Pennsylvania Standards Alignment Grades One through Eleven

Transcription

1 Pennsylvania Standards Alignment Grades One through Eleven Trademark of Renaissance Learning, Inc., and its subsidiaries, registered, common law, or pending registration in the United States and other countries. P.O. Box 8036 Wisconsin Rapids, WI Phone: (800) Fax: (715)

2 Pennsylvania Standards Alignment The Report is a standards-oriented document showing the entire list of standards for the subject and grade on the left side of the report with the aligning product objectives on the right side. This alignment report shows the breadth of standards coverage for the purpose and focus of this product. Note to Educator... iii Grade Grade Grade Grade Grade Grade Grade Grade Algebra 1 Keystone Exams...99 Algebra 2 Keystone Exams Geometry Keystone Exams Grade by Renaissance Learning, Inc. All rights reserved. No portion of this document may be reproduced, by any process or technique, without the express written consent of Renaissance Learning, Inc. Any standards referenced in this document are the property of their respective copyright holders. ii

3 P.O. Box 8036 Wisconsin Rapids, WI Phone: (800) Fax: (715) Note to Educator: Thank you for your interest in Renaissance Learning technology. The attached document contains the alignment between the software and/or instructional materials and the skills described in the state standards documentation. At Renaissance Learning, we recognize the impact that the standards-based reform movement and high-stakes standardized testing have on schools, and we share the concerns of educators and administrators that students perform well on high-stakes assessments. We hope this report answers your questions regarding the alignment of Renaissance Learning technology and materials to your state standards. If you have any questions about the attached document, please feel free to call us at (800) Sincerely, Renaissance Sales and Funding Staff iii

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5 Accelerated Math Grade 1 Pennsylvania, Math, 2008, 1st Grade, Early Learning Standards, State Accelerated Math Second Edition Grade 1 PA Numbers, Number Systems and Number Relationships PA 2.1.A - The learner will: Count using whole numbers to 100 by 1's, 2's, 5's, 10's and 25's PA 2.1.B - The learner will: Use whole numbers and fractions (halves, thirds and fourths) to represent quantities PA 2.1.C - The learner will: Represent equivalent forms of the same number through the use of concrete objects, drawings, word names and symbols to 100 Topic 1 - Numbers and Topic 1 - Numbers and Topic 1 - Numbers and Obj. 5 - Count objects to 20 Obj. 6 - Count on by ones from a number less than 100 Obj Count by 2s to 50 starting from a multiple of 2 Obj Count by 5s or 10s to 100 starting from a multiple of 5 or 10, respectively Obj. 5 - Count objects to 20 Obj Count objects grouped in tens and ones Obj. 1 - Read a whole number to 30 Obj. 2 - Read a whole number from 31 to 100 Obj. 3 - Determine the word form of a whole number to 30 Obj. 4 - Determine the word form of a whole number from 31 to 100 Obj. 9 - Identify a number to 20 represented by a point on a number line Obj Model a number to 100 using tens and ones Obj Recognize a number from a model of tens and ones to 100 PA 2.1.D - The learner will: Use drawings or models to show the concept of a fraction as part of a whole Page 1 of 168 Topic 1 - Numbers and Obj Represent a 2-digit number as tens and ones Obj Determine the 2-digit number represented as tens and ones Obj Recognize equivalent forms of a 2-digit number using tens and ones Obj Determine equivalent forms of a number, up to 10 Obj Identify a shape divided into equal parts

6 Accelerated Math Grade 1 Pennsylvania, Math, 2008, 1st Grade, Accelerated Math Second Edition Grade 1 Early Learning Standards, State PA 2.1.E - The learner will: Count, compare and make change up to one dollar using a collection of coins (pennies, nickels, dimes and quarters) PA 2.1.F - The learner will: Apply number patterns (even and odd) and compare numbers on the hundred chart PA 2.1.G - The learner will: Use concrete objects to count, order and group to 100 Topic 1 - Numbers and Topic 1 - Numbers and Topic 1 - Numbers and PA 2.1.H - The learner will: Topic 1 - Numbers and Demonstrate an understanding of one-to-one correspondence up to 100 Obj Determine the value of a collection of like coins Obj Determine the value of a collection of mixed coins Obj Identify odd and even numbers less than 100 Obj. 5 - Count objects to 20 Obj Count objects grouped in tens and ones Obj Locate a number to 20 on a number line PA 2.1.I - The learner will: Apply Topic 1 - Numbers and place-value concepts and numeration to counting and ordering numbers up to 100 PA 2.1.J - The learner will: Estimate and approximate number quantities in at least a set of ten PA 2.1.K - The learner will: Recognize the inverse relationship between addition and subtraction PA 2.1.L - The learner will: Demonstrate knowledge of basic addition and subtraction facts Page 2 of 168 Topic 1 - Numbers and Topic 1 - Numbers and Obj Order whole numbers to 100 in ascending order Obj Order whole numbers to 100 in descending order Obj Complete an addition and subtraction fact family Obj Apply the inverse relationship between addition facts and subtraction facts Obj Relate a picture model to a basic addition fact Obj Determine the basic addition fact shown by a picture model Obj Relate a number-line model to a basic addition fact Obj Determine the basic addition fact shown by a number-line model Obj Relate a picture model to a basic subtraction fact Obj Determine the basic subtraction fact shown by a picture model

