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Common Core State Standards Pacing Guide 2nd Edition

Math

First Grade — 2nd Nine Week Period

2nd Edition: Laura Taft, Donna Boyle, Mindy Tapia

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Mr. Stan Rounds, Superintendent

Dr. Steven Sanchez, Associate Superintendent for Learning, Teaching & Research

Prepared By: Lydia Polanco, Coordinator of Elementary Instruction

1st

Edition: Laura Taft, Camilla Housinger, Mindy Tapiia

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Math Pacing Guide

Las Cruces Public Schools

Understanding Mathematics: Standards define what students should understand and be able to do in their study of mathematics. Asking students to

understand something means asking teachers to assess whether the student has understood it.1 Mathematical understanding and procedural skill are equally

important.2

Description of the Pacing Guide: A pacing guide is an interval based description of what teachers teach in a particular grade or course; the order in which it is

taught, and the amount of time dedicated to teaching the content.

Purpose of a Pacing Guide: The purpose of a pacing guide is to ensure that all of the standards are addressed during the academic year. Each pacing guide is

nine weeks in duration.

Components of the Pacing Guide:

Critical Areas- Each grade level has identified Critical Areas. These areas are woven throughout the standards and should receive additional time and

attention.

Mathematical Practice Standards (8)- Based on the NCTM Process Standards, these standards describe the variety of "processes and proficiencies"

students should master while working with the Grade Level Content Standards.

Domains are larger groups of related Content Standards. Standards from different domains may sometimes be closely related.3

Clusters are groups of related standards. Note that standards from different clusters may sometimes be closely related, because mathematics is a

connected subject.4

Grade level standards define what students should know and be able to do by the end of each grade level.

Unpacked standards provide a clear picture for the teacher as he/she implements the CCSS

Resources—includes but not limited to current district core resources

1 www.corestandards.org, Mathematics, Introduction, p. 4

2 See #1

3 See #1

4 www.corestandards.org, Mathematics, Introduction, p. 5

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Depth of Knowledge — (DOK) Criteria for systematically analyzing the alignment between standards and standardized assessments

Key Points in Mathematics

• The K-5 standards provide students with a solid foundation in whole numbers, addition, subtraction, multiplication, division, fractions and decimals—which help young students build the foundation to successfully apply more demanding math concepts and procedures, and move into applications.

• In First Grade, the standards follow successful international models and recommendations from the National Research Council’s Early Math Panel report, by focusing kindergarten work on the number core: learning how numbers correspond to quantities, and learning how to put numbers together and take them apart (the beginnings of addition and subtraction).

• The K-5 standards build on the best state standards to provide detailed guidance to teachers on how to navigate their way through knotty topics such as fractions, negative numbers, and geometry, and do so by maintaining a continuous progression from grade to grade.

• The standards stress not only procedural skill but also conceptual understanding, to make sure students are learning and absorbing the critical information they need to succeed at higher levels - rather than the current practices by which many students learn enough to get by on the next test, but forget it shortly thereafter, only to review again the following year.

• Having built a strong foundation K-5, students can do hands on learning in geometry, algebra and probability and statistics.

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Mathematical Practice Standards: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Looks for and make sense of structure 8. Look for and express regularity in repeated reasoning

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Common Core State Standards

LCPS

Pacing Guides

Core Math Program

enVision

Supplemental Technology Based

program to prepare for PARCC

(First in Math, FASTT Math, etc.)

Other Resources

STANDARDS-BASED,

STANDARDS-DRIVEN

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Grade Level: First Quarter: 2nd Nine Weeks

These standards can be taught using enVision Topics 4 and 5 in their entirety.

Standard Q1 Q2 Q3 Q4 1.OA.1 I/P I/P P R 1.OA.2 X I/P P R 1.OA.3 I/P P R R 1.OA.4 I/P P R R 1.OA.6 I/P I/P I/P P

Domain: 1.OA Operations and Algebraic Thinking

1.OA.1 & 1.OA.2 Cluster: Represent and solve problems involving addition and subtraction

1.OA.3 & 1.OA.4 Cluster: Understand and Apply Properties of Operations and the Relationship between Addition and Subtraction

1.OA.6 Cluster: Add and Subtract within 20

Critical Areas: #1: Strong Connection #2: Some Connection #3: No Connection #4: No Connection

Grade Level Content Standard Mathematical Practice Standard

1.OA.1 Use addition and subtraction within 20 (10) to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. (See Glossary Table 1, pg. 88 CCSS)

MP.2. Reason abstractly and quantitatively. De-contextualize (equations) and contextualize (make meaning In a word problem) quantitative relationships. Create a logical representation of the problem. Attends to the meaning of quantities, not just how to compute them. MP.4. Model with mathematics. Understand this is a way to reason quantitatively and abstractly (able to de-contextualize and contextualize). Apply the mathematics they know to solve everyday problems. Reflect on whether the results make sense, possibly improving/revising the model. See: LCPS Pacing Guide Appendix B

1.OA.2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to (12), e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

1.OA.3 Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) (Students need not use formal terms for these properties.)

