SY 18-19

OSTP Mathematics Data

Interpretation Guidebook

OSDE ASSESSMENT AND DATA LITERACY TOOLKIT: A RESOURCE FOR EDUCATORS

1 OSTP Mathematics Data Interpretation Guide- OSDE Assessment and Data Literacy/ March 2019

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2 OSTP Mathematics Data Interpretation Guide- OSDE Assessment and Data Literacy/ March 2019

Table of Contents

Introduction.................................................................................................................................................................. 3

About the Oklahoma School Testing Program (OSTP) ................................................................................................ 4

About OSTP Data .......................................................................................................................................................... 5

OSTP Performance Level Data: Are we on track? ....................................................................................................... 7

Oklahoma Performance Index Scores (OPI): Are we porgressing? .......................................................................... 15

OSTP Reporting Category Indicators: Where are our strengths? ............................................................................. 17

Reporting Category Analysis- Grade 3- Mathematics ............................................................................................... 19

Reporting Category Analysis: Grade 4 Mathematics ................................................................................................ 21

Reporting Category Analysis: Grade 5- Mathematics ............................................................................................... 23

Reporting Category Analysis: Grade 6- Mathematics ............................................................................................... 25

Reporting Category Analysis: Grade 7- Mathematics ............................................................................................... 27

Reporting Category Analysis: Grade 8- Pre-Algebra ................................................................................................. 29

OSTP Glossary ............................................................................................................................................................. 30

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Introduction

We believe that all students can grow and all schools can improve and are committed to ensuring that state testing in Oklahoma is both effective and meaningful to families, districts, educators, and members of the community. Assessments within the Oklahoma School Testing Program (OSTP) are:

It is important to note that, while annual state assessments do not capture everything our students are capable of

or learn in school, state assessments are the most reliable way to objectively measure student performance

across the state. Statewide data allows educators and community leaders to see gaps in learning among student

groups as compared to other students across the state. These assessments also provide evidence that can inform

local educators and school and district leaders on the changes needed to strengthen student outcomes in their

district.

OSTP Assessments

Created with input from Oklahoma educators and stakeholders

Aligned to our Oklahoma Academic

Standards (OAS)

Able to provide information and data to support

state and federal accountability

Able to provide public information

about performance to support growth

and improvement

Able to track career and college

readiness over time as students move from grade-

to-grade

Able to measure student academic

growth and proficiency against

the OAS

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About the Oklahoma School Testing Program (OSTP)

Oklahoma recognizes that a robust assessment system is tied closely to students’ learning and teachers’ instructional practices by valuing and promoting local, classroom-based formative assessments that help make student learning visible. At the same time, that system should provide a strong summative assessment program that fits as a component within a multifaceted state, district and school accountability system. Oklahoma ESSA Plan pp 48-49

The Oklahoma School Testing Program (OSTP) consists of Oklahoma’s grade-level and Career- and College-Ready (CCR) summative assessments in English Language Arts (ELA), math, and science. OSTP assessments tell us how well our students are growing in the knowledge, skills, and abilities outlined in the Oklahoma Academic Standards (OAS) by supporting criterion-referenced interpretations at appropriate levels and grain size (e.g., grade, student group, teacher, building/district administrator, state). OSTP results support state and federal accountability and allow the public to know how their local schools are performing compared to others around the state.

The OSTP development process is an extensive, ongoing process that ensures our state assessments are valid and appropriate measures of student knowledge, skills, and abilities. The Oklahoma State Department of Education (OSDE) works with groups of Oklahoma educators through our contract with Measured Progress to develop the state tests as shown in the graphic below.

OSTP Development Process

OSTP Assessments

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About OSTP Data Data from state summative assessments serve as a point-in-time snapshot of what students know and are able to do relative to the standards being assessed. Measuring real-world skills like problem solving and critical thinking, the assessments are aligned to the standards so that teachers are able to teach the standards and do not have to “teach to

the test.” The Oklahoma Academic Standards for Mathematics are developed around four main content strands. Each strand provides the focus to deliver a clear, comprehensive, coherent, and developmentally appropriate set of standards for grades K-12 to guide curricular decisions.

Math Content Strand About this Strand

Number and Operations (N)

This strand provides focus on the importance of a students’ understanding of numbers, ways of representing numbers, relationships among numbers, relationships among number systems, and meanings of operations and how they relate to one another. A focus on number and operations is the cornerstone of a strong mathematics program.

Algebraic Reasoning and Algebra (A)

This strand provides focus for the PK-7 and Pre-Algebra standards around the notion that algebra is more than moving symbols around. It is about understanding patterns, relations and functions, representing and analyzing mathematical situations and structures using algebraic symbols, using mathematical models to represent and understand quantitative relationships, and analyzing change in various contexts.

Geometry and Measurement (GM)

This strand provides focus for the PK-7 and Geometry standards around the notion that geometry and measurement help students understand and represent ideas and solve problems they will encounter in their daily lives.

Data and Probability (D)

A focus on data and probability should enable all students to formulate questions that can be addressed with data and to collect, organize, and display relevant data to answer them. Students should select and use appropriate statistical methods to analyze data, develop and evaluate inferences and predictions that are based on data, and understand and apply basic concepts of probability.

In addition to the content standards, the process standards are defined as the Mathematical Actions and Processes and are comprised of the skills and abilities students should develop and be engaged in throughout their PK-12 mathematics education. The process and content standards work in concert to create clear, concise, and rigorous mathematics standards and expectations for Oklahoma students with the aim of helping them be career and college ready.

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While state summative assessments are only one measure of what students know and can do, having Oklahoma

students take standardized math assessments provides reliable data that can be compared across schools and

districts. Data from state assessment provide evidence in the form of an instructionally useful claim that serves to

support evaluation and enhancement of curriculum and programs while meeting state and federal accountability

requirements.

Claims made by the Oklahoma School Testing Program (OSTP) are reported out at three different grain sizes- Performance Level, Oklahoma Performance Index Score, and Reporting Category Indicator.

OSTP data can be accessed through the Measured Progress portal; however, a username and password are needed. Please contact your district test coordinator to find out about your school/district policy related to accessing data in the portal.

Performance Level (PL)- Are we on track?

•Reported as one of four levels: Advanced, Proficient, Basic (Limited Knowledge), or Below Basic (Unsatisfactory)

•Relates what a typical student at each level should know and be able to do relative to the Oklahoma Academic Standards (OAS) as described in the Performance Level Descriptors (PLDs)

•Provides a broad view of whether a student, program, or group is on-track with the grade level-expectations needed to be career and college ready (CCR)

Oklahoma Performance Index Scores (OPI)- Are we progressing?

•Reported as a number between 200-399

•Built on a comparable scale from 200-399 related to the Performance Level wherein 300 is always Proficient

•Provides a more specific data point that can be used to measure growth from year to year and determine where a student or program is in relation to grade-level expectations.

Reporting Category Indicators- Where are our strengths?

•Identified on the OSTP Test Blueprints and reported out as one of three indicators: Above Standard, At/Near Standard, or Below Standard

•Determined by comparing student performance on items associated with each reporting category against the expectations of Proficiency; communicates confidence regarding student ability to demonstrate the Proficient knowledge, skills, and abilities.

•Provides point-in-time data about student or program strengths and gaps

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OSTP Performance Level Data: Are we on track?

Reported as one of four levels (Advanced, Proficient, Basic, or Below Basic, performance levels provide a broad view of whether a student, program, or group is on track with grade level expectations needed to be career and college ready (CCR).

Performance levels were determined by Oklahoma educators using grade-level OAS to identify the knowledge,

skills and abilities (KSAs) students should demonstrate based on their command of grade-level standards. The

resulting Performance Level Descriptors (PLDs) and 2017 OSTP test results were used during the standard setting

process to determine the “cut scores” for each performance band. The range of scores for each performance level

band varies by grade as shown in the table below. The table communicates the range of index scores in each

performance band and the percentage of Oklahoma students that scored at each level.