7 Accelerated Math Grade 1 Pennsylvania, Math, 2008, 1st Grade, Accelerated Math Second Edition Grade 1 Early Learning Standards, State Obj Determine the basic subtraction fact shown by a numberline model Obj Relate a number-line model to a basic subtraction fact Obj Apply the relationship between addition and counting on Obj Apply the relationship between subtraction and counting back Obj Know basic addition facts to 10 plus 10 Obj Know basic subtraction facts to 20 minus 10 Obj Complete an addition and PA 2.1.a - The learner will: Count, read and write whole numbers from 1 through 100. PA 2.1.b - The learner will: Skip count by 2's, 5's, 10's and 25's. Topic 1 - Numbers and Topic 1 - Numbers and PA 2.1.c - The learner will: Match the fraction to the corresponding model (concrete and/or pictorially). PA 2.1.d - The learner will: Represent Topic 1 - Numbers and a given number less than or equal to 100 in various ways (e.g. tallies, numeral, tens and ones, addition and subtraction, etc.). subtraction fact family Obj. 1 - Read a whole number to 30 Obj. 2 - Read a whole number from 31 to 100 Obj. 6 - Count on by ones from a number less than 100 Obj Count by 2s to 50 starting from a multiple of 2 Obj Count by 5s or 10s to 100 starting from a multiple of 5 or 10, respectively Obj Model a number to 100 using tens and ones Obj Recognize a number from a model of tens and ones to 100 PA 2.1.e - The learner will: Identify fractional parts of a region or set. Page 3 of 168 Obj Represent a 2-digit number as tens and ones Obj Determine the 2-digit number represented as tens and ones Obj Recognize equivalent forms of a 2-digit number using tens and ones Obj Determine equivalent forms of a number, up to 10

8 Accelerated Math Grade 1 Pennsylvania, Math, 2008, 1st Grade, Accelerated Math Second Edition Grade 1 Early Learning Standards, State PA 2.1.f - The learner will: Represent a given fraction (halves, thirds and fourths) using drawings or concrete materials. PA 2.1.g - The learner will: Read and write fractions. PA 2.1.h - The learner will: Identify the name and value of pennies, nickels, dimes and quarters. PA 2.1.i - The learner will: Count, compare and record the value of a collection of coins up to one dollar. PA 2.1.j - The learner will: Count coins and make change in real life situations. PA 2.1.k - The learner will: Use different sets of coins to represent the same amount of money (up to one dollar). PA 2.1.l - The learner will: Differentiate between even and odd numbers. PA 2.1.m - The learner will: Order a set of whole numbers from least to greatest or from greatest to least up through 100. PA 2.1.n - The learner will: Count sets of objects to at least 100. PA 2.1.o - The learner will: Count objects using 1-1 correspondence. PA 2.1.p - The learner will: Compare two sets of objects using 1-1 correspondence to determine greater than/less than. PA 2.1.q - The learner will: Match a symbolic representation of numbers to appropriate whole numbers up to 100 (e.g. base-ten blocks). Topic 1 - Numbers and Topic 1 - Numbers and Topic 1 - Numbers and Topic 1 - Numbers and Topic 1 - Numbers and Topic 1 - Numbers and Topic 1 - Numbers and Obj Determine the value of a collection of like coins Obj Determine the value of a collection of mixed coins Obj Identify odd and even numbers less than 100 Obj Order whole numbers to 100 in ascending order Obj Order whole numbers to 100 in descending order Obj. 5 - Count objects to 20 Obj. 5 - Count objects to 20 Obj Compare sets of objects using words Obj Count objects grouped in tens and ones Obj Model a number to 100 using tens and ones Obj Recognize a number from a model of tens and ones to 100 Page 4 of 168

9 Accelerated Math Grade 1 Pennsylvania, Math, 2008, 1st Grade, Accelerated Math Second Edition Grade 1 Early Learning Standards, State PA The teacher will: For each stated skill the teacher will provide and incorporate opportunities in both everyday occurrences and planned, purposeful instruction; model and incorporate appropriate language and vocabulary; supply students with manipulatives (e.g. counters, base ten blocks, pattern blocks, coins, hundred chart, etc.). PA Computation and Estimation PA 2.2.A - The learner will: Solve addition and subtraction in everyday situations using concrete objects with one and two digit numbers (no regrouping) PA 2.2.B - The learner will: Solve addition and subtraction in everyday situations with one and two digit numbers (no regrouping) PA 2.2.C - The learner will: Determine the sum of the same three one-digit numbers (e.g., 5+5+5) Topic 1 - Numbers and Obj Determine the missing portion in a partially screened (hidden) collection of up to 10 objects Obj WP: Use basic addition or subtraction facts to solve problems Obj WP: Add or subtract a 1- and 2-digit number without regrouping Obj WP: Add or subtract two 2- digit numbers without regrouping PA 2.2.D - The learner will: Determine the difference by forming equal groups PA 2.2.E - The learner will: Make estimates of objects in a set up to and including 100 using groups of ten as a reference and verify estimate PA 2.2.F - The learner will: Compare estimate with verified answer PA 2.2.G - The learner will: Explain and describe the process of addition and subtraction Topic 1 - Numbers and Obj Determine equivalent addition or subtraction expressions involving words or symbols Page 5 of 168

10 Accelerated Math Grade 1 Pennsylvania, Math, 2008, 1st Grade, Accelerated Math Second Edition Grade 1 Early Learning Standards, State PA 2.2.a - The learner will: Use concrete objects, including number lines, to find the solution to addition and subtraction problems with one and two digit numbers (no regrouping). PA 2.2.b - The learner will: Find the solution to addition and subtraction problems with one and two digit numbers (no regrouping). Topic 1 - Numbers and Topic 1 - Numbers and Obj Determine the missing portion in a partially screened (hidden) collection of up to 10 objects Obj Relate a picture model to a basic addition fact Obj Determine the basic addition fact shown by a picture model Obj Relate a number-line model to a basic addition fact Obj Determine the basic addition fact shown by a number-line model Obj Relate a picture model to a basic subtraction fact Obj Determine the basic subtraction fact shown by a picture model Obj Determine the basic subtraction fact shown by a numberline model Obj Relate a number-line model to a basic subtraction fact Obj Add multiples of 10, sums to 90 Obj Subtract multiples of 10 up to 90 Obj Add zero to any number less than 100 Obj Subtract zero from any number less than 100 Obj Add a 2-digit and a 1-digit number without regrouping Obj Add two 2-digit numbers without regrouping Obj Subtract a 1-digit number from a 2-digit number without regrouping Obj Subtract a 2-digit number from a 2-digit number without regrouping Obj WP: Add or subtract a 1- and 2-digit number without regrouping Obj WP: Add or subtract two 2- digit numbers without regrouping Page 6 of 168

