Grade 7 Math Curriculum Notebook.docx

Statistics and Probability 7SP4
Core Content
Cluster Title: Draw Informal comparative inferences about two populations
Standard 4: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book
MASTERY Patterns of Reasoning:
Conceptual:
• Understand that measures of center and variability can be used to make inferences about two populations
Procedural:
• Make comparative inferences about two populations using measures of center and variability
Representational:
• Represent the measures of center and variability of two populations graphically Supports for Teachers
Critical Background Knowledge
Conceptual:
• Know Measures of Center (median and/or mean)
• Know Measures of Variability (interquartile range and/or mean absolute deviation) Procedural:
• Find Measures of Center (median and/or mean)
• Find Measures of Variability (interquartile range and/or mean absolute deviation) Representational:
• Represent Measures of Center (median and/or mean) graphically Academic Vocabulary and Notation
Inference
In small groups, compare and contrast similar data
from two populations to make inferences http://www.learnzillion.com/lessons/371-
learn-which-measure-of-central-tendency- to-use
Assessment Tasks Used
Skill-based Task: Problem Task:
Measure the heights of the girls versus boys in your Decide whether girls or boys take longer to class. Calculate the measures of center and get ready for school in the morning. Justify measures of variability for each group. What your answer using measures of center and inferences can you make about the height of girls spread.
versus boys? Will these inferences be the same your Senior year? Support your answer with a description of the overlap of the two distributions and numerical calculations for means and variability
Instructional Strategies Used
Resources Used
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Statistics and Probability 7SP5
Core Content
Cluster Title: Investigate chance processes and develop, use, and evaluate probability models
Standard 5: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
MASTERY Patterns of Reasoning:
Conceptual:
• Understand that a probability of 0 is impossible
• Understand that probabilities near 0 are unlikely to occur
• Understand that probabilities of .5 are equally likely and unlikely
• Understand that probabilities near 1 are more likely to occur
• Understand that a probability of 1 is certain.
Procedural:
• Represent the probability of an event as a fraction or decimal from 0 to 1 or percent from 0% to 100%.
Representational:
• represent probability with area Supports for Teachers
Critical Background Knowledge
Conceptual:
• Understand that 1 = 100% Procedural:
• Recognize when a number is close to 0, close to 1⁄2, or close to 1. Representational:
•
Academic Vocabulary and Notation
Probability, event, chance event, likelihood, outcome
Brainstorm possible events that fit on the continuum from impossible to certain.
Assessment Tasks Used
Skill-based Task: Problem Task:
The weatherman said that there is a 90% Using a six-sided number cube, have students chance of snow today. Describe the likelihood create events that are impossible, unlikely, as of it snowing today likely as unlikely, likely, and certain
Instructional Strategies Used
Resources Used
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Statistics and Probability 7SP6
Core Content
Cluster Title: Investigate chance processes and develop, use, and evaluate probability models
Standard 6. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.
MASTERY Patterns of Reasoning:
Conceptual:
• Know how to approximate probabilities Procedural:
• Perform an experiment and collect data on a chance event
• Relate the results of an experiment to the theoretical relative frequency of an event
• Use the results of an experiment to estimate the probability of an even
• Estimate the long-run relative frequency of an event given the probability of the event
Representational:
• Represent the collected data in tables or charts Supports for Teachers
Critical Background Knowledge
Conceptual:
• Understand the probability of a chance event as a number between 0 and 1 that expresses likelihood. (7.SP.5)
Procedural:
• Summarize numerical data sets by reporting the number of observations. (6.SP.5) Representational:
•
Academic Vocabulary and Notation
Theoretical probability, experimental probability, relative frequency
Instructional Strategies Used
Resources Used
Have students compare experimental and theoretical probability using coins, dice, or spinners
Assessment Tasks Used
Skill-based Task:
You roll a fair die 200 times. How many outcomes should be even?
Web Simulations
Coins, number cubes, spinners, cards National Library of Virtual Manipulatives
Problem Task:
If Portia were to flip a coin one hundred times could the outcomes be 80 heads and 20 tails? Explain your reasoning.
