Grade 2 Mathematics Curriculum Document

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Grade 2

Mathematics Curriculum Document

2016-2017

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Cover Page Pg. 1

Table of Contents Pg. 2

Trouble Shooting Guide Pg. 3

Best Practices in the Math Classroom Pg. 4

Problem Solving 4-Square Model Pg. 6

Problem Solving with Pictorial Modeling/ Strip Diagrams Pg. 7

Number Sense/ Number Talks Pg. 8

Year at a Glance Pg. 11

Mathematics Process Standards Pg. 12

Math Instructional Resources Pg. 13

Bundle 1: Basic Fact Strategies and Problem Solving Pg. 14

Bundle 2: Representing and Comparing Whole Numbers to 1,200 Pg. 19 Bundle 3: 2-Digit Addition and Subtraction (Strategies and Problem Solving) Pg. 28

Bundle 4: Money Pg. 35

Bundle 5: Understanding Contextual Multiplication and Division Pg. 39

Bundle 6: Data Analysis Pg. 44

Bundle 7: 3-Digit Addition and Subtraction (Strategies and Problem Solving) Pg. 50 Bundle 8: Exploring the Addition and Subtraction Algorithms and Problem Solving Pg. 57

Bundle 9: Geometry Pg. 64

Bundle 10: Fractions Pg. 70

Bundle 11: Measurement Pg. 75

Bundle 12: Personal Financial Literacy Pg. 82

Bundle 13: Extended Learning Pg. 88

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Trouble Shooting Guide

• The 2015-2016 Mathematics Curriculum Document for Grade 2 includes the following features:

• The NISD Curriculum Document is a TEKS-Based Curriculum.

• Year at a Glance Indicating Bundle Titles and Number of Days for Instruction

• Color Coding: Green- Readiness Standards, Yellow- Supporting Standards, Blue- Process Standards, Purple- ELPS, Strike-Out- Portion of TEKS not Taught in Current Bundle

• NISD Math Instructional Focus Information

• The expectation is that teachers will share additional effective resources with their campus Curriculum &

Instructional Coach for inclusion in the document.

• The NISD Curriculum Document is a working document. Additional resources and information will be added as they become available.

• **The resources included here provide teaching examples and/or meaningful learning experiences to address the District Curriculum. In order to address the TEKS to the proper depth and complexity, teachers are encouraged to use resources to the degree that they are congruent with the TEKS and

research-based best practices. Teaching using only the suggested resources does not guarantee student mastery of all standards. Teachers must use professional judgment to select among these and/or other resources to teach the district curriculum.

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NISD Math Focus

Best Practices in the Math Classroom

• Teaching for Conceptual Understanding: Math instruction should focus on developing a true understanding of the math concepts being presented in the classroom. Teachers should avoid teaching “quick tricks” for finding the right answers and instead focus on developing student understanding of the “why” behind the math. Math is not a list of arbitrary steps that need to be memorized and performed, but is, rather, a logical system full of deep connections. When students see math as a set of disconnected steps to follow they tend to hold many misconceptions, make common mistakes, and do not retain what they have learned. However, when students understand the connections they have fewer misconceptions, make less errors, and tend to retain what they have learned.

• Developing Student Understanding through the Concrete-Pictorial-Abstract Approach: When learning a new math concept, students should be taken through a 3-step process of concept development. This process is known as the Concrete-Pictorial-Abstract approach. During the concrete phase, students should participate in hands-on activities using manipulatives to develop an understanding of the concept. During the pictorial phase, students should use pictorial representations to demonstrate the math concepts. This phase often overlaps with the

concrete phase as students draw a representation of what they are doing with the manipulatives. During the abstract phase, students use symbols and/or numbers to represent the math concepts. This phase often overlaps with the pictorial phase as students explain their thinking in pictures, numbers, and words. If math concepts are only taught in the abstract level, students attain a very limited understanding of the concepts. However, when students go through the 3-step process of concept development they achieve a much deeper level of understanding.

• Developing Problem Solving Skills through Quality Problem Solving Opportunities: Students should be given opportunities to develop their problem solving skills on a daily basis. One effective approach to problem solving is the think-pair-share approach. Students should first think about and work on the problem independently. Next, students should be given the opportunity to discuss the problem with a partner or small group of other students. Finally, students should be able to share their thinking with the whole group. The teacher can choose students with different approaches to the problem to put their work under a document camera and allow them to talk through their thinking with the class. The focus of daily problem solving should always be Quality over Quantity. It is more important to spend time digging deep into one problem than to only touch the surface of multiple problems.

• Developing Problem Solving Skills through Pictorial Modeling: One of the most important components of students’ problem solving development is the ability to visualize the problem. Students should always draw a pictorial representation of the problem they are trying to solve. A pictorial model helps students to better visualize the problem in order to choose the correct actions needed to solve it. Pictorial modeling in math can be done with pictures as simple as sticks, circles, and boxes. There is no need for detailed artistic representations. One of the most effective forms of pictorial modeling is the strip diagram (or part-part-whole model in lower grades). This type of model allows students to see the relationships between the numbers in the problem in order to choose the proper operations.

