math amp summative framework final 1 15 15 assessment...alaska measures of progress mathematics...

Alaska Measures of Progress Mathematics Summative Assessment Framework The Alaska Mathematics Standards is a set of specific, rigorous expectations that build students’ skills across grades in mathematics content as well as mathematical practices. The standards are designed to develop a logical progression of mathematical fluency, conceptual understanding, and real-world applications. Building on the Alaska Mathematics Standards, test development for the AMP assessment is focusing item development on broader skills and strategies rather than individual standards and discrete skills—a method more reflective of both the holistic approaches teachers use to teach and the ways students learn. This document includes information about the content emphases and the item specifications of AMP. While documents such as these are typically created for the teams of test developers and content specialists who write and review test questions, they can also provide helpful information for teachers. The Summative Assessment Framework combines test development documents and adapts the information for use by educators. The Framework provides an overview of the assessment for each grade, using tables to identify accompanying Claims and thoroughly define Targets, including statements of the evidence required.

The Summative Assessment Framework

The AMP Summative Assessment Framework shows the percentage and relative emphasis for Claims and Targets for the summative assessments. The AMP Summative Assessment Frameworks for both Mathematics and English Language Arts (ELA) do three very specific things:

1. Organize the standards around big ideas (Claims). A Claim is a broad statement that outlines the outcomes that demonstrate mastery of the standards.

2. Describe the specific skills required of students in order to be successful on AMP through Targets. Targets are groups of related standards.

3. Create a content emphasis to form a bridge between standards, assessment, and instruction. This bridge can help educators analyze how a lesson or unit engages a student’s cognitive process and what level of cognitive rigor (Depth of Knowledge) it requires.

AMP The Alaska Measures of Progress assessment is a computer-based assessment for grades 3-10 aligned to the Alaska English Language Arts and Mathematics Standards (adopted in 2012).

Claims and Targets Claims are broad statements about student mastery of the standards.

Targets are groups of related standards that can be measured.

Claims The Claims are the broadest categories of knowledge, skills, and abilities that can have inferences drawn about them. These broad statements outline outcomes that demonstrate mastery of the standards. In Mathematics, the Claims follow the pattern of the Clusters, the boldfaced items in the Alaska Mathematics Standards. There are four Claims in Mathematics that will be assessed by AMP: Claim 1: Concepts and Procedures (65-70%). Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency. Claim 2: Problem Solving (8-12%). Students can solve a range of complex, well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies. Claim 3: Communicating and Reasoning (8-12%). Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others. Claim 4: Modeling and Data Analysis (8-12%). Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems. In Claims 2, 3, and 4, students will focus on deeper problem-solving strategies and mathematical practices.

Targets Targets (or Assessment Targets) break the Claims down into groups of similar standards. Each Target within a Claim is followed by evidence statements, which outline the skills students need to master. Arranging standards into Targets more accurately reflects how students learn and teachers teach. For example, students who are solving a division word problem will need to draw on their previous understanding of multiplication and incorporate Mathematical Practice 6 (Attend to precision) to accurately solve the problem. The Claims are built from Targets, which are drawn from groups of the Alaska Standards. In addition, groupings of standards are given for each Target. Although the numbered standards are listed with the Targets and Claims, the test blueprint cannot be derived by counting up the number of times a particular standard is listed. There are cases where part of a standard is in one Target, and another part of the standard is in another Target. While not all Targets will be equally emphasized in the test, all of the content described by the standards is important. Some of the content in a Target may also be reflected in another Target, or the content in a Target in the current grade

Blueprint A test blueprint is used by test creators to ensure that multiple forms of the test cover the same content in the same proportions.

may be a critical foundation skill for success in subsequent grades. Thus, attempts to pattern instruction on the perceived or actual numbers of items in a test may not adequately serve students’ needs. Assessing at the Target level, rather than the individual standard level, makes it possible to highlight student understanding through a more meaningful and holistic grouping. Individual standards, while important, are impossible to sufficiently measure with limited testing time. By assessing at the Target level, it is possible to highlight student understanding of the connected material contained in the standards through this meaningful grouping. Targets are drawn from one or more of the numbered standards and are accompanied by descriptions of evidence required, or evidence statements. These evidence statements are used to guide item writers in creating test questions that will give students the opportunity to demonstrate mastery of that Target. For example, for Grade 3, Target F: Develop understanding of fractions as numbers, one evidence statement is, “The student expresses whole numbers as fractions and recognizes fractions equal to whole numbers” (Grade 3, Claim 1, Target F, Evidence Statement 5). High School Claim 1 Targets - Rationale The Alaska Mathematics Standards are organized into conceptual categories, which means there are no specific grades associated with any standard within a grade cluster. In order to measure student growth, the assessment needs to have vertical alignment. For this reason, some Targets appear in both grades 9 and 10. In an effort to distinguish the differences between the expectations of these Targets in the two grades, each Target in Claim 1 contains a clarifying focus statement that describes how the Target will be measured differently in the two grades. Vertical alignment between grades 9 and 10 requires that each test focus largely on algebra, but also include geometry and statistics. However, Claims 2, 3, and 4 for grade 10 will emphasize geometry. Relative Emphasis The focus, coherence, and rigor of the Alaska Standards are captured through the emphases of High, Medium, or Low on particular Targets, as shown on the Summative Assessment Framework. Relative Emphasis is related to the frequency with which items aligned to that Target would appear on an item-adaptive test. It should NOT be interpreted as a basis for making curricular decisions. Targets with a Low Relative Emphasis should be considered important for instruction because they may include skills associated with Medium or High Targets in the same grade, or they may be important building blocks and are key to success in later grades. For example, in Grade 3, Target E: Use place value understanding and properties

Evidence Statements Specific, observable activities that provide students an opportunity to show mastery of a Target.

of operations to perform multi-digit arithmetic has Low Relative Emphasis. The place value skills in Target E are important to accurately compute problems in Targets having a high emphasis, such as Target D: Solve problems involving the four operations, and identify and explain patterns in arithmetic. Depth of Knowledge The Summative Assessment Framework also identifies the cognitive rigor expected of students for the Targets by providing a Depth of Knowledge (DOK) level. DOK offers a common language to understand "rigor," or cognitive demand, in assessments, as well as curricular units, lessons, and tasks. By using DOK, tasks can be categorized according to the complexity of thinking required to successfully complete them. The categories are defined below:

DOK 1: Recall & Reproduction Tasks at this level require recall of facts or rote application of simple procedures. A Mathematics example is learning multiplication facts. DOK 2: Skills and Concepts Tasks at this level require more than one mental step and expect students to apply knowledge to compare, organize, summarize, or predict. A Mathematics example is extending a pattern. DOK 3: Strategic Thinking Tasks at this level require the use of planning and evidence to support more abstract thinking. A Mathematics example is analyzing and drawing conclusions from data, citing evidence to support the conclusions. DOK 4: Extended Thinking Tasks at this level involve the synthesis of information from multiple sources, often over an extended period of time, or the transfer of knowledge from one domain to solve problems in another.

The DOK in the Framework is provided as a general reference for the projected maximum DOK of items on AMP. Typically, machine-scorable items are DOK 1, 2, or 3 as supported by the content being measured and by the context of the problem. DOK 4 is generally reserved for performance tasks. The maximum DOK of items is typically determined by the depth of cognitive complexity suggested by the content standards. While this is

DOK Depth of Knowledge is a way to categorize the cognitive complexity of a content standard, a Target, or a test question.

AMP Items Machine-scorable items on AMP include traditional multiple choice, multi-select multiple choice, and technology-enhanced items (i.e., highlighting, drag and drop, graphs).

the maximum DOK for summative test items, it should not be interpreted as a limit to the Depth of Knowledge for instructional activities. When assessments are used in a high-stakes environment, it would be unfair to include items that tap into higher levels of DOK than indicated by the state’s content standards. Similarly, in order to accurately measure achievement for all students, some items will be included at lower DOK levels than indicated by the state’s content standards. For example, if a standard said, “Students will be able to jump over a three-foot-high obstacle,” mastery could be measured by determining if students were successful in jumping over something three feet high. Students who were unsuccessful at three feet could have their performance measured by including obstacles of lower heights, to provide information for possible remediation. However, when receiving instruction for this activity, the students should practice jumping over obstacles at different heights, starting off with lower heights and building up to heights greater than three feet. Furthermore, it would be unfair to have the actual test be to jump over something five feet high, since the expectation of the standard is three feet.

.

Grade 3 M

athematics

Claim 1: Concepts and Procedures. Students can explain and apply m

athematical concepts and interpret and carry out

mathem

atical procedures with precision and fluency.

Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not used in this grade.

A. R

epresent and solve problems involving m

ultiplication and division.

Evidence Required:

1. The student uses multiplication and division up to

100 to solve straightforward one-step w

ord problems in

situations involving equal groups, arrays, and m

easurement quantities such as length, liquid volum

e, and m

asses of objects. 2. The student determ

ines an unknown w

hole number

in a multiplication or division equation relating three

whole num

bers with single-digit factors up to 100.

3.OA.1, 3.O

A.2, 3.O

A.3, 3.OA.4

2 H

igh 60-65%

Grade: the grade level the

Framew

ork describes.

Claim

: a short description of the C

laim that sum

marizes its

main topic

Focus: in grades 9 and 10, the C

onceptual Category from

the Alaska Standards that is the prim

ary source of the Target. The Focus provides another connection betw

een the Alaska Standards and the Targets.

Target: Targets in Mathem

atics are draw

n from the C

lusters in the Alaska Standards. Targets describe an overall them

e of a group of related standards.

Standards: a list of the standards w

hich are addressed by the Target.

Goal D

OK: the m

aximum

D

epth of Knowledge for

assessment suggested by the

Target and its associated standards

Relative E

mphasis: categorizes

Targets as High, M

edium, or

Low em

phasis for item

development. H

owever, this

should not be interpreted as a reflection of or suggestion for a pattern of em

phasis for instruction. %

: the proportion of the machine-

scorable part of the assessment

that will be draw

n from each C

laim

How to Read This Docum

ent: This document is organized by grade. An excerpt from

Grade 3 is provided as an exam

ple.

