Pennsylvania Alternate Standards - Pennsylvania's Alternate System of Assessment

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Alternate Academic Content Standards for Reading
Alternate Academic Content Standards for Mathematics

Introduction

This document includes the Reading Standard: 1.1. Learning to Read Independently
Re-interpreted for students with the most significant cognitive disabilities
The Alternate Reading Standards describe what students with the most significant cognitive disabilities should know and be able to do in literacy-related areas at four grade spans (third/fourth, fifth/sixth, seventh/eighth and eleventh). The standards for each grade span were derived from the general education content standards for the equivalent grade that appear in the Chapter 4 Academic Standards for Reading, Writing, Listening, and Speaking as approved by the Pennsylvania Board of Education for all students, at the same grade levels as originally listed (the reference number to the original Chapter 4 Standard is provided in parentheses) The third/fourth grade alternate standards link to the third grade Chapter 4 standards; the eleventh grade alternate standards link to the eleventh grade Chapter 4 standards; and so on. The alternate grade-level content standards provide the targets for instruction and student learning essential for success in the environments in and out of school that students with severe disabilities are likely to encounter. Although the standards are not a curriculum or a prescribed series of activities, school programs for students with the most significant disabilities will use them to develop a local curriculum that will meet local students needs.
Literacy is the process by which students learn about and make sense of their world. Students do not just read printed or Braille text; they "read" everything they see or touch, including objects, pictures, and media of all sorts. Therefore, these Reading Standards address "reading" in its broadest sense. When students look at an object or touch an object and recognize what it is, or what it is for, or what it belongs with, they are "reading" the object. When students name a picture, or recognize a picture, or describe what is happening in a picture, they are "reading" the picture. And when students make meaning from print or Braille, they are also "reading." The standards define the skills and strategies employed by students with the most significant disabilities who have attained proficiency in literacy skills defined very broadly; all teachers who interact with these students will assist them in learning these skills and strategies through multiple classroom situations in all the subject areas.
The Alternate Reading Standards also provide parents and community members with information about what students with the most significant disabilities should know and be able to do as they progress through their educational program and at graduation. With a clearly defined target provided by the standards, parents, students, educators and community members become partners in learning success.

NOTE: The system used in this document to reference the standards is as follows.
Standards listed in boldface are the same standards that appear in the Chapter 4 Academic Standards for Mathematics as approved by the Pennsylvania Board of Education for all students, at the same grade levels as originally listed (the reference number to the original Chapter 4 Standard is provided in parentheses.).
Specific skills that define the reinterpreted content standard for students with the most severe cognitive disabilities are provided in italics

1.1. A. Learning to Read Independently

GRADE 3/4	GRADE 5/6	GRADE 7/8	GRADE 11
Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:
A. Identify the purposes and types of text (e.g., literature, information) before reading. (1.1.3.A) Identifies books Identifies books as source of information Predicts topic of story or book based on pictures	A. Identify the purposes for reading a type of text (e.g., literature, information) before reading. (1.1.5.A) Identifies books Identifies books as source of information Predicts topic of story or book based on pictures	A. Locate appropriate texts (literature, information, documents) for an assigned purpose before reading. (1.1.8.A) Chooses correct source for needed information	A. Locate various texts, media and traditional resources for assigned and independent projects before reading. (1.1.11.A) Identifies content of material Chooses correct source for needed information

1.1. B Learning to Read Independently

GRADE 3/4	GRADE 5/6	GRADE 7/8	GRADE 11
Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:
B. Preview the text formats (e.g., title, headings, chapters and table of contents). (1.1.3.B) Orients towards materials Locates parts of book (title, etc.)	B. Select texts for a particular purpose using the format of the text as a guide. (1.1.5.B) Identifies correct source for information	B. Identify and use common structures and graphic features to comprehend information. (1.1.8.B) Matches identical pictures, icons, words Locates pictures, icons, words named Uses titles, pictures etc to identify content of source	B. Analyze the structure of informational materials (1.1.11.B) Uses titles, pictures, etc to identify content of source

