Kindergarten Mathematics Curriculum Document 2016-2017

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Kindergarten Mathematics Curriculum Document

2016-2017

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Table of Contents Cover Page Pg. 1 Table of Contents Pg. 2 Trouble Shooting Guide Pg. 3 Best Practices in the Math Classroom Pg. 4 Problem Solving with Pictorial Modeling/ Strip Diagrams Pg. 6 Number Sense/ Number Talks Pg. 8 Year at a Glance Pg. 10 Mathematics Process Standards Pg. 11 Math Instructional Resources Pg. 12 Bundle 1: Representing and Comparing Whole Numbers 0-10 Pg. 13 Bundle 2: Representing and Comparing Whole Numbers 11-20 Pg. 22 Bundle 3: Addition and Subtraction Pg. 31 Bundle 4: Geometry Pg. 36 Bundle 5: Measurement and Expanded Addition and Subtraction Pg. 42 Bundle 6: Data Analysis and Personal Financial Literacy Pg. 48

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Trouble Shooting Guide

• The 2015-2016 Mathematics Curriculum Document for Kinder 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.

• **Theresourcesincludedhereprovideteachingexamplesand/ormeaningfullearningexperiencestoaddresstheDistrictCurriculum.InordertoaddresstheTEKStotheproperdepthandcomplexity,teachersareencouragedtouseresourcestothedegreethattheyarecongruentwiththeTEKSandresearch-basedbestpractices.Teachingusingonlythesuggestedresourcesdoesnotguaranteestudentmasteryofallstandards.Teachersmustuseprofessionaljudgmenttoselectamongtheseand/orotherresourcestoteachthedistrictcurriculum.

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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 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.

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

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

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

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

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

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

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Part/Whole Mat

Whole

Part

Part

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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

Kinder Number Talks will focus on composing and decomposing numbers 3-10. Teachers should provide students with opportunities to explore these numbers through dot images, rekenreks, and 5- and 10- frames. For the first half of the year, teachers should focus on one number for 1-3 weeks at a time. Once all numbers have been explored, teachers should spend the remainder of the year building on students’ fluency with composing and decomposing numbers 3-10. Below are samples of Number Talks for the number 7 using dot images, rekenreks, and 5- and 10- frames. Dot Images Ask: “How many dots do you see?” “How do you see them?”

Some students may see this as 4 and 3. Other students may see this as 2, 2, 2, and 1. Others may see 3, 3, and 1. All represent different ways of composing and decomposing 7.

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Rekenreks Ask: “How many beads do you see?” “How do you see them?” Show a rekenrek with 5 on top and 2 on bottom. Students should see 7 beads made up of 5 and 2. 10-Frames Ask: “How many dots do you see?” “How do you see them?”

Students should see 7 dots. 3 on top and 4 on bottom.

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Year at a Glance

First Semester Second Semester 1st 6-Weeks 4th 6-Weeks

• Bundle #1- Representing and Comparing Whole Numbers 0-10 (29 days)

• Bundle #4- Geometry (28days)

2nd 6-Weeks 5th 6-Weeks • Bundle #2- Representing and Comparing Whole Numbers 11-20

(30 days)

• Bundle # 5- Measurement and Expanded Addition and Subtraction (33 days)

3rd 6-Weeks 6th 6-Weeks

• Bundle #3- Addition and Subtraction (29 days)

• Bundle #6- Data Analysis and Personal Financial Literacy (28 days)

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

K.1A K.1B K.1C K.1D K.1E K.1F K.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/#/ Thinking Blocks Online Online Problem Solving Practice with Strip Diagrams http://www.mathplayground.com/thinkingblocks.html Kinder Grade Math Games Print Collection of Engaging and Low-Prep Math Games for Skill Practice http://maccss.ncdpi.wikispaces.net/file/view/Kgrade_GAMES.pdf/522022884/Kgrade_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-Kindergarten.pdf/466936720/CCSSMathTasks-Kindergarten.pdf Math Learning Center (Bridges) Print Collection of Engaging and Rigorous Math Lessons http://catalog.mathlearningcenter.org/catalog/supplemental-materials-elementary/lessons-activities-grade-k-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: Kinder Math Bundle 1: Representing and Comparing Whole Numbers 0-10

Dates: August 22nd- September 30th (29 days)

TEKS

K.2A: count forward and backward to at least 20 with and without objects (numbers 0-10 only) K.2B: read, write, and represent whole numbers from 0 to at least 20 with and without objects or pictures (numbers 0-10 only) K.2C: count a set of objects up to at least 20 and demonstrate that the last number said tells the number of objects in the set regardless of their arrangement or order (numbers 0-10 only) K.2D: recognize instantly the quantity of a small group of objects in organized and random arrangements K.2E: generate a set using concrete and pictorial models that represents a number that is more than, less than, and equal to a given number up to 20 (numbers 0-10 only) K.2F: generate a number that is one more than or one less than another number up to at least 20 (numbers 0-10 only) K.2G: compare sets of objects up to at least 20 in each set using comparative language (numbers 0-10 only) K.2H: use comparative language to describe two numbers up to 20 presented as written numerals (numbers 0-10 only) K.2I: compose and decompose numbers up to 10 with objects and pictures (numbers 0-10 only) K.5: The student applies mathematical process standards to identify the pattern in the number word list. The student is expected to recite numbers up to at least 100 by ones and tens beginning with any given number.