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• Developing Students’ Number Sense: The development of number sense is a critical part of a student’s learning in the mathematics

classroom. The ability to reason about numbers and their relationships allows students the opportunity to think instead of just following a rote set of procedures. The standard algorithms for computation may provide students with a quick answer, but they do not allow for development of student thinking and reasoning. The standard algorithms should not be abandoned completely, but should be used as one of many ways of approaching a computation problem. It is, however, very important that students have the opportunity to develop their number sense through alternative computation strategies before learning the standard algorithm in order to prevent students from having a limited view of number relationships.

• Creating an Environment of Student Engagement: The most effective math classrooms are places in which students have chances to interact with their teacher, their classmates, and the math content. Students should be given plenty of opportunities to explore and investigate new math concepts through higher-order, rigorous, and hands-on activities. Cooperative learning opportunities are critical in order for

students to talk through what they are learning. The goal should be for the student to work harder than the teacher and for the student to do more of the talking.

• Higher Level Questioning: The key to developing student thinking is in the types of questions teachers ask their students. Teachers should strive to ask questions from the top three levels of Bloom’s Taxonomy to probe student thinking.

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NISD Math Focus

Developing Problem Solving through a 4-Square Model Approach

• The 4-square problem solving model should be used to help guide students through the problem solving process. It is important that students complete step 2 (pictorial modeling) before attempting to solve the problem abstractly (with computation). When students create a visual model for the problem they are better able to recognize the appropriate operation(s) for solving the problem.

Dragon Problem Solving

What does the question ask me? This is the picture in my mind.

This is how I solve the problem. I know I am right because...

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NISD Math Focus

Developing Problem Solving through Pictorial Modeling/ Strip Diagrams

• Visual models for addition and subtraction situations help students see relationships between quantities. In the model, students place object, then later draw dots, then later write numbers.

Joining/ Combining

There are 3 birds. 2 more fly in. How many birds in all?

?

There are 3 birds. More fly in. Then there are 5 in all. How many flew in?

5

There are some birds. 2 more fly in. Then there are 5 in all. How many were there to begin with?

5 Separating

There are 7 birds. 3 birds fly away. How many are left?

7 3 ?

There are 7 birds. Some fly away. Then 4 birds are left. How many flew away?

7 ? 4

There are some birds. 3 birds fly away. Then 4 birds are left. How many were there to begin with?

?

3 4

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NISD Math Focus

Developing Number Sense through Number Talks

What is a Number Talk?

A Number Talk is a short, ongoing daily routine that provides students with meaningful ongoing practice with computation. A Number Talk is a powerful tool for helping students develop computational fluency because the expectation is that they will use number relationships and the structures of numbers to add, subtract, multiply and divide.

Number Talks should be structured as short sessions alongside (but not necessarily directly related to) the ongoing math curriculum. It is important to keep Number Talks short, as they are not intended to replace current curriculum or take up the majority of the time spent on mathematics. In fact, teachers need to spend only 5 to 15 minutes on Number Talks. Number Talks are most effective when done every day.

A Rationale for Number Talks

http://www.mathsolutions.com/documents/9781935099116_ch1.pdf

Number Talks 6-Weeks Strategy Focus

Operation Strategies

1^st 6-Weeks Addition Doubles/Near Doubles, Making 10s, Making Landmark or Friendly Numbers, Breaking Each Number into Its Place Value (Decomposing Each Number), Compensation, Adding Up in Chunks (Decomposing One Number)

2^nd 6-Weeks Addition Doubles/Near Doubles, Making 10s, Making Landmark or Friendly Numbers, Breaking Each Number into Its Place Value (Decomposing Each Number), Compensation, Adding Up in Chunks (Decomposing One Number)

3^rd 6-Weeks Addition Doubles/Near Doubles, Making 10s, Making Landmark or Friendly Numbers, Breaking Each Number into Its Place Value (Decomposing Each Number), Compensation, Adding Up in Chunks (Decomposing One Number)

4^th 6-Weeks Addition Doubles/Near Doubles, Making 10s, Making Landmark or Friendly Numbers, Breaking Each Number into Its Place Value (Decomposing Each Number), Compensation, Adding Up in Chunks (Decomposing One Number)

5^th 6-Weeks Subtraction Adding Up, Removal/ Counting Back 6^th 6-Weeks Subtraction Adding Up, Removal/ Counting Back

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Number Talks

Addition and Subtraction Strategy Examples

Operation Strategy Example

Addition Doubles/ Near Doubles Use a known double to solve an unknown near-double 8 + 8 = 16

8 + 9 = 17 because 8 + 9 is the same as 8 + (8 + 1) or (8 + 8) + 1 8 + 7 = 15 because 8 + 7 is the same as 8 + (8 – 1) or (8 + 8) - 1 Addition Making Tens Decompose a number to make a ten

8 + 4 = 8 + (2 + 2) = (8 + 2) + 2 = 10 + 2 = 12

8 + 2 = 10 10 + 2 = 12 Addition Making Landmark or Friendly

Numbers Decompose a number to make a friendly number (usually a multiple of 10) 19 + 15 = 19 + (1 + 14) = (19 + 1) + 14= 20 + 14 = 34

19 + 1 = 20 20 + 14 = 34 Addition Breaking Each Number into Its

Place Value (Decomposing Each Number)

24 + 21

20 + 20 = 40 4 + 1 = 5 40 + 5 = 45

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Addition Compensation 18 + 23