1.1. C Learning to Read Independently

GRADE 3/4	GRADE 5/6	GRADE 7/8	GRADE 11
Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:
C. Use knowledge of phonics, word analysis (e.g., root words, prefixes and suffixes), syllabication, picture and context clues to decode and understand new words during reading. (1.1.3.C) Makes discriminations between objects, pictures, icons, words, sounds Matches identical objects, pictures, icons, words Labels objects pictures, icons and words Discriminates beginning sound of objects and words	C. Use knowledge of phonics, syllabication, prefixes, suffixes, the dictionary or context clues to decode and understand new words during reading. Use these words accurately in writing and speaking. (1.1.5.C) Matches identical objects, pictures, icons, words Identifies words that rhyme Labels objects, pictures, icons and words Discriminates beginning sounds of objects and words Demonstrates letter- sound knowledge	C. Use knowledge of phonics, syllabication, prefixes, suffixes, root words as well as context clues and glossaries to understand vocabulary during reading. (1.1.8.C) Discriminates beginning sounds of objects and words Demonstrates letter- sound knowledge Identifies words that rhyme Uses pictures and context to identify words	C. Use knowledge of root words and words from literary works to recognize and understand the meaning of new words during reading. Use these words accurately in speaking and writing. (1.1.11.C)

1.1. D Learning to Read Independently

GRADE 3/4	GRADE 5/6	GRADE 7/8	GRADE 11
Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:
D. Acquire a reading vocabulary by identifying and correctly using words (e.g., antonyms, synonyms, categories of words). Use a dictionary when appropriate. (1.1.3.E) Labels items, pictures, icons, words Identifies commonality of items and groups them accordingly	D. Identify the basic ideas and facts in text using strategies (e.g., prior knowledge, illustrations and headings) and information from other sources to make predictions about text. (1.1.5.D) Predicts topic of text from pictures/words	D. Expand a reading vocabulary (1.1.8.E) Identifies similar and related pictures/words Identifies categories of pictures/words Identifies function of pictures/words Identifies picture based on characteristics named/described Reads complex pictures Reads words in isolation	D. Establish a reading vocabulary by identifying and correctly using new words acquired through the study of their relationships to other words. Use a dictionary or related reference. (1.1.11.E) Identifies similar and related pictures/words Identifies categories of pictures/words Identifies function of pictures/words Identifies picture based on characteristics named/described Reads complex pictures Reads words in isolation

1.1. E Learning to Read Independently

GRADE 3/4	GRADE 5/6	GRADE 7/8	GRADE 11
Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:
E. Understand the meaning of and use correctly new vocabulary learned in various subject areas. (1.1.3.F) Identifies items, pictures (simple and complex), icons, or words described Identifies similar and related items, pictures, icons or words Identifies object by function described Indicates function of item	E. Acquire a reading vocabulary by correctly identifying and using words (e.g., synonyms, homophones, homographs, words with roots, suffixes, prefixes). Use a dictionary or related reference. (1.1.5.E) Labels items, pictures (simple and complex), icons, words Identifies like items Defines terms Identifies terms with similar meanings Identifies tense of words	E. Understand the meaning of and apply key vocabulary across the various subject areas. (1.1.8.F) Identifies function of item presented as object, picture or word Defines words with examples Demonstrates meaning of word by categorizing	E. Understand the meaning of and apply key vocabulary across the various subject areas. (1.1.11.F) Identifies function of item presented as object, picture or word Defines words with examples Demonstrates meaning of word by categorizing

1.1. F Learning to Read Independently

GRADE 3/4	GRADE 5/6	GRADE 7/8	GRADE 11
Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:
F. Demonstrate understanding and interpretation of word/text (1.1.3.G). Defines words Categorizes words by meaning Chooses word to complete phrase/sentence	F. Identify, understand the meaning of and use correctly key vocabulary from various subject areas. (1.1.5.F) Labels items, pictures, icons and word across functional and academic curriculum Identifies similar and related items, pictures, icons or words across functional and academic curriculum