1.OA.4 Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8.

1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10 (+0's, +1's, and doubles were to be mastered during the 1st quarter, In the 2nd quarter add in the other addition facts within 10). Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13

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Unpacked Content Standard: 1.OA.1 In the 1st quarter, this standard was Introduced for addition and subtraction within 10. During the 2nd quarter, students will work on addition and subtraction within 10 with unknowns in all 3 positions, using symbols for the unknowns. (Students will work on this Standard for both the 2nd and 3rd quarter.) The unknown symbols should include boxes, lines, question marks, or pictures, but not letters. Teachers should be aware of the three types of problems and provide multiple experiences for their students solving ALL three types of problems: Result Unknown, Change Unknown, and Start Unknown. Students should become familiar with, and begin to use, the strategies: Add to, Take From, Put Together, Take Apart, and Compare. (CCSS Math Standards Table 1, page 88) Subtizing, the ability to recognize the number of objects in a set without counting, is a helpful strategy for students to recognize sets of objects in either random arrangements (1-5 objects) or in common patterned arrangements such as 10 Frames or Dominoes (1-10/12 objects). Investigations Quick Images is a resource for students to practice subtizing.

1.OA.2 This Standard asks students to add (join) three numbers whose sum is less than or equal to 20, using a variety of mathematical representations. This objective also addresses multi-step word problems. In the 2nd quarter, students are expected to become proficient at adding three numbers whose sum is within 10, and begin seeing two step word problems. Example: There are cookies on the plate. There are 4 oatmeal raisin cookies, 2 chocolate chip cookies, and 2 gingerbread cookies. How many cookies are there total?

Student 1: Adding with a Ten Frame and Counters I put 4 counters on the 10 Frame for the oatmeal raisin cookies. Then, I put 2 different color counters on the 10-Frame for the chocolate chip cookies. Then, I put another 2 color counters out for the gingerbread cookies. There are still 2 empty frames left, so I know the answer is 8.

Student 2: Using Known equations (Doubles) I know that 2 and 2 equal 4, so the chocolate chip cookies and gingerbread equals 4 cookies. Then, I add the 4 and 4 to get 8 total cookies.

Student 3: Number Line I counted on the number line. First, I counted 4, then I counted 2 more and landed on 6. Then, I counted 2 more and landed on 8. So there were 8 total cookies.

1.OA.3 Students were introduced to this Standard in the 1st quarter when they learned to use and apply the Commutative Property, using Fact Families for both addition and subtraction. In the 2nd quarter, students will also learn to use the Associative Property (4 + 2 + 4 = 10, 4 + 4 + 2 = 10) as they begin to add three numbers in Standard 1.OA.2 (see above). Students should use the strategy of re-arranging the order of the addends in order to use known equations (Double, Near Doubles, Making 10, and other memorized addition facts (See Standard 1.OA.6). While this Standard calls for students to apply the properties of operations as strategies to add and subtract, students do not need to use formal terms for these properties. Students should use manipulatives, such as cubes and counters, and mathematical tools, such as the number line and a 100/120 chart to model these ideas.

1.OA.4 This Standard asks for students to use subtraction in the context of unknown addend problems. When determining the answer to a subtraction problem, 12 - 5, students think, "If I have 5, how many more do I need to make 12?"‖ Encouraging students to record this symbolically, 5 + ? = 12, will develop their understanding of the relationship between addition and subtraction. Some strategies they may use are counting objects, creating drawings, counting up, using a number line or using two 10 Frames to determine the answer. When teaching subtraction as an unknown addend: students can always solve subtraction problems by a forward method that finds the unknown. The counting down, or back, method is more difficult and error-prone. Help children learn and use this more accurate forward method. See 1.OA.6: 1st Quarter-within 10 and 2nd Quarter- within 20

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1.OA.6 In the 1st quarter, this standard was Introduced for both addition and subtraction equations within 10 using the strategies Count On, Decomposing/ Making 10, Using the relationship between addition and subtraction, and using knowledge of easier or known sums (such as combinations of 10 and doubles.) Students will practice addition and subtraction equations this quarter within 20, and are expected to become Proficient at this Standard during the 3rd quarter. This standard introduces subtraction, especially how subtraction is related to Addition (See Standard 1.OA.4 above). By studying patterns and relationships in addition facts and relating addition and subtraction as inverse operations, students build a foundation for fluency with addition and subtraction facts.