11 Accelerated Math Grade 1 Pennsylvania, Math, 2008, 1st Grade, Accelerated Math Second Edition Grade 1 Early Learning Standards, State PA 2.2.c - The learner will: Write a number sentence to represent a picture/story problem. PA 2.2.d - The learner will: Determine the sum of the same three addends. PA 2.2.e - The learner will: Understand subtraction as separating sets to form equal groups. PA 2.2.f - The learner will: Form a group of ten and use as a reference to make an estimate. PA 2.2.g - The learner will: Count to verify the estimate. PA 2.2.h - The learner will: Compare estimate with verification. PA 2.2.i - The learner will: Recognize when estimation is or is not reasonable. PA 2.2.j - The learner will: Explore and state the concept of addition and subtraction as the joining and separating of sets. PA The teacher will: For each stated skill the teacher will provide and incorporate opportunities in both everyday occurrences and planned, purposeful instruction; model and incorporate appropriate language and vocabulary; supply students with manipulatives (e.g. counters, base ten blocks, etc.). PA The teacher will: Teachers will demonstrate and develop students' abilities to find differences using related addition facts. Topic 2 - Algebraic Thinking Obj WP: Determine a basic addition- or subtraction-fact number sentence for a given situation PA Measurement and Estimation PA 2.3.A - The learner will: Compare two objects using direct comparison Topic 3 - Geometry and Measurement Obj Compare objects using the vocabulary of measurement Obj Compare and order objects by attributes of height or length PA 2.3.B - The learner will: Estimate, measure and compare the lengths of objects using non-standard units Topic 3 - Geometry and Measurement Obj Estimate length in nonstandard units Page 7 of 168

12 Accelerated Math Grade 1 Pennsylvania, Math, 2008, 1st Grade, Accelerated Math Second Edition Grade 1 Early Learning Standards, State PA 2.3.C - The learner will: Estimate, measure and compare the lengths of objects using standard units of measure PA 2.3.D - The learner will: Determine and compare lengths of time PA 2.3.E - The learner will: Tell time (analog and digital) to the minute Topic 3 - Geometry and Measurement Topic 3 - Geometry and Measurement Topic 3 - Geometry and Measurement Obj Compare and order objects by attributes of height or length Obj Know the approximate time it takes to complete a task Obj Tell time to the hour PA 2.3.F - The learner will: Determine appropriate unit of measure PA 2.3.G - The learner will: Demonstrate that a single object has different attributes that can be measured in different ways (e.g., length, mass/ weight, time, area, temperature, capacity, perimeter) PA 2.3.a - The learner will: Collect two objects and compare them by a defined attribute (length, capacity or weight). PA 2.3.b - The learner will: Determine and use an appropriate non standard measuring tool (for example, an appropriate nonstandard measuring tool would be a finger to measure the length of a piece of paper, not the length of a hallway). (Crayons, unifix cubes, paper clips.) PA 2.3.c - The learner will: Estimate and measure the lengths and heights of objects using non-standard units. Topic 3 - Geometry and Measurement Topic 3 - Geometry and Measurement Obj Tell time to the half hour Obj Compare objects using the vocabulary of measurement Obj Compare and order objects by attributes of height or length Obj Estimate length in nonstandard units PA 2.3.d - The learner will: Estimate and measure the lengths and heights of objects to the nearest inch. PA 2.3.e - The learner will: Estimate and measure the lengths and heights of objects to the nearest foot using a 12 inch ruler. PA 2.3.f - The learner will: Estimate and measure the length of objects in centimeters using a ruler. Page 8 of 168

13 Accelerated Math Grade 1 Pennsylvania, Math, 2008, 1st Grade, Accelerated Math Second Edition Grade 1 Early Learning Standards, State PA 2.3.g - The learner will: Estimate and determine the distance around a shape using non-standard units (paper clips) and standard units (inches). PA 2.3.h - The learner will: Estimate, measure and compare the capacities of various containers. PA 2.3.i - The learner will: Compare the capacities of cups, pints and quarts. PA 2.3.j - The learner will: Compare the capacity of containers to one liter. PA 2.3.k - The learner will: Estimate, measure and compare the weights of different objects using a balance scale. PA 2.3.l - The learner will: Compare the weights of objects to one pound. PA 2.3.m - The learner will: Determine the appropriate unit for measuring an object using gram or kilogram. PA 2.3.n - The learner will: Determine temperatures on a thermometer. PA 2.3.o - The learner will: Recognize the divisions of time: morning, afternoon and evening, before and after. PA The teacher will: Model, using the appropriate language/vocabulary, the process of comparing objects using a specified attribute and measuring using standard and non-standard tools and units. PA The teacher will: Provide materials/opportunities and support learners in making estimations, determine the appropriate measurement tool and explore and apply understanding of estimation throughout the school day. PA The teacher will: Provide authentic opportunities for measuring such as cooking and mixing simple recipes. Page 9 of 168