18 + 23 +2 - 2 20 + 21 = 41

36 + 9 36 + 9 - 1 +1 35 + 10 = 45 Addition Adding Up in Chunks

(Decomposing One Number) 35 + 42 35 + 10 = 45 45 + 10 = 55 55 + 10 = 65 65 + 10 = 75 75 + 2 = 77

Subtraction Adding Up 40 – 28 = ____ or 28 + ____ = 40 28 + 2 = 30

30 + 10 = 40

28 + 12 = 40 so 40 – 28 = 12

Subtraction Removal/ Counting Back 45 – 28 45 – 10 = 35 45 – 10 = 25 25 – 5 = 20 20 – 3 = 17

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Year at a Glance

First Semester Second Semester

1^st 6-Weeks 4^th 6-Weeks

• Bundle #1- Basic Fact Strategies and Problem Solving (14 days)

• Bundle #2- Representing and Comparing Whole Numbers to 1,200 (15 days)

• Bundle #7- 3-Digit Addition and Subtraction (Strategies and Problem Solving) (14 days)

• Bundle #8- Exploring the Addition and Subtraction Algorithms and Problem Solving (10 days)

• Bundle #9- Geometry (4 days)

2^nd 6-Weeks 5^th 6-Weeks

• Bundle #2 (cont.)- Representing and Comparing Whole Numbers to 1,200 (4 days)

• Bundle #3- 2-Digit Addition and Subtraction (Strategies and Problem Solving (15 days)

• Bundle #4- Money (10 days)

• Bundle #9 (cont.)- Geometry (10 days)

• Bundle #10- Fractions (15 days)

• Bundle #11- Measurement (8 days)

3^rd 6-Weeks 6^th 6-Weeks

• Bundle #4 (cont.)- Money (5 days)

• Bundle #5- Understanding Contextual Multiplication and Division (15 days)

• Bundle #6- Data Analysis (9 days)

• Bundle #11 (cont.)- Measurement (10 days)

• Bundle #12- Personal Financial Literacy (10 days)

• Bundle #13- Extended Learning (8 days)

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Mathematical Process Standards

• Process standards MUST be integrated within EACH bundle to ensure the success of students.

2.1A 2.1B 2.1C 2.1D 2.1E 2.1F 2.1G

apply

mathematics to problems arising in everyday life, society, and the workplace

use a problem- solving model that

incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem- solving

process and the reasonableness of the solution

select

tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math,

estimation, and number sense as appropriate, to solve problems

communicate mathematical ideas,

reasoning, and their

implications using multiple representations, including symbols,

diagrams, graphs, and language as appropriate

create and use representations to organize, record, and communicate mathematical ideas

analyze mathematical relationships to connect and communicate mathematical ideas

display, explain, and

justify mathematical ideas and

arguments using precise

mathematical language in written or oral communication

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Math Instructional Resources

Resource Print/Online Description

EnVision Both Textbook Adoption

https://www.pearsontexas.com/#/

Motivation Math Both Supplemental Curriculum

https://www.mentoringminds.com/customer/account/login/

Engaging Mathematics Print Collection of Mini-Lessons for All TEKS from Region IV http://www.region4store.com/catalog.aspx?catid=1171582

Thinking Blocks Online Online Problem Solving Practice with Strip Diagrams http://www.mathplayground.com/thinkingblocks.html

2^nd Grade Math Games Print Collection of Engaging and Low-Prep Math Games for Skill Practice http://maccss.ncdpi.wikispaces.net/file/view/2ndgrade_GAMES.pdf/522022874/2ndgrade_GAMES.pdf

Epic! For Educators Online Search for Literature Connections for Math Content https://www.getepic.com/educators

Number Talks (Sherry Parrish) Print Develop Number Sense Through a Daily Number Talk Routine Lessons for Learning (North Carolina) Print Collection of Engaging and Rigorous Math Lessons

http://maccss.ncdpi.wikispaces.net/file/view/CCSSMathTasks-Grade2.pdf/464833262/CCSSMathTasks-Grade2.pdf Math Learning Center (Bridges) Print Collection of Engaging and Rigorous Math Lessons http://catalog.mathlearningcenter.org/catalog/supplemental-materials-elementary/lessons-activities-grade-2-free

NCTM Illuminations Online Search for Engaging and Rigorous Math Lessons by Grade and Topic http://illuminations.nctm.org/

Math Coach’s Corner Online Math Blog from a Master Texas Math Teacher, Coach, and Consultant http://www.mathcoachscorner.com/

Promethean Planet Online Tools and Lessons for Interactive Whiteboard http://www.prometheanplanet.com/en-us/

Interactive Math Glossary Online TEA Interactive Math Glossary http://www.texasgateway.org/resource/interactive-math-

glossary?field_resource_keywords_tid=math%20teks&sort_by=title&sort_order=ASC&items_per_page=5 TEKS Information for Teachers

TEA Math Resources Online TEA Supporting Information for Math TEKS

http://tea.texas.gov/Curriculum_and_Instructional_Programs/Subject_Areas/Mathematics/Resources_for_the_Revised_Mathematics_TEKS/

Lead4Ward Resources Online Math TEKS Instructional Resources and Supporting Information http://lead4ward.com/resources/

TEKS Resource System Online Math TEKS Instructional Resources and Supporting Information http://www.teksresourcesystem.net/module/profile/Account/LogOn

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Course: Grade 2 Math Bundle 1: Basic Fact Strategies and Problem Solving

Dates: August 22^nd -September 9^th (14 days)