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Statistics and Probability 7SP7
Core Content
Cluster Title: Investigate chance processes and develop, use, and evaluate probability models
Standard 7: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.
a) Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.
b) Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies? MASTERY Patterns of Reasoning:
Conceptual:
• Understand why an observed frequency and theoretical probabilities may not agree
• Understand definitions of theoretical and experimental probability Procedural:
• Use theoretical probabilities to create a probability model (e.g. table showing the potential outcomes of an experiment or random process with their corresponding probabilities) in which all outcomes are equally likely (uniform)
• Use observed frequencies to create a probability model for the data generated from a chance process
• Use probability models to find probabilities of events
• Compare theoretical and experimental probability. Representational:
• Represent the data of observed frequencies graphically or in tables Supports for Teachers
Critical Background Knowledge
Conceptual:
• Know Theoretical and experimental probability Procedural:
• Collect data for random samples Representational:
• Represent data from random samples in charts or tables
Academic Vocabulary and Notation
Probability model, uniform probability, discrepancy, sample space, event
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Instructional Strategies Used
Resources Used
Create a game based on a model, predict the winner, play the game. Compare observed frequencies with the prediction and explain discrepancies.
Sample Formative
Assessment Tasks Used
Skill-based Task:
Juan rolled 15 fours when rolling a fair die 60 times. Would you expect this result? Justify your answer.
Problem Task:
The results of a spinner experiment are 50% red, 10% blue, 20% yellow, and 20% green. Draw the spinner.
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Statistics and Probability 7SP7
Core Content
Cluster Title: Investigate chance processes and develop, use, and evaluate probability models
Standard 8: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
a) Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
b) Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.
c) Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?
MASTERY Patterns of Reasoning:
Conceptual:
• Understand the definition of sample space
• Understand the definition of compound events Procedural:
• Find the sample space of a compound event.
• Generate frequencies for compound events using random number generators (e.g.
tables, calculators, manipulatives).
Representational:
• Represent probabilities of simple and compound events as a fraction, decimal, or percent
• Create organized lists, tables, tree diagrams, and simulations to determine the probability of compound events
Supports for Teachers
Critical Background Knowledge
Conceptual:
• Know what probability of simple events are Procedural:
• Compute the probability of a simple event
• Use lists and tables to organize data
• Read tree diagrams
Representational:
• Create lists and tables to organize data
• Create tree diagrams
Academic Vocabulary and Notation
Simple event, compound events, tree diagram, simulation, sample space
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Instructional Strategies Used
Resources Used
Use playing cards to simulate the results of compound events. (e.g. use 4 hearts and 6 clubs to simulate 40% of donors with type A blood)
Assessment Tasks Used
Skill-based Task:
What is the probability of a family with five children having exactly two boys?
Random Number Generator
Problem Task:
Create a tree diagram for illustrating the outcomes for a car that has two or four doors and is red, black, or silver. Create questions that can be answered based on the diagram.
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Pacing Guide
Pacing Guide for Mathematics Essentials
Term 1
The Number System: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Solve real-world and mathematical problems involving the four operations with rational numbers.
7NS1 7NS2 7NS3
Term 2
Ratios and Proportional Reasoning: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. Recognize and represent proportional relationships between quantities. Use proportional relationships to solve multi-step ratio and percent problems.
7RP1 7RP2 7RP3
Term 3
Expressions and Equations: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations to solve problems by reasoning about the quantities.
7EE1 7EE3 7EE4
Geometry: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
7G1 7G5
Term 4
Geometry: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
7G4 7G6
Statistics and Probability: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long- run relative frequency, and predict the approximate relative frequency given the probability.
7SP1 7SP5 7SP6
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Units
Planning Guide: Jay McTighe, an expert in unit planning and author of Understanding by Design, has written four point to consider when planning units. They are presented below.
UbD Design Standards Stage 1 – To what extent does the design:
1. focus on the “Big ideas” of targeted content? Consider: are . . .
– the targeted understandings enduring, based on transferable, big ideas at the heart of the
discipline and in need of “uncoverage”?
– the targeted understandings framed as specific generalizations?
– the “big ideas” framed by questions that spark meaningful connections, provoke genuine
inquiry and deep thought, and encourage transfer?
– appropriate goals (e.g., content standards, benchmarks, curriculum objectives) identified? – valid and unit-relevant knowledge and skills identified?
Stage 2 – To what extent do the assessments provide:
2. fair, valid, reliable and sufficient measures of the desired results? Consider: are . . .
– students asked to exhibit their understanding through “authentic” performance tasks? – appropriate criterion-based scoring tools used to evaluate student products and
performances?