Decomposing/Making 10: 5 + 15 =? I know that 5 + 5 = 10, so I decomposed (broke apart) the 15 into 10 + 5, now I have two 10s. I know that 10 + 10 = 20.

Using Knowledge of Easier or Known Sums/ Using the Relationship between Addition and Subtraction: 18 - 3 = __ I know that 3 + 5 = 8, so 3 + 15 = 18.

This standard also deals with building Computational Fluency1 with addition facts within 10. 1Fluency means accuracy (correct answer), efficiency (within 4-5 seconds), and flexibility (quickly using mental strategies such as making 5 or making 10.

Quarter Add/Subtract within 20 Computational Fluency within 10 Examples

1 + / - within 10 + / - 0's, 1's 10+0, 9+0, 9+1, 8+0, 8+1.....

2 + / - within 20 Addition Doubles, Near Doubles, + / - within 5

5+5, 4+4, 4+3, 3+3, 3+2, 2+2 5-5, 5-4, 5-3, 5-2,

3 + / - within 20 All addition within 10 & Subtraction of 10's 10-1, 10-2, 10-3, 10-4.....

4 Reinforce and Review All addition & subtraction within 10 All addition and subtraction facts where 10 is the largest number in the equation

Vocabulary:

enVisions Topic 1:

order, addition sentence, addend, plus sign (+), equals (=), plus sign, sum, in all, inside, outside, part, whole, double, join

enVisons Topic 4:

near Double, 2 less than, 1 less than, 0 less than

enVisons Topic 5:

Doubles, plus 1, plus 2,

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Resources: DOK: enVision Topic 4 Test (page 159) enVision Benchmark Test Topics 1-4

enVision Topic 5 Test (page 201)

1.OA.1 enVisons Topic 4: (1 lesson) 4-10 enVisons Topic 5: (1 lesson) 5-4 Also See enVisions Topics 1- 3 from the 1st quarter. enVision Topics 4 & 5: As teachers begin each new topic and Domain, it is very helpful to read the "MATH BACKGROUND" pages to gain an understanding of the mathematic principals, get a clear understanding of some of the Math vocabulary found in the lessons, and see suggestions on how to teach difficult concepts. enVision Topics 4 & 5: "THE LANGUAGE OF MATH" page gives excellent ideas for connecting Reading skills and comprehension to Mathematics and the Problem Solving needed to be an effective mathematician at first grade. enVision Topics 4 & 5: Each enVisions Topic includes an "INTERACTIVE MATH STORY". This should be used as Day 1 when starting a new Topic. enVision Topics 4 & 5: The "TOPIC OPENER" and game should be used as Day 2 for each Topic. Also included on these pages are information on sending home a Parent Letter introducing the Standards taught in the Topic, a reminder to use the Vocabulary cards, an interactive game for students to play, a suggested Mat h Project,

1.OA.1 DOK 2: In addition to workbook style, multiple choice questions, students should also be assessed through authentic means where they must show not only their answer, but the strategies used to solve the problems. Assessments should include "ACE" type word problems where students must provide an Answer, Calculations, and Explanation.

Word Problems

1. There were 4 boys on the swings. Some girls were also on the swings. All together, there were 8 boys and girls on the swings. How many girls were there? 4 + ? = 8 (Change Unknown)

2. Some red apples were in the basket. 6 green apples were in the basket. There were 10 apples all together. How many red apples were in the basket? __ + 6 = 10 (Start Unknown)

3. 3 cars were in the parking lot. 4 trucks were in the parking lot. How many cars and

trucks were in the parking lot all together? 3 + 4 = (Result Unknown)

Discovery Item:

Tracy wants to write thank you letters for her birthday gifts. She has written 6 letters. There were 13 girls at her party. How many more letters does she need to write?

Which number sentence shows how to solve this problem?