1.1. G Learning to Read Independently

GRADE 3/4	GRADE 5/6	GRADE 7/8	GRADE 11
Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:
G. Demonstrate after reading understand of fiction. (1.1.3.G) Answers literal who, what, where, when comprehension questions after text is read Sequences pictures based on text Locates pictures illustrating text meaning Follows 1-2 step instructions	G. Demonstrate understanding and interpretation of both fiction and nonfiction text. (1.1.5.G) Identifies events in pictures/text Orders events Identifies picture/ story details	G. Demonstrate after reading understanding and interpretation of both fiction and nonfiction text, including public documents. (1.1.8.G) Identifies main event in picture/text Identifies next event in picture/text Sequences events Identifies detail in picture/text Identifies facts in narrative/expository text Locates information in text Identifies topic of story from picture/title Identifies function of word Identifies last word to complete sentence/passage Orders 3 phrases representing main ideas from text	G. Demonstrate after reading understanding and interpretation of both fiction and nonfiction text, including public documents. (1.1.11.G) Identifies main event in picture/text Identifies next event in picture/text Sequences events Identifies detail in picture/text Identifies facts in narrative/expository text Locates information in text Identifies topic of story from picture/title Identifies function of word Identifies last word to complete sentence/passage Orders phrases representing main ideas from text

1.1. H Learning to Read Independently

GRADE 3/4	GRADE 5/6	GRADE 7/8	GRADE 11
Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:
H. Demonstrate fluency and comprehension in reading. (1.1.3.H) Reads words in isolation Reads words in context	H. Demonstrate fluency and comprehension in listening and reading. (1.1.5.H) Reads pictures, icons, word, phrases, and sentences Answers literal comprehension questions based on listening to and reading text Follows directions based on listening to and reading text	H. Demonstrate fluency and comprehension in reading. (1.1.8.H) Reads words paired with pictures Reads words in context Read words in sentences/paragraphs Answers literal and inferential questions after text is read to student Answers comprehension questions after reading text Reads and/or follows 1-2 step directions	H. Demonstrate fluency and comprehension in reading. (1.1.8.H) Reads words paired with pictures Reads words in context Read words in sentences/paragraphs Answers literal and inferential questions after text is read to student Answers comprehension questions after reading text Reads and/or follows 1-2 step directions

Introduction

2.1. Numbers, Number Systems and Number Relationships
2.2. Computation and Estimation
2.3. Measurement and Estimation
2.6. Statistics and Data Analysis
2.7. Probability and Predictions
2.8. Algebra and Functions

The Alternate Mathematics Standards describe what students with the most severe cognitive disabilities should know and be able to do at four grade level spans (third/fourth, fifth/sixth, seventh/eighth, and eleventh). The standards for each grade span were derived from the general education content standards for the equivalent grade that appear in the Chapter 4 Academic Standards for Mathematics as approved by the Pennsylvania Board of Education for all students, at the same grade levels as originally listed (the reference number to the original Chapter 4 Standard is provided in parentheses). The third/fourth grade alternate standards link to the third grade Chapter 4 standards; the eleventh grade alternate standards link to the eleventh grade Chapter 4 standards; and so on. Those Chapter 4 grade-level content standards have been reinterpreted to be appropriate learning targets for students with the most severe cognitive disabilities, and at the same time link the learning goals for these students with those of their non-disabled grade-mates. The alternate academic content standards delineated in this document provide the targets for instruction and student learning essential for success in the environments in and out of school that students with severe disabilities are likely to encounter. Although the standards are not a curriculum or a prescribed series of activities, school programs for students with the most severe cognitive disabilities will use them to develop a local school curriculum that will meet local student's needs.
The Alternate Mathematics Standards define the skills and strategies employed by students with the most severe cognitive disabilities who have attained proficiency in numeracy skills defined very broadly; all teachers who interact with these students will assist them in learning these skills and strategies through multiple classroom situations in all the subject areas. The Alternate Mathematics Standards also provide parents and community members with information about what students with the most severe cognitive disabilities should know and be able to do as they progress through their educational program and at graduation. With a clearly defined target provided by the standards, parents, students, educators and community members become partners in learning success.