Grade: the grade level the Framework describes Claim: a short description of the Claim that summarizes its main topic Focus: in grades 9 and 10, the Conceptual Category from the Alaska Standards that is the primary source of the Target. The Focus provides another connection between the Alaska Standards and the Targets. Target: Targets in Mathematics are drawn from the Clusters in the Alaska Standards. Targets describe an overall theme of a group of related standards.

● Targets are followed by statements of Evidence Required, describing the types of things a student could do to demonstrate mastery of the skills that contribute to the indicated Target. Items may address more than one Evidence requirement.

Standards: a list of the standards which are addressed by the Target. The references to the standards show how the Target is connected to the Alaska Standards. Goal DOK: the maximum Depth of Knowledge for assessment suggested by the Target and its associated standards Relative Emphasis: categorizes Targets as High, Medium, or Low emphasis for item development. However, this should not be interpreted as a reflection of or suggestion for a pattern of emphasis for instruction.

● The Relative Emphasis column may also include comments about the tested content specific to the machine-scorable part of the assessment.

%: the proportion of the machine-scorable part of the assessment that will be drawn from each Claim. Again, this should not be interpreted as a reflection of or suggestion for a pattern of emphasis for instruction.

Grade 3 Mathem

atics

Alaska Department of Education &

Early Development

1

Claim

1: Concepts and Procedures. Students can explain and apply mathem

atical concepts and interpret and carry out m

athematical procedures w

ith precision and fluency.

Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

N

ot used in

this grade.

A. Represent and solve problem

s involving multiplication and division.

Evidence Required: 1.

The student used multiplication and division up to 100 to solve straightforw

ard one-step w

ord problems in situations involving equal groups, arrays, and

measurem

ent quantities such as length, liquid volume and m

asses of objects. 2.

The student determines an unknow

n whole num

ber in a multiplication or

division equation relating three whole num

ber with single-digit factors up to

100.

3.OA.1,

3.OA.2, 3.O

A.3, 3.O

A.4 2

High

60-65%

B. U

nderstand properties of multiplication and the relationship betw

een m

ultiplication and division. Evidence Required: 1.

The student uses properties of operations (Comm

utative Property of M

ultiplication, Associative Property of Multiplication, and Distributive Property)

as strategies to multiply and divide.

2. The student w

ill represent division as an unknown-factor problem

.

3.OA.5, 3.O

A.6 1

High

C. M

ultiply and divide up to 100. Evidence Required: 1.

The student accurately multiplies single-digit factors w

ithin 100. 2.

The student accurately divides within 100 using single-digit divisors and single

digit quotients. 3.

The student connect multiplication and division to target fluencies.

3.OA.7

1 High

D. Solve problem

s involving the four operations, and identify and explain patterns in arithm

etic. Evidence Required: 1.

The student identifies arithmetic patterns including input/output m

odels, num

ber lines, addition tables, and multiplication tables.

3.OA.8, 3.O

A.9 2

High

Grade 3 Mathem

atics


Early Development

2

Claim





Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

N

ot used in

this grade.

E. U

se place value understanding and properties of operations to perform m

ulti-digit arithm

etic. Evidence Required: 1.

The student solves non-contextual problems using place value understanding to

round whole num

bers to the nearest 10 or 100. 2.

The student solves non-contextual problems by adding and/or subtracting

within 1000, using strategies and algorithm

s based on place value, properties of operations, and /or the relationship betw

een addition and subtraction. 3.

The student solves non-contextual computation problem

s by multiplying gone-

digit whole num

bers by multiples of 10 in the range of 10-90 using strategies

based on place value and properties of operations.

3.NBT.1, 3.N

BT.2, 3.N

BT.3 1

Low

Claim

1 cont.

60-65%

F. Develop understanding of fractions as num

bers. Evidence Required: 1.

The student identifies a fraction 1/b as 1 part of a whole that is partitioned into

b equal parts and a fraction a/b is a quantity formed by a parts of size 1/b using

a model. For this evidence statem

ent, a/b may be greater than, less than, or

equal to 1. 2.

The student identifies and represents fractions on a number line using the

interval 0-1 as a whole w

ith or without partitioning.

3. The student identifies tw

o fractions as equal if they are the same size or the

same point on a num

ber line. 4.

The student generates simple equal fractions using a visual fraction m

odel. 5.

The student expresses whole num

bers as fractions and recognizes fractions equal to w

hole numbers.

6. The student com

pares two fractions w

ith the same num

erator or the same

denominator using the sym

bols <, +, >.

3.NF.1, 3.N

F.2, 3.N

F.3 2

High

Grade 3 Mathem

atics


Early Development

3

Claim





Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

N

ot used in

this grade.

G. Solve problem

s involving measurem

ent and estimation of intervals of tim

e, liquid volum

es, and masses of objects.


The student tells and writes tim

e to the nearest minute.

2. The student solves one-step w

ork problems w

ith addition and subtraction including tim

e intervals in minutes.

3. The student solves one-step w

ord problems involving liquid volum

es (liters) and m

ass (grams, kilogram

s) using the four operations. 4.

The student selects and appropriate unit of English, metric, or non-standard

measurem

ent to estimate length, tim

e, weight, or tem

perature.

3.MD.1, 3.M

D.2, 3.M

D.3 2

High

Claim

1 cont.

60-65%

H. Represent and interpret data. Evidence Required: 1.

The student creates a scaled picture graph and a scaled bar graph to represent a data set w

ith up to four categories. 2.

The student solves one-and tow-step “how

many m

ore” and “how m

any less” problem

s using information presented ins called bar graphs.

3. The student generates m

easurement data by m

easuring lengths using rulers m

arked with halves and fourths of an inch and m

akes a line plot with fractional

measurem

ent values. 4.

The student can determine the classification of date from

real-world problem

s show

n in graphical representation, using the terms m

inimum

and maxim

um.

3.MD.4, 3.M

D.5, 3.M

D.6 3

Medium

I. Geom

etric measurem

ent: understand concepts of area and relate area to m

ultiplication and to addition. Evidence Required: 1.

The student measures areas by counting unit squares.

2. The student finds areas of rectilinear figures by decom

posing them into non-

overlapping rectangles and adding the areas of the non-overlapping parts. 3.

The student finds the area of a rectangle with w

hole-number side lengths by

tiling it, and shows that the area is the sam

e as would be found by m

ultiplying the side lengths.

3.MD.7, 3.M

D.8, 3.M

D.9 2

High

Grade 3 Mathem

atics


Early Development

4

Claim





Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

N

ot used in

this grade.

J. Geom

etric measurem

ent: recognize perimeter as an attribute of plane figures and

distinguish between linear and area m

easures. Evidence Required: 1.

The student solves real-world and m

athematical problem

s involving finding the perim

eter of a polygon given the side lengths. 2.

The student distinguishes between area and perim

eter of a rectangle.

3.MD.10

2 Low

Claim

1 cont.

60-65%

K.

Reason with shapes and their attributes.


The student identifies, draws, and classifies shapes (e.g., rhom

buses, rectangles, and others) according to their attributes (e.g., having four sides), and recognizes that shared attributes can define a classification category.

2. The student partitions shapes into parts w

ith equal areas and can express the area of each part as a unit fraction of the w

hole.

3.G.1, 3.G.2 2

Medium

Grade 3 Mathem

atics


Early Development

5

Claim

2: Problem Solving. Students can solve a range of com

plex well-posed problem

s in pure and applied mathem

atics, making

productive use of knowledge and problem

s solving strategies.

Focus Target

Standard G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade.

A-D A.

Represent and solve problems involving m

ultiplication and division. B.

Understand properties of m

ultiplication and the relationship between

multiplication and division.

C. M

ultiply and divide up to 100. D.

Solve problems involving the four operations, and identify and explain patterns in

arithmetic.

Focus Clusters: 3.O

A.A, 3.OA.D,

3.NBT.A, 3.M

D.A, 3.M

D.B*, 3.MD.C,

3.MD.D*

*denotes minor

clusters

3

Tasks limited

to machine-

scorable responses, so not all Targets

may be

addressed.

8-12%

Grade 3 Mathem

atics


Early Development

6

Claim

3: Comm

unicating Reason. Students can clearly and precisely construct viable arguments to support their ow

n reasoning and to critique the reasoning of other.

Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade.

A-F A.






C. M



arithmetic.

E. U


ulti-digit arithm

etic. F.

Develop understanding of fractions as numbers.

Focus Clusters/ Standards:

3.OA.B, 3.N

F.A, 3.N

F.2, 3.NF.3,

3.MD.A, 3.M

D.7 3

Tasks limited

to machine-


may be

addressed.

8-12%

Grade 3 Mathem

atics


Early Development

7

Claim

4: Modeling and Data Analysis. Students can analyze com

plex, real-world scenarios and can construct and use m

athematical

models to interpret and solve problem

s.

Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

A-G

A.






C. M



arithmetic.

E. U


ulti-digit arithm

etic. F.

Develop understanding of fractions as numbers.

G. Solve problem

s involving measurem

ent and estimation of intervals of tim

e, liquid volum

es, and masses of objects.

Focus Clusters: 3.O

A.A 3.OA.D,

3.MD.A, 3.M

D.C, 3.M

D.D* *denotes m

inor clusters

3

Tasks limited

to machine-


may be

addressed.

8-12%

Grade 4 Mathem

atics


Early Development

1



mathem


Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade.

A. U

se the four operations with w

hole numbers to solve problem

s. Evidence Required: 1.

The student solves contextual problems involving m

ultiplicative comparisons,

e.g., by using drawings and equations w

ith a symbol for the unknow

n number

to represent the problem.

2. The student solves straightforward, contextual problem

s using the four operations.

4.OA.1, 4.O

A.2, 4.O

A.3 2

High

60-65%

B. Gain fam

iliarity with factors and m

ultiples. Evidence Required: 1.

The student determines one or m

ore factors or factor pairs for a given whole

number (from

1 to 100). 2.

The student recognizes that a whole num

ber (from 1 to 100) is a m

ultiple of each of its factors.