1. 6 + 13 = 19

2. 7 - 6 = 1

3. 13 - 5 = 7

4. 13 - 6 = 7

Keep in mind that many students will apply their understanding that addition and subtraction are related, inverse operations, and use the equation: 6 + ? = 13 to solve this word problem.

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and the Essential Question that students should be able to answer by the end of the Topic.

1.OA.2 enVisons Topic 5: (1 lesson) 5-9 Also See enVisions Topics 1- 3 from the 1st quarter.

1.OA.2 DOK 2: Discovery Items:

1. Write a number problem from the number line.

2. David ate 2 cookies. Sam ate 3 cookies. Juan ate 1 cookie. The dog ate 2 cookies.

How many did they eat all together?

1.OA.3 enVisons Topic 4: (1 lesson) 4-1 enVisons Topic 5: (1 lesson) 5-8 Also See enVisions Topics 1- 3 from the 1st quarter.

1.OA.3 DOK 3: Teacher Observation: As student solves the following word problem, does s/he use the Associative Property?

Word Problem

1. Beth did 6 jumping jacks, Ben did 5 jumping jacks, and Patty did 4 jumping jacks. How many jumping jacks in all?

Student should re-arrange the word problem to the easier equation: 6 + 4 = 10; 10 + 5 = 15

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1.OA.4 enVisons Topic 4: (3 lessons) 4-7, 4-8, 4-9 Also See enVisions Topics 1- 3 from the 1st quarter.

1.OA.4 DOK 3: Teacher Observation/Questions: 1. Understand the Relationship between Addition and Subtraction, including

Understanding Subtraction Problems as an Unknown Addend Problem

Student 1 I used a Ten Frame. I started with 3 counters. I know that I had to have 10, which is one full ten frame. I needed 7 counters, so 10 – 3 = 7

Student 2 Draw a number line. I started at 3 and counted until I reached 10. I counted 7 numbers, so I knew that 10 – 3 = 7.

Provide student with the subtraction problem: 10 - 3 = __. Observe how the student solves this problem. While students do not necessarily need to solve the problem as an unknown addend addition problem, students should be able to explain how the problem could also be solved in this manner.

1.OA.6 enVisons Topic 4: (4 lessons) 4-2, 4-3, 4-4, 4-5 enVisons Topic 5: (6 lessons) 5-1, 5-2, 5-3, 5-5, 5-6, 5-7 Also See enVisions Topics 1- 3 from the 1st quarter. Computational Fluency

Fasst Math

Timed Math Fact Tests

Flash Cards

1.OA.6 DOK 2: Teacher Observation:

Count On

Show me how you would solve this problem: 6 + 3 = ?

Is student able to use the Count On Strategy? Student can count out 6, pointing to that set and saying "6"... then counting on: "7, 8, 9"

Decomposing/Making 10

Show me how you would solve this problem: 5 + 7 = __

Is student able to use the Making 10 Strategy? Student can decompose either the 5 or the 7 and explain that 5 + 5 = 10, and 2 more makes 12 or 7 + 3 = 10, and 2 more = 12

Using the Relationship between Addition and Subtraction

Show me an Addition problem that could help you solve this problem: 7 - 4 = __

Is student able to use the addition problem 4 + = 7 to solve?

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Grade Level: First Quarter: 2nd Nine Weeks

These standards can be taught using Portions of enVision Topics 9 and 10 and Topic 11 in its entirety.

Standard Q1 Q2 Q3 Q4

1.NBT.5

X P R R

1.NBT.6 X P R R

Domain: Number and Operations in Base Ten Cluster: Use Place Value Understanding and Properties of Operations to Add and Subtract Critical Areas: #1: No Connection #2: Some

Connection #3: No Connection #4: No Connection

Grade Level Content Standard Mathematical Practice Standard

1.NBT.5 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.

MP.2. Reason abstractly and quantitatively.

De-contextualize (equations) and contextualize (make meaning

In a word problem) quantitative relationships.

Create a logical representation of the problem.

Attends to the meaning of quantities, not just how to compute them. MP.7. Look for and make use of structure.

Apply general mathematical rules to specific situations.

Look for the overall structure and patterns in mathematics.

See complicated things as single objects or as being composed of several objects.