Math Performance Bands and % of OK Students Scoring at Band by Grade Level (2017-18)

Grade

Below Basic % at Band

Basic

% at Band

Proficient % at Band

Advanced % at Band

Gr 3 200-273 24% 274-299 35% 300-320 26% 321-399 15%

Gr 4 200-272 27% 273-299 37% 300-321 25% 322-399 11%

Gr 5 200-265 25% 266-299 45% 300-320 20% 321-399 10%

Gr 6 200-266 29% 267-299 43% 300-329 23% 330-399 5%

Gr 7 200-278 34% 279-299 32% 300-328 26% 329-399 8%

Gr 8 200-276 52% 277-299 28% 300-315 10% 316-399 10%

2018 Performance Level Look-Up Table used to determine performance level bands in the table

Below Basic

Students have not performed at least at the basic level

Basic

Students demonstrate partial mastery of the essential knowledge and skills that are foundational for proficient work at their grade level or course and that students are not on track to be career and college ready (CCR)

Proficient

Students demonstrate mastery over challenging grade-level subject matter, can analyze and apply such knowledge to real-world situations, are ready for the next grade, course, or level, and are on-track to be career and college ready (CCR)

Advanced

Students demonstrate superior performance on challenging subject matter

Source: Senate Bill 1197

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Performance Level claims inform stakeholders of how to interpret student test scores in relation to the OAS through Performance Level Descriptor (PLD). PLDs define the intended interpretations of state tests scores by providing a narrative account of the knowledge, skills, and abilities students should demonstrate at each grade and in each level of achievement.

3rd Grade Math Performance Level Descriptors by Level

Below Basic Basic Proficient Advanced

Students have not performed at least at the Basic level.

Students demonstrate partial mastery of the essential knowledge and skills appropriate to their grade level. Students scoring at the Basic level typically:

Students demonstrate mastery over appropriate grade-level subject matter and readiness for the next grade level. Students scoring at the Proficient level typically:

Students demonstrate superior performance on challenging subject matter. In addition to demonstrating a broad and in-depth understanding and application of all skills at the Proficient level, students scoring at the Advanced level typically:

Represent whole

numbers. Complete simple

addition, subtraction, and multiplication problems.

Read and write fractions. Determine the value of a

set of coins or bills. Determine rules to

describe simple patterns. Determine unknowns in

simple equations. Identify right angles. Choose an appropriate

instrument to measure an object.

Read and write time from a digital clock.

Compare and order whole numbers.

Complete addition, subtraction, and multiplication problems and recognize the relationship between multiplication and division.

Construct and compare fractions using models.

Select the fewest number of coins for a given amount of money.

Determine rules to describe basic patterns.

Determine unknowns in equations and apply number properties.

Classify angles. Sort three-dimensional

figures and determine the perimeter of polygons.

Determine the area of two-dimensional figures.

Read and analyze length, temperature, and time.

Summarize a data set and analyze the data to solve problems.

Solve real-world problems and employ problem-solving strategies of identifying and using appropriate information.

Complete complex addition, subtraction, and multiplication problems and model division facts.

Order fractions using models and compose and decompose fractions related to the same whole.

Extend patterns and generate real-world situations to represent number sentences.

Determine volume and elapsed time.

Summarize complex data sets and analyze the data to solve problems.

Solve complex and non-routine real-world problems, draw logical conclusions and justify solutions.

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4th Grade Math Performance Level Descriptors by Level

Below Basic Basic Proficient Advanced

Students have not performed at least at the Basic level.

Students demonstrate partial mastery of the essential knowledge and skills appropriate to their grade level. Students scoring at the Basic level typically:

Students demonstrate mastery over appropriate grade-level subject matter and readiness for the next grade level. Students scoring at the Proficient level typically:

Students demonstrate superior performance on challenging subject matter. In addition to demonstrating a broad and in-depth understanding and application of all skills at the Proficient level, students scoring at the Advanced level typically:

Demonstrate the ability

to estimate and solve simple mathematical problems.

Use models to determine simple equivalent fractions, compare and order whole numbers and simple fractions, and decompose fractions.

Read and write simple decimals and compare and order whole numbers and decimals.

Determine change using whole dollars.

Determine a rule and extend a simple pattern.

Determine unknown values in simple mathematical problems.

Identify quadrilaterals and determine the area of simple polygons.

Identify appropriate units and tools to measure.

Estimate and solve mathematical problems.

Use models to determine equivalent fractions, compare and order fractions, and add and subtract fractions.

Read and write decimals and make connections between decimals and fractions.

Determine change using coins.

Determine rules and extend patterns.

Determine unknown values in mathematical problems.

Describe parts of geometrical figures and identify similarities in three-dimensional figures.

Decompose and determine the area of polygons.

Solve measurement problems.

Represent data sets and solve problems involving the data.

Solve real-world problems and employ problem-solving strategies of identifying and using appropriate information.

Estimate and solve complex mathematical problems and determine the unknown in non-equivalent expressions.

Compare decimals and fractions.

Solve complex money problems.

Determine a rule and extend a complex pattern.

Determine and represent unknown values in complex problems

Determine volume. Solve complex measurement

problems. Represent complex data sets

and solve problems involving the data.

Solve complex and non-routine real-world problems, draw logical conclusions and justify solutions.

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5th Grade Math Performance Level Descriptors by Level

Below Basic Basic Proficient Advanced

Students have not performed at least at the Basic level.

Students demonstrate partial mastery of the essential knowledge and skills appropriate to their grade level. Students scoring at the Basic level typically:

Students demonstrate mastery over appropriate grade-level subject matter and readiness for the next grade level. Students scoring at the Proficient level typically:

Students demonstrate superior performance on challenging subject matter. In addition to demonstrating a broad and in-depth understanding and application of all skills at the Proficient level, students scoring at the Advanced level typically:

Estimate and solve

division problems with remainders and solve addition and subtraction real-world problems.

Recognize basic equivalent decimals and fractions, represent whole numbers, and compare and order fractions or decimals.

Add and subtract decimals and fractions with like denominators.

Describe simple patterns of change and identify ordered pairs on a coordinate plane.

Evaluate simple equivalent numerical expressions or equations.

Describe and classify geometric figures.

Solve simple volume and perimeter problems.

Choose an appropriate instrument to measure objects and read and analyze the length of objects.

Read and analyze the measure of angles.

Read simple graphs.

Estimate and solve division problems with the remainder represented as a fraction or decimal.

Generate equivalent decimals and fractions, represent whole numbers or decimals, and compare fractions and decimals, including mixed numbers.

Estimate, add, and subtract decimals and fractions.

Describe patterns of change and graph these patterns as ordered pairs on a coordinate plane.

Evaluate expressions, equations, and inequalities.

Solve volume and perimeter problems and simple surface area problems.

Determine reasonable values for the perimeter of shapes with curves.

Compare angles. Recognize relationships within

a measurement system. Determine the mean, median,

mode, and range of a data set and analyze simple graphs.

Solve real-world problems and employ problem-solving strategies of identifying and using appropriate information.

Interpret the remainder of division problems within the context of the problem.

Order decimals, fractions, and whole numbers.

Evaluate complex expressions, equations, and inequalities.

Construct geometric figures and identify them in various contexts.

Compare the volume, perimeter, or surface area of geometric figures.

Analyze complex graphs. Solve complex and non-

routine real-world problems, draw logical conclusions and justify solutions

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6th Grade Math Performance Level Descriptors by Level

Below Basic Basic Proficient Advanced

Students have not performed at least at the Basic level.

Read, order, represent, and

explain rational numbers expressed as fractions, decimals, percents, and ratios.

Write positive integers as products of factors.

Illustrate or simplify the addition and subtraction of integers.

Identify and compare quantities, determine unit rates, and find equivalent fractions and percents.

Multiply and divide non-negative rational numbers.

Graph ordered pairs in all quadrants.

Represent reflective relationships between varying quantities.

Evaluate the value of a variable in expressions, equations, and inequalities.

Use number sense and properties of operations to solve equations and graph the solution.

Determine the area of parallelograms and triangles.

Identify angle relationships by name.

Identify and display the effect of transformations.

Identify lines of symmetry. Calculate measures of

central tendency, determine the sample space of simple experiments, and identify possible outcomes.

Estimate, illustrate, and simplify the addition and subtraction of integers and assess the reasonableness of an answer.

Solve ratio and unit rate problems.

Estimate and illustrate the multiplication and division of non-negative rational numbers.