3. The student determ

ines if a whole num

ber (from 1 to 100) is a m

ultiple of a given one-digit num

ber. 4.

The student determines if a w

hole number (from

1 to 100) is prime or

composite.

4.OA.4

1 M

edium

C. Generate and analyze patterns. Evidence Required: 1.

The student generates number patterns.

2. The student generates shape patterns.

3. The student analyzes a num

ber pattern or shape pattern, showing

understanding of the pattern rule and features other than the pattern rule.

4.OA.5, 4.O

A.6 3

Low

Grade 4 Mathem

atics


Early Development

2



mathem


Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade

D. Generalize place value understanding for m

ulti-digit whole num

bers. Evidence Required: 1. The student com

pares two m


bers in the same form

using >, <, and = sym

bols. 2. The student rounds m


bers to any place. 3. The student identifies m


bers that, when rounded to a given

place value, will be closest to a given num

ber. 4. The student com

pares two m


bers in different forms.

5. The student explains the difference between the values of a num

eral in the tens and the ones place, the hundreds place and the tens place, or the thousands place and the hundreds place in m

athematical situations.

4.NBT.1, 4.N

BT.2, 4.N

BT.3 2

High

Claim 1

cont. 60-65%

E. U


ulti-digit arithm

etic. Evidence Required: 1. The student adds or subtracts m


bers in non-contextual m

athematics problem

s. 2. The student m

ultiplies whole num

bers (up to four digits by one digit or two digits

by two digits) using strategies based on place value and the properties of

operations. 3.

The student finds whole num

bers quotients and remainders (up to four-digit

dividends and one-digit divisors) using strategies based on place value, the properties of operations, and/or the relationship betw

een multiplication and

division.

4.NBT.4, 4.N

BT.5, 4.N

BT.6 2

High

Grade 4 Mathem

atics


Early Development

3



mathem


Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade

F. Extend understanding of fraction equivalence and ordering. Evidence Required: 1.

The student recognizes when tw

o or more fractions are equivalent.

2. The student generates equivalent fractions given an initial fraction or fraction m

odel. 3.

The student uses the symbols <, >, and – to com

pare fractions with different

numerators and different denom

inators.

4.NF.1, 4.N

F.2 2

High

Claim 1

cont. 60-65%

G. Build fractions from

unit fractions by applying and extending previous understandings of operations on w

hole numbers.


The student adds and subtracts fractions with like denom

inators by joining and separating parts referring to the sam

e whole.

2. The student expresses an equivalent form

of a fraction or mixed num

ber by considering each as a sum

of fractions with the sam

e denominator.

3. The student solves contextual problem

s involving addition and subtraction of fractions referring to the sam

e whole and having like denom

inators by using visual fraction m

odels and equations to represent the problem.

4. The student represents a fraction a/b as a m

ultiple of 1/b. 5.

The student multiplies a fraction by a w

hole number.

6.

The student solves contextual problems involving the m

ultiplication of a fraction by a w

hole number by using visual fraction m

odels and equations to represent the problem

.

4.NF.3, 4.N

F.4 2

High

Grade 4 Mathem

atics


Early Development

4



mathem


Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade

H. U

nderstand decimal notation for fractions, and com

pare decimal fractions.


The student expresses a fraction with denom

inator 10 as an equivalent fraction w

ith denominator 100.

2. The student adds tw

o fractions with respective denom

inators 10 and 100. 3.

The student uses decimal notation to represent fractions w

ith denominators 10

or 100. 4.

The student locates decimal num

bers to the hundredths place on a number

line. 5.

The student compares tw

o decimals to the hundredths place by reasoning

about their size, using the symbols <, >, or =.

4.NF.5, 4.N

F.6, 4.N

F.7 2

High

Claim 1

cont. 60-65%

I.

Solve problems involving m

easurement and conversion of m

easurements from

a larger unit to a sm

aller unit, and involving time.


The student converts measurem

ents from larger units to sm

aller units within a

single system of units.

2. The student records m

easurement equivalents in a tw

o-column table.

3. The student identifies m

easurement quantities from

diagrams, such as num

ber line diagram

s that feature a measurem

ent scale, and uses the information to

solve word problem

s. 4.

The student applies the area and perimeter form

ulas for rectangles to solve m

athematical and real-w

orld problems.

4.MD.1, 4.M

D.2, 4.M

D.3, 4.MD.4

2 M

edium

Grade 4 Mathem

atics


Early Development

5



mathem


Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade

J. Represent and interpret data. Evidence Required: 1.

The student completes a line plot to display a data set of m

easurements in

fractions of a unit (1/2, 1/4, 1/8). 2.

The student solves problems involving addition and subtraction of fractions

with like denom

inators by using information presented in line plots.

4.MD.5, 4.M

D.6 2

Medium

Claim 1

cont. 60-65%

K. Geom

etric measurem

ent: understand concepts of angle and measure angles.


The student relates the concept of an angle to the fraction of a circular arc betw

een two points on a circle.

2. The student uses a protractor to m

easure angles (composed of one-degree

angles) and construct angles to whole-num

ber degrees. 3.

The student decomposes an angle into sm

aller non-overlapping parts and adds the m

easures of these smaller parts to find the m

easure of the whole angle.

4. The student solves addition and subtraction problem

s to find unknown angles

on a diagram in real w

orld and mathem

atical problems.

4.MD.7, 4.M

D.8, 4.M

D.9 2

Low

L. Draw

and identify lines and angles, and classify shapes by properties of their lines and angles. Evidence Required: 1.

The student draws points, lines, line segm

ents, rays, and angles and identifies these in tw

o-dimensional figures.

2. The student classifies tw

o-dimensional figures based on the presence or

absence of parallel/perpendicular line segments and angles of a specified size,

including identifying right triangles. 3.

The student identifies and draws lines of sym

metry in line-sym

metric figures,

and distinguishes line-symm

etric figures from line-asym

metric figures.

4.G.1, 4.G.2, 4.G.3 2

Low

Grade 4 Mathem

atics


Early Development

6

Claim 2: Problem

Solving. Students can solve a range of complex w

ell-posed problems in pure and applied m

athematics, m

aking productive use of know

ledge and problems solving strategies.

Focus Target

Standard G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade.

A-D A.

Apply mathem

atics to solve well-posed problem

s in pure mathem

atics and arising in everyday life, society, and the w

orkplace. B.

Select and use appropriate tools strategically. C.

Interpret results in the context of a situation. D.

Identify important quantities in a practical situation and m

ap their relationships (e.g., using diagram

s, two-w

ay tables, graphs, flowcharts, or form

ulas).

Focus Clusters: 4.O

A.A, 4.NBT.B,

4.NF.A, 4.N

F.B, 4.N

F.C, 4.MD.A*,

4.MD.C*

*denotes minor

clusters

3

Tasks limited

to machine-


may be

addressed.

8-12%

Grade 4 Mathem

atics


Early Development

7

Claim 3: Com

municating Reason. Students can clearly and precisely construct viable argum

ents to support their own reasoning and

to critique the reasoning of other.

Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade.

A-F A.

Test propositions or conjectures with specific exam

ples. B.

Construct, autonomously, chains of reasoning that w

ill justify or refute propositions or conjectures.

C. State logical assum

ptions being used. D.

Use the technique of breaking an argum

ent into cases. E.

Distinguish correct logic or reasoning from that w

hich is flawed and—

if there is a flaw

in the argument—

explain what it is.

F. Base argum

ents on concrete referents such as objects, drawings, diagram

s, and actions.

Focus Clusters/Standards:

4.OA.3, 4.N

BT.A, 4.N

BT.5, 4.NBT.6,

4.NF.A, 4.N

F.1, 4.N

F.2, 4.NF.3a,

4.NF.3b, 4.N

F.3c, 4.N

F.4a, 4.NF.4b,

4.NF.C, 4.N

F.7

3

Tasks limited

to machine-


may be

addressed.

8-12%

Grade 4 Mathem

atics


Early Development

8

Claim 4: M

odeling and Data Analysis. Students can analyze complex, real-w

orld scenarios and can construct and use mathem

atical m

odels to interpret and solve problems.

Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade.

A-G

A. Apply m

athematics to solve problem

s arising in everyday life, society, and the w

orkplace. B.

Construct, autonomously, chains of reasoning to justify m

athematical m

odels used, interpretations m

ade, and solutions proposed for a complex problem

. C.

State logical assumptions being used.

D. Interpret results in the context of a situation.

E. Analyze the adequacy of and m

ake improvem

ents to an existing model or develop

a mathem

atical model of a real phenom

enon. F.



s, two-w


ulas). G.

Identify, analyze, and synthesize relevant external resources to pose or solve problem

s. (performance tasks only)

Focus Clusters: 4.O

A.A 4.NF.B

4.MD.A* 4.M

D.B* 4.M

D.C* *denotes m

inor clusters

3

Tasks limited

to machine-


may be

addressed.

8-12%

Grade 5 Mathem

atics


Early Development

1



mathem


Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade.

A. W

rite and interpret numerical expressions.


The student writes or identifies a num

erical expression that records a calculation represented w

ith words.

2. The student interprets num

erical expressions in words w

ithout evaluating them

. 3.

The student evaluates numerical expressions w

ith grouping symbols.

5.OA.1, 5.O

A.2 1

Low

65-75%

B. Analyze patterns and relationships. Evidence Required: 1.

Given two rules, the student identifies and explains apparent relationships

between corresponding term

s of two related num

erical patterns. 2.

Given two rules, the student represents corresponding term

s from tw

o related num

erical patterns as ordered pairs and plots them on a coordinate plane.

5.OA.3

2 Low

C. U

nderstand the place value system.


The student represents powers of 10 by using w

hole-number exponents.

2. The student reads and w

rites decimals to the thousandths using base-ten

numerals, num

ber names, and expanded form

. 3.

The student compares tw

o decimals to the thousandths by using >, =, and <

symbols.

4. The student rounds decim

als to the nearest whole num

ber, tenth, hundredth, or thousandth.