ELPS

Learning Strategies 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 2E: use visual, contextual, and linguistic support to enhance and confirm understanding of increasingly complex and elaborated spoken language 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

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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 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 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

Vocabulary

Unit Vocabulary Backward Decompose More than Compare Equal to Numbers 0-10 Compose Forward Ones Counting words Greater than Tens Counting words 0-100 Less than

Cognitive Complexity Verbs: count, read, write, represent, demonstrate, recognize, generate, compare, use, compose, decompose, recite Academic Vocabulary by Standard: K.2A: backward, forward, numbers 0-10 (oral and written representations) K.2B: numbers 0-10 (oral and written representations) K.2C: numbers 0-10 (oral and written representations) K.2D: counting words K.2E: equal to, less than, more than K.2F: less than, more than K.2G: compare, equal to, greater than, less than, more than K.2H: equal to, greater than, less than, more than K.2I: compose, decompose K.5: counting words 0-100, ones, tens

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Suggested Math Manipulatives Ten Frames/ Double Ten Frames 2-Color Counters Rekenreks 100s Chart Number Lines Snap Cubes Dot Images Counters Color Tiles

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Bundle 1: Vertical Alignment

K.2A: count forward and backward to at least 20 with and without objects (numbers 0-10 only)

K.2B: read, write, and represent whole numbers from 0 to at least 20 with and without objects or pictures (numbers 0-10 only)

K.2C: count a set of objects up to at least 20 and demonstrate that the last number said tells the number of objects in the set regardless of their arrangement or order (numbers 0-10 only)

K.2D: recognize instantly the quantity of a small group of objects in organized and random arrangements

1.2A recognize instantly the quantity of structured arrangements

K.2E: generate a set using concrete and pictorial models that represents a number that is more than, less than, and equal to a given number up to 20 (numbers 0-10 only)

K.2F: generate a number that is one more than or one less than another number up to at least 20 (numbers 0-10 only)

1.2D generate a number that is greater than or less than a given whole number up to 120 2.2C generate a number that is greater than or less than a given whole number up to 1,200

K.2G: compare sets of objects up to at least 20 in each set using comparative language (numbers 0-10 only)

1.2E use place value to compare whole numbers up to 120 using comparative language 2.2D use place value to compare and order whole numbers up to 1,200 using comparative language, numbers, and symbols (>,<,=)

K.2H: use comparative language to describe two numbers up to 20 presented as written numerals (numbers 0-10 only)


K.2I: compose and decompose numbers up to 10 with objects and pictures (numbers 0-10 only)

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

K.5: The student applies mathematical process standards to identify the pattern in the number word list. The student is expected to recite numbers up to at least 100 by ones and tens beginning with any given number.

1.5A recite numbers forward and backward from any given number between 1 and 120

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Bundle 1: Teacher Notes

TEKS/Student Expectations

Instructional Implications Distractor Factors Supporting Readiness Standards

TEA Supporting Information

K.2A: count forward and backward to at least 20 with and without objects (numbers 0-10 only)

The counting sequence is a rote procedure. However, the understanding of relative position and magnitude of numbers related to counting is the key conceptual idea. Therefore, students must associate the counting words “one, two, three, four, etc.” with a one-to-one correspondence of touching manipulatives (see K.2B). Moving students from counting forward to counting on and/or backward will be a developmental progression. Frequent short practice routines are recommended. With the inclusion of “at least” within the standard, the minimum expectation is that all students will count to 20 but students are not limited to 20.

Counting numbers backward and forward with and without objects develops the contextual understanding of value of numbers. This learning will support future comparing/ ordering of numbers and informally develop a student’s understanding of place value, the relative position of numbers, and the magnitude of numbers. 1.2G represent the comparison of two numbers to 100 using the symbols >, <, or = K.2H use comparative language to describe two numbers up to 20 presented as written numerals

Students are expected to count by ones, starting at any number with and without objects. Students are expected to count backward with and without objects.

K.2B: read, write, and represent whole numbers from 0 to at least 20 with and without objects or pictures (numbers 0-10 only)

Helping students read and write numerals is similar to teaching them to read and write letters of the alphabet. Instruction often involves engaging forms of repetition (i.e. making numerals out of clay, tracing numerals in shaving cream, representing numerals on the calculator, matching games, etc.). Whole students are developing the writing of numerals, they can select from a stack of pre-made number cards to read and represent the total number of objects in a set. Students must also be given a whole number and asked to represent the quantities with given objects/manipulatives.

* Students may write numerals backwards but understand the value of the number. * Students may be able to read a number but not represent its value. * Students may be able to read a number but not write the number. * Students may be able to write a number but not associate a set of objects to its value. *Students may be able to represent a number with a set of objects but not be able to identify and/or write the numeric representation. * Students may recite the numbers, such as 1 through 20, without associating the number name with appropriate number or value. * Students may confuse number

The student is expected to read and write numbers as numerals. Based on the student’s reading readiness, it might be appropriate for the student to learn the numbers as sight words.

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names that are homophones (one/won, two/to/too, four/for, eight/ate). * Students may not consider zero a number.