See: LCPS Pacing Guide Appendix B

1.NBT.6 Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Unpacked Content Standard: 1.NBT.5 was Introduced in the 1st quarter during Daily Math Routines and students become Proficient in the 2nd quarter. This standard builds on students’ work with tens and ones and requires them to understand and apply the concept of 10 by mentally adding ten more and ten less than any number less than 100. This understanding leads to future place value concepts. It is critical for students to do this without counting. Prior use of models such as base ten blocks, number path, and 100 charts helps facilitate understanding. Ample experiences with ten frames will also help students see the pattern involved when adding or subtracting 10 and USE these patterns to solve such problems. Examples: There are 74 birds in the park. 10 birds fly away. How many are left?

Student 1: Student 2: More Examples:

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I used a 100s board. I started at 74. Then, because 10 birds flew away. I moved back one row. I landed on 64. So, there are 64 birds left in the park.

I pictured 7 ten frames and 4 left over in my head. Since 10 birds flew away. I took one of the ten frames away. That left 6 ten frames and 4 left over. So, there are 64 birds left in the park.

10 more than 43 is 53 because, 53 is one more 10 than 43 10 less than 43 is 33 because 33 is one 10 less than 43

1.NBT.6 was Introduced in the 1st quarter during Daily Math Routines and students become Proficient in the 2nd quarter. This standard calls for students to use concrete models, drawings and place value strategies to subtract multiples of 10 from decade numbers (e.g., 30, 40, 50). This standard is foundational for future work in subtraction with more complex numbers. Students should have multiple experiences representing numbers that are multiples of 10 (e.g. 90) with models or drawings. Then they subtract multiples of 10 (e.g. 20) using these representations or strategies based on place value. These opportunities develop fluency of addition and subtraction facts and reinforce counting up and back by 10s. Examples:

70 - 30: Seven 10s take away three 10s is four 10s

80 - 50: 80, 70 (one 10), 60 (two 10s), 50 (three 10s), 40 (four 10s), 30 (five 10s)

60 - 40: I know that 4 + 2 is 6 so four 10s + two 10s is six 10s so 60 - 40 is 20 Examples: There are 60 students in the gym. 30 students leave. How many students are still in the gym?

Student 1 I used a hundreds chart and started at 60. I moved up 3 rows to land on 30. There are 30 students left.

Student 2 I used place value blocks or Unifix cubes to build towers of 10. I started with 6 towers of 10 and removed 3. Had 3 towers left. 3 towers have a value of 30. There are 30 students left.

Student 3 Students mentally apply their knowledge of addition to solve this subtraction problem. I know that 30 plus 30 is 60, so 60 minus 30 equals 30. There are 30 students left.

Student 4 I used a number path. I started at 60 and moved back 3 tens and landed on 30. There are 30 students left.

Students may use interactive versions of models (base ten blocks, 100s charts, number path, etc.) to demonstrate and justify their thinking.

Vocabulary: more, less, mental math, regroup, place value, ones, tens, digit

Resources

Depth of Knowledge enVision Topic 11 Test- p 381

1.NBT.5 enVision Math- Topic 9- Lesson 9-1 Topic 10- Lessons- 10-2, 10-3, 10-4 120 Chart Counter

DOK 2: Provide students with access to a 100/120 Chart; ask students to find numbers that are 10 more or 10

less than given two-digit number. Observe how students find the answer.

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Cubes Number line 10 Frames Routine #2: Fluency and Patterns in Counting:

student use the Chart? Does student have to count up?

(knowing that only the digit in the 10's place changes.) Student A I thought about a 100s board. I started at 74. Then, because 10 birds flew away, I moved back one row for

a total of 10 spaces. I landed on 64. So, there are 64 birds left in the park.

1.NBT.6 enVision Topic 11: (All lessons) enVision Topic 11, pages 353A As teachers begin each new topic and Domain, it is very helpful to read the “MATH BACKGROUND” pages to gain an understanding of the mathematic principals, get a clear understanding of some of the Math vocabulary found in the lessons, and see suggestions on how to teach difficult concepts. enVision Topic 11, page 353D: “THE LANGUAGE OF MATH” page gives excellent ideas for connecting Reading skills and comprehension to Mathematics and the Problem Solving needed to be an effective mathematician at first grade. enVision Topic 11, page 353E Each envision Topic includes an “INTERACTIVE MATH STORY”. This should be used as Day 1 when starting a new Topic.

DOK 2: Example: There are 60 students in the gym. 30 students leave. How many students are still in the gym?

Student A- I used a number line. I started at 60 and moved back 3 jumps of 10 and landed on 30. There

are 30 students left.