5.NBT.1, 5.N

BT.2, 5.N

BT.3, 5.NBT.4

2 High

Grade 5 Mathem

atics


Early Development

2



mathem


Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade.

D. Perform

operations with m


bers and with decim

als to hundredths. Evidence Required: 1.

The student multiplies m


bers. 2.

The student determines w

hole-number quotients of w

hole numbers w

ith up to four-digit dividends and tw

o-digit divisors using strategies based on place value, the properties of operations, and/or the relationship betw

een multiplication

and division. 3.

The student adds, subtracts, multiplies, and divides decim

als to the hundredths using concrete m

odels or drawings and strategies based on place value,

properties of operations, and/or the relationship between addition and

subtraction.

5.NBT.5, 5.N

BT.6, 5.N

BT.7 2

High

Claim

1 cont.

65-75%

E. U

se equivalent fractions as a strategy to add and subtract fractions. Evidence Required: 1.

The student adds or subtracts fractions with unlike denom

inators (including m

ixed numbers) by using visual fraction m

odels or equations to represent the problem

. 2.

The student identifies and explains the use of equivalent fractions when adding

or subtracting fractions with unlike denom

inators (including mixed num

bers).

5.NF.1, 5.N

F.2 2

High

F. Apply and extend previous understandings of m

ultiplication and division to multiply

and divide fractions. Evidence Required: 1.

The student interprets a fraction as division of the numerator by the

denominator.

2. The student solves problem

s involving division of whole num

bers leading to quotients in the form

of fractions or mixed num

bers, with or w

ithout fraction m

odels.

5.NF.3, 5.N

F.4, 5.N

F.5, 5.NF.6,

5.NF.7

2

High

Grade 5 Mathem

atics


Early Development

3



mathem


Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

N

ot used in

this grade.

F. continued 3.

The student multiplies a fraction or w

hole number by a fraction.

4. The student m

ultiplies fractional side lengths to find areas of rectangles. 5.

The student compares the size of a product to the size of one factor on the

basis of the size of the other factor, without perform

ing the indicated m

ultiplication. 6.

The student solves real-world problem

s involving multiplication of fractions and

mixed num

bers, with or w

ithout visual fraction models.

7. The student solves real-problem

s involving division of unit fractions by non-zero w

hole numbers and division of w

hole numbers by unit fractions, w

ith or w

ithout visual fraction models.

5.N

F.3, 5.NF.4,

5.NF.5, 5.N

F.6, 5.N

F.7

2

High

Claim

1 cont.

65-75%

G. Convert like m

easurement units w

ithin a given measurem

ent system and solve

problems involving tim

e. Evidence Required: 1.

The student converts units of linear measure w

ithin a single measurem

ent system

. 2.

The student converts units of weight/m

ass measure w

ithin a single m

easurement system

. 3.

The student converts units of liquid volume m

easure within a single

measurem

ent system.

1. The student converts units of tim

e measure w

ithin a single measurem

ent system

. 4.


s involving elapsed time betw

een world

time zones.

5.MD.1, 5.M

D.2 1

Medium

Grade 5 Mathem

atics


Early Development

4



mathem


Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade.

H. Represent and interpret data. Evidence Required: 1.

The student completes or identifies line plot w

ith fractional units to display a data set.

2. The student uses operations on fractions to solve problem

s involving inform

ation presented in line plots. 3.

The student explains the classification of data from real-w

orld problems show

n in graphical representations including the use of term

s mean and m

edian with a

given set of data.

5.MD.3, 5.M

D.4 2

Medium

Claim 1

cont. 65-75%

I. Geom

etric measurem

ent: understand concepts of volume and relate volum

e to m

ultiplication and to addition. Evidence Required: 1.

The student determines the volum

e of a right rectangular prism w

ith whole-

number side lengths by counting or packing unit cubes.

1. The student applies the form

ulas V = l × w × h and V = b × h to solve real w

orld and m

athematical problem

s involving volumes of right rectangular prism

s.

5.MD.5, 5.M

D.6, 5.M

D.7 2

High

J. Graph points on the coordinate plane to solve real-w

orld and mathem

atical problem


The student interprets coordinate values of points graphed on a coordinate plane, or in the context of a given situation.

2. The student graphs points on the coordinate plane representing real w

orld or m

athematical problem

s.

5.G.1, 5.G.2 1

Low

K. Classify tw

o-dimensional (plane) figures into categories based on their properties.


The student classifies two-dim

ensional figures into categories and/or subcategories based on attributes and properties.

5.G.3, 5.G.4 2

Low

Grade 5 Mathem

atics


Early Development

5

Claim 2: Problem

Solving. Students can solve a range of complex w

ell-posed problems in pure and applied m

athematics, m

aking productive use of know

ledge and problems solving strategies.

Focus Target

Standard G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade.

A-D A.

Apply mathem


s in pure mathem


orkplace. B.





s, two-w


ulas).

Focus Clusters: 5.N

BT.B, 5.NF.A,

5.NF.B, 5.M

D.A*, 5.M

D.C, 5.G.A* *denotes m

inor clusters

3

Tasks limited

to machine-


may be

addressed.

8-12%

Grade 5 Mathem

atics


Early Development

6

Claim 3: Com

municating Reason. Students can clearly and precisely construct viable argum

ents to support their own reasoning and

to critique the reasoning of other.

Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade.

A-F A.


ples. B.






ent into cases. E.



if there is a flaw

in the argument—

explain what it is.

F. Base argum


s, and actions.

Focus Clusters/Standards: 5.N

BT.2, 5.NBT.6,

5.NBT.7, 5.N

F.1, 5.N

F.2, 5.NF.B,

5.NF.3, 5.N

F.4, 5.N

F.7a, 5.NF.7b,

5.MD.C, 5.M

D.5a, 5.M

D.5b, 5.G.B*, 5.G.4*

*denotes minor

clusters

3

Tasks limited

to machine-


may be

addressed.

8-12%

Grade 5 Mathem

atics


Early Development

7

Claim 4: M

odeling and Data Analysis. Students can analyze complex, real-w

orld scenarios and can construct and use mathem

atical m

odels to interpret and solve problems.

Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

A-G

A.

Apply mathem

atics to solve problems arising in everyday life, society, and the

workplace.

B. Construct, autonom

ously, chains of reasoning to justify mathem

atical models

used, interpretations made, and solutions proposed for a com

plex problem.



Interpret results in the context of a situation. E.

Analyze the adequacy of and make im

provements to an existing m

odel or develop a m

athematical m

odel of a real phenomenon.

F. Identify im

portant quantities in a practical situation and map their relationships

(e.g., using diagrams, tw

o-way tables, graphs, flow

charts, or formulas).

G. Identify, analyze, and synthesize relevant external resources to pose or solve problem


Focus Clusters: 5.N

BT.B, 5.NF.A,

5.NF.B, 5.M

D.A* 5.M

D.B* 5.MD.C,

5.G.A* *denotes m

inor clusters

3

Tasks limited

to machine-


may be

addressed.

8-12%

Grade 6 Mathem

atics


Early Development

1

Claim





Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade.

A. U

nderstand ratio concepts and use ratio reasoning to solve problems.


The student uses ratio language to describe a ratio relationship. 2.

The student determines the unit rate associated w

ith a real-world ratio.

3. The student finds m

issing values in tables of equivalent ratios. 4.

The student plots coordinate pairs to represent equivalent ratios. 5.

The student makes tables of equivalent ratios relating quantities w

ith whole-

number m

easurements.

6. The student solves real-w

orld problems involving unit rate.

7. The student solves m

athematical problem

s involving finding the whole, given a

part and the percent. 8.


athematical problem

s involving finding a percent of a quantity as a rate per 100.

9. The student uses ratio reasoning to convert m

easurement units.

10. The student uses ratio reasoning to manipulate and transform

units appropriately w

hen multiplying or dividing quantities.

6.RP.1, 6.RP.2, 6.RP.3

2 High

65-75%

B. Apply and extend previous understandings of m

ultiplication and division to divide fractions by fractions. Evidence Required: 1.

The student interprets quotients of fractions using visual fraction models,

equations, and the relationship between m

ultiplication and division. 2.


athematical one-step problem

s involving division of fractions by fractions.

6.NS.1

2 High

C. Com

pute fluently with m

ulti-digit numbers and find com

mon factors and m

ultiples. Evidence Required: 1.

The student divides multi-digit num

bers. 2.

The student adds, subtracts, multiplies, and divides m

ulti-digit decimals.


ines the greatest comm

on factor of two w

hole numbers.


ines the least comm

on multiple of tw

o whole num

bers. The student uses the distributive property to express a sum

of two w

hole numbers

with a com

mon factor as a m

ultiple of a sum of tw

o whole num

bers with no

comm

on factor.

6.NS.2, 6.N

S.3, 6.N

S.4 1

Low

Grade 6 Mathem

atics


Early Development

2

Claim





Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade

D. Apply and extend previous understandings of num

bers to the system of rational

numbers.


The student uses positive and negative numbers to represent quantities in real-

world contexts.

2. The student can identify the location of ordered pairs on the coordinate plane based on the signs of the num

bers in an ordered pair. 3.

The student locates and positions integers and other rational numbers on a

number line.

4. The student positions ordered pairs of integers and other rational num

bers on a coordinate plane.

5. The student interprets statem

ents about inequalities as relative position on a num

ber line. 6.

The student writes and interprets statem

ents about the order of rational num

bers in real-world contexts.

7. The student represents the absolute value of a rational num

ber as the distance from

zero on a number line.

8. The student can m

ake comparisons of absolute value from

statements about

order. 9.


athematical problem

s by graphing ordered pairs on a coordinate plane and using coordinates and absolute value to find the distances betw

een points with sam

e first coordinate or same second

coordinate.

6.NS.5, 6.N

S.6, 6.N

S.7, 6.NS.8

2 High

Claim 1

cont. 65-75%

Grade 6 Mathem

atics


Early Development

3

Claim





Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade

E. Apply and extend previous understandings of arithm

etic to algebraic expressions. Evidence Required: 1.

The student evaluates numerical expressions involving w

hole-number

exponents. 2.