14 Accelerated Math Grade 1 Pennsylvania, Math, 2008, 1st Grade, Accelerated Math Second Edition Grade 1 Early Learning Standards, State PA The learner will: Encourage and support learners in explaining how they applied their skills during mathematical tasks. PA Mathematical Reasoning and Connections PA 2.4.A - The learner will: Make, check and verify predictions about the quantity, size and shape of objects and groups of objects PA 2.4.B - The learner will: Use measurements in everyday situations PA 2.4.a - The learner will: Make estimates of objects in a set up to and including 100. PA 2.4.b - The learner will: Make estimates of quantity and verify by counting. PA 2.4.c - The learner will: Sort, classify and order objects by 2 or more attributes including color, size, shape (including two- and threedimensional geometric shapes) and number properties (odd/even, numbers said when counting by 5s 10s) using standard and nonstandard units. PA 2.4.d - The learner will: Explain and identify how a set or group of items has been sorted. PA 2.4.e - The learner will: Estimate the length or weight of an object. PA 2.4.f - The learner will: Select an appropriate unit and/or tool for the attribute being measured. Topic 1 - Numbers and Topic 3 - Geometry and Measurement Topic 4 - Data Analysis and Statistics Topic 3 - Geometry and Measurement Topic 3 - Geometry and Measurement Obj Count by 5s or 10s to 100 starting from a multiple of 5 or 10, respectively Obj Determine the rule used to sort geometric shapes Obj Determine the rule used to sort objects Obj Estimate length in nonstandard units Obj Select the appropriate measurement tool for length, weight, temperature, time, or capacity PA 2.4.g - The learner will: Compare objects according to length, weight or volume. PA 2.4.h - The learner will: Tell time (analog) to the hour and half hour. PA 2.4.i - The learner will: Tell time to the nearest 1/2 hour. Page 10 of 168 Topic 3 - Geometry and Measurement Topic 3 - Geometry and Measurement Topic 3 - Geometry and Measurement Obj Estimate length in nonstandard units Obj Compare and order objects by attributes of height or length Obj Tell time to the hour Obj Tell time to the half hour Obj Tell time to the half hour

15 Accelerated Math Grade 1 Pennsylvania, Math, 2008, 1st Grade, Accelerated Math Second Edition Grade 1 Early Learning Standards, State PA 2.4.j - The learner will: Use a ruler to measure to the nearest inch. PA 2.4.k - The learner will: Measure objects to the nearest inch or centimeter. PA The teacher will: Model, using appropriate vocabulary, the process of estimating and verifying groups of objects. PA The teacher will: Create and provide opportunities for learners to make comparisons of objects by at least 2 attributes. PA The teacher will: Engage learners in recognizing and applying estimation in everyday situations. PA The teacher will: Facilitate classroom discussion to encourage learners to explain how a set of items has been sorted. PA The teacher will: Provide opportunities for learners to explore and apply an understanding of estimating and measurement. PA Mathematical Problem Solving and Communication PA 2.5.A - The learner will: Use appropriate problem-solving strategies (e.g., make a model, draw a picture, guess and check, working backwards) Topic 1 - Numbers and Topic 2 - Algebraic Thinking Obj WP: Use basic addition or subtraction facts to solve problems Obj WP: Add or subtract a 1- and 2-digit number without regrouping Obj WP: Add or subtract two 2- digit numbers without regrouping Obj WP: Determine a missing addend or subtrahend in a basic addition- or subtraction-fact number sentence Obj WP: Determine a basic addition- or subtraction-fact number sentence for a given situation PA 2.5.B - The learner will: Determine when sufficient information is present to solve a problem and explain how to solve a problem Page 11 of 168

16 Accelerated Math Grade 1 Pennsylvania, Math, 2008, 1st Grade, Accelerated Math Second Edition Grade 1 Early Learning Standards, State PA 2.5.C - The learner will: Select and use an appropriate method, materials and strategy to solve problems, including mental mathematics, paper and pencil and concrete objects PA 2.5.a - The learner will: Identify and think about possible solutions to solve daily problems occurring in and out of the classroom. PA 2.5.b - The learner will: Determine appropriate strategies to solve various problems. PA 2.5.c - The learner will: Utilize the strategies to solve the problems. PA 2.5.d - The learner will: Describe the steps necessary to solve a problem. Communicate these steps orally. PA 2.5.e - The learner will: Identify the correct operations to solve a word problem. PA 2.5.f - The learner will: Analyze problem situations to choose a correct operation. PA 2.5.g - The learner will: Invent different strategies and approaches to solve daily problems occurring in and out of the classroom. PA 2.5.h - The learner will: Determine what is the best method to solve a single step problem. PA The teacher will: Model, using the appropriate language/ vocabulary, the process of identifying and solving a problem. Topic 1 - Numbers and Topic 2 - Algebraic Thinking Obj WP: Use basic addition or subtraction facts to solve problems Obj WP: Add or subtract a 1- and 2-digit number without regrouping Obj WP: Add or subtract two 2- digit numbers without regrouping Obj WP: Determine a missing addend or subtrahend in a basic addition- or subtraction-fact number sentence Obj WP: Determine a basic addition- or subtraction-fact number sentence for a given situation Page 12 of 168

17 Accelerated Math Grade 1 Pennsylvania, Math, 2008, 1st Grade, Accelerated Math Second Edition Grade 1 Early Learning Standards, State PA The teacher will: Facilitate classroom discussion to identify the necessary steps and the appropriate order to solve problems occurring in and out of the classroom. PA The teacher will: Create and provide opportunities for learners to engage in problem solving activities. PA The teacher will: Highlight the process versus the product of an activity (give specific examples). PA The teacher will: Ask openended questions, encourage conversations and create classroom activities that encourage learners to explore a variety of possible solutions (setup situations). PA The teacher will: Encourage and support learners to explain their mathematical thinking and work. PA The teacher will: Provide opportunities for learners to explore and apply understanding of problem solving throughout the school day. PA The teacher will: Provide the students with examples on how to utilize the best method to solve a multiple step problem. PA Statistics and Data Analysis PA 2.6.A - The learner will: Formulate and answer questions that can be proven with data (bar graphs, pictographs and/or tally charts) Page 13 of 168 Topic 4 - Data Analysis and Statistics Obj Read a 2-category tally chart Obj Answer a question using information from a 2-category tally chart Obj Read a picture graph Obj Answer a question using information from a picture graph Obj Read a pictograph (1 symbol = 1 object) Obj Answer a question using information from a pictograph (1 symbol = 1 object)

