Read Guide to Pacing and Standardized Assessment text version

Connected Mathematics 2

Guide to Pacing and Standardized Assessment (GPSA) Grade 7:

WHAT DO YOU EXPECT?

Office of Mathematics Office of Teaching + Learning Chicago Public Schools 2010-2011

Acknowledgments

We would like to thank Pearson Prentice Hall, publisher of Connected Mathematics, and the University of Illinois at Chicago, who provided valuable assistance in the production of this document, along with the Chicago Public Schools Office of Mathematics and its Acting Director, Jesch Reyes, for their support for the production of this document. Special acknowledgment goes to the following organizations and personnel who helped develop and review this document.

Pearson Prentice Hall Office of Mathematics & Science

Faylesha L. Porter

Chicago Public School Teachers and Specialists Anne Agostinelli

Lynn Polite Susan Shaughnessy

All Learn Mathematics (ALM); University of Illinois at Chicago

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Introduction

This document provides pacing and other information for Chicago Public School teachers and administrators in schools that use Connected Mathematics 2 (CMP2) in grades 6-8. Connected Mathematics 2 is the elementary school math curriculum developed at Michigan State University and published by Pearson Prentice Hall. This document should be used along with the Teachers Guide that is part of CMP2. It does not replace the detailed information found in the Teachers Guide. The order of some lessons has been changed to provide students with content experiences prior to the Illinois Standards Achievement Test (ISAT). The content in some lessons prepares students for mathematics concepts covered in depth in later grades; therefore, these lessons may not include a reference to the grade level Illinois Assessment Framework (IAF) but are critical in developing a students understanding of the mathematics. Some Grade 7 units are used in Grade 8. The detailed GPSA includes the applicable Grade 7 IAF statements for each lesson and the numbers (in parentheses) to the corresponding Grade 8 IAF statements. Teachers are advised to use the Summary Pacing Guide (page iv) and the detailed Guide to Pacing and Standardized Assessment (that follows) to develop their own pacing for the year. Pacing should be based upon 60 minutes of mathematics per day. All Connected Mathematics 2 units address the content and process standards: Numbers and Operations Problem Solving Algebra Reasoning and Proof Geometry Communication Measurement Connections Data Analysis and Probability Representation A high fidelity implementation of Connected Mathematics 2 incorporates the use of all components of the math curriculum: Investigations ACE Questions Mathematical Reflections Assessments This document can be useful in several ways. It can help teachers: In their pacing so they cover the concepts required for that particular grade level and help them get through the curriculum by the end of the school year. This guide provides a reasonable schedule for completing CMP2 lessons within the CPS calendar. Use CMP2 to address the Illinois Learning Standards. See the connections between the lessons, the Illinois Learning Standards and the Illinois Assessment Frameworks. See the connection between CMP2 lessons and items that may appear on standardized tests. Making this connection explicit emphasizes that the most effective preparation for a standardized test is to do a good job teaching a high-quality math curriculum that is aligned with the standards the test is assessing. We look forward to feedback from teachers who will be using this document during the 2010-2011 school year.

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Connected Mathematics 2 ­ 7th Grade Guide to Pacing and Standardized Assessment (GPSA) 2010-2011

Illinois Learning Standards:

Office of Mathematics Chicago Public Schools

What Do You Expect?

Investigation 1: Evaluating Games

Problem / Activity Mathematical Goals Problem 1.1 Matching Colors Mathematical Goals: Review basic probability concepts, such as fair game, experimental probability, theoretical probability, and fraction notation for expressing probabilities Include a payoff in consideration of the fairness of a game