Evaluate the validity of the value of a variable.

Generate expressions, equations, and inequalities.

Interpret the solution of an equation and assess the reasonableness of the solution.

Determine the area of polygons and composite figures.

Use relationships between angles and the triangle sum theorem to solve problems.

Estimate and solve problems requiring unit conversion.

Predict transformations, analyze lines of symmetry, and use the distance between points and transformations to solve problems involving congruent figures.

Explain and justify which measure of central tendency provides the most descriptive information for a data set.

Create and analyze box-and-whisker plots and explain and compare possible outcomes of simple experiments.

Estimate and solve complex problems requiring unit conversions.

Use the distance between points and transformations to solve complex problems involving congruent figures.

Analyze the differences between two outcomes of simple experiments.

Solve complex and non-routine real-world problems, draw logical conclusions and justify solutions.

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7th Grade Math Performance Level Descriptors by Level

Below Basic Basic Proficient Advanced

Students have not performed at least at the Basic level.

Recognize, compare, and

order rational numbers. Create equivalent

representations of rational numbers.

Calculate and model mathematical problems involving rational numbers and exponents.

Calculate the absolute value of a rational number.

Describe and identify a proportional relationship.

Identify and solve problems involving ratios and unit rates.

Represent, solve, and write simple equations.

Represent, write, and graph simple inequalities.

Evaluate expressions using the order of operations.

Determine the surface area and volume of rectangular prisms and calculate the area and perimeter of trapezoids.

Calculate the circumference and area of circles.

Describe the effect of dilations and transformations.

Calculate the measures of central tendencies and range and determine appropriate data displays.

Calculate theoretical probability.

Estimate solutions of problems involving rational numbers and assess the reasonableness of the solutions.

Differentiate between proportional and inversely proportional relationships and identify the constant of proportionality.

Represent proportional relationships in a variety of ways.

Use representations to identify and compare unit rates.

Solve problems involving proportional relationships and assess the reasonableness of solutions.

Represent, solve, and write equations.

Solve simple inequalities. Generate and evaluate

equivalent expressions with justification of steps.

Interpret theoretical probability and draw conclusions.

Apply the effect of dilations and transformations.

Solve real-world problems and employ problem-solving strategies of identifying and using appropriate information

Interpret equations and inequalities involving variables and rational numbers.

Make connections between circumference and area to solve problems involving circles.

Analyze, apply, and display the effect of dilations and multiple transformations.

Use central tendencies and range, predict data and select an appropriate data display, and predict theoretical probability.

Solve complex and non-routine real-world problems, draw logical conclusions and justify solutions.

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8th Grade Math Performance Level Descriptors by Level

Below Basic Basic Proficient Advanced

Students have not performed at least at the Basic level.

Simplify and generate

simple equivalent expressions, including expressions in scientific notation.

Translate between standard form and scientific notation.

Identify and compare real numbers.

Recognize if a graph represents a linear function.

Identify intercepts and slope from the graph of a line.

Identify the effect on the graph of a linear function when characteristics are changed.

Solve and graph equations and inequalities.

Use the Pythagorean Theorem to identify right triangles and to find the length of the hypotenuse.

Calculate the surface area and volume of solids.

Identify the outliers of a data set.

Identify the line of best fit from a given scatterplot and determine if the rate of change is positive or negative.

Calculate the experimental probability of single events, identify sample spaces, and classify events as independent or dependent.

Solve complex and non-routine real-world problems, draw logical conclusions and justify solutions.

Generate, simplify, and evaluate equivalent expressions.

Classify and explain operational closure of rational and irrational numbers.

Distinguish between a linear and nonlinear function.

Identify independent and dependent variables.

Describe, analyze, and represent linear functions with two variables and translate between representations.

Use and apply the Pythagorean Theorem.

Describe the impact on central tendencies of a data set with an outlier and when inserting or deleting a data point.

Interpret a scatterplot, determine the rate of change, and use a line of best fit to make predictions.

Calculate, interpret, and predict experimental probability and generalize samples to populations.

Generate, simplify, and evaluate complex equivalent expressions.

Make connections between volume and surface area to solve problems involving solids.

Compare the volume and surface area of different solids.

Describe the impact on central tendencies of a data set with multiple outliers and when inserting or deleting multiple data points.

Solve complex and non-routine real-world problems, draw logical conclusions and justify solutions.

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Performance level claims serve as a starting point for discussions and analysis related to the overall

Performance and readiness of programs, classes, and groups of students to move to the next grade, course, or level.

State, District, Site, Teacher Level Insights

● Where students are as a whole ● Equity gaps across student groups ● Patterns or trends across groups of students and/or grade levels ● Vertical alignment across grade levels ● Horizontal alignment across teachers or student groups ● Comparison to the state ● How data from local assessments compares ● How other evidence of student learning fits

Student Level Considerations

Performance level data tells only part of the student’s story and other relevant information should be considered when making student level decisions.

Other relevant information includes: o Student work samples o Course grades o Teacher observations

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Oklahoma Performance Index Scores (OPI): Are we progressing? Oklahoma Performance Index (OPI) scores supplement performance-level data by pin-pointing where a score is relative to the performance level band.

Built on a comparable scale from 200-399, wherein 300 is always proficient, OPI scale scores allow for numerical comparison between test takers taking the same test. OPI scores also allow us to compare individual student performance from one year to the next as a measure of growth. Performance level score ranges differ by grade and subject area as shown in the performance level lookup table linked here.

Grade 2017 Mean OPI 2018 Mean OPI Cohort Change

3 295 293 4 293 289 -6

5 288 285 -8 6 287 282 -6

7 287 287 No change

8 276 275 -12 OPI scores are obtained by statistically adjusting and converting raw scores onto a common scale to account for differences in difficulty across different assessment forms. This allows for consistency in score interpretation. When combined across a student population, mean OPI scores can be used to describe state, district, and school level changes in performance, as well as identify gaps in achievement among different groups of students.

+ + + + + + + /8 = Mean OPI Score Also referred to as an average, the mean OPI score is calculated by adding all the individual student scores and dividing by the number of total scores and communicates the average performance for a group of students.

Cohort change can be

found by finding the

difference in Mean OPIs

for the same group of

students from one year

to the next.

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Performance index scores add information to the conversation started with performance levels by pin-

pointing where a grade, student group, or class is relative to the next level along a continuum.

State, District, Site, Teacher Insights

● Changes in achievement gaps overtime

● Changes in student growth from year to year

● Equity gaps across student groups

● Trends and patterns across groups of students and/or grade levels

● Alignment across grade levels

● Comparison to state and other districts

● Relation to local level evidence of learning

Student Level Considerations

Performance level data tells only part of the student’s story and other relevant information should be considered when making student level decisions.

Other relevant information includes:

o Student work samples

o Course grades

o Teacher observations

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OSTP Reporting Category Indicators: Where are our strengths?

Oklahoma Academic Standards measured by the OSTP assessment are outlined on the OSTP Blueprints. Each

OSTP math assessment has four reporting categories. Reporting categories represent groups of similar student

skills assessed within each grade level and subject area. Reporting Category Performance is reported with an

indicator that represents a confidence level of the student’s likelihood of being able to demonstrate the proficient

level Knowledge, Skills, and Abilities (KSAs) found in the Performance Level Descriptor (PLD) and assessed

through at least five items. Indicators include Below Standard, At/Near Standard, and Above Standard.

Reporting category indicators communicate strand level performance on a subset of items within the state test.

Strand level information can help you gauge where groups of students or programs are relative to the proficient

level KSAs needed to be ready for the next grade, course, or level. State averages for each strand and grade level

for the 2017-18 state test are shown in the table below.