18 Accelerated Math Grade 1 Pennsylvania, Math, 2008, 1st Grade, Accelerated Math Second Edition Grade 1 Early Learning Standards, State Obj Answer a question using PA 2.6.B - The learner will: Collect, organize and display relevant data to answer questions PA 2.6.C - The learner will: Discuss whether a prediction or statement is likely or unlikely based on a comparison to the data PA 2.6.a - The learner will: Participate in classroom graphing activities. PA 2.6.b - The learner will: Read and compare data shown on bar graphs, pictographs and/or tally charts (guiding questions may include: How many? How many more? How many less? Equal? Why? What? How do you know?). PA 2.6.c - The learner will: Sort and classify objects according to their attributes and organize data about these objects. PA 2.6.d - The learner will: Represent data using concrete objects, pictures and graphs. PA 2.6.e - The learner will: Discuss why a prediction or statement based on data is either likely or unlikely. Topic 4 - Data Analysis and Statistics Topic 4 - Data Analysis and Statistics Topic 4 - Data Analysis and Statistics Topic 4 - Data Analysis and Statistics information from a bar graph Obj Use a 2-category tally chart to represent groups of objects (1 symbol = 1 object) Obj Use a picture graph to represent groups of objects (1 symbol = 1 object) Obj Use a pictograph to represent groups of objects (1 symbol = 1 object) Obj Use a bar graph to represent groups of objects Obj Read a 2-category tally chart Obj Read a picture graph Obj Read a pictograph (1 symbol = 1 object) Obj Read a bar graph Obj Determine the group in which an object belongs Obj Determine the rule used to sort objects Obj Use a picture graph to represent groups of objects (1 symbol = 1 object) Obj Use a pictograph to represent groups of objects (1 symbol = 1 object) Obj Use a bar graph to represent groups of objects PA The teacher will: Provide easy to read data sets for the students. Page 14 of 168

19 Accelerated Math Grade 1 Pennsylvania, Math, 2008, 1st Grade, Accelerated Math Second Edition Grade 1 Early Learning Standards, State PA The teacher will: Assist (as needed) learners in reading the data, deducing information, drawing conclusions and applying data to future events/behaviors. PA The teacher will: Pose open-ended questions to engage learners in reading the data on a graph. PA The teacher will: Provide opportunities for learners to see graphs used in the real world. PA The teacher will: Encourage and support learners in explaining how they applied their skills during mathematical work. PA The teacher will: Provide opportunities for learners to create and interpret graphs throughout the school day. PA The teacher will: Model and verbalize, using language/ vocabulary appropriate to the learners, the process of graphing. PA Probability and Predictions PA 2.7.A - The learner will: State and explain the likelihood of an event using the terms certain, likely, unlikely or impossible PA 2.7.B - The learner will: Discuss why a spinner is fair or unfair PA 2.7.C - The learner will: Discuss the results of an experiment PA 2.7.a - The learner will: Determine the likelihood of events occurring. PA 2.7.b - The learner will: Example: the teacher flips a coin and the students predict the likelihood of the coin landing "heads up." PA 2.7.c - The learner will: When presented with various spinners and activities with the spinners, students discuss why certain spinners are either fair or unfair. PA 2.7.d - The learner will: Predict what the results of an experiment will be. Page 15 of 168

20 Accelerated Math Grade 1 Pennsylvania, Math, 2008, 1st Grade, Accelerated Math Second Edition Grade 1 Early Learning Standards, State PA 2.7.e - The learner will: Discuss the results of an experiment for which the teacher has recorded or graphed the results. PA The teacher will: Model and verbalize (as needed), using language/vocabulary appropriate to the students, the process of determining the likelihood of an event and/or why a spinner is either fair or unfair. PA The teacher will: Explain examples of activities that are most likely to occur at certain times of the year. PA The teacher will: Explain/demonstrate the meaning of the words certain, likely, unlikely and impossible. PA The teacher will: Facilitate predictions of possible results by referring to previous events. PA The teacher will: Encourage and support learners in explaining how they applied their skills during mathematical tasks. PA Algebra and Functions PA 2.8.A - The learner will: Topic 2 - Algebraic Thinking Recognize and extend patterns based on shape, size, color, sound or number PA 2.8.B - The learner will: Identify the rule for a repeating pattern that could be extended infinitely PA 2.8.C - The learner will: Identify the rule for a number sequence that could be extended infinitely PA 2.8.D - The learner will: Choose the correct operation (addition or subtraction) to solve a story problem Obj Extend a repeating picture pattern Obj Extend a pictorial growth pattern Obj Complete a pattern on a 1 to 100 chart Topic 2 - Algebraic Thinking Obj Determine a pattern on a 1 to 100 chart Topic 2 - Algebraic Thinking Obj Determine a pattern on a 1 to 100 chart Topic 1 - Numbers and Obj WP: Use basic addition or subtraction facts to solve problems Page 16 of 168 Obj WP: Add or subtract a 1- and 2-digit number without regrouping Obj WP: Add or subtract two 2- digit numbers without regrouping