Student B-I used a hundreds chart and started at 60. I moved back 3 rows of ten to land on 30. There

are 30 students left.

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enVision Topic 11, pages 353 The “TOPIC OPENER” and game should be used as Day 2 for each Topic. Also included on these pages are information on sending home a Parent Letter introducing the Standards taught in the Topic, a reminder to use the Vocabulary cards, an interactive game for students to play, a suggested Mat h Project, and the Essential Question that students should be able to answer by the end of the Topic.

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Grade Level: First Grade Quarter: 2nd Nine Weeks

Standard Q1 Q2 Q3 Q4

1.MD.4 I I/P I I/P

Domain: Measurement and Data Cluster: Represent and interpret data. Critical Areas: #1: No Connection #2: No Connection #3: Some Connection #4: No Connection

Grade Level Content Standard Mathematical Practice Standard

1.MD.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

MP.2. Reason abstractly and quantitatively.

De-contextualize (equations) and contextualize (make meaning

In a word problem) quantitative relationships.

Create a logical representation of the problem.

Attends to the meaning of quantities, not just how to compute them. MP.4. Model with mathematics.

Understand this is a way to reason quantitatively and abstractly (able to de-contextualize and contextualize).

Apply the mathematics they know to solve everyday problems.

Reflect on whether the results make sense, possibly improving/revising the model. See: LCPS Pacing Guide Appendix B

Unpacked Content Standard: 1.MD.4 In the 1st quarter, 1.MD.4 was introduced. Students had practice representing data on a chart and graph with three categories during Daily Math Routines #3. During the 2nd quarter, students are expected to become Proficient at this type of representation as well as be able to ask/answer questions on the graphs and charts (How many more than, less than.) During the 3rd and 4th quarters, students will continue to work on this standard, moving to using a question to survey and collect data, then represent the data collected on a self-created chart or graph. This Standard calls for students to create graphs and tally charts using data relevant to their lives (e.g. categorical data--favorite ice cream, how I get to school, pets, etc). Graphs may be constructed by groups of students as well as by individual students. Then, they work with the data by organizing, representing and interpreting data. Students should have experiences posing a question with 3 possible responses and then work with the data that they collect. In order to begin this type of work in the 3rd quarter, students need experiences in the 2nd quarter being responsible for deciding on the survey questions and/or categories. Counting objects should be reinforced when collecting, representing, and interpreting data. Students describe the object graphs and tally charts they create. They should also ask and answer questions based on these charts or graphs that reinforce other mathematics concepts such as sorting and comparing. The data chosen or questions asked give students opportunities to reinforce their understanding of place value, identifying ten more and ten less, relating counting to addition and subtraction and using comparative language and symbols: greater than (>), less than (>), and equal to (=).

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What is your favorite Ice Cream Flavor?

Chocolate 10

Vanilla 9

Strawberry 5

Example: Students pose a question and the 3 possible responses.

Which is your favorite flavor of ice cream? Chocolate, vanilla or strawberry?

Students collect their data by using tallies or another way of keeping track of responses.

Students organize their data by representing and totaling each category in a chart or table.

Vocabulary: data, interpret, how many

Resources Depth of Knowledge

Daily Routine #3: Surveying and Graphing

In the 3rd Quarter, enVision Topic 14 will expand upon this standard to

include student created graphs and charts.

DOK:2

“What is your favorite flavor of ice cream?” is posed and recorded. The categories

chocolate, vanilla and strawberry are determined as anticipated responses and written

down on the recording sheet. When asking each classmate about their favorite flavor,

the student’s name is written in the appropriate category. Once the data are collected,

the student counts up the amounts for each category and records the amount. The

student then analyzes the data by carefully looking at the data and writes 4 sentences

about the data.

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LCPS Pacing Guide Appendices

Appendix A Balanced Classroom Assessment Strategies

Selected Response

Constructed Response

Performance Assessment

Informal Assessment

Multiple Choice

Fill-in-the-blank (words, phrases)

Presentation

Oral questioning

True–False

Essay Movement

Observation

Matching

Short answer (sentences, paragraphs)

Exhibition Interview

Diagram

Model Conference

Web

Dramatization

Process description

Concept Map

Enactment

Checklist

Flowchart

Project

Rating scale

Graph

Debate

Journal sharing

Table

Thinking aloud process

Matrix

Student self-assessment

Illustration

Peer review

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Mathematical Practice Standards Appendix B

Summary of Standards for Mathematical Practice Questions to Develop Mathematical Thinking

1. Make sense of problems and persevere in solving them. Interpret and make meaning of the problem to find a starting point.