Your Pacing

Notes

Days 158159

6.A.3 Represent fractions, decimals, percentages, exponents and scientific notation in equivalent forms. 6.B.3a Solve practical computation problems involving whole numbers, integers, and rational numbers. 6.C.3a Select computational procedures and solve problems with whole numbers, fractions, decimals, of Chance percents, and proportions. 10.C.3a Determine the probability and odds of events using fundamental counting principles. 10.C.3b Analyze problem situations and make predictions about results. IL Assessment Pre- and Post-ISAT IL Performance Descriptors Practice Test Items Frameworks Guidance 6D - Students who meet the standard can Opportune time to May Ling has two spinners, as shown below. 6.7.14 (6.8.15) solve problems using comparison of Create and explain review fractional parts of She will spin each arrow once and add the quantities, ratios, proportions, and percents. ratios that represent a a whole; and percentresults. given situation. decimal - fraction 6D.1 Work flexibly with fractions, equivalents. decimals, and percents to solve number 6.7.15 (6.8.16) Use sentences and word problems. proportional ACE 2: fractional reasoning to model 10B - Students who meet the standard can notation to express and solve problems. formulate questions, design data collection probability. methods, gather and analyze data, and 10.7.06 (10.8.06) communicate findings. Solve problems ACE 14: ordering points involving the Which of the following sets represents every 10B.1 Select and use appropriate data on a number line probability of a possible outcome? gathering techniques. (possible whole-class simple or compound problem) 10C - Students who meet the standard can event, including A. {25, 30, 35, 40} determine, describe and apply the representing the ACE 15-18: fractional probabilities of events. (Probability, B. {15, 20, 25, 30, 35, 40} probability as a parts of whole and including counting techniques) fraction, decimal, or equivalent fractions. C. {20, 25, 30, 35, 40, 45} 10C.1 Discuss odds versus probability. percent. D. {10, 15, 20, 25, 30, 35, 10C.2 Make and test conjectures about the 10.7.07 Represent all 40, 45, 50} results of experiments and simulations possible outcomes using proportionality and basic (sample space) for MCAS Item understanding of probability. simple or compound events (e.g., tables, 10C.3 Compute probabilities for simple grids, tree diagrams). compound events using methods such as organized lists and tree diagrams. 10C - Students who meet the standard can determine, describe and apply the probabilities of events. (Probability, including counting techniques) 10C.2 Make and test conjectures about the results of experiments and simulations using proportionality and basic understanding of probability. 10C.3 Compute probabilities for simple compound events using methods such as organized lists and tree diagrams. 10.7.06 (10.8.06) Solve problems involving the probability of a simple or compound event, including representing the probability as a fraction, decimal, or percent. 10.7.07 Represent all possible outcomes Opportunity to review: The use of ,,or and ,,and in mathematical statements; Multiplication of fractions. ACE 3, 10, 21: multistep problems. An eighth-grade class will perform the first four acts in the annual talent show. Every student is in exactly one of the four acts. The order in which the acts will be presented is to be decided by a drawing so that each act has an equal chance of being drawn. a. Chantal is a member of the eighth-grade class. What is the probability that her act will be presented first? b. Chantal's act was chosen to be presented first. Make a tree diagram, chart, or list

Days 160161

Problem 1.2 Red and Blue is a Winner! Mathematical Goals: To use probability and payoff to calculate the longterm average result of a game of chance.

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Connected Mathematics 2 ­ 7th Grade Guide to Pacing and Standardized Assessment (GPSA) 2010-2011

Illinois Learning Standards:

Office of Mathematics Chicago Public Schools

What Do You Expect?

Investigation 1: Evaluating Games

Problem / Activity Mathematical Goals

Your Pacing

Notes

6.A.3 Represent fractions, decimals, percentages, exponents and scientific notation in equivalent forms. 6.B.3a Solve practical computation problems involving whole numbers, integers, and rational numbers. 6.C.3a Select computational procedures and solve problems with whole numbers, fractions, decimals, of Chance percents, and proportions. 10.C.3a Determine the probability and odds of events using fundamental counting principles. 10.C.3b Analyze problem situations and make predictions about results. IL Assessment Pre- and Post-ISAT IL Performance Descriptors Practice Test Items Frameworks Guidance (sample space) for showing all the possible orders in which the simple or compound other three acts could be presented. Use the events (e.g., tables, letters A, B, and C to represent these three grids, tree diagrams). acts. c. Rory, Jesse, and Chantal are all members of the eighth-grade class who will each perform an act. What is the probability that Rory's act will immediately follow Jesse's? Explain how you found your answer. MCAS Item Silas has the cards shown below. All cards are the same size and shape. He put the cards into a bag.