The student writes num

erical expressions involving whole-num

ber exponents, algebraic expressions, and expressions from

formulas in real-w

orld problems.

3. The student uses m

athematical term

s to describe expressions. 4.

The student evaluates algebraic expressions and expressions from form

ulas in real-w

orld problems.

5. The student creates equivalent expressions by applying properties of operations.

6. The student identifies w

hen expressions are equivalent by utilizing properties of operations.

6.EE.1, 6.EE.2, 6.EE.3, 6.EE.4

2 High

Claim 1

cont. 65-75%

F.

Reason about and solve one-variable equations and inequalities. Evidence Required: 1.

The student uses substitution in one-variable equations and inequalities. 2.

The student writes one-variable equations and inequalities and solves one-

variable equations in real-world and m

athematical problem

s. 3.

The student represents solutions of inequalities in real-world and m

athematical

problems on a num

ber line.

6.EE.5, 6.EE.6, 6.EE.7, 6.EE.8

G. Represent and analyze quantitative relationships betw

een dependent and independent variables. Evidence Required: 1.

The student writes an equation to express one quantity versus another quantity

using dependent and independent variables. 1.

The student identifies the relationship between dependent and independent

variables from graphs and tables and relates them

to equations.

6.EE.9

Grade 6 Mathem

atics


Early Development

4

Claim





Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade

H. Solve real-w

orld and mathem

atical problems involving area, surface area, and

volume.


The student determines the area of triangles, special quadrilaterals, and

polygons using composition and decom

position in solving real-world and

mathem

atical problems.


ines the volume of right rectangular prism

s with fractional

edge lengths in solving real-world and m

athematical problem

s. 3.

The student draws polygons in the coordinate plane, given coordinates for the

vertices in the context of solving real-world and m

athematical problem

s. 4.

The student determines the length of a side of a polygon in the coordinate

plane, given coordinates for the vertices in the context of solving real-world and

mathem

atical problems.


ines the surface area of three-dimensional figures form

ed by nets of polygons in the context of solving real-w

orld and mathem

atical problem

s. 6.

The student identifies, compares, or describes attributes and properties of

circles (radius, and diameter).

6.G.1, 6.G.2, 6.G.3, 6.G.4, 6.G.5

2 M

edium

Claim 1

cont. 65-75%

I. Develop an understanding of statistics variability. Evidence Required 1.

The student recognizes a statistical question as one that anticipates variability. 2.

The student identifies statements that describe the center and/or spread,

and/or overall shape of a set of data. 3.

The student recognizes that a measure of center for a num

erical data set sum

marizes all of its values w

ith a single number, w

hile a measure of variation

describes how its values vary w

ith a single number.

6.SP.1, 6.SP.2, 6.SP.3

2 Low

Grade 6 Mathem

atics


Early Development

5

Claim





Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade

J. Sum

marize and describe distributions.


The student displays numerical data on line plots, dot plots, histogram

s, and box plots.

2. The student sum

marizes num

erical data sets by describing the nature of the attribute under investigation, including how

it was m

easured, its units of m

easurement, and num

ber of observations. 3.

The student summ

arizes numerical data sets by determ

ining quantitative m

easures of center (median and/or m

ean) and variability (interquartile range, range, and/or m

ean absolute deviation). 4.

The student summ

arizes numerical data sets by describing any overall pattern

and any striking deviations from the overall pattern in reference to the

quantitative measures.

5. The student sum

marizes num

erical data sets by relating the choice of measures

of center and variability to the shape of the data distribution or context data gathered.


ines whether a gam

e is mathem

atically fair or unfair by explaining the probability of all possible outcom

es. 7.

The student solves or identifies solutions to problems involving possible

combinations.

6.SP.4, 6.SP.5, 6.SP.6, 6.SP.7

2 Low

Claim

1 cont.

65-75%

Grade 6 Mathem

atics


Early Development

6

Claim




atics, making



Focus Target

Standard G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade.

A-D A.

Apply mathem


s in pure mathem


orkplace. B.





s, two-w


ulas).

Focus Clusters: 6.RP.A, 6.N

S.A, 6.N

S.C, 6.EE.A, 6.EE.B, 6.EE.C,

6.G.A* *denotes m

inor clusters

3

Tasks limited

to machine-


may be

addressed.

8-12%

Grade 6 Mathem

atics


Early Development

7

Claim

3: Comm



Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade.

A-F A.


ples. B.






ent into cases. E.



if there is a flaw

in the argument—

explain what it is.

F. Base argum


s, and actions.


6.RP.A, 6.RP.3, 6.N

S.A, 6.NS.1,

6.NS.C, 6.N

S.5, 6.N

S.6, 6.NS.7,

6.EE.A, 6.EE.3, 6.EE.4, 6.EE.B, 6.EE.6, 6.EE.9

3

Tasks limited

to machine-


may be

addressed.

8-12%

Grade 6 Mathem

atics


Early Development

8

Claim



athematical


s.

Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade.

A-G

A. Apply m



orkplace. B.


athematical m



. C.




ake improvem


a mathem


enon. F.



s, two-w


ulas). G.




S.A, 6.N

S.C, 6.EE.B, 6.EE.C, 6.G.A*,

6.SP.A*, 6.SP.B* *denotes m

inor clusters

3

Tasks limited

to machine-


may be

addressed.

8-12%

Grade 7 Mathem

atics


Early Development

1

Claim





Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade.

A. Analyze proportional relationships and use them

to solve real-world and

mathem

atical problems.


The student computes unit rates and finds the constant of proportionality of

proportional relationships in various forms.


ines whether tw

o quantities, shown in various form

s, are in a proportional relationship.

3. The student represents proportional relationships betw

een quantities using equations.

4. The student interprets specific values from

a proportional relationship in the context of a problem

situation. 5.

The student computes w

ith percentages in context.

7.RP.1, 7.RP.2, 7.RP.3

2 High

65-75%

B. Apply and extend previous understandings of operations w

ith fractions to add, subtract, m

ultiply, and divide rational numbers.


The student interprets rational number values on a num

ber line, including m

odeling addition and subtraction expressions. 2.

The student applies properties of operations as strategies to add and subtract rational num

bers. 3.

The student applies properties of operations as strategies to multiply and divide

rational numbers.

4. The student converts from

a fractional form of rational num

bers to a decimal

form of rational num

bers. 5.


athematical problem

s involving the four operations w

ith rational numbers.

7.NS.1, 7.N

S.2, 7.N

S.3

Grade 7 Mathem

atics


Early Development

2

Claim





Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade.

C. U

se properties of operations to generate equivalent expressions. Evidence Required: 1.

The student adds and subtracts linear expressions with rational coefficients.

2. The student factors linear expressions w

ith rational coefficients. 3.

The student expands linear expressions with rational coefficients.

4. The student generates equivalent linear expressions using a com

bination of addition and subtraction, factoring, and expansion.

7.EE.1, 7.EE.2 1

High

Claim 1

cont. 65-75%

D. Solve real-life and m

athematical problem

s using numerical and algebraic

expressions and equations. Evidence Required: 1.

The student identifies equivalency between tw

o rational numbers.

2. The student applies properties of operations to evaluate num

eric expressions, including converting betw

een different forms of rational num

bers. 3.

The student solves word problem

s leading to equations of the form px + q = r

and p(x + q) = r, where p, q, and rare specific rational num

bers. 4.

The student solves word problem

s leading to inequalities of the form px + q > r

and px + q < r, where p, q, and rare specific rational num

bers. 5.

The student graphs the solution set of an inequality on a number line.

7.EE.3, 7.EE.4 2

High

E. Draw

, construct, and describe geometrical figures and describe the relationships

between them

. Evidence Required: 1.

The student creates scale drawings.

2. The student solves problem

s involving scale drawings using proportional

reasoning. 3.

The student draws, constructs, or describes geom

etric shapes given certain conditions.

4. The student describes a tw

o-dimensional figure resulting from

slicing a three-dim

ensional figure by a plane.

7.G.1, 7.G.2, 7.G.3 3

Low

Grade 7 Mathem

atics


Early Development

3

Claim





Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade.

F. Solve real-life and m

athematical problem

s involving angle measure, area, surface

area, and volume.


The student solves real-life and mathem

atical problems for the circum

ference and area of circles.

2. The student solves real-life and m

athematical problem

s involving angle m

easure including problems requiring w

riting and solving equations. 3.

The student solves real-life and mathem

atical problems for the area of tw

o-dim

ensional objects composed of polygons.

4. The student solves real-life and m

athematical problem

s for the volume and

surface area of three-dimensional objects com

posed of right prisms and cubes.

7.G.4, 7.G.5, 7.G.6 2

Low

Claim 1

cont. 65-75%

G. U

se random sam

pling to draw inferences about a population.



hether a sample is representative of a population.

2. The student draw

s inferences about a population using data from a random

sam

ple.

7.SP.1, 7.SP.2 2

Medium

H. Draw

informal com

parative inferences about two populations.


The student makes com

parisons between tw

o numerical data distributions.

2. The student uses m

easures of center and measures of variability to m

ake statem

ents that form the basis for inform

al comparative inferences.

7.SP.3, 7.SP.4 2

Low

Grade 7 Mathem

atics


Early Development

4

Claim





Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade.

I. Investigate chance processes and develop, use, and evaluate probability m

odels. Evidence Required: 1.

The student understands the likelihood of an event as a probability between 0

and 1. 2.

The student finds probabilities of simple events.

3. The student com

pares predicted probabilities to observed frequencies. 4.

The student finds probabilities of compound events.

7.SP.5, 7.SP.6, 7.SP.7, 7.SP.8

2 M

edium

Claim 1

cont. 65-75%

Grade 7 Mathem

atics


Early Development

5

Claim




atics, making



Focus Target

Standard G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade.

A-D A.

Apply mathem


s in pure mathem


orkplace. B.





s, two-w


ulas).


S.A, 7.EE.A, 7.EE.B, 7.G.A*, 7.G.B*

*denotes minor

clusters

3

Tasks limited

to machine-


may be

addressed.

8-12%

Grade 7 Mathem

atics


Early Development

6

Claim

3: Comm



Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade.