21 Accelerated Math Grade 1 Pennsylvania, Math, 2008, 1st Grade, Accelerated Math Second Edition Grade 1 Early Learning Standards, State PA 2.8.E - The learner will: Write an equation to solve a story problem Topic 2 - Algebraic Thinking Obj WP: Determine a basic addition- or subtraction-fact number sentence for a given situation PA 2.8.F - The learner will: Use concrete objects and trial and error to solve addition or subtraction number sentences and check if solutions are accurate PA 2.8.G - The learner will: Find a missing addend that makes a number sentence true PA 2.8.H - The learner will: Explain how solutions to equations or missing addends are determined PA 2.8.I - The learner will: Identify the missing symbol (+,-, =) that makes a number sentence true PA 2.8.a - The learner will: Construct patterns with a repeating pattern with concrete objects such as geometric shapes or connecting cubes. Topic 2 - Algebraic Thinking Obj Determine a missing addend in a basic addition-fact number sentence Obj Determine equivalent addition or subtraction expressions involving 1-digit numbers Obj Determine a missing addend in an addition sentence with three 1-digit numbers Obj WP: Determine a missing addend or subtrahend in a basic addition- or subtraction-fact number sentence PA 2.8.b - The learner will: Describe a repeating pattern and be able to extend it beyond the pattern shown. Topic 2 - Algebraic Thinking Obj Extend a repeating picture pattern PA 2.8.c - The learner will: Describe how patterns are alike. PA 2.8.d - The learner will: Create their own repeating pattern and be able to describe the pattern. PA 2.8.e - The learner will: Describe and extend a number pattern that is a constant sequence, such as 1,4,7,... or 2,4,6,... Topic 2 - Algebraic Thinking Obj Determine a pattern on a 1 to 100 chart PA 2.8.f - The learner will: Solve a variety of story problems by first identifying the operation involved. Page 17 of 168 Obj Complete a pattern on a 1 to 100 chart

22 Accelerated Math Grade 1 Pennsylvania, Math, 2008, 1st Grade, Accelerated Math Second Edition Grade 1 Early Learning Standards, State PA 2.8.g - The learner will: Use concrete manipulatives and/or draw pictures to determine missing addends. PA 2.8.h - The learner will: Progress from the use of manipulative and drawings to use symbols and write equations to solve story problems and equations. Topic 2 - Algebraic Thinking Obj WP: Determine a missing addend or subtrahend in a basic addition- or subtraction-fact number sentence Obj WP: Determine a basic addition- or subtraction-fact number sentence for a given situation PA 2.8.i - The learner will: Use a variety of strategies to solve problems involving addition or subtraction. PA 2.8.j - The learner will: Provide explanations for the solutions and strategies used in solving story problems and/or equations. PA The teacher will: Provide a variety of materials for sorting, classifying and creating patterns (connecting cubes, beads, buttons, lids, etc.). PA The teacher will: Demonstrate and explain the concept of recognizing, describing, repeating and extending a pattern or sequence. Topic 1 - Numbers and Obj WP: Use basic addition or subtraction facts to solve problems Obj WP: Add or subtract a 1- and 2-digit number without regrouping Obj WP: Add or subtract two 2- digit numbers without regrouping PA The teacher will: Provide opportunities and support learners in recognizing, describing and extending patterns and sequences. PA The teacher will: Demonstrate solving story problems through providing a variety of manipulatives and drawings to solve addition and subtraction story problems. PA The teacher will: Demonstrate how story problems can be represented with equations. Page 18 of 168

23 Accelerated Math Grade 1 Pennsylvania, Math, 2008, 1st Grade, Accelerated Math Second Edition Grade 1 Early Learning Standards, State PA The teacher will: Provide meaningful demonstrations to establish the meaning of symbols in equations. PA The teacher will: Provide opportunities for students to explain their strategy for solving story problems or equations (missing addends). PA Geometry PA 2.9.A - The learner will: Name and label geometric shapes in two and three dimensions (e.g., circle, square, triangle, rectangle, sphere, cube, pyramid and prism) PA 2.9.B - The learner will: Build geometric shapes using concrete objects PA 2.9.C - The learner will: Create two- and three-dimensional shapes PA 2.9.D - The learner will: Find and describe geometric figures in real life Topic 3 - Geometry and Measurement Obj Identify a circle, a triangle, a square, or a rectangle PA 2.9.E - The learner will: Identify and draw lines of symmetry in geometric figures Topic 3 - Geometry and Measurement PA 2.9.F - The learner will: Identify lines of symmetry in nature PA 2.9.G - The learner will: Fold paper to demonstrate the reflection of a line PA 2.9.H - The learner will: Show relationships between and among figures using reflections PA 2.9.I - The learner will: Predict how shapes can be changed by combining or dividing them PA 2.9.a - The learner will: Identify Topic 3 - Geometry and two and three-dimensional figures Measurement and describe their specific attributes. PA 2.9.b - The learner will: Compare, contrast and sort two- and threedimensional shapes. PA 2.9.c - The learner will: Relate faces of three-dimensional figures to two-dimensional shapes. Page 19 of 168 Topic 3 - Geometry and Measurement Obj Identify a line of symmetry Obj Determine the common attributes in a set of geometric shapes Obj Determine the common attributes in a set of geometric shapes Obj Determine the group in which a geometric shape belongs Obj Determine the rule used to sort geometric shapes