Days 162

Problem 1.3 Playing the Multiplication Game Mathematical Goals: Use probability and payoff to calculate the long-term average result of a game of chance

6D - Students who meet the standard can solve problems using comparison of quantities, ratios, proportions, and percents. 6D.1 Work flexibly with fractions, decimals, and percents to solve number sentences and word problems. 10C - Students who meet the standard can determine, describe and apply the probabilities of events. (Probability, including counting techniques) 10C.2 Make and test conjectures about the results of experiments and simulations using proportionality and basic understanding of probability. 10C.3 Compute probabilities for simple compound events using methods such as organized lists and tree diagrams.

.

Opportunity to review line plots. ACE 11-13: extended response practice. ACE 24-28: number sense and reasoning. The Additional Practice and Skills Workbook provides exercises for additional practice and/or assessment of the skills addressed in this investigation.

Silas will pull one card out of the bag without looking. a. Will the number on the card Silas pulls out more likely be an even number or more likely be an odd number? Show or explain how you got your answer. b. What is the probability that the card Silas pulls out will have a 3 on it? Show or explain how you got your answer. c. Silas will perform this experiment a total of 72 times, replacing the card after each pull. What is the total number of times he should expect to pull out a card with a 7 on it? Show or explain how you got your answer. MCAS Item

Day 163 Day 164

Mathematical Reflections and Review Check Up 1

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Connected Mathematics 2 ­ 7th Grade Guide to Pacing and Standardized Assessment (GPSA) 2010-2011

Office of Mathematics Chicago Public Schools

What Do You Expect?

Investigation 2: Analyzing Situations Using an Area Model

Your Pacing

Illinois Learning Standards:

10.C.3a Determine the probability and odds of events using fundamental counting principles. 10.C.3b Analyze problem situations and make predictions about results. IL Assessment Frameworks Pre- and Post-ISAT Guidance Opportunity to review addition of fractions. ACE 14: operations with negative integers. Practice Test Items Use the spinner shown below to answer question 12.

Day 165

Problem / Activity Mathematical Goals Problem 2.1 Making Purple Mathematical Goals: Use an area model to analyze the theoretical probabilities for twostage outcomes.

Notes

IL Performance Descriptors 7C - Students who meet the standard can select and use appropriate technology, instruments, and formulas to solve problems, interpret results, and communicate findings. 7C.7 Develop and discuss strategies to find the area of combined shapes. 10C - Students who meet the standard can determine, describe and apply the probabilities of events. (Probability, including counting techniques) 10C.1 Discuss odds versus probability. 10C.2 Make and test conjectures about the results of experiments and simulations using proportionality and basic understanding of probability. 10C.3 Compute probabilities for simple compound events using methods such as organized lists and tree diagrams. 7C - Students who meet the standard can select and use appropriate technology, instruments, and formulas to solve problems, interpret results, and communicate findings. (Progression from selection of appropriate tools and methods to application of measurements to solve problems) 7C.7 Develop and discuss strategies to find the area of combined shapes 10A - Students who meet the standard can organize, describe and make predictions from existing data. (Data Analysis) 10A.3 Construct an equivalent data representation given data in a different form. 10B - Students who meet the standard can formulate questions, design data collection methods, gather and analyze data, and communicate findings. (Data Collection)

Melinda and Henry are playing a game with this three-color spinner. Henry thinks that the probability of landing on gold is 1/3. Is Henry correct? If he is correct, explain how you know. If he is not correct, give the correct probability and explain how you know it is correct. MCAS Item

Days 166167

Problem 2.2 Choosing Paths Mathematical Goals: Simulate and analyze probability situations involving two-stage outcomes Distinguish between equally likely and non-equally likely outcomes by collecting data and analyzing experimental probabilities Use an area model to analyze the theoretical probabilities for two-

. 10.7.08 Solve simple problems involving the number of ways objects can be arranged

The area model provides opportunity to assess students facility with fractions (especially, equivalent fractions; and addition and multiplication of fractions). ACE 21: interpreting data presented in a line plot. ACE 22: determining fractional parts of a whole.