A-F A.


ples. B.






ent into cases. E.



if there is a flaw

in the argument—

explain what it is.

F. Base argum


s, and actions.


7.RP.2, 7.NS.A,

7.NS.1, 7.N

S.2, 7.EE.1, 7.EE.2

3

Tasks limited

to machine-


may be

addressed.

8-12%

Grade 7 Mathem

atics


Early Development

7

Claim



athematical


s.

Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade.

A-G

A. Apply m



orkplace. B.


athematical m



. C.




ake improvem


a mathem


enon. F.



s, two-w


ulas). G.




S.A, 7.EE.B, 7.G.A*,

7.G.B*, 7.SP.A*, 7.SP.B*, 7.SP.C* *denotes m

inor clusters

3

Tasks limited

to machine-


may be

addressed.

8-12%

Grade 8 Mathem

atics


Early Development

1

Claim





Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade.

A. Know

that there are numbers that are not rational, and approxim

ate them by

rational numbers.


The student classifies real numbers as rational or irrational.

2. The student converts a repeating decim

al into a fraction. 3.

The student writes approxim

ations of irrational numbers as rational num

bers. 4.

The student compares the sizes of irrational num

bers by using rational approxim

ations of irrational numbers.

5. The student approxim

ates the locations of irrational numbers on the num

ber line by using rational approxim

ations of irrational numbers.

6. The student identifies or w

rites the prime factorization of a num

ber using exponents.

8.NS.1, 8.N

S.2, 8.N

S.3 1

Medium

65-75%

B. W

ork with radicals and integer exponents.


The student generates equivalent numerical expressions by applying the

properties of integer exponents. 2.

The student represents solutions to equations of the form x² = p using square

root symbols.

3. The student represents solutions to equations of the form

x³ = p using cube root sym

bols. 4.

The student states how m

any times as large or as sm

all one number, w

ritten as a single digit tim

es a power of 10, is than another, to estim

ate very large or very sm

all quantities. 5.

The student performs operations w

ith numbers expressed in scientific notation,

including problems w

here both decimal and scientific notation are used.

8.EE.1, 8.EE.2, 8.EE.3, 8.EE.4

1 High

Grade 8 Mathem

atics


Early Development

2

Claim





Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade.

C. U

nderstand the connections between proportional relationships, lines, and linear

equations. Evidence Required: 1.

The student graphs proportional relationships. 2.

The student interprets the unit rate as the slope of the graph of a proportional relationship.

3. The student com

pares two different proportional relationships represented in

different formats.

4. The student uses sim

ilar triangles to determine that the slope m

is the same

between any tw

o distinct points on a non-vertical line in the coordinate plane. 5.

The student finds the equation 𝑦=𝑚𝑥 or 𝑦

=𝑚𝑥+

𝑏 for a line.

8.EE.5, 8.EE.6

2 High

Claim 1

cont. 65-75%

D. Analyze and solve linear equations and pairs of sim

ultaneous linear equations. Evidence Required: 1.

The student identifies and writes exam

ples of linear equations in one variable w

ith one solution, infinitely many solutions, or no solutions.

2. The student solves linear equations in in one variable w

ith rational number

coefficients, including equations with solutions that require expanding

expressions using the distributive property and collecting like terms.

3. The student estim

ates solutions by graphing systems of tw

o linear equations in tw

o variables. 4.

The student recognizes when a system

of two linear equations in tw

o variables has one solution, no solution, or infinitely m

any solutions. 5.

The student solves a system of tw

o linear equations in two variables

algebraically, or solves real-world and m

athematical problem

s leading to two

linear equations in two variables.

8.EE.7, 8.EE.8

Grade 8 Mathem

atics


Early Development

3

Claim





Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade.

E. Define, evaluate, and com

pare functions. Evidence Required The student recognizes that a function is a rule that assigns to each input exactly one output. 1.

The student identifies or produces input and output pairs for given functions. 2.

The student recognizes the same function w

ritten in different functional forms

(algebraic, graphic, tabular, or verbal). 3.

The student compares properties of tw

o functions, each represented in a different w

ay (algebraic, graphic, tabular, or verbal). 4.

The student interprets the equation 𝑦=𝑚𝑥+

𝑏 as defining a linear function w

ith a graph that is a straight line. 5.

The student recognizes and gives examples of functions that are not linear.

8.F.1, 8.F.2, 8.F.3 2

High

Claim 1

cont. 65-75%

F.

Use functions to m

odel relationships between quantities.


The student constructs a function to model a linear relationship betw

een two

quantities. 2.

The student determines the rate of change and initial value of a function, either

from a description of a relationship or from

two (x, y) values, including reading

the rate of change and/or the value of the function from a table or a graph.

3. The student interprets features of a linear function, such as rate of change and initial value, in term

s of the situation it models, its graph, or a table of values.

4. The student qualitatively describes the functional relationship betw

een two

quantities by analyzing a graph (e.g., whether the function is increasing or

decreasing, or whether the graph is linear or nonlinear).

5. The student draw

s a graph that exhibits the qualitative features of a function that has been described in w

riting.

8.F.4, 8.F.5 2

Medium

Grade 8 Mathem

atics


Early Development

4

Claim





Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this grade.

G. U

nderstand congruence and similarity using physical m

odels, transparencies, or geom

etry software.


The student verifies that rigid transformations preserve distance and angle

measures.

2. The student describes sequences of rotations, reflections, translations, and dilations that can verify w

hether two dim

ensional figures are similar or

congruent to each other. 3.

The student constructs a new figure after the original figure is dilated, rotated,

reflected, or translated. 4.

The student describes the effect of dilations, translations, rotations, and reflections on tw

o-dimensional figures using coordinates.

8.G.1, 8.G.2, 8.G.3, 8.G.4, 8.G.5

2 High

Claim 1

cont. 65-75%

H. U

nderstand and apply the Pythagorean Theorem.


The student solves real–world and m

athematical problem

s of right triangles in tw

o and three dimensions by applying the Pythagorean Theorem

and its converse.

2. The student finds the distance betw

een two points in a coordinate system

by applying the Pythagorean Theorem

.

8.G.6, 8.G.7, 8.G.8 2

High

I. Solve real-w

orld and mathem

atical problems involving volum

e of cylinders, cones, and spheres. Evidence Required: 1.


s by applying the formulas for the

volumes of cylinders, cones, and spheres.

2. The student solves m

athematical problem

s by applying the formulas for the

volumes of cylinders, cones, and spheres.

8.G.9 2

Low

Grade 8 Mathem

atics


Early Development

5

Claim





Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this grade.

J. Investigate patterns of association in bivariate data. Evidence Required: 1.

The student interprets patterns of association between tw

o quantities in a scatter plot (clustering in reference to the line of best fit, positive or negative association, linear association, nonlinear association, and the effect of outliers) and interprets the slope and y-intercept in term

s of the context. 2.

The student identifies the slope (rate of change) and intercept (initial value) of a line suggested by exam

ining bivariate measurem

ent data in a scatter plot. 3.

The student constructs and interprets a two-w

ay table summ

arizing data on tw

o categorical variables collected from the sam

e subjects.

8.SP.1, 8.SP.2, 8.SP.3, 8.SP.4

2 M

edium

Claim 1

cont. 65-75%

Grade 8 Mathem

atics


Early Development

6

Claim




atics, making



Focus Target

Standard G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade.

A-D A.

Apply mathem


s in pure mathem


orkplace. B.





s, two-w


ulas).

Focus Clusters: 8.EE.B, 8.EE.C,

8.F.A, 8.F.B*, 8.G.A, 8.G.B, 8.G.C*

*denotes minor

clusters

3

Tasks limited

to machine-


may be

addressed.

8-12%

Grade 8 Mathem

atics


Early Development

7

Claim

3: Comm



Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade.

A-F A.


ples. B.






ent into cases. E.



if there is a flaw

in the argument—

explain what it is.

F. Base argum


s, and actions.


8.EE.1, 8.EE.5, 8.EE.6, 8.EE.7a,

8.EE.7b, 8.EE.8a, 8.F.1, 8.F.2, 8.F.3,

8.G.1, 8.G.2, 8.G.4, 8.G.5, 8.G.6, 8.G.8

3

Tasks limited

to machine-


may be

addressed.

8-12%

Grade 8 Mathem

atics


Early Development

8

Claim



athematical


s.

Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade.

A-G

A. Apply m



orkplace. B.


athematical m



. C.




ake improvem


a mathem


enon. F.



s, two-w


ulas). G.



Focus Clusters: 8.EE.3, 8.EE.4, 8.EE.B, 8.EE.C, 8.F.B*, 8.G.B,

8.G.C*, 8.SP.A* *denotes m

inor clusters

3

Tasks limited

to machine-


may be

addressed.

8-12%

Grade 9 Mathem

atics


Early Development

1

Claim





Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

N-RN

.A

A. Extend the properties of exponents to rational exponents and w

ork with radicals and

integer exponents. Evidence Required: 1.

The student rewrites expressions in radical form

into an equivalent expression with

rational exponents. 2.

The student rewrites expressions w

ith rational exponents into an equivalent expression in radical form

. 3.

The student uses the properties of exponents to write equivalent expressions involving

radicals and rational exponents. 4.

The student states how m

any times as large or as sm

all one number, w

ritten as a single digit tim

es a power of 10, is than another, to estim

ate very large or very small

quantities. 5.

The student performs operations w

ith numbers expressed in scientific notation,

including problems w

here both decimal and scientific notation are used.

Focus: Solve equations with square and cube roots, rew

rite rational and radical expressions.

N-RN

.2 2

Low

65-75%

N-Q

.A

C. Reason quantitatively and use units to solve problem


The student chooses units consistently in formulas.

2. The student chooses the scales for graphs and data displays.

Focus: Use and interpret units in real w

orld and mathem

atical situations.

N-Q

.1 2

Medium

A-SSE.A

D. Interpret the structure of expressions. Evidence Required: 1.

The student identifies key features of a function. 2.

The student uses the structure of an expression to identify ways of rew

riting it. Focus: Identify parts of a function and use properties of the function to help rew

rite it.