2017-18 Mathematics Reporting Categories by Grade Level and Indicator

Strand- Number and Operations (N) 3rd 4th 5th 6th 7th 8th Below Standard 40% 53% 57% 56% 44% 57%

At/Near Standard 38% 20% 22% 31% 36% 27%

Above Standard 22% 27% 21% 13% 19% 16%

Strand- Algebraic Reasoning and Algebra (A) 3rd 4th 5th 6th 7th 8th Below Standard 27% 46% 45% 44% 47% 63%

At/Near Standard 44% 37% 32% 33% 31% 22%

Above Standard 29% 17% 23% 23% 22% 15%

Strand- Geometry and Measurement (GM) 3rd 4th 5th 6th 7th 8th Below Standard 41% 44% 54% 38% 40% 58%

At/Near Standard 33% 33% 22% 49% 41% 23%

Above Standard 26% 23% 23% 13% 19% 19%

Strand- Data and Probability (D) 3rd 4th 5th 6th 7th 8th Below Standard 31% 27% 38% 51% 46% 48%

At/Near Standard 38% 62% 45% 20% 34% 45%

Above Standard 31% 12% 17% 29% 20% 6%

Below Standard

This student is UNLIKELYto possess the KSAs necessary to be Proficient with respect to the content represented in the standard.

At/Near Standard

This student is LIKELY to possess the KSAs necessary to be Proficient with respect to the content represented in the standard.

Above Standard

We are CONFIDENT that this student possesses the KSAs necessary to be Proficient with respect to the content represented in the standard.

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Reporting category indicator claims have the smallest grain size and can provide an additional piece

of evidence to inform instructional and programmatic decisions by bringing to the surface what is

working and what may need to change relative to the standards.

As with all OSTP data, other relevant information such as student work samples and local level standards-based

assessments should be considered when making decisions.

State, District, Site, and Teacher Level Insights

● Where strengths and gaps may exist in the curriculum

● Equity gaps across student groups

● Effectiveness of differentiation

● Needs for enhancement

● Alignment across grade levels

● Comparison to state and other districts

Student Level Considerations

Performance level data tells only part of the student’s story and other relevant information should be considered when making student level decisions. ● Other relevant information includes:

o Student work samples

o Course grades

o Teacher observations

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Reporting Category Analysis: Grade 3 Mathematics Reporting Category indicator claims can best be interpreted by linking the Oklahoma Academic Standards measured on the assessment with proficient level knowledge, skills, and abilities (KSAs) described in the grade level performance level descriptor (PLD). PLDs define the intended interpretations of tests scores by describing what students should know and be able to do in each level of achievement. PLDs reflect the standards but should not be the emphasis of instruction.

*Click on each standard to show the full breadth and depth that should be included to focus instruction.

GR 3- NUMBER AND OPERATIONS (N) On Track Knowledge, Skills, and Abilities

3.N.1 Number Sense- Compare and represent whole numbers up to 100,000 with an emphasis on place value and equality 3.N.2 Number Operations- Add and subtract multi-digit whole numbers; multiply with factors up to 10; represent multiplication and division in various ways; solve real-world and mathematical problems through the representation of related operations 3.N.3 Fractions- Understand meanings and uses of fractions in real-world and mathematical situations 3.N.4 Money- Determine the value of a set of coins or bills

Students receiving At/Near or Above Standard indicators are likely to be able to employ problem-solving strategies of identifying and using appropriate information to

represent, compare, and order whole numbers complete addition, subtraction, and multiplication

problems recognize the relationship between multiplication and

division read and write fractions construct and compare fractions using models determine the value of a set of coins or bills

select the fewest number of coins for a given amount of money

Gr 3- ALGEBRAIC REASONING AND ALGEBRA (A) On Track Knowledge, Skills, and Abilities (KSAs)

3.A.1 Numerical and Geometric Patterns- Describe and create representations of numerical and geometric patterns 3.A.2 Equations- Use number sentences involving multiplication and unknowns to represent and solve real-world and mathematical problems

Students receiving At/Near or Above Standard indicators are likely to be able to employ problem-solving strategies of identifying and using appropriate information to

determine rules to describe basic patterns determine unknowns in equations and apply number

properties

Gr 3- GEOMETRY AND MEASUREMENT (GM) On Track Knowledge, Skills, and Abilities (KSAs)

3.GM.1 Describe and Create Shapes- Use geometric attributes to describe and create shapes in various contexts 3.GM.2 Measurement- Understand measurable attributes of real-world and mathematical objects using various tools 3.GM.3 Time- Solve problems by telling time to the nearest 5 minutes

Students receiving At/Near or Above Standard indicators are likely to be able to employ problem-solving strategies of identifying and using appropriate information to

classify angles sort three-dimensional figures determine the perimeter of polygons determine the area of two-dimensional figures choose an appropriate instrument to measure an object read and analyze length, temperature, and time

Gr 3- DATA AND PROBABILITY (D) On Track Knowledge, Skills, and Abilities (KSAs)

3.D.1 Data Analysis- Summarize, construct, and analyze data

summarize a data set analyze the data to solve problems

In addition, on track 3rd grade students actively utilize the mathematical processes needed to be mathematically literate and can:

20 OSTP Mathematics Data Interpretation Guide- OSDE Assessment and Data Literacy/ March 2019

Develop a Deep and Flexible Conceptual Understanding

Build upon the knowledge they have and applying it in more complex mathematical contexts. For example, students use their place value knowledge when rounding numbers and estimating. They also recognize the relationships between addition and subtraction / multiplication and division to help determine which operation and strategy to use when solving word problems. They recognize connections in math that help them further their understanding of a concept and make sense of it (ex: skip counting by 5’s when telling time or recognizing fraction patterns on a number line and ruler).

Develop Accurate and Appropriate Procedural Fluency

Distinguish when to use certain operations, strategies, and/or properties to solve a problem most efficiently. Students develop mastery of basic math facts in addition, subtraction, and multiplication and then apply that knowledge when solving multi-digit equations. They also learn to use tools that are important to everyday life, such as rulers, thermometers, and clocks.

Develop Strategies for Problem Solving

Develop a toolbox of strategies for problem solving. They apply these strategies when finding solutions to real world problems. They analyze the problem, select a strategy to solve, and check their answers. Students recognize that there can be multiple ways to justify an answer with numbers, words, pictures, symbols, charts, graphs, etc; if their representation does not make sense, they reevaluate and try another strategy.

Develop Mathematical Reasoning

Defend their thinking based on logical strategies. They ask questions such as “Does this make sense?” and “How did you get that?” when participating in mathematical discourse with peers. They use their reasoning to evaluate the validity of an answer and if there is a better way to solve the problem. They apply their mathematical reasoning in many contexts, such as analyzing function machines and tables, classifying shapes, estimating lengths and values, and determine logical combinations of coins to represent a given amount.

Develop a Productive Mathematical Disposition

Recognize that math skills such as telling time, paying with money, and finding measurements are evident in everyday life. They begin to see the usefulness of mathematics in other contexts as well. They also understand that problem solving can lead to frustration, but continue to work through in order to find accurate solutions.

Develop the Ability to Make Conjectures, Model, and Generalize

Use tables, graphs, pictures, manipulatives, symbols and words to solve problems efficiently and accurately. They notice patterns and relationships in their representations that help them draw conclusions when analyzing data, finding missing values, and continuing numerical and geometric sequences. Students begin to predict solutions based on previous problems and are able to form generalizations that are helpful in other mathematical situations.

Develop the Ability to Communicate Mathematically

Describe their process of problem solving using appropriate vocabulary. They justify their answers, but also listen and consider other students’ strategies. Students discuss mathematics as a way of further understanding the content and eliminating misconceptions. Communicating during the problem solving process is a powerful way for students to evaluate if their answers make sense and determine if they need to readjust their thinking.

Source: Grade 3 Math Frameworks- The OSDE frameworks are curricular tools and resources

developed by Oklahoma teachers that may be helpful to educators as they evaluate, select and implement instruction, curriculum and local-level classroom assessments aligned to standards.

21 OSTP Mathematics Data Interpretation Guide- OSDE Assessment and Data Literacy/ March 2019

Reporting Category Analysis: Grade 4 Mathematics Reporting Category indicator claims can best be interpreted by linking the Oklahoma Academic Standards measured on the assessment with proficient level knowledge, skills, and abilities (KSAs) described in the grade level performance level descriptor (PLD). PLDs define the intended interpretations of tests scores by describing what students should know and be able to do in each level of achievement. PLDs reflect the standards but should not be the emphasis of instruction.

*Click on each standard to show the full breadth and depth that should be included to focus instruction.

