forces on a particular object in a system.

Practice 3: Planning and Carrying Out Investigations

Students should have opportunities to plan and carry out several different kinds of investigations during their K-12 years. At all levels, they should engage in investigations that range from those structured by the teacher—in order to expose an issue or question that they would be unlikely to explore on their own (e.g., measuring specific properties of materials) — to those that emerge from students’ own questions.

Practice 4: Analyzing and Interpreting Data

Once collected, data must be presented in a form that can reveal any patterns and relationships and that allows results to be communicated to others. Because raw data as such have little meaning, a major practice of scientists is to organize and interpret data through tabulating, graphing, or statistical analysis. Such analysis can bring out the meaning of data—and their relevance—so that they may be used as evidence.

Engineers, too, make decisions based on evidence that a given design will work; they rarely rely on trial and error. Engineers often analyze a design by creating a model or prototype and collecting extensive data on how it performs, including under extreme conditions. Analysis of this kind of data not only informs design decisions and enables the prediction or assessment of performance but also helps define or clarify problems, determine economic feasibility, evaluate alternatives, and investigate failures.

Practice 5: Using Mathematics and Computational Thinking

Although there are differences in how mathematics and computational thinking are applied in science and in engineering, mathematics often brings these two fields together by enabling engineers to apply the mathematical form of scientific theories and by enabling scientists to use powerful information technologies designed by engineers. Both kinds of professionals can thereby accomplish investigations and analyses and build complex models, which might otherwise be out of the question.

Practice 6: Constructing Explanations and Designing Solutions

“The goal of science is the construction of theories that provide explanatory accounts of the world. A theory becomes accepted when it has multiple lines of empirical evidence and greater explanatory power of phenomena than previous theories.”

Asking students to demonstrate their own understanding of the implications of a scientific idea by developing their own explanations of phenomena, whether based on observations they have made or models they have developed, engages them in an essential part of the process by which
conceptual change can occur.

In engineering, the goal is a design rather than an explanation. The process of developing a design is iterative and systematic, as is the process of developing an explanation or a theory in science. Engineers’ activities, however, have elements that are distinct from those of scientists. These elements include specifying constraints and criteria for desired qualities of the solution, developing a design plan, producing and testing models or prototypes, selecting among alternative design features to optimize the achievement of design criteria, and refining design ideas based on the performance of a prototype or simulation.

Practice 7: Engaging in Argument from Evidence

The study of science and engineering should produce a sense of the process of argument necessary for advancing and defending a new idea or an explanation of a phenomenon and the norms for conducting such arguments. In that spirit, students should argue for the explanations they construct, defend their interpretations of the associated data, and advocate for the designs they propose.

Practice 8: Obtaining, Evaluating, and Communicating Information

Any education in science and engineering needs to develop students’ ability to read and produce domain-specific text. As such, every science or engineering lesson is in part a language lesson, particularly reading and producing the genres of texts that are intrinsic to science and engineering.

NGSS: Science and Engineering Practices

Physical Science

PS.1 Matter and Its Interactions

PS.1.A: Structure & Properties of Matter
PS.1.B: Chemical Reactions
PS.1.C: Nuclear Processes

PS.2 Motion and Stability: Forces and Interactions

PS.2.A: Forces and Motion
PS.2.B: Types of Interactions
PS.2.C: Stability and Insatability

PS.3 Energy

PS.3.A: Definitions of Energy
PS.3.B: Energy: Conservation & Transfer
PS.3.C: Energy & Forces
PS.3.D: Energy in Chemical Processes & Life

PS.4 Waves and Their Applications in Technologies for Information Transfer

PS.4.A: Wave Properties
PS.4.B: Electromagnetic Radiation
PS.4.C: Information Technologies

Earth and Space Science

ESS.1 Earth’s Place in the Universe

ESS.1.A: The Universe & Its Stars
ESS.1.B: Earth & the Solar System
ESS.1.C: History of the Planet Earth

ESS.2 Earth’s Systems

ESS.2.A: Earth Materials & Systems
ESS.2.B: Plate Tectonics/Large Scale Systems
ESS.2.C: Role of Water on Earth
ESS.2.D: Weather & Climate
ESS.2.E: Biogeology

ESS.3 Earth and Human Activity

ESS.3.A: Natural Resources
ESS.3.B: Natural Hazards
ESS.3.C: Human Impacts on Earth Systems
ESS.3.D: Global Climate Change

Life Science

LS.1 From Molecules to Organisms: Structures and Processes

LS.1.A: Structure and Function
LS.1.B: Growth and Development
LS.1.C: Organization in Organisms
LS.1.D: Information Processing

LS.2 Ecosystems: Interactions, Energy, and Dynamics

LS2.A: Relationships in Ecosystems
LS2.B: Cycles in Ecosystems
LS2.C: Ecosystem Dynamics
LS2.D: Social Interactions & Behavior

LS.3 Hereditary: Inheritance and Variation of Traits

LS.3.A: Inheritance of Traits
LS.2.B: Variation of Traits

LS.4 Biological Evolution: Unity and Diversity

LS.4.A: Evidence of Common Ancestry
LS.4.B: Natural Selection
LS.4.C: Adaptation
LS.4.D: Biodiversity & Humans

Crosscutting Concepts

1. Patterns

Observed patterns of forms and events guide organization and classification, and they prompt questions about relationships and the factors that influence them.

2. Cause and effect: Mechanism and explanation

Events have causes, sometimes simple, sometimes multifaceted. A major activity of science is investigating and explaining causal relationships and the mechanisms by which they are mediated. Such mechanisms can then be tested across given contexts and used to predict and explain events in new contexts.

3. Scale, proportion, and quantity

In considering phenomena, it is critical to recognize what is relevant at different measures of size, time, and energy and to recognize how changes in scale, proportion, or quantity affect a system’s structure or performance.

4. Systems and system models

Defining the system under study—specifying its boundaries and making explicit a model of that system—provides tools for understanding and testing ideas that are applicable throughout science and engineering.

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

Tracking fluxes of energy and matter into, out of, and within systems helps one understand the systems’ possibilities and limitations.

6. Structure and function

The way in which an object or living thing is shaped and its substructure determine many of its properties and functions.

7. Stability and change

For natural and built systems alike, conditions of stability and determinants of rates of change or evolution of a system are critical elements of study.

NGSS Crosscutting Concepts

Matrix of Disciplinary Core Ideas in NGSS

social studies mission, vision & essential agreements

Dimension 1: Developing Questions and Planning Inquiries

Individually and with others, students construct compelling questions, and…

Explain how a question reflects an enduring issue in the field.
Explain points of agreement and disagreement experts have about interpretations and applications of disciplinary concepts and ideas associated with a compelling question.

Individually and with others, students construct supporting questions, and…

Explain points of agreement and disagreement experts have about interpretations and applications of disciplinary concepts and ideas associated with a supporting question.
Explain how supporting questions contribute to an inquiry and how, through engaging source work, new compelling and supporting questions emerge.