K.2C: count a set of objects up to at least 20 and demonstrate that the last number said tells the number of objects in the set regardless of their arrangement or order (numbers 0-10 only)

In conjunction with K.2B, students will learn to count objects and identify the associated counting word to represent the quantity. In order to adhere to this standard, students must have an understanding of the cardinality principle (the last number stated is the total amount of objects). When students count a set of objects and respond with the appropriate counting number this does not mean they understand the cardinality principle. For example, after rearranging that same number of objects a different way and asking students how many objects are in the set, the student should respond with the same number without recounting as the amount of objects did not change. Should a student need to recount using one-to-one correspondence each time the objects are moved, he/she does not understand the cardinality principle. This understanding will support future learning of how to add basic facts more fluidly (i.e. 8 + 4 =___; with the understanding of the cardinality rule, students can begin counting on from 8 to determine four more (9, 10, 11, 12) without having to count to eight and then 4 more (1,2,3,4,5,6,7,8, 9, 10, 11,12).

Applying one-to-one correspondence to counting a set of objects up to 20 and understanding the cardinality rule will support students’ ability to develop strategies to recall basic facts to solve addition/ subtraction problems. 1.3F generate and solve problem situations when given a number sentence involving addition or subtraction of numbers within 20 1.5G apply properties of operations to add and subtract two or three numbers

Students are expected to form connections between counting with a set of objects and the number that describes a set of objects. Once the student has determined the number of objects in the set, he or she must understand that if the objects are simply rearranged, the quantity does not change.

K.2D: recognize instantly the quantity of a small group of objects in organized and random

Students learn to recognize dot arrangements on standard dice due to the many board games they have

Being able to recognize the quantity of structured and random arrangements will support students in

Organized arrangements include ten frames and the arrangements of dots on

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arrangements played. Similar instant recognition can be developed for other patterns as well (i.e. dominos, fingers, five/ten frame). Quantities up to 10 can be known and named without the routine of counting. Some students may continue to rely on physically counting using one-to-one correspondence to determine the total number of objects. However, with continuous exposure to pattern sets, students will begin to rely less on their counting skills and more on their spatial reasoning. A fun game of jacks can reinforce such understanding.

visually comparing two numbers. 1.2G represent the comparison of two numbers to 100 using the symbols >, <, or =

random number generators. The number of items in a group should be ten or fewer. This SE builds to 1.2A where students use this understanding to quickly decompose sets and make connections to basic facts.

K.2E: generate a set using concrete and pictorial models that represents a number that is more than, less than, and equal to a given number up to 20 (numbers 0-10 only)

Students counting forward and backward from a given number or given set of objects (see K.2A) begin the foundational understanding of comparisons using the phrases “more than” and “less than.” Instruction should include students being given a set of objects and asking them to create a set that is “one more, one less, two more, two les, etc.” The idea of equivalence could include giving the students a set of objects and prompting them to generate a representation that is equal to a give number (i.e. given 3 color tiles, prompt students to create a set of color tiles that would be equal to 8 color tiles). This understanding will support students with the future learning of the strategy “adding on” for addition/subtraction (i.e. 3 + ___ = 8; 8 – 3 = ___).

Generating a number greater than, less than or equal to a given whole number with a set of concrete objects develops in students the understanding of the magnitude of whole numbers which will support their ability to compare/order numbers. K.2H use comparative language to describe two numbers up to 20 presented as written numerals 1.2G represent the comparison of two numbers to 100 using the symbols >, <, or =

This SE introduces students to the concepts of both equality and inequality, without symbols. It also lays the foundation for the work students will do when solving both equations and inequalities. For example, when given a number such as 18, the student may be expected to use objects or pictures to create a set that it more than 18, less than18, or equal to 18. This SE builds to K.2F where students generate a number without models.

K.2F: generate a number that is one more than or one less than another number up to at least 20 (numbers 0-10 only)

As students become comfortable using manipulatives to generate a number that is more than, less than, or equal to a given number (see K.2E), instruction should then move to the abstract where students are just given a number (without an image/object) and asked to generate

In generating a number greater than, less than, or equal to a given whole number, students will develop the understanding of magnitude of whole numbers which will support their ability to compare/ order numbers. K.2H use comparative language to

This SE allows students to apply their understandings from K.2E to generate a number without the use of models. This SE builds to 1.2D and 2.2C where students are

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a number more than and/or less than an object.

describe two numbers up to 20 presented as written numerals 1.2G represent the comparison of two numbers to 100 using the symbols >, <, or =

expected to generate a number that is more than or less than a given whole number.

K.2G: compare sets of objects up to at least 20 in each set using comparative language (numbers 0-10 only)

Students will compare two sets of objects using the correct academic vocabulary (i.e. 12 color tiles is more than 9 color tiles). It is important for students to recognize the inverse comparison statement as well (i.e. 9 color tiles is less than 12 color tiles). Encourage students to articulate both comparison statements during activities. In adherence to the standard, the minimum state expectation is to compare numbers through 20. However, with the inclusion of the phrase “at least,” instruction may extend beyond 20 for those students that are developmentally ready.