Gr 4- NUMBER AND OPERATIONS (N) On Track Knowledge, Skills, and Abilities (KSAs)

4.N.1 Number Operations- Solve real-world and mathematical problems using multiplication and division 4.N.2 Rational Numbers- Represent and compare fractions and decimals in real-world and mathematical situations; use place value to understand how decimals represent quantities 4.N.3 Money- Determine the value of coins in order to solve monetary transactions

estimate and solve mathematical problems use models to determine equivalent fractions, compare

and order whole numbers and fractions add and subtract fractions, and decompose fractions read and write decimals compare and order whole numbers and decimals make connections between decimals and fractions determine change using whole dollars and coins

Gr 4- ALGEBRAIC REASONING AND ALGEBRA (A) On Track Knowledge, Skills, and Abilities (KSAs) 4.A.1 Numerical Patterns- Use multiple representations of patterns to solve real-world and mathematical problems 4.A.2 Equations- Use multiplication and division with unknowns to create number sentences representing a given problem situation

determine rules and extend patterns determine unknown values in mathematical problems

Gr 4- GEOMETRY AND MEASUREMENT (GM) On Track Knowledge, Skills, and Abilities (KSAs)

4.GM.1 Polygons and Polyhedra- Name, describe, classify and construct polygons, and three- dimensional figures 4.GM.2 Measurement- Understand angle, length, and area as measurable attributes of real- world and mathematical objects. Use various tools to measure angles, length, area, and volume

4.GM.3 Time-Determine elapsed time and convert

between units of time

describe and classify quadrilaterals describe parts of geometrical figures and identify

similarities in three-dimensional figures decompose and determine the area of polygons identify appropriate units and tools to measure solve measurement problems

Gr 4- DATA AND PROBABILITY (D) On Track Knowledge, Skills, and Abilities (KSAs)

4.D.1 Data Analysis- Collect, organize, and analyze data

represent data sets and solve problems involving the

data

22 OSTP Mathematics Data Interpretation Guide- OSDE Assessment and Data Literacy/ March 2019

In addition, on track 4th grade students actively utilize the mathematical processes needed to be mathematically literate and can:

Develop a Deep and Flexible Conceptual Understanding

Continue to build upon previous knowledge of basic multiplication and begin applying it to division, multi-digit multiplication and later, long division. They will apply their knowledge of operations to real world situations, establishing when a specific operation is appropriate. Students will make connections between fractions and decimals using number lines and manipulatives. They will also dive deeper into geometry, exploring angles, line segments, rays, and lines, as well as quadrilaterals

Develop Accurate and Appropriate Procedural Fluency

Recall basic multiplication and division facts with factors up to 12. They will appropriately and accurately solve real world problems using both basic and multi-digit equations including addition, subtraction, multiplication, and division. Students will identify quadrilaterals and their properties. They will also read and write fractions and decimals up to hundredths

Develop Strategies for Problem Solving

Predict, check, and justify their answers with real world problems including, but not limited to, decimals, fractions, multi-digit multiplication, and long division. Students will recognize multiple entry points and identify logical steps when solving multi-step equations.

Develop Mathematical Reasoning

Monitor their own work and make adjustments as needed to reach a logical solution. They will evaluate other students work and critique or defend the work. Students will also be able to question another’s work as well as answer questions about their own reasoning.

Develop a Productive Mathematical Disposition

Recognize the importance of decimals, fractions, and geometric patterns as part of their everyday life. They will view struggle as part of the problem solving process, understanding the importance of perseverance and active engagement.

Develop the Ability to Make Conjectures, Model, and Generalize

Use graphs, tables, pictures, words, and symbols to strategize and solve real world problems. Make generalizations about the powers of 10 and use them to help estimate and reason. Create input/output tables and other graphs and charts to recognize patterns and express them in writing as well as verbally.

Develop the Ability to Communicate Mathematically

Appropriately use vocabulary regarding time, decimals, money, fractions, multi-digit multiplication and division, when solving problems and defending their answer. Students will strategically solve problems by listening and responding to their peers.

Source: Grade 4 Math Frameworks- The OSDE frameworks are curricular tools and resources

developed by Oklahoma teachers that may be helpful to educators as they evaluate, select and implement instruction, curriculum and local-level classroom assessments aligned to standards.

23 OSTP Mathematics Data Interpretation Guide- OSDE Assessment and Data Literacy/ March 2019

Reporting Category Analysis: Grade 5- Mathematics Reporting Category indicator claims can best be interpreted by linking the Oklahoma Academic Standards measured on the assessment with proficient level knowledge, skills, and abilities (KSAs) described in the grade level performance level descriptor (PLD). PLDs define the intended interpretations of tests scores by describing what students should know and be able to do in each level of achievement. PLDs reflect the standards but should not be the emphasis of instruction. *Click on each standard to understand the full breadth and depth that should be used to focus instruction.

Gr 5- NUMBER AND OPERATIONS On Track Knowledge, Skills, and Abilities (KSAs) 5.N.1 Division of Multi-digit Numbers- Divide multi-digit numbers and solve real-world and mathematical problems using arithmetic 5.N.2 Fractions and Decimals- Read, write, represent, and compare fractions and decimals; recognize and write equivalent fractions; convert between fractions and decimals; use fractions and decimals in real-world and mathematical situations 5.N.3 Add and Subtract Rational Numbers- Add and subtract fractions with like and unlike denominators, mixed numbers and decimals to solve real-world and mathematical problems

estimate and solve division problems with remainders, including those represented by fractions or decimals

generate equivalent decimals and fractions represent whole numbers or decimals compare fractions and decimals, including mixed numbers estimate, add, and subtract decimals and fractions

Gr 5- ALGEBRAIC REASONING AND ALGEBRA On Track Knowledge, Skills, and Abilities (KSAs)

5.A.1 Numerical Patterns and Graphs- Describe and graph patterns of change created through numerical patterns 5.A.2 Equations and Inequalities- Understand and interpret expressions, equations, and inequalities involving variables and whole numbers, and use them to represent and evaluate real-world and mathematical problems

describe patterns of change and graph these patterns as ordered pairs on a coordinate plane

evaluate expressions, equations, and inequalities

Gr 5- GEOMETRY AND MEASUREMENT On Track Knowledge, Skills, and Abilities (KSAs) 5.GM.1 Polygons and Polyhedra- Describe, classify, and draw representations of two- and three-dimensional figures 5.GM.2 Volume and Surface Area- Understand how the volume of rectangular prisms and surface area of shapes with polygonal faces are determined by the dimensions of the object and that shapes with varying dimensions can have equivalent values of surface area or volume 5.GM.3 Angles/Length- Understand angle and length as measurable attributes of real-world and mathematical objects. Use various tools to measure angles and lengths

describe and classify geometric figures solve volume, perimeter, and simple surface area problems determine reasonable values for the perimeter of shapes with

curves read and analyze the measure of angles and compare angles choose an appropriate instrument to measure objects

and analyze the length of objects recognize relationships within a measurement system

Gr 5- DATA AND PROBABILITY (D) On Track Knowledge, Skills, and Abilities (KSAs) 5.D.1 Data Analysis- Display and analyze data to find the range and measures of central tendency (mean, median, and mode).

determine the mean, median, mode, and range of a data set and analyze simple graphs

24 OSTP Mathematics Data Interpretation Guide- OSDE Assessment and Data Literacy/ March 2019

In addition, on track 5th grade students will actively utilize the mathematical processes needed to be mathematically literate and can:

Develop a Deep and Flexible Conceptual Understanding

Pull from prior experiences and knowledge to choose strategies and procedures to access real world math problems involving fractions and decimals and other grade work content. They solve problems involving decimals and fractions by applying their understanding of operations with whole numbers. They strategize and problem solve when engaging in real world explorations of volume and graphing patterns. They also use prior knowledge to predict what kind of solution to expect in order to evaluate the reasonableness of their answers. They ask themselves probing questions while problem-solving to check their thinking and understanding

Develop Accurate and Appropriate Procedural Fluency

Draw upon their conceptual understanding to choose strategies and procedures that are appropriate for the mathematical situation. Fifth grade students apply their understanding of fractions and fraction models to represent addition and subtraction of fractions with unlike denominators as equivalent calculations with like denominators. They develop fluency in calculating sums and differences of fractions and make reasonable estimates of them. Students also use the meaning of fractions, addition, and subtraction, and the relationship between addition and subtraction to understand and explain why the procedures for adding and subtracting fractions make sense.