– a variety of appropriate assessment formats provide additional evidence of learning? Stage 3 – To what extent is the learning plan:
3. effective and engaging? Consider: will students . . .
– know where they’re going (the learning goals), why (reason for learning the content), and
what is required of them (performance requirements and evaluative criteria)?
– be hooked – engaged in digging into the big ideas (e.g., through inquiry, research, problem- solving, experimentation)?
– have adequate opportunities to explore/experience big ideas and receive instruction to equip them for the required performance(s)?
– have sufficient opportunities to rethink, rehearse, revise, and/or refine their work based upon timely feedback?
– have an opportunity to self-evaluate their work, reflect on their learning and set future goals? Consider: the extent to which the learning plan is:
– tailored and flexible to address the interests and learning styles of all students?
– organized and sequenced to maximize engagement and effectiveness?
Overall Design – to what extent is the entire unit:
4. coherent, with the elements of all 3 stages aligned?
Grant Wiggins and Jay McTighe 2005
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Assessment Standards
Utah SAGE Secondary Blueprints
Math 7
45 Operational Items
Domain
Min
Max
Ratios and Proportions
22%
26%
Expressions and Equations
16%
20%
The Number System
18%
22%
Geometry
18%
22%
Statistics and Probability
18%
22%
DOK1
12%
24%
DOK2
48%
60%
DOK3
20%
26%
Disclosure: Depth of Knowledge (DOK) and Elements of Rigor are essential components of the Utah Mathematics Core Standards. As such, DOK and Elements of Rigor are integrated into the Student Assessment of Growth and Excellence (SAGE) assessment items. All students will see a variety of DOK and Elements of Rigor on the SAGE summative assessment. For more information about DOK and Elements of Rigor please see: http//www.schools.utah.gov/assessment/Criterion-Referenced-Tests/Math.aspx
Or http://static.pdesas.org/content/documents/M1-Slide_22_DOK_Hess_Cognitive_Rigor.pdf
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Purpose of Testing (from USBE testing ethics training)
The purpose of statewide assessment is for accountability.
When administered properly, standardized assessments allow students to demonstrate their abilities, knowledge, aptitude, or skills (see R277 – 404). Valid and reliable results from uniform assessments provide information used by:
Students, to determine how well they have learned the skills and curriculum they are expected to know;
Parents, to know whether their student is gaining the skills and competencies needed to be competitive and successful;
Teachers, to gauge their students’ understanding and identify potential areas of improvement in their teaching;
LEAs (districts or charter schools), to evaluate programs and provide additional support;
State, for school accountability; and
Public, to evaluate schools and districts.
As educators, we are obligated to provide students with an opportunity to demonstrate their knowledge and skills fairly and accurately.
Educators involved with the state – wide assessment of students must conduct testing in a fair and ethical manner (see Utah Code 53A-1-608; R277-404).
The best test preparation a teacher can provide is good instruction throughout the year that covers the breadth and depth of the standards for a course, using varied instructional and assessment activities tailored to individual students.
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Ethical Assessment Practices (USBE ethics training) Licensed Utah Educators should:
• Ensure students are enrolled in appropriate courses and receive appropriate instruction
• Provide instruction to the intended depth and breadth of the course curriculum
• Provide accommodations throughout instruction to eligible students as identified by an
ELL, IEP, or 504 team.
• Use a variety of assessments methods to inform instructional practices
• Introduce students to various test-taking strategies throughout the year
• Provide students with opportunities to engage with available training test to ensure that
they can successfully navigate online testing systems, and to ensure that local
technology configurations can successfully support testing.
• Use formative assessments throughout the year using high-quality, non-secure test
questions aligned to Utah Standards.
Licensed Utah Educators shall ensure that:
• An appropriate environment reflective of an instructional setting is set for testing to limit distractions from surroundings or unnecessary personnel.
• All students who are eligible for testing are tested.
• A student is not discouraged from participating in state assessments, but upon a
parent’s opt-out request (follow LEA procedures), the student is provided with a
meaningful educational activity.
• Tests are administered in-person and testing procedures meet all test administration
requirements.
• Active test proctoring occurs: walking around the room to make sure that each
student has or is logged into the correct test; has appropriate testing materials
available to them; and are progressing at an appropriate pace.
• No person is left alone in a test setting with student tests left on screen or open.
• The importance of the test, test participation, and the good faith efforts of all
students are not undermined.
• All information in the Test Administration Manual (TAM) for each test administered
is reviewed and strictly followed (see 53A-1-608; R277-404).