As students compare sets of objects, they need to use the appropriate academic vocabulary (greater than, less than, equal to) before moving to the abstract use of comparison symbols (<, >, =) in 1st grade. K.2H use comparative language to describe two numbers up to 20 presented as written numerals 1.2G represent the comparison of two numbers to 100 using the symbols >, <, or =

Students may be expected to compare two or more sets using comparative language including “more than,” “same number as,” and “two less than.” This builds to K.2H.

K.2H: use comparative language to describe two numbers up to 20 presented as written numerals (numbers 0-10 only)

As students become comfortable using manipulatives to compare values (see K.2G), instruction should then move to the abstract where students are just given a written numeral (without an image/object) and asked to compare it to another written numeral. Encourage students to give two statements to describe each comparison (i.e. 9 is more than 6 and 6 is less than 9).

* Due to developmental reasons, students may not be able to compare written representations of numerals. * Students may view a comparison statement and its inverse as two different comparison statements (i.e. forty-five is greater than forty-one; forty-one is less than forty-five).

This SE builds upon K.2G and builds to 1.2E. However, students are only asked to compare two numbers using comparative language including “more than,” “greater than,” or “equal to.”

K.2I: compose and decompose numbers up to 10 with objects and pictures (numbers 0-10 only)

The composing and decomposing of numbers develops a student’s understanding of relationships within the numeration system. Instruction may begin with the use of two different colored cubes and asking students to make different combinations for four cubes (i.e. 4 blue; 4 yellow; 3 blue and 1 yellow; 3 yellow and 1 blue; 2 blue

* Students may confuse the creation of patterns (i.e. repeating pattern; blue, yellow, blue, yellow) with the composing/decomposing of numbers (i.e. 1 yellow + 3 blue = a value of 4).

This SE provides groundwork for making ten, compatible numbers, and factoring. It also leads to the concept of subtraction in a more abstract form. For example, the objects or pictures may be arranged to show a group of 8 and a

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and 2 yellow). Visually representing a given number as many different ways as possible will support students with developing number concepts. Students may begin to informally discover the commutative property (i.e. the total of the train of 3 blue and 1 yellow is the same train as 1 yellow and 3 blue). As students become secure with composing and decomposing sums through 10 with two addends, instruction should extend to the use of three addends. Students will be provided three different color cubes to represent the value of 4 (i.e. 1 red, 2 blue, and 1 yellow; 1 red, 1 blue, 2 yellow; 2 red, 1 blue, 1 yellow).

group of 2 to make 10. A student may also compose and decompose in a variety of ways such as making a group of 5 and another group of 5 or by making a group of 2, a group of 3, and a group of 5 to make 10. This builds to 1.2B.


The counting sequence is a rote procedure. Therefore, counting to 100 will become routine for students. However, this standard requires students to develop patterns within the number system, so they may be able to begin counting by ones or tens starting at any number (i.e. counting by ones starting at 32; counting by tens starting at 30). The use of a 100s chart may be a helpful tool for students to begin recognizing these patterns. The TEKS also require students to identify patterns in the number word list. Students are not required to read or write number words, but they are required to recognize the patterns. Therefore, instruction needs to include exposure to the number word version (i.e. twenty-four) in addition to the symbolic representation (i.e. 24).

Reciting numbers by ones and tens starting at any given number will informally introduce the ones and tens place value. This understanding will be critical in being able to develop algorithms based on place vale in order to solve addition/subtraction problems.

Reciting numbers should be developed through counting so that students have meaning behind the recitation. This recitation builds automaticity when counting by ones or by tens. The given number, when reciting by tens, should be a multiple of ten (50, 60, 70, …..). This builds to 1.5A where students recite numbers forwards and backwards from any given number.

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Course: Kinder Math Bundle 2: Representing and Comparing Whole Numbers 11-20

Dates: October 4th-November 11th (29 days)

TEKS K.2A: count forward and backward to at least 20 with and without objects K.2B: read, write, and represent whole numbers from 0 to at least 20 with and without objects or pictures K.2C: count a set of objects up to at least 20 and demonstrate that the last number said tells the number of objects in the set regardless of their arrangement or order K.2D: recognize instantly the quantity of a small group of objects in organized and random arrangements K.2E: generate a set using concrete and pictorial models that represents a number that is more than, less than, and equal to a given number up to 20 K.2F: generate a number that is one more than or one less than another number up to at least 20 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 K.2I: compose and decompose numbers up to 10 with objects and pictures K.5: The student applies mathematical process standards to identify the pattern in the number word list. The student is expected to recite numbers up to at least 100 by ones and tens beginning with any given number.

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 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) 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 2E: use visual, contextual, and linguistic support to enhance and confirm understanding of increasingly complex and elaborated spoken language 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

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Speaking 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 3E: share information in cooperative learning interactions 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 Reading 4C: develop basic sight vocabulary, derive meaning of environmental print, and comprehend English vocabulary and language structures used routinely in written classroom materials 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 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 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

Vocabulary

Unit Vocabulary Backward Decompose More than Compare Equal to Numbers 0-20 Compose Forward Ones Counting words Greater than Tens Counting words 0-100 Less than