24 Accelerated Math Grade 1 Pennsylvania, Math, 2008, 1st Grade, Accelerated Math Second Edition Grade 1 Early Learning Standards, State PA 2.9.d - The learner will: Identify and create figures that are the same size and same shape (congruent). PA 2.9.e - The learner will: Use various materials to draw, build and make two-dimensional and threedimensional shapes. PA 2.9.f - The learner will: Recognize two-dimensional shapes within other two-dimensional shapes. PA 2.9.g - The learner will: Combine two-dimensional shapes to make new shapes. PA 2.9.h - The learner will: Draw and label parallelogram, trapezoid and hexagon. PA 2.9.i - The learner will: Recognize Topic 3 - Geometry and sides, vertices (angles), corners and Measurement curves in two-dimensional shapes. PA 2.9.j - The learner will: Name and label two- and three-dimensional shapes. PA 2.9.k - The learner will: Recognize and identify two- and threedimensional shapes in the environment. PA 2.9.l - The learner will: Match twoand three-dimensional shapes to twoand three-dimensional shapes in real life. PA 2.9.m - The learner will: Identify lines of symmetry in shapes and objects. PA The teacher will: Provide an environment rich in geometric design. PA The teacher will: Use appropriate manipulatives (i.e. geoboards) and activities to create shapes and form congruent plane figures. PA The teacher will: Create a chart with attributes of each object. Topic 3 - Geometry and Measurement Topic 3 - Geometry and Measurement Obj Determine the common attributes in a set of geometric shapes Obj Identify a circle, a triangle, a square, or a rectangle Obj Identify a line of symmetry Page 20 of 168

25 Accelerated Math Grade 1 Pennsylvania, Math, 2008, 1st Grade, Accelerated Math Second Edition Grade 1 Early Learning Standards, State PA The teacher will: Use appropriate manipulatives (i.e. pattern blocks, building blocks, etc.) to allow for exploration and construction of new shapes while engaging the student in dialogue about the attributes of the new shape. PA The teacher will: Provide opportunities to identify and name the properties of two- and threedimensional shapes using plane figures and geometric solids. PA The teacher will: Use real objects as examples of geometric solids. PA The teacher will: Provide opportunities to explore shapes that involves folding and/or drawing lines of symmetry. PA The teacher will: Provide opportunities to explore reflections using appropriate manipulatives (i.e. mirrors, graph paper, geoboards). PA The teacher will: Provide shapes for exploration. PA Trigonometry PA 2.10.A - The learner will: Identify and give examples of corner angles PA 2.10.B - The learner will: Identify a triangle that has one corner. Recognize that a line drawn from one vertex to the opposite vertex in a rectangle or square divides it into two triangles, each with a corner angle PA Calculus PA 2.11.A - The learner will: Describe how you can get closer and closer to a point or line and not reach or cross it PA 2.11.a - The learner will: Football penalty activity (if an offense is on the 5 yard line and the defense gets a penalty that equals "half the distance to the end zone" for the offense...will the offense ever cross the end zone if the defense keeps getting penalties?) Page 21 of 168

26 Accelerated Math Grade 1 Pennsylvania, Math, 2008, 1st Grade, Accelerated Math Second Edition Grade 1 Early Learning Standards, State PA 2.11.b - The learner will: Approaching a tape 1/2 distance each move. Page 22 of 168

27 Accelerated Math Grade 2 Pennsylvania, Math, 2008, 2nd Grade, Early Learning Standards, State Accelerated Math Second Edition Grade 2 PA Numbers, Number Systems and Number Relationships PA 2.1.A - The learner will: Count using whole numbers to 1000 by 1's, 2's, 5's, 10's and 25's PA 2.1.B - The learner will: Use whole numbers and simple fractions to represent quantities PA 2.1.C - The learner will: Represent equivalent forms of the same number through the use of concrete objects, drawings, word names and symbols to 1000 Topic 1 - Number Sense and Topic 1 - Number Sense and Topic 1 - Number Sense and Obj. 3 - Complete a skip pattern starting from a multiple of 2, 5, or 10 Obj. 4 - Complete a skip pattern of 2, 5, or 10 starting from any number Obj Recognize a number from a model of hundreds, tens, and ones to 1,000 Obj. 1 - Read a whole number to 1,000 Obj. 2 - Determine the word form of a whole number to 1,000 Obj Model a number using hundreds, tens, and ones to 1,000 Obj Recognize a number from a model of hundreds, tens, and ones to 1,000 Obj Represent a 3-digit number as hundreds, tens, and ones PA 2.1.D - The learner will: Use drawings or models to show the concept of a fraction as part of a whole PA 2.1.E - The learner will: Count, compare and make change using a collection of coins and one dollar bills PA 2.1.F - The learner will: Apply number patterns (even and odd) and compare numbers on the hundred chart Topic 1 - Number Sense and Topic 1 - Number Sense and Topic 1 - Number Sense and Obj Determine the 3-digit number represented as hundreds, tens, and ones Obj Recognize equivalent forms of a 3-digit number using hundreds, tens, and ones Obj Identify a unit fraction as part of a whole Obj Identify a fraction as part of a whole Obj Determine the value of a collection of bills and coins Obj. 6 - Identify odd and even numbers between 100 and 1,000 Obj. 7 - Solve problems involving the concept of odd and even numbers Page 23 of 168

28 Accelerated Math Grade 2 Pennsylvania, Math, 2008, 2nd Accelerated Math Second Edition Grade 2 Grade, Early Learning Standards, State PA 2.1.G - The learner will: Use concrete objects to count, order and group to 1000 PA 2.1.H - The learner will: Demonstrate an understanding of one-to-one correspondence up to 1000 PA 2.1.I - The learner will: Apply Topic 1 - Number Sense and place-value concepts and numeration to counting, ordering and grouping numbers up to 1000 PA 2.1.J - The learner will: Estimate and approximate number quantities as groups of ten and 100 PA 2.1.K - The learner will: Describe the inverse relationship between addition and subtraction PA 2.1.L - The learner will: Demonstrate knowledge of basic addition and subtraction facts PA 2.1.M - The learner will: Use various models to demonstrate the concept of multiplication PA 2.1.a - The learner will: Count, read and write whole numbers from 1 through 100. PA 2.1.b - The learner will: Skip count by 2's, 3's, 5's, 25's and 100's. Topic 1 - Number Sense and Topic 1 - Number Sense and Obj. 9 - Determine the value of a digit in a 3-digit number Obj Determine which digit is in a specified place in a 3-digit whole number Obj Determine the result of changing a digit in a 3-digit whole number Obj Determine the sum of equal groups using pictures Obj Represent repeated addition as multiplication Obj Relate a multiplication sentence to an array model Obj. 3 - Complete a skip pattern starting from a multiple of 2, 5, or 10 Obj. 4 - Complete a skip pattern of 2, 5, or 10 starting from any number PA 2.1.c - The learner will: Match the fraction to the corresponding model (concrete and /or pictorially). Page 24 of 168 Topic 1 - Number Sense and Obj. 5 - Count on by 100s from any number Obj Identify a unit fraction as part of a whole Obj Identify a unit fraction as part of a set of objects Obj Identify a fraction as part of a set of objects