Della is chosen as a contestant on a game show. The host gives her two red marbles, two green marbles, and two yellow marbles. Della will put the marbles into two identical cans in any way she chooses. The host will then rearrange the cans, leaving the marbles as Della placed them. Della will then select a can and choose a marble. If she chooses a red marble, she wins a prize. How should Della arrange the marbles so she has the best chance of choosing a red marble? ACE Question #27 from p. 36

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Connected Mathematics 2 ­ 7th Grade Guide to Pacing and Standardized Assessment (GPSA) 2010-2011

Office of Mathematics Chicago Public Schools

What Do You Expect?

Investigation 2: Analyzing Situations Using an Area Model

Your Pacing

Illinois Learning Standards:

10.C.3a Determine the probability and odds of events using fundamental counting principles. 10.C.3b Analyze problem situations and make predictions about results. IL Assessment Frameworks Pre- and Post-ISAT Guidance Practice Test Items

Problem / Activity Mathematical Goals stage outcomes

Notes

IL Performance Descriptors 10B.1 Select and use appropriate data gathering techniques. 10B.2 Formulate new questions using conjectures, and plan new studies to answer them. 10C - Students who meet the standard can determine, describe and apply the probabilities of events. (Probability, including counting techniques) 10C.2 Make and test conjectures about the results of experiments and simulations using proportionality and basic understanding of probability. 10C.3 Compute probabilities for simple compound events using methods such as organized lists and tree diagrams. 6D - Students who meet the standard can solve problems using comparison of quantities, ratios, proportions, and percents. 6D.1 Work flexibly with fractions, decimals, and percents to solve number sentences and word problems. 10C - Students who meet the standard can determine, describe and apply the probabilities of events. (Probability, including counting techniques) 10C.2 Make and test conjectures about the results of experiments and simulations using proportionality and basic understanding of probability. 10C.3 Compute probabilities for simple compound events using methods such as organized lists and tree diagrams.

Day 168

Problem 2.3 Finding the Best Arrangement Mathematical Goals: Use an area model to analyze the theoretical probabilities for twostage outcomes

representing the probability 10.7.08 (10.8.08) Solve simple problems involving the number of ways objects can be arranged.

ACE 23: fractional parts of a whole; addition of fractions. The Additional Practice and Skills Workbook provides exercises for additional practice and/or assessment of the skills addressed in this investigation.

A box contains 3 chips numbered 1 through 3. One chip will be taken at random from the box and then put back into the box. Then a second chip will be taken from the box. In the space provided below, list all possible pairs of chips Number on First Chip Number on Second Chip

NAEP Item

Day 169 Day 170

Mathematical Reflections and Review Partner Quiz

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Connected Mathematics 2 ­ 7th Grade Guide to Pacing and Standardized Assessment (GPSA) 2010-2011

Illinois Learning Standards:

Office of Mathematics Chicago Public Schools

What Do You Expect?

Investigation 3: Expected Value

Your Pacing

6.A.3 Represent fractions, decimals, percentages, exponents and scientific notation in equivalent forms. 6.B.3a Solve practical computation problems involving whole numbers, integers, and rational numbers. 10.C.3a Determine the probability and odds of events using fundamental counting principles. 10.C.3b Analyze problem situations and make predictions about results. IL Performance Descriptors 6D - Students who meet the standard can solve problems using comparison of quantities, ratios, proportions, and percents. 7C - Students who meet the standard can select and use appropriate technology, instruments, and formulas to solve problems, interpret results, and communicate findings. 7C.7 Develop and discuss strategies to find the area of combined shapes. 10A - Students who meet the standard can organize, describe and make predictions from existing data. (Data Analysis) 10A.3 Construct an equivalent data representation given data in a different form. 10C - Students who meet the standard can determine, describe and apply the probabilities of events. (Probability, including counting techniques) 10C.2 Make and test conjectures about the results of experiments and simulations using proportionality and basic understanding of probability. 10C.3 Compute probabilities for simple compound events using methods such as organized lists and tree diagrams. 6D - Students who meet the standard can solve problems using comparison of quantities, ratios, proportions, and percents. 6D.1 Work flexibly with fractions, decimals, and percents to solve number sentences and work problems. 10A - Students who meet the standard can organize, describe and make predictions from existing data. (Data Analysis) 10A.1 Construct, read, interpret, infer, predict, draw conclusions, and evaluate data from IL Assessment Frameworks 10.7.08 (10.8.08) Solve simple problems involving the number of ways objects can be arranged. Pre-and Post-ISAT Guidance Opportunity to assess students facility with percents and decimals (especially multiplication). ACE 1-2; 12-14: percents Practice Test Items