Develop Strategies for Problem Solving

Make and test predictions in varied real-world mathematical problems. They will recognize when an adaptation is needed, and check and justify their solution. They may problem solve by drawing pictures, guessing and checking, acting out, working backward or utilizing other invented strategies. They will routinely be able to develop and test more than one strategy to find solutions, and will identify when multiple solutions to a real world problem are possible. They may check their thinking by asking themselves, “What is the most efficient way to solve the problem?”, “Does this make sense?”, and “Can I solve the problem in a different way?”

Develop Mathematical Reasoning

Identify efficient methods to find solutions to problems where no clear-cut strategy is evident and ask questions to deepen understanding. They extend their understanding from whole numbers to their work with fractions and decimals. They actively examine the work of peers, asking clarifying questions in order to constructively critique the strategies. They will engage in and create real world mathematical problems and recognize when particular strategies, methods, and algorithms will aid in a solution.

Develop a Productive Mathematical Disposition

Recognize that math is evident in everyday life and apply mathematical thinking and problem solving in other areas of academics and outside of the classroom. They actively engage in critical thinking and view struggle as part of the process. They are willing to take chances, adapt, revise plans and persevere, until at least one solution is found. When composing and decomposing numbers and shapes and working within grade level content, they investigate, describe and draw logical conclusions aiding in the development of a bank of strategies to utilize when embarking on the problem-solving process.

Develop the Ability to Make Conjectures, Model, and Generalize

Connect place value and their prior work with operations to understand algorithms to fluently multiply multi-digit numbers and perform all operations with decimals to hundredths. They explore operations with fractions with visual models and begin to formulate generalizations. Fifth graders explore representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures, using objects, making charts, lists, or graphs, and creating equations. They use these models to recognize patterns and structures in order to formulate rules

and generalizations.

Develop the Ability to Communicate Mathematically

Actively listen and communicate when collaborating with peers. They are able to defend their thinking when solving real world problems involving three-digit division, rational numbers, geometrical solids, data and other grade level concepts. While collaborating they respectfully critique others' strategies, ideas and solutions by asking questions like “How did you get that”” and “Why is that true?

Source: Grade 5 Math Frameworks- The OSDE frameworks are curricular tools and resources

developed by Oklahoma teachers that may be helpful to educators as they evaluate, select and implement instruction, curriculum and local-level classroom assessments aligned to standards.

25 OSTP Mathematics Data Interpretation Guide- OSDE Assessment and Data Literacy/ March 2019

Reporting Category Analysis: Grade 6 Mathematics Reporting Category indicator claims can best be interpreted by linking the Oklahoma Academic Standards measured on the assessment with proficient level knowledge, skills, and abilities (KSAs) described in the grade level performance level descriptor (PLD). PLDs define the intended interpretations of tests scores by describing what students should know and be able to do in each level of achievement. PLDs reflect the standards but should not be the emphasis of instruction. *Click on each standard to understand the full breadth and depth that should be used to focus instruction.

Gr 6- NUMBER AND OPERATIONS On Track Knowledge, Skills, and Abilities (KSAs)

6.N.1 Number Sense of Integers and Rational Numbers- Read, write, and represent integers and rational numbers expressed as fractions, decimals, percents, and ratios; write positive integers as products of factors; use these representations

in real-world and mathematical situations. 6.N.2 Addition and Subtraction of Integers- Add and

subtract integers in order to solve real-world and mathematical problems 6.N.3 Ratios- Understand the concept of ratio and its relationship to fractions and percents and to the multiplication and division of whole numbers. Use ratios to solve real-world and mathematical problems. 6.N.4 Multiplication and Division of Rational Numbers- Multiply and divide decimals, fractions, and mixed numbers; solve

real-world and mathematical problems with rational numbers.

read, order, represent, and explain rational numbers expressed as fractions, decimals, percents, and ratios

write positive integers as products of factors estimate, illustrate, and simplify the addition and subtraction

of integers and assess the reasonableness of an answer identify and compare quantities and find equivalent fractions

and percents solve ratio and unit rate problems calculate, estimate, and illustrate the multiplication and

division of non-negative rational numbers

Gr 6- ALGEBRAIC REASONING AND ALGEBRA On Track Knowledge, Skills, and Abilities (KSAs)

6.A.1 Algebraic Representations- Recognize and represent relationships between varying quantities; translate from one representation to another; use patterns, tables, graphs and rules

to solve real-world and mathematical problems. 6.A.2 Algebraic Expressions-Use properties of arithmetic to

generate equivalent numerical expressions and evaluate

expressions involving positive rational numbers. 6.A.3 Equations and Inequalities- Use equations and

inequalities to represent real-world and mathematical problems and use the idea of maintaining equality to solve equations. Interpret solutions in the original context.

graph ordered pairs and represent reflective relationships between varying quantities

evaluate the validity of the value of a variable in expressions, equations, and inequalities

generate expressions, equations, and inequalities solve, graph, and interpret the solution of an equation

assessing the reasonableness of the solution

Gr 6- GEOMETRY AND MEASUREMENT On Track Knowledge, Skills, and Abilities (KSAs)

6.GM.1 Area of Parallelograms and Triangles- Calculate

area of squares, parallelograms, and triangles to solve real-world and mathematical problems. 6.GM.2 Angle Relationships on Intersecting Lines- Understand and use relationships between angles in geometric figures 6.GM.3 Units of Measurement and Unit Conversions- Choose appropriate units of measurement and use ratios to convert within measurement systems to solve real-world and mathematical problems. 6.GM.4 Congruency and Symmetry of Transformations- Use translations, reflections, and rotations to establish congruency and understand symmetries.

Students receiving At/Near or Above Standard indicators are likely to be able to employ problem-solving strategies of identifying

and using appropriate information to

determine the area of polygons and composite figures identify angle relationships by name use relationships between angles and the triangle sum

theorem to solve problems estimate and solve problems requiring unit conversion identify, predict, and display the effect of transformations

use the distance between points and transformations to solve analyze lines of symmetry

problems involving congruent figures

26 OSTP Mathematics Data Interpretation Guide- OSDE Assessment and Data Literacy/ March 2019

Gr 6- DATA AND PROBABILITY (D) On Track Knowledge, Skills, and Abilities (KSAs)

6.D.1 Data Analysis- Display and analyze data

6.D.2 Probability- Use probability to solve real-world and

mathematical problems; represent probabilities using

fractions and decimals.

calculate measures of central tendency

explain and justify which measure of central tendency provides the most descriptive information for a data set

create and analyze box-and-whisker plots

determine the sample space of simple experiments and identify possible outcomes

explain and compare possible outcomes of simple experiments

In addition, on track 6th grade students will actively utilize the mathematical processes needed to be mathematically literate and can:

Develop a Deep and Flexible Conceptual Understanding

Continue to explore the relationships between real-world situations and mathematical expressions, equations and inequalities involving variables and rational numbers through the use of inverse operations, the associative, commutative, and distributive properties, and visual representations on number lines or a coordinate plane. They define equivalence using substitution, variables, congruency, and conversion between fractions, decimals, and percents. They use deconstruction to determine the area of polygons and create prime factorizations.

Develop Accurate and Appropriate Procedural Fluency

Choose appropriate algorithms to add and subtract integers or multiply and divide fractions, decimals, and mixed numbers. They use exponents to represent prime factorizations, and follow the order of operations when solving expressions or equations. They choose the most appropriate representation of a quantity including formulas for area of rectangles, parallelograms, and triangles.

Develop Strategies for Problem Solving

Recognize relationships, apply rules or formulas, use known information to find missing values, break problems into smaller components, and make connections to real world situations. Students construct models, use manipulatives, and select appropriate tools to enhance their understanding of the problem or formulate appropriate questions. They are aware of their thinking patterns and processes as they work through problems individually or in groups, recognizing that there may be more than one approach to reaching an acceptable solution.

Develop Mathematical Reasoning

Use estimation to assess reasonableness of answers. They express why they have chosen the strategy, algorithm, or representation as the best fit for mathematical situations. They make predictions of the effects of translations, rotations, and reflections. They determine similarities/differences, whether a substitution results in a true or false inequality or equation, and relate measures of central tendency to real-world data sets and probability to real world sample spaces.