Analyze what is given in order to explain to themselves the meaning of the problem.

Plan a solution pathway instead of jumping to a solution.

Monitor their progress and change the approach if necessary.

See relationships between various representations.

Relate current situations to concepts or skills previously learned and connect mathematical ideas to one another.

Continually ask themselves, “Does this make sense?”

Understand various approaches to solutions.

How would you describe the problem in your own words?

How would you describe what you are trying to find?

What do you notice about...?

What information is given in the problem?

Describe the relationship between the quantities.

Describe what you have already tried. What might you change?

Talk me through the steps you’ve used to this point.

What steps in the process are you most confident about?

What are some other strategies you might try?

What are some other problems that are similar to this one?

How might you use one of your previous problems to help you begin?

How else might you organize...represent... show...?

2. Reason abstractly and quantitatively.

Make sense of quantities and their relationships.

De-contextualize (represent a situation symbolically and manipulate the symbols) and contextualize (make meaning of the symbols in a problem) quantitative relationships.

Understand the meaning of quantities and are flexible in the use of operations and their properties.

Create a logical representation of the problem.

Attends to the meaning of quantities, not just how to compute them.

What do the numbers used in the problem represent?

What is the relationship of the quantities?

How is _______ related to ________?

What is the relationship between ______and ______?

What does _______ mean to you? (e.g. symbol, quantity, diagram)

What properties might we use to find a solution?

How did you decide in this task that you needed to use...?

Could we have used another operation or property to solve this task? Why or why not?

Summary of Standards for Mathematical Practice Questions to Develop Mathematical Thinking

3. Construct viable arguments and critique the reasoning of others.

Analyze problems and use stated mathematical assumptions, definitions, and established results in constructing arguments.

What mathematical evidence would support your solution?

How can we be sure that..? How could you prove that..? Will it still work if..?

How did you decide to try that strategy?

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Justify conclusions with mathematical ideas.

Listen to the arguments of others and ask useful questions to determine if an argument makes sense.

Ask clarifying questions or suggest ideas to improve/revise the argument.

Compare two arguments and determine correct or flawed logic.

How did you test whether your approach worked?

How did you decide what the problem was asking you to find?

Did you try a method that did not work? Why didn’t it work? Would it ever work? Why or why not?

What is the same and what is different about...?

How could you demonstrate a counter-example?

4. Model with mathematics.

Understand this is a way to reason abstractly and quantitatively (able to contextualize- put into a real life situation or word problem, and de-contextualize- put into an equation).

Apply the mathematics they know to solve everyday problems.

Are able to simplify a complex problem and identify important quantities to look at relationships.

Represent mathematics to describe a situation either with an equation or a diagram and interpret the results of a mathematical situation.

Ask themselves, “How can I represent this mathematically?”

What number model could you construct to represent the problem?

What are some ways to represent the quantities?

What is an equation or expression that matches the diagram, number line.., chart..., table..?

Where did you see one of the quantities in the task in your equation or expression?

How would it help to create a diagram, graph, table...?

What are some ways to visually represent...?

What formula might apply in this situation?

5. Use appropriate tools strategically.

Use available tools recognizing the strengths and limitations of each.

Use estimation and other mathematical knowledge to detect possible errors.

Identify relevant external mathematical resources to pose and solve problems.

Use technological tools to deepen their understanding of mathematics.

What mathematical tools could we use to visualize and represent this?

What information do you have?

What do you know that is not stated in the problem?

What approach are you considering trying first?

What estimate did you make for the solution?

In this situation would it be helpful to use...a graph..., number line..., ruler..., diagram..., calculator..., manipulative? Why was it helpful to use...?

What can using a ______ show us that _____may not? In what situations

6. Attend to precision.

Communicate precisely with others and try to use clear mathematical language when discussing their reasoning.

Understand the meanings of symbols used in mathematics and can label quantities appropriately.

Express numerical answers with a degree of precision appropriate for the problem context.

Calculate efficiently and accurately.

What mathematical terms apply in this situation?

How did you know your solution was reasonable?

Explain how you might show that your solution answers the problem.

What would be a more efficient strategy?

How are you showing the meaning of the quantities?

What symbols or mathematical notations are important in this problem?

What mathematical language ,definitions, properties can you use to explain?

How could you test your solution to see if it answers the problem?