NOTE: The system used in this document to reference the standards is as follows. Standards listed in boldface are the same standards that appear in the Chapter 4 Academic Standards for Mathematics as approved by the Pennsylvania Board of Education for all students, at the same grade levels as originally listed (the reference number to the original Chapter 4 Standard is provided in parentheses).
Standards listed in regular print are standards that are continued into additional grades for ongoing instruction for students with the most severe cognitive disabilities.
Specific skills that define the reinterpreted content standard for students with the most severe cognitive disabilities are provided in italics.

2.1. A, B, & C Numbers, Number Systems and Number Relationships

2.2. A, B, & C Computation and Estimation

GRADE 3/4	GRADE 5/6	GRADE 7/8	GRADE 11
Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:
A. Count using whole numbers (to 10,000) and by 2's, 3's, 5's, 10's, 25's and 100's. (2.1.3.A) B. Use concrete objects to count, order and group. (2.1.3.G) C. Demonstrate an understanding of one-to-one correspondence. (2.1.3.H) Rationally counts by 1s up to 9 Rationally counts single set of items by 1s up to 9 with and without teacher pointing Rationally counts groups of sets Orders sets of items by quantity Sorts objects into groups Creates sets of items (e.g., each set has one) Counts out quantity named up to 9	A. Count using whole numbers (to 10,000) and by 2's, 3's, 5's, 10's, 25's and 100's. B. Use concrete objects to count, order and group. C. Demonstrate an understanding of one-to-one correspondence Rote counts by 1s, 2s, and 5s up to 19 Rationally counts by 1s, 2s, 5s up to 19 with and without teacher pointing; fixed/movable array Rationally counts groups of sets Orders sets of items by quantity Sorts items into groups Creates sets of items (e.g., each set has one) Counts out quantity named up to 19	A. Count using whole numbers (to 10,000) and by 2's, 3's, 5's, 10's, 25's and 100's. B. Use concrete objects to count, order and group. C. Demonstrate an understanding of one-to-one correspondence Rote counts by 1s, 2s, 5s, 10s, 20s, and 25s up to 99 Rationally counts by 1s, 2s, 5s, 10s, 20s and 25s up to 99; fixed/movable array Counts out quantity named up to 99	A. Count using whole numbers (to 10,000) and by 2's, 3's, 5's, 10's, 25's and 100's B. Use concrete objects to count, order and group. C. Demonstrate an understanding of one-to-one correspondence Rote counts by 1s, 2s, 5s,10s, 20s, 25s, and 100s up to 500 Rationally counts by 1s , 2s, 5s, 10s, 20s, 25s, and 100s up to 500 Counts out quantity named up to 500

2.1. D Numbers, Number Systems and Number Relationships

2.2. D Computation and Estimation

GRADE 3/4	GRADE 5/6	GRADE 7/8	GRADE 11
Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:
D. Use whole numbers and fractions to represent quantities. (2.1.3.B) Identifies numerals (0 - 9) Matches numbers to quantities (0 - 9)	D. Use whole numbers and fractions to represent quantities. Identifies numerals (0 - 19) Matches numbers to quantities (0 - 19) Locates numerals in an array	D. Use whole numbers and fractions to represent quantities. Identifies numerals (0 - 99) Matches numbers to quantities (0 - 99)	D. Use whole numbers and fractions to represent quantities. Identifies numerals (0 - 500) Matches numbers to quantities (0 - 500)

2.1. E Numbers, Number Systems and Number Relationships

2.2. E Computation and Estimation

GRADE 3/4	GRADE 5/6	GRADE 7/8	GRADE 11
Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:
E. Represent equivalent forms of the same number through the use of concrete objects, drawings, word names and symbols. (2.1.3.C) Matches numerals to quantities (0 - 9) Matches sets with identical quantities Reads numerals	E. Apply number theory concepts to rename a number quantity (e.g., six, 6, , 3 x 2, 10 - 4). (2.1.5.B) Matches equivalent numerals, sets, notations (0-19) Matches numerals to word (3 to three)	E. Apply number theory concepts to rename a number quantity (e.g., six, 6, , 3 x 2, 10 - 4). Matches equivalent numerals, sets, notations (0-99) Matches numerals to word (3 to three)	E. Apply number theory concepts to rename a number quantity (e.g., six, 6, , 3 x 2, 10 - 4). Matches equivalent numerals, sets, notations (0-500) Matches numerals to word (3 to three