Develop a Productive Mathematical Disposition

Make personal connections between math and things beyond the classroom. They develop discipline to write each step when solving expressions and equations or when making conversions while focusing on the process and reasons behind the algorithm or strategy. They are willing to work collaboratively, take risks, and revise thinking or processes as needed, building confidence on their successes.

Develop the Ability to Make Conjectures, Model, and Generalize

Write an expression, equation, or inequality that represents a real world situation or apply math rules beyond the classroom. They represent varying quantities in multiple ways, graph solutions, and model concepts such as area, congruency, and distance. Students make predictions about experimental outcomes using probability. They understand that multiplicative and additive properties work the same for fractions, decimals, and percents as they do with whole numbers.

Develop the Ability to Communicate Mathematically

Communicate effectively with peers and teacher using appropriate vocabulary in writing, through discussions in pairs or small groups, and by presenting to the class. Students translate words into mathematical sentences and vice versa. They explain differences, rules, procedures, and how to apply each state while providing the reason for choosing the particular strategy or representation over other options. They describe mathematical situations and how these relate to the real world. They generate purposeful questions to further their knowledge, reframing ideas presented by others to identify gaps in their understanding.

Source: Grade 6 Math Frameworks- The OSDE frameworks are curricular tools and resources

27 OSTP Mathematics Data Interpretation Guide- OSDE Assessment and Data Literacy/ March 2019

Reporting Category Analysis: Grade 7 Mathematics Reporting Category indicator claims can best be interpreted by linking the Oklahoma Academic Standards measured on the assessment with proficient level knowledge, skills, and abilities (KSAs) described in the grade level performance level descriptor (PLD). PLDs define the intended interpretations of tests scores by describing what students should know and be able to do in each level of achievement. PLDs reflect the standards but should not be the emphasis of instruction. *Click on each standard to understand the full breadth and depth that should be used to focus instruction.

Gr 7- NUMBER AND OPERATIONS On Track Knowledge, Skills, and Abilities (KSAs)

7.N.1 Representation and Comparison of Rational Numbers- Read, write, represent, and compare rational numbers, expressed as integers, fractions, and decimals 7.N.2 Number Operations and Absolute Value- Calculate with integers and rational numbers, with and without positive integer exponents, to solve real- world and mathematical problems; explain the relationship between absolute value of a rational number and the distance of that number from zero

recognize, compare, and order rational numbers create equivalent representations of rational numbers calculate, model, and estimate solutions of problems

involving rational numbers and exponents assessing the reasonableness of solutions

calculate the absolute value of a rational number Gr 7- ALGEBRAIC REASONING AND ALGEBRA (A) On Track Knowledge, Skills, and Abilities (KSAs)

7.A.1 Proportional Relationships-Understand the concept of proportionality in real-world and mathematical situations, and distinguish between proportional and other relationships 7.A.2 Proportions, Rates and Ratios-Recognize proportional relationships in real-world and mathematical situations; represent these and other relationships with tables, verbal descriptions, symbols, and graphs; solve problems involving proportional relationships and interpret results in the original context. 7.A.3 Linear Equations and Inequalities- Represent and solve linear equations and inequalities 7.A.4 Order of Operations- Use order of operations and properties of operations to generate equivalent numerical and algebraic expressions containing rational numbers and grouping symbols; evaluate such expressions

describe and identify a proportional relationship identifying the constant of proportionality

represent proportional relationships in a variety of ways differentiate between proportional and inversely

proportional relationships represent proportional relationships in a variety of ways

solve problems involving proportional relationships and assess the reasonableness of solutions

identify and solve problems involving ratios and unit rates generate and evaluate equivalent expressions with

justification of steps represent, solve, and write equations evaluate expressions using the order of operations represent, write, solve, and graph simple inequalities

Gr 7- GEOMETRY AND MEASUREMENT On Track Knowledge, Skills, and Abilities (KSAs) 7.GM.1 Surface Area and Volume of Rectangular Prisms-Develop and understand the concept of surface area and volume of rectangular prisms 7.GM.2 Trapezoids and Composite Figures-Determine the area of trapezoids and area and perimeter of composite figures 7.GM.3 Circles- Use reasoning with proportions and ratios to determine measurements, justify formulas, and solve real-world and mathematical problems involving circles and related geometric figures 7.GM.4 Transformations-Analyze the effect of dilations, translations, and reflections on the attributes of two-dimensional figures on and off the coordinate plane

determine the surface area and volume of rectangular prisms

calculate the area and perimeter of trapezoids calculate the circumference and area of circles

describe and apply the effect of dilations and transformations

28 OSTP Mathematics Data Interpretation Guide- OSDE Assessment and Data Literacy/ March 2019

Gr 7- DATA AND PROBABILITY (D) On Track Knowledge, Skills, and Abilities (KSAs)

7.D.1 Data Analysis- Display and analyze data in a variety of ways

7.D.2 Probability- Calculate probabilities and reason about

probabilities using proportions to solve real-world and mathematical

problems.

calculate the measures of central tendencies and range and determine appropriate data displays

calculate and interpret theoretical probability drawing conclusions

In addition, on track 7th grade students will actively utilize the mathematical processes needed to be mathematically literate and can:

Develop a Deep and Flexible Conceptual Understanding

Continue to apply mathematical concepts to their everyday lives. They will apply the concept of proportionality to the real world to understand and explain the relationship between tables, graphs, symbols, and verbal descriptions. Comparisons and links between unit rates, proportions, rates of change, and slope are front and center as students move between multiple representations. Students are able to flow freely between percents, decimals, and fractions

Develop Accurate and Appropriate Procedural Fluency

Begin to build algorithms and functionally applying them to their conceptual knowledge. Formulas and procedures are discovered and developed to determine areas of trapezoids, find area and perimeter of composite figures, and calculate circumference and area of circles so that students can make sense of how these concepts apply to real life. As students begin using symbols to solve mathematical situations, they will apply an understanding of properties of operations and how they allow building of equivalent expressions as well as order of operations. This ensures the ability to check for reasonableness when using technological tools like calculators.

Develop Strategies for Problem Solving

Use concepts and procedures to make decisions on how to approach challenging real-world situations. They determine reasonableness of different approaches of problem solving and judge the efficiency of multiple modes. Students begin designing experiments, collecting data, and making predictions about measures of central tendency, scale representations, and probability. They are using a variety of tools in mathematics and can determine when it is useful and necessary to use technology and tools to deal with data.

Develop Mathematical Reasoning

Develop sound abilities to explain real world situations mathematically using words, symbols, graphical representations, and tables. They apply proportional reasoning to assess whether solutions are mathematically sound.

Develop a Productive Mathematical Disposition

Understand that math is useful and worthwhile. They will be able to use strategies and reason to overcome mathematical obstacles as they continue to apply the idea of proportionality to everyday life. Tables, graphs, symbols, and verbal descriptions find their place in students’ lives, as they understand the usefulness of each in different situations.

Develop the Ability to Make Conjectures, Model, and Generalize

Begin to develop algorithms and procedures through the actions of identifying patterns, making tables, predicting how identified information will apply to unknown situations, and then establishing future processes. Measures of central tendency and graphic representations help students to draw conclusions and apply their findings to rationalize the real world.

Develop the Ability to Communicate Mathematically

Use mathematical terminology to describe their surroundings and real life situations. They are able to communicate effectively with peers and teachers as well as those without a thorough mathematical background to explain their understanding of mathematical concepts. Students should be provided with opportunities to engage in explorations and discussion on a regular basis both orally and in writing.

Source: Grade 7 Math Frameworks- The OSDE frameworks are curricular tools and resources

29 OSTP Mathematics Data Interpretation Guide- OSDE Assessment and Data Literacy/ March 2019

Reporting Category Analysis: Grade 8- Pre-Algebra Reporting Category indicator claims can best be interpreted by linking the Oklahoma Academic Standards measured on the assessment with proficient level knowledge, skills, and abilities (KSAs) described in the grade level performance level descriptor (PLD). PLDs define the intended interpretations of tests scores by describing what students should know and be able to do in each level of achievement. PLDs reflect the standards but should not be the emphasis of instruction. *Click on each standard to understand the full breadth and depth that should be used to focus instruction.