Days 171 172

Problem / Activity Mathematical Goals Problem 3.1 One-and-One FreeThrows Mathematical Goals: Understand the difference between the probability of an outcome and the long-term average of many trials in a situation with a payoff Determine the expected value in a probability situation Use probability to make decisions

Notes

Days 173174

Problem 3.2 Finding Expected Value Mathematical Goals: Determine the expected value in a probability situation

ACE 7, 17, 25, 26, 28: percents ACE 16: ratios and proportions ACE 18, 19: addition and multiplication of positive and negative integers

From a shipment of 500 batteries, a sample of 25 was selected at random and tested. If 2 batteries in the sample were found to be dead, how many dead batteries would be expected in the entire shipment? A. B. C. D. E. 10 20 30 40 50

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WHAT DO YOU EXPECT?

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Connected Mathematics 2 ­ 7th Grade Guide to Pacing and Standardized Assessment (GPSA) 2010-2011

Illinois Learning Standards:

Office of Mathematics Chicago Public Schools

What Do You Expect?

Investigation 3: Expected Value

Your Pacing

6.A.3 Represent fractions, decimals, percentages, exponents and scientific notation in equivalent forms. 6.B.3a Solve practical computation problems involving whole numbers, integers, and rational numbers. 10.C.3a Determine the probability and odds of events using fundamental counting principles. 10.C.3b Analyze problem situations and make predictions about results. IL Performance Descriptors various displays, including box and whiskers plots. 10A.3 Construct an equivalent data representation given data in a different form. 10C - Students who meet the standard can determine, describe and apply the probabilities of events. (Probability, including counting techniques) 10C.2 Make and test conjectures about the results of experiments and simulations using proportionality and basic understanding of probability. 10C.3 Compute probabilities for simple compound events using methods such as organized lists and tree diagrams. IL Assessment Frameworks Pre-and Post-ISAT Guidance Practice Test Items NAEP Item

Problem / Activity Mathematical Goals

Notes

Days 175176

Problem 3.3 Choosing Pay Plans Mathematical Goals: Practice determining the expected value in a probability situation Use probability to make decisions

10C - Students who meet the standard can determine, describe and apply the probabilities of events. (Probability, including counting techniques) 10C.2 Make and test conjectures about the results of experiments and simulations using proportionality and basic understanding of probability.

ACE 21: extended response ACE 22: visual representation of fractional parts of whole The Additional Practice and Skills Workbook provides exercises for additional practice and/or assessment of the skills addressed in this investigation.

To win a game, Yepa must get a sum of 8 on her next two spins of the arrow on the spinner shown below. All the sections of the spinner are of equal size.

What is the probability that the results of Yepas next two spins will have a sum of 8? A. 0

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WHAT DO YOU EXPECT?

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Connected Mathematics 2 ­ 7th Grade Guide to Pacing and Standardized Assessment (GPSA) 2010-2011

Illinois Learning Standards:

Office of Mathematics Chicago Public Schools

What Do You Expect?

Investigation 3: Expected Value

Your Pacing

6.A.3 Represent fractions, decimals, percentages, exponents and scientific notation in equivalent forms. 6.B.3a Solve practical computation problems involving whole numbers, integers, and rational numbers. 10.C.3a Determine the probability and odds of events using fundamental counting principles. 10.C.3b Analyze problem situations and make predictions about results. IL Performance Descriptors IL Assessment Frameworks Pre-and Post-ISAT Guidance Practice Test Items B. C. D.

Problem / Activity Mathematical Goals

Notes

MCAS Item Day 177 Day 178 Mathematical Reflections and Review Administer Check Up 2

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WHAT DO YOU EXPECT?