Cognitive Complexity Verbs: count, read, write, represent, demonstrate, recognize, generate, compare, use, compose, decompose, recite Academic Vocabulary by Standard: K.2A: backward, forward, numbers 0-20 (oral and written representations) K.2B: numbers 0-20 (oral and written representations) K.2C: numbers 0-20 (oral and written representations) K.2D: counting words K.2E: equal to, less than, more than K.2F: less than, more than K.2G: compare, equal to, greater than, less than, more than K.2H: equal to, greater than, less than, more than K.2I: compose, decompose K.5: counting words 0-100, ones, tens

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Suggested Math Manipulatives

Ten Frames/ Double Ten Frames 2-Color Counters Rekenreks 100s Chart Number Lines Snap Cubes Dot Images Counters Color Tiles

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K.2A: count forward and backward to at least 20 with and without objects

K.2B: read, write, and represent whole numbers from 0 to at least 20 with and without objects or pictures

K.2C: count a set of objects up to at least 20 and demonstrate that the last number said tells the number of objects in the set regardless of their arrangement or order


1.2A recognize instantly the quantity of structured arrangements

K.2E: generate a set using concrete and pictorial models that represents a number that is more than, less than, and equal to a given number up to 20

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

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


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


1.5A recite numbers forward and backward from any given number between 1 and 120

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K.2A: count forward and backward to at least 20 with and without objects

The counting sequence is a rote procedure. However, the understanding of relative position and magnitude of numbers related to counting is the key conceptual idea. Therefore, students must associate the counting words “one, two, three, four, etc.” with a one-to-one correspondence of touching manipulatives (see K.2B). Moving students from counting forward to counting on and/or backward will be a developmental progression. Frequent short practice routines are recommended. With the inclusion of “at least” within the standard, the minimum expectation is that all students will count to 20 but students are not limited to 20.

Counting numbers backward and forward with and without objects develops the contextual understanding of value of numbers. This learning will support future comparing/ ordering of numbers and informally develop a student’s understanding of place value, the relative position of numbers, and the magnitude of numbers. 1.2G represent the comparison of two numbers to 100 using the symbols >, <, or = K.2H use comparative language to describe two numbers up to 20 presented as written numerals

Students are expected to count by ones, starting at any number with and without objects. Students are expected to count backward with and without objects.

K.2B: read, write, and represent whole numbers from 0 to at least 20 with and without objects or pictures

Helping students read and write numerals is similar to teaching them to read and write letters of the alphabet. Instruction often involves engaging forms of repetition (i.e. making numerals out of clay, tracing numerals in shaving cream, representing numerals on the calculator, matching games, etc.). Whole students are developing the writing of numerals, they can select from a stack of pre-made number cards to read and represent the total number of objects in a set. Students must also be given a whole number and asked to represent the quantities with given objects/manipulatives.

* Students may write numerals backwards but understand the value of the number. * Students may be able to read a number but not represent its value. * Students may be able to read a number but not write the number. * Students may be able to write a number but not associate a set of objects to its value. *Students may be able to represent a number with a set of objects but not be able to identify and/or write the numeric representation. * Students may recite the numbers, such as 1 through 20, without associating the number name with appropriate number or value. * Students may confuse number

The student is expected to read and write numbers as numerals. Based on the student’s reading readiness, it might be appropriate for the student to learn the numbers as sight words.

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names that are homophones (one/won, two/to/too, four/for, eight/ate). * Students may not consider zero a number.

K.2C: count a set of objects up to at least 20 and demonstrate that the last number said tells the number of objects in the set regardless of their arrangement or order

In conjunction with K.2B, students will learn to count objects and identify the associated counting word to represent the quantity. In order to adhere to this standard, students must have an understanding of the cardinality principle (the last number stated is the total amount of objects). When students count a set of objects and respond with the appropriate counting number this does not mean they understand the cardinality principle. For example, after rearranging that same number of objects a different way and asking students how many objects are in the set, the student should respond with the same number without recounting as the amount of objects did not change. Should a student need to recount using one-to-one correspondence each time the objects are moved, he/she does not understand the cardinality principle. This understanding will support future learning of how to add basic facts more fluidly (i.e. 8 + 4 =___; with the understanding of the cardinality rule, students can begin counting on from 8 to determine four more (9, 10, 11, 12) without having to count to eight and then 4 more (1,2,3,4,5,6,7,8, 9, 10, 11,12).

Applying one-to-one correspondence to counting a set of objects up to 20 and understanding the cardinality rule will support students’ ability to develop strategies to recall basic facts to solve addition/ subtraction problems. 1.3F generate and solve problem situations when given a number sentence involving addition or subtraction of numbers within 20 1.5G apply properties of operations to add and subtract two or three numbers

Students are expected to form connections between counting with a set of objects and the number that describes a set of objects. Once the student has determined the number of objects in the set, he or she must understand that if the objects are simply rearranged, the quantity does not change.


Students learn to recognize dot arrangements on standard dice due to the many board games they have played. Similar instant recognition can be developed for other patterns as well (i.e. dominos, fingers,

Being able to recognize the quantity of structured and random arrangements will support students in visually comparing two numbers. 1.2G represent the comparison of

Organized arrangements include ten frames and the arrangements of dots on random number generators. The number of items in a

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five/ten frame). Quantities up to 10 can be known and named without the routine of counting. Some students may continue to rely on physically counting using one-to-one correspondence to determine the total number of objects. However, with continuous exposure to pattern sets, students will begin to rely less on their counting skills and more on their spatial reasoning. A fun game of jacks can reinforce such understanding.

two numbers to 100 using the symbols >, <, or =

group should be ten or fewer. This SE builds to 1.2A where students use this understanding to quickly decompose sets and make connections to basic facts.