29 Accelerated Math Grade 2 Pennsylvania, Math, 2008, 2nd Accelerated Math Second Edition Grade 2 Grade, Early Learning Standards, State Obj Identify a fraction as part of a whole Obj Relate a fraction equal to a PA 2.1.d - The learner will: Represent a given number less than or equal to 1000 in various ways (e.g. tallies, numerals, hundreds, tens and ones, addition and subtraction, etc.). Topic 1 - Number Sense and whole to a pictorial model Obj Model a number using hundreds, tens, and ones to 1,000 Obj Recognize a number from a model of hundreds, tens, and ones to 1,000 Obj Represent a 3-digit number as hundreds, tens, and ones PA 2.1.e - The learner will: Identify fractional parts of a region or set. PA 2.1.f - The learner will: Represent a given fraction (sixths, eighths) using drawings or concrete materials. Topic 2 - Algebraic Thinking Topic 1 - Number Sense and Obj Determine the 3-digit number represented as hundreds, tens, and ones Obj Recognize equivalent forms of a 3-digit number using hundreds, tens, and ones Obj Determine a number pair that totals 100 Obj Determine a number pair that totals 1,000 Obj Determine equivalent addition expressions involving 2-digit numbers Obj Identify a unit fraction as part of a whole Obj Identify a unit fraction as part of a set of objects Obj Identify a fraction as part of a set of objects Obj Identify a fraction as part of a whole Obj Relate a fraction equal to a whole to a pictorial model PA 2.1.g - The learner will: Name and state the value of coins up to a half-dollar. PA 2.1.h - The learner will: Count a collection of coins less than $2.00. PA 2.1.i - The learner will: Make change for an amount up to $2.00 with no more than $.99 change. Page 25 of 168

30 Accelerated Math Grade 2 Pennsylvania, Math, 2008, 2nd Accelerated Math Second Edition Grade 2 Grade, Early Learning Standards, State PA 2.1.j - The learner will: Describe strategies for counting money. PA 2.1.k - The learner will: Identify and describe the rule for a pattern. PA 2.1.l - The learner will: Use the rule to extend the pattern. PA 2.1.m - The learner will: Order a set of whole numbers from least to greatest or from greatest to least up to 999. PA 2.1.n - The learner will: Describe when we use ordinal numbers. PA 2.1.o - The learner will: Count objects using one-to-one correspondence up to 999. PA 2.1.p - The learner will: Match a symbolic representation of numbers to appropriate whole numbers up to 999 (ex. using base ten cubes). Topic 2 - Algebraic Thinking Topic 2 - Algebraic Thinking Topic 1 - Number Sense and Topic 1 - Number Sense and Obj Determine an addition or subtraction number pattern given a rule Obj Determine the rule for an addition or subtraction number pattern Obj Determine a repeating pattern corresponding to the same pattern expressed using different elements Obj Extend a number pattern involving addition Obj Extend a number pattern involving subtraction Obj Extend a pattern given a table of related number pairs Obj Order whole numbers to 1,000 in ascending order Obj Order whole numbers to 1,000 in descending order Obj Model a number using hundreds, tens, and ones to 1,000 Obj Recognize a number from a model of hundreds, tens, and ones to 1,000 Obj Represent a 3-digit number as hundreds, tens, and ones Obj Determine the 3-digit number represented as hundreds, tens, and ones Obj Recognize equivalent forms of a 3-digit number using hundreds, tens, and ones Page 26 of 168

31 Accelerated Math Grade 2 Pennsylvania, Math, 2008, 2nd Accelerated Math Second Edition Grade 2 Grade, Early Learning Standards, State PA The teacher will: For each stated standard provide and incorporate opportunities in everyday occurrences and planned direct instruction; model, the process/skill being presented using appropriate language/vocabulary; create authentic (real life situations) for learners to practice the skill; supply learners with appropriate manipulatives (e.g. uni-fix cubes, counters, pattern blocks, part-towhole chart, coins etc.) as indicated by the standard. PA Computation and Estimation PA 2.2.A - The learner will: Solve addition and subtraction problems in everyday situations with two- and three-digit numbers, with or without regrouping PA 2.2.B - The learner will: Solve addition problems with 3 two-digit numbers with regrouping PA 2.2.C - The learner will: Solve subtraction problems with doubledigit numbers with regrouping Page 27 of 168 Topic 1 - Number Sense and Topic 1 - Number Sense and Topic 1 - Number Sense and Obj WP: Add or subtract numbers without regrouping Obj WP: Add or subtract up to 2- digit numbers with one regrouping Obj Add two 3-digit numbers without regrouping Obj Add a 2-digit number to a 1- digit number with regrouping Obj Add two 2-digit numbers with regrouping Obj Add three 2-digit numbers with one regrouping, sum less than 100 Obj Add 2- and 3-digit numbers with no more than one regrouping Obj Add two 3-digit numbers with one regrouping Obj Subtract a 3-digit number from a 3-digit number without regrouping Obj Subtract money values using cents or dollars with one regrouping Obj Subtract a 1- or 2-digit number from a 2-digit number with one regrouping Obj Subtract a 1- or 2-digit number from a 3-digit number with one regrouping