TEKS 2.4A: recall basic facts to add and subtract within 20 with automaticity

2.7C: represent and solve addition and subtraction word problems where unknowns may be any one of the terms in the problem ELPS

Learning Strategies

1A: use prior knowledge and experiences to understand meanings in English

1B: monitor oral and written language production and employ self-corrective techniques or other resources Listening

2C: learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions

2I: demonstrate listening comprehension of increasingly complex spoken English by following directions, retelling or summarizing spoken messages, responding to questions and requests, collaborating with peers, and taking notes commensurate with content and grade-level needs

Speaking

3B: expand and internalize initial English vocabulary by learning and using high-frequency English words necessary for identifying and describing people, places, and objects, by retelling simple stories and basic information represented or supported by pictures, and by learning and using routine language needed for classroom communication

3C: speak using a variety of grammatical structures, sentence lengths, sentence types, and connecting words with increasing accuracy and ease as more English is acquired

3D: speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency

Reading

4D: use pre-reading supports such as graphic organizers, illustrations, and pre-taught topic-related vocabulary and other pre-reading activities to enhance comprehension of written text

4E: read linguistically accommodated content area material with a decreasing need for linguistic accommodations as more English is learned

4F: use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language

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Vocabulary Unit Vocabulary

Add/addition Difference Number sentence Sum Unknown

Basic facts Equation Subtract/subtraction Term

Cognitive Complexity Verbs: recall, represent Academic Vocabulary by Standard:

2.4A: add, basic facts, difference, subtract, sum

2.7C: addition, difference, number sentence, equation, subtraction, sum, term, unknown Suggested Math Manipulatives

Cuisenaire Rods Dice Dominoes Hundreds Chart Part/Whole Mat

Number Lines Counters Rekenreks Ten Frames Snap Cubes

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Bundle 1: Vertical Alignment

1.3D apply basic fact strategies to add and subtract within 20, including making 10 and decomposing a number leading to a 10

2.4A: recall basic facts to add and subtract within 20 with automaticity

3.4A solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction 4.4A add and subtract whole numbers and decimals to the hundredths place using the standard algorithm

1.5D represent word problems involving addition and subtraction of whole numbers up to 20 using concrete and pictorial models and number sentences

1.5E understand that the equal sign represents a

relationship where expressions on each side of the equal sign represent the same value(s)

1.5F determine the unknown whole number in an addition or subtraction equation when the unknown may be any one of the three or four terms in the equation

2.7C: represent and solve addition and subtraction word problems where unknowns may be any one of the terms in the problem

3.5A represent one- and two-step problems involving addition and subtraction of whole numbers to 1,000 using pictorial models, number lines, and equations

4.5A represent multi-step problems involving the four operations with whole numbers using strip diagrams and equations with a letter standing for the unknown quantity

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Bundle 1: Teacher Notes TEKS/Student

Expectations

Instructional Implications Distractor Factors Supporting Readiness Standards

TEA Supporting Information

2.4A: recall basic facts to add and subtract within 20 with automaticity

In conjunction with 1.3D, students will continue to apply the following strategies to recall basic facts:

Addition:

- Make Ten with the use of two tens frames as a model

(i.e. 9 + 8 = ___; can be rewritten as

9 + 1 + 7 = ___; 10 + 7 = 17)

- Make Ten with the use of an open number line

(i.e. 9 + 8 = ___; 9 + 1 + 7 = ___; 10 + 7 = ___;

10 + 7 = 17)

- Doubles: (i.e. 6 + 8 = 6 + 6 + 2 = ___; 12 + 2 = ___; 12 + 2 = 14)

- Count On: (i.e. 3 + 8 = ___; 8, 9, 10, 11; 3 + 8

= 11) Subtraction:

- Think Addition/ Count One: (i.e. 12 – 9 = ___;

9 + ___ = 12; 9 + 3 = 12).

- Make Ten: (i.e. 12 – 9 = 12 – 2 – 7 = 10 – 7 = 3).

- Compensation (i.e. 12 – 9 = 12 - 10 + 1 = 2 + 1

= 3).

Efficiency and accuracy with basic addition/subtraction facts will be a critical foundation for students to be able to solve multi-step addition and subtraction problems using place value strategies.

2.2D: use place value to compare and order whole numbers up to 1,200 using comparative language, numbers, and symbols (>, <, or =)

2.4C: solve one-step

and multi-step word problems involving addition and subtraction within 1,000 using a variety of strategies based on place

value, including algorithms

The level of skill with

“automaticity” requires quick recall of basic facts within 20 with speed and accuracy at an unconscious level.

Automaticity is part of

procedural fluency and, as such, should not be overly emphasized as an isolated skill.

Automaticity with basic addition and subtraction facts allows students to explore richer applications of addition and subtraction.

When paired with 2.1A, students may be expected to apply these basic facts.

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- Count Back: (i.e. 12 – 3 = ___; 12, 11, 10, 9;

12 – 3 = 9)

In adherence to this grade level standard, students will continue to practice using these strategies in order to recall their basic facts with automaticity.