Summary of Standards for Mathematical Practice Questions to Develop Mathematical Thinking

7. Look for and make use of structure. What observations do you make about...?

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Apply general mathematical rules to specific situations.

Look for the overall structure and patterns in mathematics.

See complicated things as single objects or as being composed of several objects.

What do you notice when...?

What parts of the problem might you eliminate..., simplify...?

What patterns do you find in...?

How do you know if something is a pattern?

What ideas that we have learned before were useful in solving this problem?

What are some other problems that are similar to this one?

How does this relate to...?

In what ways does this problem connect to other mathematical concepts?

8. Look for and express regularity in repeated reasoning.

See repeated calculations and look for generalizations and shortcuts.

See the overall process of the problem and still attend to the details.

Understand the broader application of patterns and see the structure in similar situations.

Continually evaluate the reasonableness of their intermediate results

Explain how this strategy work in other situations?

Is this always true, sometimes true or never true?

How would we prove that...? What do you notice about...?

What is happening in this situation? What would happen if...?

Is there a mathematical rule for...?

What predictions or generalizations can this pattern support?

What mathematical consistencies do you notice ?

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Appendix C Daily Math Routines:

The following Daily Classroom Math Routines are recommended to begin on the first day of the school year. Students build fluency and flexibility in counting, understanding place value, telling time, and representing/interpreting data through daily exposures to these concepts.

Daily Classroom Math Routines Standards Classroom Routine- Do these activities everyday during a "Calendar/Morning Math" time

or the Launch part of your Math Lesson 1.NBT.2a, b, c

Daily Routine #1: Place Value, Bundles of Ten: Keep track of the number of School Days using straws, popsicle sticks, etc. to count the schools days. Have students add one straw/stick daily, counting the total number of straws/sticks each day, initially by one's, but eventually by ten's and left over ones. As you collect 10's, bundle the straws or sticks into a bundle of 10 and discuss how 10 ones becomes one unit of ten. Demonstrate how tens and ones are represented when writing two-digit numbers. Other Activities that Support this Concept:

Bundling Straws

Days in School

http://blog.pcieducation.com/index.php/2010/03/bundles-of-straws-place-value-made-simple/

1.OA.5 1.NBT.1 1.NBT 2c 1.NBT.5 1.NBT.6

Daily Routine #2: Fluency and Patterns in Counting: Use both a number line to 120 and a 120's Chart for this routine. Teacher, or student helper, will identify a number between 1-120. Students will begin at this number and Count On a designated amount. Start Number: 34, Count On: 10- Students will say "34" then count on 35, 36, 37, 38, 39, 40, 41, 42, 43, 44. Teacher, or student helper, will keep track of the number being counted on (10) with tallies. When starting this daily routine, begin with Start Numbers less than 60 and Count On Numbers less than 10. Gradually increase both. Other Activities that Support this Concept:

Start With, Get To

Patterns in Counting

Number Line

120 Chart

Tell A Story

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The following Daily Classroom Math Routines are recommended to begin on the first day of the school year. Students build fluency and flexibility in counting, understanding place value, telling time, and representing/interpreting data through daily exposures to these concepts.

Daily Classroom Math Routines Standards Classroom Routine- Do these activities everyday during a "Calendar/Morning Math" time

or the Launch part of your Math Lesson 1.MD.4

Daily Routine #3: Surveying and Graphing: Post a daily question that students can respond to, representing their answers on graph and charts, using tallies, Xs, etc. with three categories (example: How do you get to school? On the bus, In a car, walk or bike? What is your favorite flavor of ice cream? (Chocolate, Vanilla, Other) Once all students have responded to the survey question, have students ask and answer questions to interpret the data represented on class graphs. (How many students take the bus? How many more students like chocolate ice cream than vanilla? How many students get to school either on the bus or in a car?) Other Activities that Support this Concept:

Quick Survey and Graphing

Data Interpretation

Weather Charting

1.MD.3

Daily Routine #4: Telling Time: Provide students with daily opportunities to practice reading time by posting and reviewing a daily schedule (example: 10:30 - PE, Math- 1:00-2:15). Provide students with daily opportunities to practice telling time, on both digital and analog clocks by using a Judy Clock. Ask students to set the clock hands to match a time on the Daily Schedule, or other time to the hour and half hour. Other Activities that Support this Concept

Daily Schedule

Time and Calendar

http://www.educationworld.com/a_lesson/03/lp312-01.shtml