K.2E: generate a set using concrete and pictorial models that represents a number that is more than, less than, and equal to a given number up to 20

Students counting forward and backward from a given number or given set of objects (see K.2A) begin the foundational understanding of comparisons using the phrases “more than” and “less than.” Instruction should include students being given a set of objects and asking them to create a set that is “one more, one less, two more, two les, etc.” The idea of equivalence could include giving the students a set of objects and prompting them to generate a representation that is equal to a give number (i.e. given 3 color tiles, prompt students to create a set of color tiles that would be equal to 8 color tiles). This understanding will support students with the future learning of the strategy “adding on” for addition/subtraction (i.e. 3 + ___ = 8; 8 – 3 = ___).

Generating a number greater than, less than or equal to a given whole number with a set of concrete objects develops in students the understanding of the magnitude of whole numbers which will support their ability to compare/order numbers. K.2H use comparative language to describe two numbers up to 20 presented as written numerals 1.2G represent the comparison of two numbers to 100 using the symbols >, <, or =

This SE introduces students to the concepts of both equality and inequality, without symbols. It also lays the foundation for the work students will do when solving both equations and inequalities. For example, when given a number such as 18, the student may be expected to use objects or pictures to create a set that it more than 18, less than18, or equal to 18. This SE builds to K.2F where students generate a number without models.

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

As students become comfortable using manipulatives to generate a number that is more than, less than, or equal to a given number (see K.2E), instruction should then move to the abstract where students are just given a number (without an image/object) and asked to generate a number more than and/or less than an object.

In generating a number greater than, less than, or equal to a given whole number, students will develop the understanding of magnitude of whole numbers which will support their ability to compare/ order numbers. K.2H use comparative language to describe two numbers up to 20 presented as written numerals

This SE allows students to apply their understandings from K.2E to generate a number without the use of models. This SE builds to 1.2D and 2.2C where students are expected to generate a number that is more than or less than a given whole

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

number.

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

Students will compare two sets of objects using the correct academic vocabulary (i.e. 12 color tiles is more than 9 color tiles). It is important for students to recognize the inverse comparison statement as well (i.e. 9 color tiles is less than 12 color tiles). Encourage students to articulate both comparison statements during activities. In adherence to the standard, the minimum state expectation is to compare numbers through 20. However, with the inclusion of the phrase “at least,” instruction may extend beyond 20 for those students that are developmentally ready.

As students compare sets of objects, they need to use the appropriate academic vocabulary (greater than, less than, equal to) before moving to the abstract use of comparison symbols (<, >, =) in 1st grade. K.2H use comparative language to describe two numbers up to 20 presented as written numerals 1.2G represent the comparison of two numbers to 100 using the symbols >, <, or =

Students may be expected to compare two or more sets using comparative language including “more than,” “same number as,” and “two less than.” This builds to K.2H.

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

As students become comfortable using manipulatives to compare values (see K.2G), instruction should then move to the abstract where students are just given a written numeral (without an image/object) and asked to compare it to another written numeral. Encourage students to give two statements to describe each comparison (i.e. 9 is more than 6 and 6 is less than 9).

* Due to developmental reasons, students may not be able to compare written representations of numerals. * Students may view a comparison statement and its inverse as two different comparison statements (i.e. forty-five is greater than forty-one; forty-one is less than forty-five).

This SE builds upon K.2G and builds to 1.2E. However, students are only asked to compare two numbers using comparative language including “more than,” “greater than,” or “equal to.”

K.2I: compose and decompose numbers up to 10 with objects and pictures

The composing and decomposing of numbers develops a student’s understanding of relationships within the numeration system. Instruction may begin with the use of two different colored cubes and asking students to make different combinations for four cubes (i.e. 4 blue; 4 yellow; 3 blue and 1 yellow; 3 yellow and 1 blue; 2 blue

* Students may confuse the creation of patterns (i.e. repeating pattern; blue, yellow, blue, yellow) with the composing/decomposing of numbers (i.e. 1 yellow + 3 blue = a value of 4).

This SE provides groundwork for making ten, compatible numbers, and factoring. It also leads to the concept of subtraction in a more abstract form. For example, the objects or pictures may be arranged to show a group of 8 and a

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and 2 yellow). Visually representing a given number as many different ways as possible will support students with developing number concepts. Students may begin to informally discover the commutative property (i.e. the total of the train of 3 blue and 1 yellow is the same train as 1 yellow and 3 blue). As students become secure with composing and decomposing sums through 10 with two addends, instruction should extend to the use of three addends. Students will be provided three different color cubes to represent the value of 4 (i.e. 1 red, 2 blue, and 1 yellow; 1 red, 1 blue, 2 yellow; 2 red, 1 blue, 1 yellow).

group of 2 to make 10. A student may also compose and decompose in a variety of ways such as making a group of 5 and another group of 5 or by making a group of 2, a group of 3, and a group of 5 to make 10. This builds to 1.2B.