2.7C: represent and solve addition and subtraction word problems where unknowns may be any one of the terms in the problem

In conjunction with 2.4, students continue to demonstrate their understanding of addition and subtraction with the appropriate number sentence. Instruction should vary the context of +/- type problems provided to students (see 2.4C for examples). In adherence to the standard, students should represent the same word problem with a variety of number sentences (i.e. 17 + 18 = ___; 18 + 17 = ___;

___ = 18 + 17; ___ = 17 + 18); (i.e. 42 – 16 = ___; ___ = 42 – 16; 16 + ___ = 42; 42 = ___ + 16).

Relating addition and subtraction number

sentences/equations supports a student’s ability to represent and solve addition and subtraction problems.

2.4D: generate and

solve problem situations for a given mathematical number sentence involving addition and subtraction of whole numbers within 1,000

When paired with 2.1C and 2.1D, the students are expected to represent problems with objects, manipulatives, diagrams, language, and number. Students may be expected to solve problems using number sense, mental math, and algorithms based on place value and properties of operations.

For example, Jasmine has 87 books. She has some paperback books and 39 hardback books.

How many paperback books does Jasmine have?

Represent: 87 = { } + 39

Solve: 87 = 40 + 40 + 7 = 39 + (1 + 40 + 7) = 39 + 48

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Course: Grade 2 Math Bundle 2: Representing and Comparing Whole Numbers to 1,200

Dates: September 12^th-October 7^th (19 days) TEKS

2.2A: use concrete and pictorial models to compose and decompose numbers up to 1,200 in more than one way as a sum of so many thousands, hundreds, tens, and ones

2.2B: use standard, word, and expanded forms to represent numbers up to 1,200

2.2C: generate a number that is greater than or less than a given whole number up to 1,200

2.2D: use place value to compare and order whole numbers up to 1,200 using comparative language, numbers, and symbols (>, <, or =) 2.2E: locate the position of a given whole number on an open number line

2.2F: name the whole number that corresponds to a specific point on a number line

2.7A: determine whether a number up to 40 is even or odd using pairings of objects to represent the number

2.7B: use an understanding of place value to determine the number that is 10 or 100 more or less than a given number up to 1,200 2.9C: represent whole numbers as distances from any given location on a number line

ELPS

1A: use prior knowledge and experiences to understand meanings in English

1D: speak using learning strategies such as requesting assistance, employing non-verbal cues, and using synonyms and circumlocution (conveying ideas by defining or describing when exact English words are not known)

1F: use accessible language and learn new and essential language in the process Listening

2C: learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions 2D: monitor understanding of spoken language during classroom instruction and interactions and seek clarification as needed

Speaking

3D: speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency

3F: ask and give information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments 3G: express opinions, ideas, and feelings ranging from communicating single words and short phrases to participating in extended discussions on a variety of

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social and grade-appropriate academic topics Reading

4C: develop basic sight vocabulary, derive meaning of environmental print, and comprehend English vocabulary and language structures used routinely in written classroom materials

4G: demonstrate comprehension of increasingly complex English by participating in shared reading, retelling or summarizing material, responding to questions, and taking notes commensurate with content area and grade level needs

10 less Equal to (=) Hyphen Ones Standard form

10 more Even Least to greatest Open number line Tens

100 less Expanded form Less than (<) Pairing Thousands

100 more Greater than (>) Location Period Whole numbers

Digit Greatest to least Number line Place value Word form

Distance Hundreds Odd

Cognitive Complexity Verbs: use, compose, decompose, represent, generate, compare, order, locate, name, determine Academic Vocabulary by Standard:

2.2A: digit, place value, thousands, hundreds, tens, ones

2.2B: digit, expanded form, hyphen, period, place value, thousands, hundreds, tens, ones, standard form, word form 2.2C: digit, greater than, less than, equal to, place value, value of a number

2.2D: digit, equal to (=), greater than (>), greatest to least, less than (<), least to greatest, place value, thousands, hundreds, tens, ones 2.2E: open number line, place value, whole numbers

2.2F: number line, place value, whole numbers 2.7A: even, odd, pairing

2.7B: place value, ten more, ten less, 100 more, 100 less 2.9C: distance, location, number line, place value, whole numbers

Suggested Math Manipulatives

Base 10 Blocks Place Value Disks Place Value Chart Hundreds Chart

Counters Snap Cubes Number Lines

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Bundle 2: Vertical Alignment K.2I compose and decompose numbers up to 10 with

objects and pictures

1.2B use concrete and pictorial models to compose and decompose numbers up to 120 in more than one way as so many hundreds, so many tens, and so many ones

2.2A: use concrete and pictorial models to compose and decompose numbers up to 1,200 in more than one way as a sum of so many thousands, hundreds, tens, and ones

3.2A compose and decompose numbers up to 100,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens, and so many ones using objects, pictorial models, and numbers, including expanded notation as appropriate

4.2B represent the value of the digit in whole numbers through 1,000,000,000 and decimals to the hundredths using expanded notation and numerals

1.2C use objects, pictures, and expanded and standard forms to represent numbers up to 120

2.2B: use standard, word, and expanded forms to represent numbers up to 1,200

3.2A compose and decompose numbers up to 100,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens, and so many ones using objects, pictorial models, and numbers, including expanded notation as appropriate

4.2B represent the value of the digit in whole numbers through 1,000,000,000 and decimals to the hundredths using expanded notation and numerals

K.2F generate a number that is one more than or one less than another number up to at least 20

1.2D generate a number that is greater than or less than a given whole number up to 120

K.2G compare sets of objects up to at least 20 in each set using comparative language