Gr 8- NUMBER AND OPERATIONS On Track Knowledge, Skills, and Abilities (KSAs)

PA.N.1 Real Number Operations- Read, write, compare, classify, and represent real numbers and use them to solve problems in various contexts

identify, compare, and classify real numbers explain operational closure of rational and irrational

numbers generate, simplify, and evaluate equivalent expressions,

including expressions in scientific notation Gr 8- ALGEBRAIC REASONING AND ALGEBRA (A) On Track Knowledge, Skills, and Abilities (KSAs)

PA.A.1 Linear and Non-Linear Functions- Understand the concept of function in real-world and mathematical situations, and distinguish between linear and nonlinear functions PA.A.2 Linear Function Representations and Problem Solving- Recognize linear functions in real-world and

mathematical situations; represent linear functions and other

functions with tables, verbal descriptions, symbols, and graphs;

solve problems involving linear functions and interpret results in

the original context PA.A.3 Algebraic Expressions- Generate equivalent

numerical and algebraic expressions and use algebraic

properties to evaluate expressions

PA.A.4 Equations and Inequalities- Represent real world

and mathematical problems using equations and inequalities involving linear expressions. Solve and graph equations and inequalities symbolically and graphically. Interpret solutions in the original context

describe, analyze, and represent linear functions with two variables and translate between representations

distinguish between a linear and nonlinear function identify independent and dependent variables identify the effect on the graph of a linear function when

characteristics are changed solve and graph equations and inequalities

Gr 8- GEOMETRY AND MEASUREMENT On Track Knowledge, Skills, and Abilities (KSAs)

PA.GM.1 Pythagorean Theorem - Solve problems involving

right triangles using the Pythagorean Theorem. PA.GM.2 Surface Area and Volume- Calculate surface area and volume of three-dimensional figures

use and apply the Pythagorean Theorem calculate the surface area and volume of solids

Gr 8- DATA AND PROBABILITY (D) On Track Knowledge, Skills, and Abilities (KSAs)

30 OSTP Mathematics Data Interpretation Guide- OSDE Assessment and Data Literacy/ March 2019

PA.D.1 Data Analysis and Scatter Plots- Display and

interpret data in a variety of ways, including using

scatterplots and approximate lines of best fit. Use line of

best fit and average rate of change to make predictions

and draw conclusions about data PA.D.2 Probability- Calculate experimental probabilities

and reason about probabilities to solve real-world and

mathematical problems

describe the impact on central tendencies of a data set with an outlier and when inserting or deleting a data point

interpret a scatterplot, determine the rate of change, and use a line of best fit to make predictions

identify sample spaces, and classify events as independent or dependent

calculate, interpret, and predict experimental probability and generalize samples to populations

In addition, on track 8th grade students will actively utilize the mathematical processes needed to be mathematically literate and can:

Develop a Deep and Flexible Conceptual Understanding

Expand applications both algebraically and geometrically of linear equations, functions and inequalities. Tools such as models, manipulatives, symbols, number lines, tables and coordinate grids aid in exploration and analysis of exponents, irrational numbers, 2-D and 3-D geometric figures, data collections, and real world tasks. The depth that these topics are covered in this course establish a conceptual foundation for future algebra, geometry, and statistics courses.

Develop Accurate and Appropriate Procedural Fluency

Develop multiple methods for solving expressions, equations, functions and inequalities with exponents and square roots. Emphasis should be focused on justification of steps used in their solutions, imploring a variety of methods to represent their solutions with context when applicable to real life situations, and checking work using substitution, graphing and estimation. Students should be developing skills to fluently apply and calculate the geometric formulas of the Pythagorean theorem, Surface Area and Volume.

Develop Strategies for Problem Solving

Use a variety of strategies to solve high-quality tasks and activities that have real world applications. The majority of problems in this course work towards creating, analyzing or applying expressions, linear equations, inequalities or formulas that model the situation presented. Students should be encouraged to persevere to formulate a strategy/strategies that fit the problem, recognize when an adaptation is needed, and then check and justify their solution using context and appropriate vocabulary.

Develop Mathematical Reasoning

Work to solidify methods of creating, solving, representing and applying multi-step equations, inequalities, and functions both algebraically and graphically in a variety of contexts. As this occurs, they should look for shared relationships between these three concepts by making justifiable conjectures and be able to explain what happens algebraically and graphically in context when changes occur.

Develop a Productive Mathematical Disposition

Recognize mathematical concepts in daily life, but are grappling with abstract ideas that do not have common familiarity for them. As more sophisticated algebraic ideas are bridged using real world examples, applications and discussions, they begin to see how they are using their prior and newly gained knowledge to use mathematics for analysis, efficiency, and reasoning. They begin to make formal conjectures, be challenged to make sense of other methods, understand that in some cases more than one answer is justifiable and ultimately realize that productive struggle is necessary for growth.

Develop the Ability to Make Conjectures, Model, and Generalize

Apply and analyze changes to multi-step equations, functions and inequalities in real world contexts. Students should be given a variety of opportunities to make predictions of what changes would look like algebraically and/or graphically. From their prediction, a formal conjecture is made with reasoning supported by data, models, and fundamental ideas to work towards a generalization that is defendable

Develop the Ability to Communicate Mathematically

Use oral and written communication of ideas and concepts. Students should be given multiple venues to share their ideas with their class from whole class discussions to collaborative real world group tasks to projects with the potential of further reaching impact. Communication of ideas should be valued and repeatedly fine-tuned to capture the essence of the concept or solution with appropriate mathematical vocabulary, context, proof and efficiency.

Source: Grade 8 Math Frameworks- The OSDE frameworks are curricular tools and resources

OSTP Glossary

31 OSTP Mathematics Data Interpretation Guide- OSDE Assessment and Data Literacy/ March 2019

criterion-referenced test: An assessment that allows its users to make score interpretations of a student’s performance in relation to specified performance standards or criteria, rather than in comparison to the performances of other test takers. See also performance standard/level. cut score: Selected points on the score scale of a test. The points are used to determine whether a particular test score is sufficient for some purpose. For example, student performance on a test maybe classified into one of several categories, such as unsatisfactory, limited knowledge, proficient or advanced on the basis of cut scores. mean: The quotient obtained by dividing the sum of a set of scores by the number of scores; also called the “average.” Mathematicians call it the “arithmetic mean.” Oklahoma Performance Index (OPI): The Oklahoma Performance Index (OPI) is a scaled score resulting from the mathematical transformation of the true score, which is associated with each of the raw scores. The OPI score is used to place students in one of four performance levels. performance level: A level of performance on a test, established by education experts, as a goal of student attainment. It may also refer to a description of the knowledge, skills, and abilities typically held by students within a performance level. performance level descriptors (PLD): Descriptors that convey the degree of student achievement in a given achievement level. Taken together with grade- and content-specific PLDs and threshold scores, they convey to educators, parents, student, and the public the meaning of assessment results relative the Oklahoma Academic Standards. performance-level score range: A range of scale scores that corresponds to one of the four performance levels: Advanced, Proficient, Below Basic, and Basic. reporting category: Groups of similar student skills or content standards assessed within each grade and subject and are communicated on the OSTP test blueprints. reporting category Indicators: Smallest grain-size OSTP data that relates student performance on a subset of items associated with a reporting category with an indicator, rather than with scale scores. These indicators are Below Standard, At/Near Standard, and Above Standard. scale scores: Scores on a single scale with intervals. The scale can be applied to all groups taking a given test, regardless of group characteristics or time of year, making it possible to compare scores from different groups of students. Scale scores are appropriate for various statistical purposes. For example, they can be added, subtracted, and averaged across test levels. Such computations permit educators to make direct comparisons among examinees or compare individual scores to groups in a way that is statistically valid. This cannot be done with percentiles or grade equivalents. standardized test: A test that is given in exactly the same way to all children taking the test. The items are the same, the instructions are the same, the timing is the same, the method of determining correctness is the same, and the scoring is the same. No variations are allowed.

32 OSTP Mathematics Data Interpretation Guide- OSDE Assessment and Data Literacy/ March 2019