• Accommodations are provided for eligible students, as identified by an ELL, IEP, or
504 team. These accommodations should be consistent with accommodations
provided during instruction throughout the instructional year.
• Any electronic devices that can be used to access non-test content or to
record/distribute test content or materials shall be inaccessible by students (e.g., cell phones, recording devices, inter-capable devices). Electronic security of tests and student information must not be compromised.
• Test materials are secure before, during and after testing. When not in use, all materials shall be protected, where students, parents cannot gain access.
No one may enter a student’s computer-based test to examine content or alter a student’s response in any way either on the computer or a paper answer document for any reason.
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Unethical Assessment Practices (USBE ethics training)
It is unethical for educators to jeopardize the integrity of an assessment or the validity of student responses.
Unethical practices include:
• Providing students with questions from the test to review before taking the test.
• Changing instruction or reviewing specific concepts because those concepts appear on
the test.
• Rewording or clarifying questions, or using inflection or gestures to help students
answer.
• Allowing students to use unauthorized resources to find answers, including dictionaries,
thesauruses, mathematics tables, online references, etc.
• Displaying materials on walls or other high visibility surfaces that provide answer to
specific test items (e.g., posters, word walls, formula charts, etc.).
• Reclassifying students to alter subgroup reports.
• Allowing parent volunteers to assist with the proctoring of a test their child is taking or
using students to supervise other students taking a test.
• Allowing the public to view secure items or observe testing sessions.
• Reviewing a student’s response and instructing the student to, or suggesting that the
student should, rethink his/her answers.
• Reproducing, or distributing, in whole or in part, secure test content (e.g., taking
pictures, copying, writing, posting in a classroom, posting publically, emailing).
• Explicitly or implicitly encouraging students to not answer questions, or to engage in
dishonest testing behavior.
• Administering tests outside of the prescribed testing window for each assessment.
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Intervention Standards
PCSD MTSS/RTI Model
Provo City School District's Academic MTSS (Multi-Tiered Systems of Support) details the system for providing Tier 1, 2, and 3 instruction; interventions; and assessment to help each student receive appropriate support. It is detailed below.
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Unpacking the Complexity of MTSS Decision Making
Successful MTSS implementation is a highly complex process that involves the following tasks:
• Gathering accurate and reliable data
• Correctly interpreting and validating data
• Using data to make meaningful instructional changes for students
• Establishing and managing increasingly intensive tiers of support
• Evaluating the process at all tiers to ensure the system is working
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Utah’s Multi-Tiered System of Supports USBE website:
http://www.schools.utah.gov/umtss/UMTSS-Model.aspx
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Supplemental Resources
Provo City School District’s Instructional Model
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• Student focus
• Educator credibility
• Meeting norms
• Professional Learning Communities (PLC)/Collaboration
• Civility policy
• Appearance and interactions
• Continual Leaning
• Testing ethics
• Research orientation
• Policy adherence
• Culture
• Safety–emotional and physical
• Physical classroom space
• Relationships
• Family connections
• Procedures
• Classroom management
• Student artifacts
• Student focus
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• Formative evaluation
• Summative evaluation
• Feedback:
• Performance of understanding
• Self-reported grades
• Student self-evaluation
• Testing ethics
• Differentiation
• Data analysis
• Response to interventions (RTI)/Multi-tiered system of success (MTSS)
• Lesson design
• Teacher clarity: share LT, share SC, share PoU
• Evidence-based instructional strategies
• Based on data
• Student engagement
• DOK – Depth of Knowledge
• Differentiation
• Student ownership of learning
• Curriculum notebook
• RTI/MTSS
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• State standards
• Curriculum map/pacing guide
• Units
• Objectives
• Curriculum Notebooks
• Course essentials
• Current
• Planning
Professional Association
The National Council of Teachers of Mathematics NCTM is the largest professional association for mathematics teachers.
Their website is at: https:// http://www.nctm.org/
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Evidence-based Pedagogical Practices
Hattie's Visible Learning
John Hattie, creator of Visible Learning, is a leading education researcher who has analyzed meta analyses in order to rank education practices (and factors) from most effective to least effective.