K.2H use comparative language to describe two numbers up to 20 presented as written numerals

1.2E use place value to compare whole numbers up to 120 using comparative language

1.2F order whole numbers up to 120 using place value and open number lines

1.2G represent the comparison of two numbers to 100 using the symbols >,

3.2D compare and order whole numbers up to 100,000 and represent comparisons using the symbols >,<,=

4.2C compare and order whole numbers to 1,000,000,000 and represent comparisons using the symbols >,<,=

4.2F compare and order decimals using concrete and visual models to the hundredths

1.2F order whole numbers up to 120 using place value and open number lines

2.2E: locate the position of a given whole number on an open number line

3.2C represent a number on a number line as being between two consecutive multiples of 10; 100; 1,000; or 10,000 and use words to describe relative size of numbers in order to round whole numbers

3.3A represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using concrete objects and pictorial models, including strip diagrams and number lines.

3.3B determine the corresponding fraction greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 given a specified point on a number line 4.2G represent fractions and decimals to the tenths or

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hundredths as distances from zero on a number line 4.2H determine the corresponding decimal to the tenths or hundredths place of a specified point on a number line 1.2F order whole numbers up to 120 using place value

and open number lines

3.2C represent a number on a number line as being between two consecutive multiples of 10; 100; 1,000; or 10,000 and use words to describe relative size of numbers in order to round whole numbers

3.3A represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using concrete objects and pictorial models, including strip diagrams and number lines.

3.3B determine the corresponding fraction greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 given a specified point on a number line 4.2G represent fractions and decimals to the tenths or hundredths as distances from zero on a number line 4.2H determine the corresponding decimal to the tenths or hundredths place of a specified point on a number line 1.5B skip count by twos, fives, and tens to determine the

total number of objects up to 120 in a set

2.7A: determine whether a number up to 40 is even or odd using pairings of objects to represent the number 1.5C use relationships to determine the number that is 10

more and 10 less than a given number up to 120

2.7B: use an understanding of place value to determine the number that is 10 or 100 more or less than a given number up to 1,200

2.9C: represent whole numbers as distances from any given location on a number line

3.7A represent fractions of halves, fourths, and eighths as distances from zero on a number line

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Bundle 2: Teacher Notes TEKS/Student

Expectations

Instructional Implications Distractor Factors Supporting Readiness Standards

TEA Supporting Information

2.2A: use concrete and pictorial models to compose

and decompose

numbers up to 1,200 in more than one way as a sum of so

many thousands, hundreds, tens, and ones

Through the use of base 10 blocks, students will begin to visually understand the magnitude of numbers (i.e. the thousand cube is ten times more than the hundred flat; the hundred flat is ten times more than the ten rod; the hundred flat is ten times smaller than the thousand cube, the ten rod is ten times smaller than the hundred flat, etc.). Students need to understand that the digit in the number represents its place value which is different from the value of the number (i.e. the number 259 can be represented as 5 hundreds, 8 tens, 9 ones or 4 hundreds, 18 tens, and 9 ones, or 5 hundreds, 7 tens, and 19 ones, etc.). This understanding will lend itself to regrouping in subtraction (i.e. 589 – 192 = ___; 589 would have to be regrouped into 4 hundreds, 18 tens, and 9 ones).

The use of concrete objects (base 10 blocks) and pictorial models to represent numbers through 1,200 will support students’ conceptual understanding of the magnitude of numbers and the relationship between the place values. This knowledge will extend to relating those visual representations to expanded notation, supporting the comparing/

ordering of numbers, and developing addition/

subtraction place value algorithms.

2.2B: use standard, word, and expanded forms

to represent numbers up to 1,200

Specificity for

representations is included with the use of concrete and pictorial models to compose and decompose numbers.

Specificity is included with

“sum of so many thousands, hundreds, tens, and ones.” It may include decomposing 787 into 7 hundreds, 8 tens, and 7 ones. It may also include decomposing 787 into the sum of 500, 200, 50, 30, and 7 to prepare for work with compatible numbers when adding whole numbers with fluency.

Students are expected to compose and decompose numbers up to 1,200.

Students are expected to use pictorial models in addition to concrete models.

2.2B: use standard, word, and expanded forms

to represent numbers up to 1,200

As students begin representing numbers through 1,200 using base ten blocks (see 2.2A), their understanding should also be associated with writing numbers in standard form (827), word form (eight hundred twenty-seven), and expanded form (i.e. 827 = 800 + 20 + 7). This type of

representation will allow students to focus on the value of each digit and support the understanding of the place value system (i.e. eight flats represent the value 800; two ten rods represent the value of 20;

seven unit cubes represent the value of 7; 800 + 20 + 7 = 827). AS grade 2 introduces the thousands period, it will be essential to explain the use of the comma to separate the periods (i.e. 1,243: the comma separates the hundreds period from the

* Students may incorrectly use the word “and” to represent numbers in words (i.e. 345 is represented as

“three hundred forty-five,”

not “three hundred and forty-five). The use of the word “and” is applied in the representations of whole number and decimal values (i.e. 3.45 is

represented as “three and forty-five hundredths).

* Students may not use the

Specificity is included for what is to be represented (read, written, and

described): “standard, word, and expanded forms” to indicate place value.

Students are expected to represent numbers up to 1,200.