2.1. F Numbers, Number Systems and Number Relationships

2.2. F Computation and Estimation

GRADE 3/4	GRADE 5/6	GRADE 7/8	GRADE 11
Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:
F. Use drawings, diagrams or models to show the concept of fraction as part of a whole. (2.1.3.D) Identifies object divided into halves	F. Use models to represent fractions. (2.1.5.D) Identifies objects divided into equal parts	F. Use models to represent fractions. Identifies largest or smallest portions Identifies diagram showing x partss of whole Identifies diagram showing x pieces of whole (halves, fourths) Identifies diagram showing sum of two portions (2 halves; 3 fourths)	F. Use models to represent fractions. Identifies largest or smallest portions Identifies diagram showing x pieces of whole (halves, thirds, fourths, eights)

2.1. G & H HNumbers, Number Systems and Number Relationships

2.2. G & H Computation and Estimation

GRADE 3/4	GRADE 5/6	GRADE 7/8	GRADE 11
Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:
G. Count, compare and make change using a collection of coins and one-dollar bills. (2.1.3.E) H. Differentiates between "money" and non money Differentiates between coins and bills Identifies currency named (1,5 dollar bill) Names currency Reads price up to $5/5¢	G. Count, compare and make change using a collection of coins and one-dollar bills. (up to 9) H. Apply estimation strategies to a variety of problems including time and money. (2.2.5.E) Identifies value of coins/bills Differentiates bills Counts pennies, one and five dollar bills Estimates costs of items (relative and actual)	G. Count, compare and make change using a collection of coins and one-dollar bills. (up to 99) H. Apply estimation strategies to a variety of problems including time and money. Identifies value of coins/bills Counts bills with mixed denominations Count bills and coins with mixed denominations Identifies sufficient amounts for purchases Estimates cost of items (relative and actual)	G. Count, compare and make change using a collection of coins and one-dollar bills. (up to 500) H. Apply estimation strategies to a variety of problems including time and money. Counts bills with mixed denominations Counts bills and coins Identifies sufficiency for purchases Estimates costs of items (relative and actual)

2.1. I Numbers, Number Systems and Number Relationships

2.2. I Computation and Estimation

GRADE 3/4	GRADE 5/6	GRADE 7/8	GRADE 11
Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:
I. Apply number patterns (even and odd) and compare values of numbers on the hundred board. (2.1.3.F) Sequentially orders consecutive numerals and quantities (0 - 9)	I. Apply number patterns (even and odd) and compare values of numbers on the hundred board. Sequentially orders consecutive and non consecutive numerals and quantities (0 - 19)	I. Apply number patterns (even and odd) and compare values of numbers on the hundred boards. Sequentially orders consecutive and non consecutive numerals and quantities (0 - 99)	I. Apply number patterns (even and odd) and compare values of numbers on the hundred board. Sequentially orders consecutive and non consecutive numerals and quantities (0 - 500)

2.1. J & K Numbers, Number Systems and Number Relationships

2.2. J & K Computation and Estimation

GRADE 3/4	GRADE 5/6	GRADE 7/8	GRADE 11
Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:
J. Apply addition and subtraction in everyday situations using concrete objects. (2.2.3.A) K. Apply place-value concepts and numeration to counting, ordering and grouping. (2.1.3.I) (1-9) Matches numerals to quantities Names numerals Writes numerals Identifies first, second, third, etc. Orders consecutive and non consecutive numbers	J. Apply addition and subtraction in everyday situations using concrete objects. K. Apply place-value concepts and numeration to counting, ordering and grouping. (0-19) Matches numerals to quantities Names numerals Writes numerals Identifies first, second, third, etc. Orders consecutive and non consecutive numbers	J. Apply addition and subtraction in everyday situations using concrete objects K. Apply place-value concepts and numeration to counting, ordering and grouping. (0-99) Matches numeral to quantity Names numerals Writes numerals Identifies first, second, third, etc. Orders consecutive and non consecutive numbers	J. Apply addition and subtraction in everyday situations using concrete objects. K. Apply place-value concepts and numeration to counting, ordering and grouping. (0-500) Matches numerals to quantities Names numerals Writes numerals Identifies first, second, third, etc. Orders consecutive and non consecutive numbers