A-SSE.1, A-SSE.2

1

Grade 9 Mathem

atics


Early Development

2

Claim





Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

A-SSE.B

E. W

rite expressions in equivalent forms to solve problem


The student factors a quadratic expression. 2.

The student understands that the factored form of a quadratic expression reveals the

zeros of the function it defines. 3.

The student uses the properties of exponents to transform exponential expressions.

Focus: Factor quadratic expressions to reveal the zeros of a function.

A-SSE.3 2

Medium

Claim 1

cont. 65-75%

A-APR.A

F. Perform

arithmetic operations on polynom

ials. Evidence Required: 1.

The student adds or subtracts polynomials.

2. The student m

ultiplies polynomials.

Focus: Add, subtract, and multiply polynom

ials of degree 2 or more.

A-APR.1 1

High

A-CED-A

G. Analyze and solve linear equations and pairs of sim

ultaneous linear equations. Create equations that describe num

bers or relationships. Evidence Required: 1.

The student recognizes when a system

of two linear equations in tw

o variables has one solution, no solution, or infinitely m

any solutions. 2.

The student solves a system of tw

o linear equations in two variables algebraically, or

solves real-world and m

athematical problem

s leading to two linear equations in tw

o variables.

3. The student creates one variable equations or inequalities arising from

linear, quadratic, sim

ple rational, and exponential functions in one variable. 4.

The student graphs equations or inequalities on coordinate axes with labels and scales

to represent the solution to a contextual problem.

5. The student creates equations in tw

o or more variables to represent relationships

between quantities.

Focus: Classify and solve linear systems, m

odel with nonlinear equations and linear

inequalities.

A-CED.1, A-CED.2, A-CED.3, A-CED.4

2 High

Grade 9 Mathem

atics


Early Development

3

Claim





Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

A-REI.A

H. U

nderstand solving multi-step linear, sim

ple radical, and simple rational equations as a

process of reasoning and explain the reasoning. Evidence Required: 1.

The student generates algebraic equations, can justify the solution, and explain the steps to solve the equation.

2. The student represents solutions to equations of the form

x² = p using square root sym

bols. 3.

The student represents solutions to equations of the form x³ = p using cube root

symbols.

4. The student solves radical and/or sim

ple rational equations in one variable, including identifying the num

ber and type of real solutions that might exist for the equation

(e.g., one, two, infinite, or no real).

5. The student evaluates proposed solutions to radical or sim

ple rational equations, and recognizes w

here extraneous solution(s) might arise during the solving of the

equation. Focus: Solve tw

o-step linear, simple radical, and sim

ple rational equations.

A-REI.1, A-REI.2

2 M

edium

Claim 1

cont. 65-75%

A-REI.B

I. Solve linear and quadratic equations in one variable and linear inequalities in one variable. Evidence Required: 1.

The student identifies and writes exam

ples of linear equations in one variable with one

solution, infinitely many solutions, or no solutions.

2. The student solves linear equations in one variable w

ith rational number coefficients,

including equations with solutions that require expanding expressions using the

distributive property and collecting like terms.

3. The student solves linear inequalities in one variable w

ith numeric and letter coefficients

or identifies appropriate value(s) of a letter coefficient given specific information about a

variable in a linear equation or inequality. 4.

The student solves quadratic equations in one variable by taking square roots, using the quadratic form

ula, or by factoring. Focus: Solve linear equations, quadratic equations, and linear inequalities in one variable. Determ

ine the number of solutions for these types of equations.

A-REI.3, A-REI.4

2 High

Grade 9 Mathem

atics


Early Development

4

Claim





Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

A-REI.D

J. Represent and solve equations and inequalities graphically. U

nderstand the connections betw

een proportional relationships, lines, and linear equations and their graphs. Evidence Required: 1.

The student compares proportional relationships represented in different form

ats and uses sim

ilar triangles to determine that the slope m

is the same betw

een any two distinct

points on a non-vertical line in the coordinate plane. 2.

The student interprets the unit rate as the slope of the graph of a proportional relationship.

3. The student finds the equation y=m

x or y=mx+b for a line and interprets the equation as

defining a linear function with a graph that is straight line.

4. The student understands that the graph of an equation in tw

o variables is the set of all its solutions plotted in the coordinate plane, often form

ing a curve (which could be a line).

5. The student graphs the solutions to a linear inequality in tw

o variables as a half-plane (excluding the boundary in the case of a strict inequality).

6. The student finds the solution(s) (either exact or approxim

ate as appropriate) to a system

of equations and graphs the solution set to a system of linear inequalities in tw

o variables as the intersection of the corresponding half-planes.

Focus: Graph linear equations and inequalities in one or two variables and understand the

solution set. Use the solution set in context to com

pare properties of lines such as comparing

slopes to determine if a system

has zero, one, or infinitely many solutions.

A-REI.10, A-REI.11, A-REI.12

1 High

Claim 1

cont. 65-75%

F-IF.A

K. U

nderstand the concept of a function and use function notation. Evidence Required: 1.

The student recognizes functions that are not linear. 2.

The student understands that a function from one set (the dom

ain) to another set (the range) assigns to each elem

ent of the domain exactly one elem

ent of the range (e.g., distinguish betw

een functions and non-functions). 3.

The student identifies or evaluates a function to produce input and output pairs for given functions.

4. The student recognizes any necessary restriction that needs to be placed on the dom

ain in order for an equation to represent a function.

Focus: Understand dom

ain, range, and any restrictions of these for a given function.

F-IF.1, F-IF.2, F-IF.3

1 Low

Grade 9 Mathem

atics


Early Development

5

Claim




atics, making



Focus Target

Standard G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade.

A-D A.

Apply mathem


s in pure mathem


orkplace. B.





s, two-w


ulas).

Focus Clusters: N

-Q.A, A-SSE.A, A-

SSE.B, A-CED.A, A-REI.A, A-REI.B, A-

REI.D, F-IF.A, F-IF.C, F-BF.A, G-SRT.C

3

Tasks limited

to machine-


may be

addressed.

8-12%

Grade 9 Mathem

atics


Early Development

6

Claim

3: Comm



Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade.

A-F A.


ples. B.






ent into cases. E.



if there is a flaw

in the argument—

explain what it is.

F. Base argum


s, and actions.

Focus Clusters/Standards: N

-RN.A, A-SSE.A, A-

APR.A, A-REI.A, A-REI.1, A-REI.2, A-

REI.10, A-REI.11, F-IF.1, F-IF.9

3

Tasks limited

to machine-


may be

addressed.

8-12%

Grade 9 Mathem

atics


Early Development

7

Claim



athematical


s.

Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

A-G

A.

Apply mathem

atics to solve problems arising in everyday life, society, and the

workplace.

B. Construct, autonom

ously, chains of reasoning to justify mathem

atical models

used, interpretations made, and solutions proposed for a com

plex problem.



Interpret results in the context of a situation. E.

Analyze the adequacy of and make im

provements to an existing m

odel or develop a m

athematical m

odel of a real phenomenon.

F. Identify im

portant quantities in a practical situation and map their relationships

(e.g., using diagrams, tw

o-way tables, graphs, flow

charts, or formulas).

G. Identify, analyze, and synthesize relevant external resources to pose or solve problem


Focus Clusters: N

-Q.A, A-SSE.B, A-

CED.A, A-REI.A, A-REI.B, F-IF.C, F-

BF.A, S-ID.A

3

Tasks limited

to machine-


may be

addressed.

8-12%

Grade 10 Mathem

atics


Early Development

1

Claim





Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

N-RN

.A

A. Extend the properties of exponents to rational exponents.


The student rewrites expressions in radical form

into an equivalent expression w

ith rational exponents. 2.

The student rewrites expressions w

ith rational exponents into an equivalent expression in radical form

. 3.

The student uses the properties of exponents to write equivalent expressions

involving radicals and rational exponents. Focus: U

se and identify properties of exponents to rewrite expressions.

N-RN

.2

2 Low

65-75%

N-RN

.B

B. U

se properties of rational and irrational numbers.


The student provides examples of addition or m

ultiplication problems that w

ill have sum

s or products of a specified type (either rational or irrational). 2.


hether the sum of tw

o numbers is a rational num

ber or an irrational num

ber. 3.


hether the product of two num

bers is a rational num

ber or an irrational number.

4. The student provides an abstract generalization that the sum

or product of any tw

o rational numbers is rational, the sum

of a rational number and an irrational

number is irrational, and the product of a nonzero rational num

ber and an irrational num

ber is irrational. Focus: Solve problem

s using square and cube roots. For example, student m

ay solve for a specified variables for equations such as distance betw

een points, surface area, and volum

e.

N-RN

.3

Grade 10 Mathem

atics


Early Development

2

Claim





Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

N-Q

.A

C. Reason quantitatively and use units to solve problem


The student chooses units consistently in formulas.

2. The student chooses the scales for graphs and data displays.

Focus: Use the context of real w

orld and mathem

atical problems to choose

appropriate units, with special em

phasis on units related to length, area, and/or volum

e of a figure.

N-Q

.1 2

Medium

Claim 1

cont. 65-75%

A-SSE.A

D. Interpret the structure of expressions.


The student uses the structure of an expression to identify ways of rew

riting it. Focus: Identify the m

eaning of parts of an expression in the context of geometric

formulas. U

se properties of these expressions to rewrite them

. Functions may include

nonlinear expressions including high degree polynomials.

A-SSE.2 1

A-SSE.B

E. W

rite expressions in equivalent forms to solve problem


The student understands that the factored form of a quadratic expression reveals

the zeros of the function it defines. 2.

The student understands that completing the square for a quadratic expression

reveals the maxim

um or m

inimum

value of the function it defines. 3.

The student uses the properties of exponents to transform exponential

expressions. Focus: Factor and com

plete the square to find the zeros, maxim

um, and m

inimum

values of a quadratic function.

A-SSE.3 2

A-APR.A

F. Perform

arithmetic operations on polynom

ials. Evidence Required: 1.

The student adds or subtracts polynomials.

2. The student m

ultiplies polynomials.