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thousands period). In representing numbers in word form, be sure to emphasize the correct use of the hyphen (i.e. twenty-three).

hyphen appropriately when representing numbers in words (i.e. 345 is represented as “three hundred forty-five”).

* Students confuse the place value a digit is in with its value (i.e. 345; the digit 4 is in the tens place value but it is valued at 40).

* Students may confuse the term digit and number.

Standard Form

787 Word

Form

Seven hundred eighty- seven Expanded

Form

700 + 80 + 7

As students become more knowledgeable with their use of the place value system in using base- ten blocks (2.2A) and expanded notation (2.2B), instruction should include students generating a number “greater than” or “less than” a given whole number. Students should be able to explain that the position of each digit in a numeral determines the quantity of a given number (i.e. given the number 437, students understand that the digit four represents the number of hundred flats and its value 400; the digit three represents the number of ten rods and its value 30). This explanation is important to ask of children before they begin abstractly

comparing two given numbers (2.2D) so students can demonstrate understanding of place value.

Generating a number greater than or less than a given whole number will allow students to focus on the value of various digits in a number before moving to the abstract use of comparison symbols (<, >, =).

This SE extends K.2F where students are expected to generate a number that is one more or one less than another number up to 20 and 1.5C where students are expected to determine the number that is 10 more and 10 less than a given number up to 120.

As students compare the value of numbers, they need to be able to relate their understanding of place value (i.e. the number 342 is greater than 226 because the digit 3 in 342 means there are 3 hundreds which is a value of 300. However, the digit 2 in 226 means there are only 2 hundreds and has a value of 200). Using expanded notation 300 + 40 + 2 is greater than 200 + 20 + 6.

Students will compare two numbers using the correct academic vocabulary (i.e. 342 is greater than 226). It is important for students to recognize the inverse comparison statement as well (i.e. 226 is less than 342). The use of the comparative language is critical before moving

* Students who rely on a trick to determine the direction of an inequality sign may not be able to read comparison symbols correctly.

* Students may view a comparison statement and its inverse as two different comparison statements (i.e. 456 > 412 is the same as 412 < 456).

Students are expected to compare and order numbers up to 1,200.

Comparative language includes greater than, less than, and equal to.

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to the symbolic representation. It is important for students to recognize how their language can be communicated using symbols (<, >, =). It is critical that students do not learn how to read each of the symbols using a tricks to remember directionality of the symbols (i.e. the alligator’s mouth eats the bigger number). Encourage students to write and articulate two comparison statements during activities (i.e. 342 > 226 and 226 < 342). The standard also has students ordering three or more numbers from least to greatest or greatest to least. The use of open number lines (see 2.2E/F) will allow students to order more efficiently. The increase in the value of numbers from left to right on a number line can be associated to ordering from least to greatest; numbers decrease from right to left on a number line can be associated to ordering from greatest to least.

* Students confuse the place value a digit is in with its value (i.e. 345;

the digit 4 is in the tens place value, but it is valued at 40).

* Students may confuse the term digit and number.

2.2E: locate the position of a given whole number on an open number line

An open number line does not have landmark numbers earmarked, does not have to begin at zero, and should include the use of arrows on both ends of the number line to indicate that the numbers continue beyond what is marked.

Students will apply their understanding of the place value system in relation to the relative position on an open number line (i.e. the number 352 would fall between 350 and 360 on a number line as 352 is expressed as 300 + 50 + 2 or the number 352 is 3 hundreds, 5 tens, and 2 ones). As students are given a specific number to locate on an open number line, you will begin to assess students’ understanding of place value (i.e. students place the number 352 between 350 and 360), the relative position of numbers (i.e. the number 350 would be indicated first and the number 360 would be indicated second on the open number line), and the magnitude of numbers (i.e. students would physically place the number 352 closer to 350 than 360).

Students can use number lines to compare/ order numbers and develop their understanding of place value, the relative position of numbers, and magnitude of numbers. The use of this tool is a critical support mechanism.

2.2D: use place value to compare and order whole numbers up to 1,200 using comparative language, numbers, and symbols (>, <, or

=)

This SE extends 1.2F where students are expected to order whole numbers up to 120 using place value.

The use of an open number line as a representation allows for the consideration of the magnitude of numbers and the place-value relationships among numbers when locating a given whole number.

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In contrast to 2.2E, specific numbers are already marked on this number line, did not have to begin at zero, and include the use of arrows on both ends of the number line to indicate how the numbers continue beyond what is marked.

Students will be provided a specific location identified on a given number line and asked to name the whole number representing its value. In conjunction with 2.2E, this activity will allow you to assess students’ understanding of place value, the relative position of number and the magnitude of numbers.

As a number line is used as a strategy to compare/order numbers and develops a student’s understanding of place value, the relative position of numbers, and the magnitude of numbers, the use of this tool will be a critical support mechanism.

2.2D: use place value to compare and order whole numbers up to 1,200 using comparative language, numbers, and symbols (>, <, or

=)

This SE and 2.9C are introductory skills that build to the various number line skills in grade 3, including 3.2C, 3.3B, and 3.3F.

2.7A: determine whether a number up to 40 is even or odd using pairings of objects to represent the number

In order to adhere to the standard, students should be provided a set of objects to group in pairs to determine if a number is even or odd. As students begin pairing objects, instruction should relate this concept to the double facts (i.e. 18 is even as there are 9 groups of pairs (2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 18); 15 is odd as there are 7 groups of pairs with one left over (2 + 2 + 2 + 2 + 2 + 2 + 2 + 1 = 15).