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Connected Mathematics 2 ­ 7th Grade Guide to Pacing and Standardized Assessment (GPSA) 2010-2011

Illinois Learning Standards:

Office of Mathematics Chicago Public Schools

What Do You Expect?

Investigation 4: Binomial Outcomes

Your Pacing

10.C.3a Determine the probability and odds of events using fundamental counting principles. 10.C.3b Analyze problem situations and make predictions about results. IL Performance Descriptors 10C - Students who meet the standard can determine, describe and apply the probabilities of events. (Probability, including counting techniques) 10C.2 Make and test conjectures about the results of experiments and simulations using proportionality and basic understanding of probability. 10C.3 Compute probabilities for simple compound events using methods such as organized lists and tree diagrams. IL Assessment Frameworks Pre-and Post-ISAT Guidance Practice Test Items You might find a tree diagram is a helpful model in this exercise. a. b. c. What are all the possible outcomes when you toss a coin three times? How many outcomes are there when you toss a coin four times? Five time? How many ways can you get five heads in five tosses? How many ways can you get zero heads in five tosses? How many ways can you get four heads? One head? Three heads? Two heads? Explain why some symmetry in your answers in part © makes sense.

Day 179180

Problem / Activity Mathematical Goals Problem 4.1 Guessing Answers Mathematical Goals: Analyze a binomial situation Practice finding expected value in a multiple-stage probability situation

Notes

d.

ACE Question #11 p. 55 Days 181 Problem 4.2 Ortonville Mathematical Goals: Analyze a binomial situation 10C - Students who meet the standard can determine, describe and apply the probabilities of events. (Probability, including counting techniques) 10C.2 Make and test conjectures about the results of experiments and simulations using proportionality and basic understanding of probability. 10C.3 Compute probabilities for simple compound events using methods such as organized lists and tree diagrams. Ensure students understand use of ,,or in mathematical statements. ACE 4-7: fractional notation to express probability. ACE 13: science connection ACE 18-22: Pascals Triangle Tess will toss a fair coin 3 times. The possible results are illustrated in the tree diagram below

Based on the information given in the tree diagram, in how many ways (outcomes) can Tess toss at least 2 heads? A. B. C. D. 2 3 4 5

Day 182-

What Do You Expect? Problem 4.3

10C - Students who meet the standard can determine, describe and apply the probabilities

ACE 16: negative/positive integers

MCAS Item Drew, the paper carrier, collects $10 per week from each customer for the paper. One

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WHAT DO YOU EXPECT?

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Connected Mathematics 2 ­ 7th Grade Guide to Pacing and Standardized Assessment (GPSA) 2010-2011

Office of Mathematics Chicago Public Schools

What Do You Expect?

Investigation 4: Binomial Outcomes

Your Pacing

Illinois Learning Standards:

10.C.3a Determine the probability and odds of events using fundamental counting principles. 10.C.3b Analyze problem situations and make predictions about results. IL Performance Descriptors of events. (Probability, including counting techniques) 10C.2 Make and test conjectures about the results of experiments and simulations using proportionality and basic understanding of probability. 10C.3 Compute probabilities for simple compound events using methods such as organized lists and tree diagrams. IL Assessment Frameworks Pre-and Post-ISAT Guidance The Additional Practice and Skills Workbook provides exercises for additional practice and/or assessment of the skills addressed in this investigation. Practice Test Items customer offers him these deals. a. Toss five coins. If there are four or more heads, the customer pays $18. Otherwise, he pays $4. Find the expected value for this deal. Decide if it is a fair deal. b. Toss five coins. If they are all the same, the customer pays $80. Other wise he pays $4. Find the expected value for this deal. Decide if it is a fair deal. ACE Question #15 p. 57

183

Problem / Activity Mathematical Goals A Baseball Series Mathematical Goals: To analyze a binomial situation with multiple-stage outcomes

Notes

Day 184 Day 185

Mathematical Reflections and Review. Please use "Looking Back and Looking Ahead," pages 63 ­ 65, to review the concepts within the unit. Administer Unit/Final Assessment

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CMP2

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