2.1. L Numbers, Number Systems and Number Relationships

2.2. L Computation and Estimation

GRADE 3/4	GRADE 5/6	GRADE 7/8	GRADE 11
Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:
L. Estimate, approximate, round or use exact numbers as appropriate. (2.1.3.J) Identifies sets with many/few; most/fewest/least Identifies subsets with all, some, most, none	L. Estimate, approximate, round or use exact numbers as appropriate Identifies sets with many/few; most/fewest/least Identifies subsets with all, some, most, none Identifies sufficiency for need	L. Estimate, approximate, round or use exact numbers as appropriate Identifies sets with many/few; most/fewest/least Identifies subsets with all, some, most, none Identifies sufficiency for need	L. Estimate, approximate, round or use exact numbers as appropriate Identifies sets with many/few; most/fewest/least Identifies subsets with all, some, most, none Identifies sufficiency for need

2.1. M, N, O & P Numbers, Number Systems and Number Relationships

2.2. M, N, O & P Computation and Estimation

GRADE 3/4	GRADE 5/6	GRADE 7/8	GRADE 11
Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:
M. Demonstrate knowledge of basic facts in four basic operations. (2.1.3.L) N. Solve single- and double-digit addition and subtraction problems with regrouping in vertical form. (2.2.3.B) O. Demonstrate the concept of multiplication as repeated addition and arrays. (2.2.3.C) P. Demonstrate the concept of division as repeated subtraction and as sharing. (2.2.3.D) (0-9) Adds/subtracts by counting Sorts items into groups	M. Demonstrate knowledge of basic facts in four basic operations. N. Solve single- and double-digit addition and subtraction problems with regrouping in vertical form O. Demonstrate the concept of multiplication as repeated addition and arrays. P. Demonstrate the concept of division as repeated subtraction and as sharing (0-19) Identify symbols +, −, ×, ÷ Writes equations for addition Writes equations for subtraction Adds 2 - 3 single digit numbers∗ Adds single digit to double digit numbers, without renaming; with renaming∗ Adds two double digit numbers, without renaming; with renaming∗ Adds two three digit numbers, without renaming; with renaming∗ Subtracts one digit numbers∗ Subtracts one and two digit numbers without renaming; with renaming∗ Subtracts two three digit numbers without renaming; with renaming∗ Continuously counts /separate sets of items ∗With or without calculator	M. Demonstrate knowledge of basic facts in four basic operations. N. Solve single- and double-digit addition and subtraction problems with regrouping in vertical form O. Demonstrate the concept of multiplication as repeated addition and arrays. P. Demonstrate the concept of division as repeated subtraction and as sharing (0-99) Identify symbols +, −, ×, ÷ Write equations for addition Write equations for subtraction Adds single digit numbers∗ Adds single digit to double digit numbers, without renaming; with renaming∗ Adds two double digit numbers, without renaming; with renaming∗ Adds two three digit numbers, without renaming; with renaming∗ Subtracts one digit numbers∗ Subtracts one and two digit numbers without renaming; with renaming∗ Subtracts two three digit numbers without renaming; with renaming∗ Multiplies numbers∗ Divides numbers∗ ∗With or without calculator	M. Demonstrate knowledge of basic facts in four basic operations. N. Solve single- and double-digit addition and subtraction problems with regrouping in vertical form O. Demonstrate the concept of multiplication as repeated addition and arrays. P. Demonstrate the concept of division as repeated subtraction and as sharing (0-500) Identify symbols +, −, ×, ÷ Write equations for addition Write equations for subtraction Adds single digit numbers∗ Adds single digit to double digit numbers, without renaming; with renaming∗ Adds two double digit numbers, without renaming; with renaming∗ Adds two three digit numbers, without renaming; with renaming∗ Subtracts one digit numbers Subtracts one and two digit numbers without renaming; with renaming∗ Subtracts two three digit numbers without renaming; with renaming∗ Multiplies numbers∗ Divides numbers∗ ∗With or without calculator