The counting sequence is a rote procedure. Therefore, counting to 100 will become routine for students. However, this standard requires students to develop patterns within the number system, so they may be able to begin counting by ones or tens starting at any number (i.e. counting by ones starting at 32; counting by tens starting at 30). The use of a 100s chart may be a helpful tool for students to begin recognizing these patterns. The TEKS also require students to identify patterns in the number word list. Students are not required to read or write number words, but they are required to recognize the patterns. Therefore, instruction needs to include exposure to the number word version (i.e. twenty-four) in addition to the symbolic representation (i.e. 24).

Reciting numbers by ones and tens starting at any given number will informally introduce the ones and tens place value. This understanding will be critical in being able to develop algorithms based on place vale in order to solve addition/subtraction problems.

Reciting numbers should be developed through counting so that students have meaning behind the recitation. This recitation builds automaticity when counting by ones or by tens. The given number, when reciting by tens, should be a multiple of ten (50, 60, 70, …..). This builds to 1.5A where students recite numbers forwards and backwards from any given number.

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Course: Kinder Math Bundle 3: Addition and Subtraction Dates: November 14th-January 12th (29 days) TEKS

K.3A: model the action of joining to represent addition and the action of separating to represent subtraction K.3B: solve word problems using objects and drawings to find sums up to 10 and differences within 10 K.3C: explain the strategies used to solve problems involving adding and subtracting within 10 using spoken words, concrete and pictorial models, and number sentences

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

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Vocabulary

Unit Vocabulary Add Equal sign Subtract Addition Join/ joining Subtraction Combine/ combining Number sentence Sum Difference Separate/ separating

Cognitive Complexity Verbs: model, solve, use, explain Academic Vocabulary by Standard: K.3A: joining/ combining (addition), separating (subtraction) K.3B: addition, add, difference, subtraction, subtract, sum K.3C: addition (joining/ combining), equal sign, number sentence, subtraction (separating)


Part/Whole Mat Snap Cubes Counters Cuisenaire Rods Ten Frames Double Ten Frames Number Line Color Tiles Dice Dominoes

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K.3A: model the action of joining to represent addition and the action of separating to represent subtraction

1.3B use objects and pictorial models to solve word problems involving joining, separating, and comparing sets within 20 and unknowns as any one of the terms in the problem such as 2 + 4 = [ ]; 3 + [ ] = 7; and 5 = [ ] - 3.

K.3B: solve word problems using objects and drawings to find sums up to 10 and differences within 10

1.3C compose 10 with two or more addends with and without concrete objects

K.3C: explain the strategies used to solve problems involving adding and subtracting within 10 using spoken words, concrete and pictorial models, and number sentences

1.3E explain strategies used to solve addition and subtraction problems up to 20 using spoken words, objects, pictorial models, and number sentences 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

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TEKS/Student Expectations Instructional Implications Distractor Factors Supporting Readiness Standards



Instruction should focus on the meaning of addition and subtraction through the lens of the terms joining and separating. Instruction should provide multiple opportunities for students to use manipulatives to act out their understanding of joining and separating to distinguish between the two operations. Instruction should include both prepared story problems for students to act out and student generated story problems to model their understanding of the difference between the two operations. Joining and separating word problems should include a variety of contexts: Joining: Sarah had 7 pencils. Juan gave her 3 more pencils. How many pencils does Sarah have now? Sarah had 7 pencils. Juan gave her some more pencils. Now Sarah has 10 pencils. How many pencils did Juan giver her? Sarah had some pencils. Juan gave her 3 pencils. Now Sarah has a total of 10 pencils. How many pencils did Sarah have to begin with? Separating: Sarah had 10 pencils. She gave 3 pencils to Juan. How many pencils does Sarah have now? Sarah had a total of 10 pencils. She gave some to Juan. Now she only has 3 pencils. How many pencils did she give to Juan? Sarah had some pencils. She gave 3 to Juan. Now Sarah has 7 pencils

The use of concrete objects and pictorial models to demonstrate joining and separating situations will support students’ understanding of the context of addition and subtraction problems. Connecting such actions to their corresponding number sentence will support students to move from concrete to the abstract understanding. K.3B: solve word problems using objects and drawings to find sums up to 10 and differences within 10 1.3F generate and solve problem situations when given a number sentence involving addition or subtraction of numbers within 20

This SE focuses on the action of joining and separating in which the result is unknown. Therefore, addition would be the more appropriate operation to solve a joining problem, and subtraction would be the more appropriate operation to solve the separation problem.

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left. How many pencils did Sarah have before?


In alignment with K.3A, students begin modeling the actions of joining and separating. Students should be provided with multiple opportunities to solve problems in order to build their understanding of addition and subtraction. The use of drawings and/or objects will be critical for developing the conceptual understanding of joining and separating. It is important that instruction begin with acting out addition/ subtraction problems with manipulatives and then associating those actions to a pictorial model. This will support students with moving from the concrete to the abstract.

* Students may not recognize a number sentence and its inverse as being equivalent (i.e. 10 – 4 = ___ is the same thing as 4 + ___ = 10).

Modeling includes the result from joining to determine sums and separating to determine differences. When paired with K.1A, students may use objects and drawings to solve problems related to real-world situations.