As students solve problems using all operations, developing patterns with even and odd solutions can support students with their computational fluency and accuracy (i.e. odd + odd = even; even + odd = odd; odd – odd = even; odd – even = odd).

This SE provides a foundation for 3.4I.

2.7B: use an understanding of place value to determine the number that is 10 or 100 more or less than a given number up to 1,200

In order to adhere to the standard, students must be able to determine 10 more/ 10 less or 100 more/

100 less (i.e. using your 100s chart, what is 10 more than 23 or what is 10 less than 45?) As students move down a row to model ten more than a number, they should begin relating how the digit in the tens place is increasing by one each move down a row in a column. As students move up a row in a column to model 10 less than a number, they should begin relating how the digit in the tens place is decreasing with each move up a row. As students become more proficient with addition/subtraction of ten, instruction can extend to 100 more/ 100 less. In accordance with the TEKS, students also need to connect their findings through the use of properties of numbers and operations (i.e. Ten more than 234 is 244 because 234 + 10 = ___; 200 + 30 + 4 + 10 = ___; 200 + 30 + 10 + 4 = 200 + 40 + 4 = 244).

Students will begin identifying patterns in determining 10 or 100 more/less than a given number. Recognizing the change in the digits will reinforce tens and hundreds place value. This standard will reinforce place value in support of comparing and ordering whole numbers.

2.2D use place value to compare and order whole numbers up to 1,200 using comparative language, numbers, and symbols (<, >, or =)

This SE provides a foundation for 2.2D and builds upon 1.5C.

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2.9C: represent whole numbers as distances from any given

location on a number line

Students will locate and name points on a number line (see 2.2E/F). Instruction needs to address that whole numbers identified on a number line represent the distance away from zero. This understanding will then be related to the use of the ruler and how the whole numbers identified on a ruler represent a measureable length (see 2.9D). In conjunction with 2.4B/C, instruction could extend the use of a number line in adding and subtracting two-digit numbers (i.e.

39 + ___ = 72).

Identifying whole numbers as distances from any given location can relate to the effective use of a ruler. This understanding will support the solving of problems involving length. Being able to represent whole number on a number line will support the comparing and ordering of numbers as larger numbers progress to the right and smaller numbers progress to the left of a number line. The understanding of whole numbers as distances from a given location will support the use of a number line as a strategy to add and subtract numbers.

2.2D use place value to compare and order whole numbers up to 1,200 using comparative language,

numbers, and symbols (<, >, =) 2.9E determine a solution to a problem involving length, including estimating lengths

This SE has added number lines as a representation of distance (length). This allows connections to linear measurement in 2.9D.

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Course: Grade 2 Math Bundle 3: 2-Digit Addition and Subtraction (Strategies and Problem Solving)

Dates: October 10^th-October 28^th (15 days) TEKS

2.4B: add up to four two-digit numbers and subtract two-digit numbers using mental strategies and algorithms based on knowledge of place value and properties of operations (algorithms will be introduced in Bundle 8)

2.4C: solve one-step and multi-step word problems involving addition and subtraction within 1,000 using a variety of strategies based on place value, including algorithms (algorithms will be introduced in Bundle 8)(3-digit addition and subtraction will be introduced in Bundle 7) 2.4D: generate and solve problem situations for a given mathematical number sentence involving addition and subtraction of whole numbers within 1,000 (3-digit addition and subtraction will be introduced in Bundle 7)

2.7C: represent and solve addition and subtraction word problems where unknowns may be any one of the terms in the problem ELPS

1A: use prior knowledge and experiences to understand meanings in English 1F: use accessible language and learn new and essential language in the process Listening

2C: learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions 2D: monitor understanding of spoken language during classroom instruction and interactions and seek clarification as needed

2I: demonstrate listening comprehension of increasingly complex spoken English by following directions, retelling or summarizing spoken messages, responding to questions and requests, collaborating with peers, and taking notes commensurate with content and grade-level needs

Speaking

3D: speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency 3F: ask and give information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and

expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments

3G: express opinions, ideas, and feelings ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics

3H: narrate, describe, and explain with increasing specificity and detail as more English is acquired Reading

4C: develop basic sight vocabulary, derive meaning of environmental print, and comprehend English vocabulary and language structures used routinely in written classroom materials

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4D: use pre-reading supports such as graphic organizers, illustrations, and pre-taught topic-related vocabulary and other pre-reading activities to enhance comprehension of written text

4G: demonstrate comprehension of increasingly complex English by participating in shared reading, retelling or summarizing material, responding to questions, and taking notes commensurate with content area and grade level needs

Addition Number sentence Properties of numbers Subtraction Term

Difference Place value Strategies Sum Unknown

Equation

Cognitive Complexity Verbs: add, subtract, use, solve, generate, represent Academic Vocabulary by Standard:

2.4B: addition, difference, place value, properties of numbers, subtraction, sum 2.4C: addition, difference, place value, strategies, subtraction, sum

2.4D: addition, difference, equation, number sentence, subtraction, sum

2.7C: addition, difference, number sentence, equation, subtraction, sum, term, unknown Suggested Math Manipulatives

Base 10 Blocks Place Value Disks Place Value Chart Hundreds Chart

Counters Snap Cubes Number Lines