2.1. Q Numbers, Number Systems and Number Relationships

2.2. Q Computation and Estimation

GRADE 3/4	GRADE 5/6	GRADE 7/8	GRADE 11
Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:
	Q. Develop and apply algorithms to solve word problems (2.2.5.B)	Q. Develop and apply algorithms to solve word problems F. Estimate amount of tips and discounts using ratios, proportions and percents. 2.2.8.D) Calculates tips∗ Calculates discounts∗ ∗With or without calculator	Q. Develop and apply algorithms to solve word problems F. Estimate amount of tips and discounts using ratios, proportions and percents. 2.2.8.D) Calculates tips∗ Calculates discounts∗ ∗With or without calculator

2.3. A Measurement and Estimation

GRADE 3/4	GRADE 5/6	GRADE 7/8	GRADE 11
Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:
A. Compare measurable characteristics of different objects on the same dimensions (e.g., time, temperature, area, length, weight, capacity, perimeter).(2.3.3.A) Identifies lightest/heaviest, smallest/biggest, shortest/furthest, shortest/tallest, longest/shortest etc.∗ Matches items identical based on length, size, volume ∗ differences are obvious and vary directly	A. Compare measurable characteristics of different objects on the same dimensions (e.g., time, temperature, area, length, weight, capacity, perimeter). Identifies lightest/heaviest, smallest/biggest, shortest/furthest, shortest/tallest, longest/shortest, a lot/a little, all/some/most, etc.∗ Matches items identical based on length, size, volume∗ ∗ differences less obvious and vary directly	A. Compare measurable characteristics of different objects on the same dimensions (e.g., time, temperature, area, length, weight, capacity, perimeter. Identifies lightest/heaviest, smallest/biggest, shortest/furthest, shortest/tallest, longest/shortest, , a lot/a little, all/some/most, etc.∗ Matches items to space Orders items by weight/size Understands meaning of temperatures Matches approximate numerals ∗ differences obvious and vary on multiple dimensions	A. Compare measurable characteristics of different objects on the same dimensions (e.g., time, temperature, area, length, weight, capacity, perimeter). Identifies lightest/heaviest, smallest/biggest, shortest/furthest, shortest/tallest, longest/shortest, coldest/hottest, a lot/a little, all/some/most, etc.∗ Orders items by weight/size Sorts by weight Understands meaning of temperatures ∗ differences less obvious vary on multiple dimensions

2.3. B & C Measurement and Estimation

GRADE 3/4	GRADE 5/6	GRADE 7/8	GRADE 11
Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:
B. Determine the measurement of objects with non-standard and standard units (e.g., US customary and metric). (2.3.3.B) C. Determine the appropriate unit of measure. (2.3.3.E) Measures in inches with fixed ruler Uses objects (blocks) to measure area and volume Selects appropriate measurement tool for activities of daily living (clock for time; cup for cooking; rulers for length, etc	B. Select and use appropriate instruments and units for measuring quantities (e.g., perimeter, volume, area, weight, time, temperature). (2.3.5.A) C. Select and use standard tools to measure the size of figures with specified accuracy, including length, width, perimeter and area. (2.3.5.B) Selects cup; identifies1 cupmeasure line Measures in cups Measures to within inch Matches measurement tool to need Identifies relative length/distance when path direct	B. Estimate, use and describe measures of distance, rate, perimeter, area. (2.3.8.D) C. Select and use standard tools to measure the size of figures with specified accuracy, including length, width, perimeter and area. Measures to within half inch Identifies 1/2,1/4 cup measures Identifies 1/2,1/4 cup line Identifies relative length when path not direct	B. Select and use appropriate units and tools to measure to the degree of accuracy required in particular measurement situations. C. Demonstrate the ability to produce measures with specified levels of precision (2.3.11.C) Identifies empty/half full/full items Measures to within quarter inch Identifies 1/2,1/4 cup measures Identifies 1/2,1/4 cup line Identifies shortest path between multiple points