Hattie's list of highest ranking factors can be found at: https://visible-learning.org/hattie-ranking-influences-effect-sizes-learning-achievement/
or
https://visible-learning.org/nvd3/visualize/hattie-ranking-interactive-2009-2011-2015.html
Hattie's original book on the topic can be found at:
https://www.amazon.com/Visible-Learning-Synthesis-Meta-Analyses- Achievement/dp/0415476186
Definitions of Hattie's factors can be found at:
https://www.amazon.com/Visible-Learning-Synthesis-Meta-Analyses- Achievement/dp/0415476186
National Reading Panel Research
The federal government commissioned a National Reading Panel to review and compile the best evidence of effective practices for reading instruction.
The full report and executive summary can be accessed at:
https://lincs.ed.gov/communications/NRP
Learning Targets
Provo City School District employs the use of learning targets, success criteria, formative assessment, and feedback. A basis of study on these topics is the book, Learning Targets, by Connie Moss and Susan Brookhart, can be found at: https://www.amazon.com/Learning-Targets-Helping-Students-Understanding- ebook/dp/B008FOKP5S.
The district has produced four videos that demonstrate elements of learning target instruction and can be found at:
http://provo.edu/teachingandlearning/learning-targets-videos/
Teacher Resource Guide
Provo City School District's Teacher Resource Guide helps teachers meet the Utah Effective Teaching Standards and includes effective teaching practices. It can be found at: http://provo.edu/teachingandlearning/wp-content/uploads/sites/4/2016/01/11182016-TRG- fixed.pdf
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Glossary
Assessment Standards
College and Career Readiness
Curriculum Resources
ELA
Essential Learning Standards
Evidence-based Pedagogical Practices
Intervention Standards
Language Standards
A set of criteria to guide the assessment of student learning in a course that is based on Standards/Essentials of the course; this might include formative assessment practices, summative assessments/practices, common assessment plans, feedback practices, and a schedule for testing.
The College and Career Readiness (CCR) anchor standards
and grade-specific standards are necessary complements—the former providing broad standards, the latter providing additional specificity—that together define the skills and understandings that all students must demonstrate.
The materials teachers use to plan, prepare, and deliver instruction, including materials students use to learn about the subject. Such materials include texts, textbooks, tasks, tools, and media. Sometimes organized into a comprehensive program format, they often provide the standards, units, pacing guides, assessments, supplemental resources, interventions, and student materials for a course.
English Language Arts, includes components of Reading, Writing, Speaking and Listening, and Language.
These are also known as power standards. They are particular standards/objectives/indicators that a school/district defines as critical for student learning. In fact, they are so critical that students will receive intervention if they are not learned. Essentials are chosen because they: 1. have endurance, 2. have leverage, and 3. are important for future learning.
A list of teaching strategies that are supported by adequate, empirical research as being highly effective.
A set of criteria to guide teachers to provide additional instruction to students who did not master the content in Tier 1 instruction. This might include: commercial intervention programs, teacher- developed intervention materials, diagnostic testing, RTI/MTSS processes, and a list of essential knowledge/skills that will prompt intervention if the student does not demonstrate mastery.
(L) A component of ELA Standards that focus on conventions of standard English grammar, usage, and mechanics as well as learning other ways to use language to convey meaning effectively.
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Math Content Standards
Mathematical Practice Standards
MTSS
Pacing Guide
Pathways of Progress
Performance of Understanding.
Provo Way Instructional Model
Reading Standards: Foundational Skills
SAGE
(MC) Math Content Standards identify the knowledge of concepts and the skills students need for college and career readiness.
The 8 Mathematical Practice Standards describe varieties of expertise that mathematics educators at all levels seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. All 8 mathematical practice standards are essential standards.
Multi-Tiered Systems of Support is an approach to academic and behavioral intervention. It is part of the intervention standards.
The order and timeline of the instruction of standards, objectives, indicators, and Essentials over the span of a course (semester or year).
(POP) An evaluation of individual student growth or improvement over time compared to other students with the same level of initial skills. It empowers educators to set goals that are meaningful, ambitious, and attainable.
(PoU). Student results that provide compelling evidence that the student has acquired the learning target. (Brookhart, 2012).
The five areas of expectations for successful instruction identified by Provo City School District.
(RF) A component of ELA Standards that focus on helping students gain a foundation where curriculum is intentionally and coherently structured to develop rich content knowledge within and across grades as well as acquiring the habits of reading independently and closely, which are essential to their future success.
Student Assessment of Growth and Excellence. This is the state end of level test for ELA and Math grades 3 – 8, and Science grades 4 – 8.
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