Focus: Add, subtract, and multiply polynom

ials in the context of finding perimeter,

area, and surface area of partial or composite figures.

A-APR.1 1

High

Grade 10 Mathem

atics


Early Development

3

Claim





Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

A-CED.A

G. Create equations that describe num

bers or relationships. Evidence Required: 1.

The student creates one variable equations arising from linear, quadratic, sim

ple rational, and exponential functions in one variable.

2. The student creates one variable inequalities arising from

linear, quadratic, sim

ple rational, and exponential functions in one variable. 3.

The student graphs equations or inequalities on coordinate axes with labels and

scales to represent the solution to a contextual problem.

4. The student creates equations in tw

o or more variables to represent relationships

between quantities.

Focus: Model relationships using nonlinear equations and linear inequalities

including but not limited to problem

s involving distance between points and sim

ilar figures.

A-CED.1, A-CED.2

2 High

Claim 1

cont. 65-75%

A-REI.A

H. U

nderstand solving equations as a process of reasoning and explain the reasoning. Evidence Required: 1.

The student solves radical and/or simple rational equations in one variable,

including identifying the number and type of real solutions that m

ight exist for the equation (e.g., one, tw

o, infinite, or no real). 2.

The student evaluates proposed solutions to radical or simple rational equations,

and recognizes where extraneous solution(s) m

ight arise during the solving of the equation.

Focus: Solve multi-step equations involving com

bining like terms and using the

distributive property.

A-REI.2 2

Medium

Grade 10 Mathem

atics


Early Development

4

Claim





Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

A-REI.B

I. Solve equations and inequalities in one variable.


The student solves linear equations in one variable with num

eric coefficients. 2.

The student solves linear inequalities in one variable with num

eric coefficients. 3.

The student solves linear inequalities in one variable with letter coefficients or

identifies appropriate value(s) of a letter coefficient given specific information

about a variable in a linear equation or inequality. 4.

The student solves quadratic equations in one variable by taking square roots, com

pleting the square, using the quadratic formula, or by factoring.

5. The student recognizes w

hen the quadratic formula gives com

plex solutions (no real solutions).

6. The student w

rites complex solutions for the quadratic form

ula in the form 𝑎±𝑏𝑖

where a and b are real num

bers. Focus: Solve linear and quadratic equations and linear inequalities in one variable w

ith emphasis on problem

s with geom

etric context such as segment lengths, angle

measures, etc.

A-REI.3, A-REI.4

2 High

Claim 1

cont. 65-75%

F-IF.A

K. U

nderstand the concept of a function and use function notation. Evidence Required:

1. The student understands that a function from

one set (the domain) to another set

(the range) assigns to each element of the dom

ain exactly one element of the range

(e.g., distinguish between functions and non-functions).

2. The student recognizes any necessary restriction that needs to be placed on the dom

ain in order for an equation to represent a function. 3.

The student understands that the graph of f is the graph of the equation y = f(x). 4.

The student recognizes that sequences are functions whose dom

ain is a subset of the integers.

Focus: Understand dom

ain, range, and their restrictions when w

orking with functions

and function notation. Compare functions using sim

ilar variables, such as area and circum

ference in relation to radius and diameter, and determ

ine any restrictions for those variables.

F-IF.1, F-IF.3 1

Low

Grade 10 Mathem

atics


Early Development

5

Claim





Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

F-IF.B

L. Interpret functions that arise in applications in term

s of the context. Evidence Required:

1. The student interprets key features of a graph or a table representing a function m

odeling a relationship between tw

o quantities. 2.

The student sketches graphs showing key features given a verbal description of a

relationship between tw

o quantities that can be modeled w

ith a function. 3.

The student relates the domain of a function to its graph and, w

here applicable, to the quantitative relationship it describes.

4. The student calculates and interprets the average rate of change of a function presented sym

bolically or as a table and estimates the rate of change of a

function from a graph.

Focus: Use applications of a function in context to interpret the solution, such as the

result of the distance formula, the m

eaning of a line’s slope, or the surface area of a figure.

F-IF.4, F-IF.5, F-IF.6

1

Low

Claim 1

cont. 65-75%

F-BF.A

N.

Build a function that models a relationship betw

een two quantities.


The student writes explicit or recursive functions to describe relationships

between tw

o quantities from a context.

2. The student translates betw

een explicit formulas and recursively defined

functions. 3.

The student understands a function as a model of the relationship betw

een two

quantities. Focus: U

se sequences and series to define patterns and relationships between

variables or similar and congruent figures.

F-BF.1, F-BF.2 2

Grade 10 Mathem

atics


Early Development

6

Claim





Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

G-SRT.C

O.

Define trigonometric ratios and solve problem

s involving right triangles. Evidence Required:

1. The student uses the definitions of trigonom

etric ratios for acute angles in a right triangle.

2. The student uses sim

ilar triangles to define and determine trigonom

etric ratios in right triangles.

3. The student explains and uses the relationship betw

een the sine and cosine of com

plementary angles.

4. The student uses the Pythagorean Theorem

and trigonometric ratios to solve

problems involving right triangles in m

athematical or real-w

orld context. Focus: U

se sine and cosine to compare properties of com

plementary angles and use

Pythagorean Theorem w

ith trigonometric ratios to solve real-w

orld and mathem

atical problem

s.

G-SRT.6, G-SRT.7, G-SRT.8

2 High

Claim 1

cont. 65-75%

S-ID.A

P. Sum

marize, represent, and interpret data on a single count or m

easurement

variable. Evidence Required:

1. The student w

ill be able to represent data on the real number line w

ith a dot plot, histogram

, or box plot. 2.

The student will be able to use statistics appropriate to the shape of the data

distribution to compare center (m

edian, mean) and spread (interquartile range,

standard deviation) of two or m

ore different data sets. 3.

The student will be able to interpret the differences in shape, center, and spread

in the context of the data sets. 4.

The student will be able to interpret the effects of outliers on the shape, center,

and spread of a data set. Focus: U

se appropriate statistics to determine shape and spread of data using

measures of center and variability.

S-ID.1, S-ID.2, S-ID.3

Grade 10 Mathem

atics


Early Development

7

Claim





Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

G-CO.C

Q.

Prove geometric theorem

s. Evidence Required:

1. The student explains proofs or reasoning related to theorem

s about lines and angles. Theorem

s include, but are not limited to: vertical angles are congruent;

when a transversal crosses parallel lines, alternate interior angles are congruent

and corresponding angles are congruent; points on a perpendicular bisector of a line segm

ent are exactly those equidistant from the segm

ent’s endpoints. 2.

The student explains proofs or reasoning related to theorems about triangles.

Theorems include, but are not lim

ited to: measures of interior angles of a triangle

sum to 180°; base angles of isosceles triangles are congruent; the segm

ent joining m

idpoints of two sides of a triangle is parallel to the third side and half the

length; the medians of a triangle m

eet at a point. 3.

The student explains proofs or reasoning related to theorems about circles.

Include proof that all circles are similar.

4. The student explains proofs or reasoning related to theorem

s about parallelogram

s. Theorems include, but are not lim

ited to: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram

bisect each other, and conversely, rectangles are parallelogram

s with congruent

diagonals. Focus: Explain proofs and reasoning related to lines, angles, triangles, circles, and parallelogram

s.

G-CO.9,

G-CO.10,

G-CO.11

2 High

Claim 1

cont. 65-75%

G-GMD.A

R. Explain volum

e formulas and use them

to solve problems.



s by applying the formulas for the volum

e of cylinders, pyram

ids, cones, and spheres. 2.

The student solves mathem

atical problems by applying the form

ulas for the volum

e of cylinders, pyramids, cones, and spheres.

Focus: Use volum

e formulas for cylinders, pyram

ids, cones, and spheres to solve problem

s.

G-GMD.1,

G-GMD.3

Grade 10 Mathem

atics


Early Development

8

Claim




atics, making



Focus Target

Standard G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade.

A-D A.

Apply mathem


s in pure mathem


orkplace. B.





s, two-w


ulas).

Focus Clusters: N

-Q.A, A-SSE.A,

A-SSE.B, A-CED.A, A-REI.2, A-REI.B, A-REI.C, A-REI.D,

F-IF.A, F-IF.B, F-IF.C, F-BF.A,

G-SRT.C, S-ID.C, S-CP.A

*denotes minor

clusters

3

Tasks limited

to machine-


may be

addressed.

8-12%

Grade 10 Mathem

atics


Early Development

9

Claim

3: Comm



Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade.

A-F A.


ples. B.






ent into cases. E.



if there is a flaw

in the argument—

explain what it is.

F. Base argum


s, and actions.


N-RN

.A, N-RN

.B, N

-RN.3, A-SSE.2,

A-APR.1, A-APR.B, A-APR.4, A-APR.6, A-REI.A, A-REI.1, A-REI.2, A-REI.C,

A-REI.10, A-REI.11, F-IF.1, F-IF.5, F-IF.9,

F-BF.3, F-BF.4a, F-TF.1, F-TF.2,

F-TF.8, G-CO.A,

G-CO.B, G-CO

.C, G-CO

.9, G-CO.10,

G-CO.11, G-SRT.A, G-SRT.B

3

Tasks limited

to machine-


may be

addressed.

8-12%

Grade 10 Mathem

atics


Early Development

10

Claim



athematical


s.

Focus Target

Standards G

oal DO

K

Relative Em

phasis/ Com

ments

%

Not

used in this

grade.

A-G

A. Apply m



orkplace. B.


athematical m



. C.




ake improvem


a mathem


enon. F.



s, two-w


ulas). G.



Focus Clusters: N

-Q.A, A-SSE.B,

A-CED.A, A-REI.A, A-REI.B, A-REI.C, F-IF.B, F-IF.C, F-

BF.A, S-ID.A, S-ID.B, S-IC.1, S-IC.B, F-LE.A, F-LE.B,

F-TF.5, G-GMD.3,

G-MG

*denotes minor

clusters

3

Tasks limited

to machine-


may be

addressed.

8-12%

math amp summative framework final 1 15 15 assessment...alaska measures of progress mathematics...

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