2.3. D & E Measurement and Estimation

GRADE 3/4	GRADE 5/6	GRADE 7/8	GRADE 11
Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:
D. Determine and compare elapsed times. 2.3.3.C) E. Tell time (analog and digital) to the minute. (2.3.3.D) Identifies clock Reads digital times to hour/half hour	D. Determine and compare elapsed times. E. Tell time (analog and digital) to the minute. Identifies clock Matches activities and seasons Matches analog and digital times to hour Reads digital times to quarter hour Reads analog time to hour	D. Determine and compare elapsed times. E. Tell time (analog and digital) to the minute. Matches activities and seasons Matches activities to time of day Matches activities with duration Matches analog and digital times to half hour Reads digital times to minute Reads analog time to quarter hour	D. Determine and compare elapsed times. E. Tell time (analog and digital) to the minute. Matches activities with duration Matches activities to time of day Identifies duration of activity given start and end time Identifies ending time given start time and duration of activity Matches analog and digital times to 5 minute Reads analog time to 5 minute

2.3. F Measurement and Estimation

GRADE 3/4	GRADE 5/6	GRADE 7/8	GRADE 11
Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:
		F. Determine the appropriateness of overestimating or underestimating in computation. (2.2.8.E) Describes consequences of having too much/ not enough in common situations	F. Determine the appropriateness of overestimating or underestimating in computation. Describes consequences of having too much/ not enough in common situations

2.6 Statistics and Data Analysis

2.7 Probability and Predictions

GRADE 3/4	GRADE 5/6	GRADE 7/8	GRADE 11
Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:
A. Answer questions based on data shown on graphs. (2.6.3.A) B. Analyze data using the concepts of largest, smallest, most often, least often and middle. (2.7.3.D) Identifies value on graph ordered by size and with and without number prompts Biggest/smallest Most often/least often/middle C. Predict and measure the likelihood of events and recognize that the results of an experiment may not match predicted outcomes. (2.7.3.D)	A. Answer questions based on data shown on graphs. B. Construct simple conclusions based on data. (2.6.5.E) Identifies value on graph with and without number prompts Biggest/smallest Most often/least often/middle C. Predict and measure the likelihood of events and recognize that the results of an experiment may not match predicted outcomes.	A. Answer questions based on data shown on graphs. B. Compare and contrast different plots of data using values mode, and range. (2.6.8.A) Identifies value on graph with and without number prompts Biggest/smallest Most often/least often/middle C. Predict and measure the likelihood of events and recognize that the results of an experiment may not match predicted outcomes. Identifies most likely outcome based on data	A. Answer questions based on data shown on graphs. B. Identifies value on graph Biggest/smallest Most often/least often/middle C. Predict and measure the likelihood of events and recognize that the results of an experiment may not match predicted outcomes. Identifies most/least likely outcome base don data

2.8. Algebra and Functions

GRADE 3/4	GRADE 5/6	GRADE 7/8	GRADE 11
Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:
A. Recognize, describe, extend, create and replicate a variety of patterns including attribute, activity, number and geometric patterns. (2.8.3.A) Sorts dissimilar items into groups with or without sample. B. Describe and interpret the data shown in tables and charts. (2.8.3.H) Locates values identified in table of 6 numbers with column or row identified.	A. Recognize, reproduce, extend, create and describe patterns, sequences and relationships verbally, numerically, symbolically and graphically, using a variety of materials. (2.8.5.A) Sorts dissimilar and similar items into groups with or without sample. B. Describe and interpret the data shown in tables and charts. Locates values identified in table of 8 numbers with column or row identified.	A. Recognize, reproduce, extend, create and describe patterns, sequences and relationships verbally, numerically, symbolically and graphically, using a variety of materials. Sorts similar items into groups with or without sample. B. Describe and interpret the data shown in tables and charts. Locates values described in table of 10 numbers with column or row identified.	A. Recognize, reproduce, extend, create and describe patterns, sequences and relationships verbally, numerically, symbolically and graphically, using a variety of materials. Sorts similar items into groups with or without sample. B. Describe and interpret the data shown in tables and charts. Locates value described in table of 12 numbers with or without column or row identified.