In conjunction with K.6A/F, as students begin solving joining and separating problems, they should explain their thought processes orally, using objects/pictures, and with number sentences. Students should orally explain how his/her picture relates to the given number sentence (i.e. in the number sentences 2 + 3 + 5 and 5 = 2 + 3; these two blue birds in the picture stand for the 2 in the number sentence. These three red birds in the pictures joined the blue birds which is the +3 in my number sentence. There is now a total of 5 birds sitting in the tree which is the same as 5 in the number sentence). Real world situations should be extended beyond two addends (i.e. There are two blue birds, one red robin, and one hummingbird in the tree. How many birds are in the tree?).

Being able to relate the manipulation of concrete objects to pictorial models to a number sentence is a critical transition to move students from the concrete to the abstract understanding of addition and subtraction. K.3B: solve word problems using objects and drawings to find sums up to 10 and differences within 10 1.3F generate and solve problem situations when given a number sentence involving addition or subtraction of numbers within 20 1.5G apply properties of operations to add and subtract two or three numbers

By pairing this SE with K.1E, students can be expected to explain and record observations which may include strategies. Students are expected to explain their thinking using spoken words, pictorial models, and number sentences.

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Course: Kinder Math Bundle 4: Geometry

Dates: January 17th- February 24th (28 days)

TEKS K.6A: identify two-dimensional shapes, including circles, triangles, rectangles, and squares as special rectangles K.6B: identify three-dimensional solids, including cylinders, cones, spheres, and cubes, in the real world K.6C: identify two-dimensional components of three-dimensional objects K.6D: identify attributes of two-dimensional shapes using informal and formal geometric language interchangeably K.6E: classify and sort a variety of regular and irregular two- and three-dimensional figures regardless of orientation or size K.6F: create two-dimensional shapes using a variety of materials and drawings

ELPS Learning Strategies 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 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 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 3E: share information in cooperative learning interactions 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 3H: narrate, describe, and explain with increasing specificity and detail as more English is acquired

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

Vocabulary

Unit Vocabulary Attribute Cylinder Shape Straight Circle Edge Side Three-dimensional Cone Face Solid Triangle Cube Polygon Sphere Two-dimensional Curved Rectangle Square (as special rectangle) Vertex/ vertices

Cognitive Complexity Verbs: identify, classify, create, use Academic Vocabulary by Standard: K.6A: attribute, curved, straight, side, vertex/vertices, polygon, shape, circle, rectangle, square (as special rectangle), triangle, two-dimensional K.6B: attributes, edge, face, vertex/vertices, solid, three-dimensional, cone, cylinder, cube, sphere K.6C: attribute, edge, side, face, vertex/vertices, polygon, shape, solid, three-dimensional, two-dimensional K.6D: attribute, side, vertex/ vertices, polygon, shape, two-dimensional K.6E: attribute, irregular, polygon, regular, shape, solid, three-dimensional, two-dimensional K.6F: attribute, shape, circle, polygon, rectangle, square (as special rectangle), triangle, two-dimensional


Pattern Blocks Popsicle Sticks, etc. Geometric Solids Attribute Blocks Geoboards Translucent Geometric Shapes Sorting Tray AngLegs

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K.6A: identify two-dimensional shapes, including circles, triangles, rectangles, and squares as special rectangles

1.6C create two-dimensional figures, including circles, triangles, rectangles, and squares, as special rectangles, rhombuses, and hexagons 2.8A create two-dimensional shapes based on given attributes, including number of sides and vertices

K.6B: identify three-dimensional solids, including cylinders, cones, spheres, and cubes, in the real world

1.6E identify three-dimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes), and triangular prisms, and describe their attributes using formal geometric language

K.6C: identify two-dimensional components of three-dimensional objects 1.6B distinguish between attributes that define a two-dimensional or three-dimensional figure and attributes that do not define the shape

K.6D: identify attributes of two-dimensional shapes using informal and formal geometric language interchangeably

1.6D identify two-dimensional shapes, including circles, triangles, rectangles, and squares, as special rectangles, rhombuses, and hexagons and describe their attributes using formal geometric language 2.8A create two-dimensional shapes based on given attributes, including number of sides and vertices

K.6E: classify and sort a variety of regular and irregular two- and three-dimensional figures regardless of orientation or size

1.6A classify and sort regular and irregular two-dimensional shapes based on attributes using informal geometric language 2.8C classify and sort polygons with 12 or fewer sides according to attributes, including identifying the number of sides and number of vertices 2.8B classify and sort three-dimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes as special rectangular prisms), and triangular prisms, based on attributes using formal geometric language

K.6F: create two-dimensional shapes using a variety of materials and drawings

1.6F compose two-dimensional shapes by joining two, three, or four figures to produce a target shape in more than one way if possible 2.8D compose two-dimensional shapes and three-dimensional solids with given properties or attributes 2.8E decompose two-dimensional shapes such as cutting out a square from a rectangle, dividing a shape in half, or partitioning a rectangle into identical triangles and identify the resulting geometric parts

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TEKS/Student Expectations Instructional Implications

Distractor Factors Supporting Readiness Standards


K.6A: identify two-dimensional shapes, including circles, triangles, rectangles, and squares as special rectangles

Students should use the attributes of given shapes (K.6D) to correctly identify a shape. A variety of shapes (i.e. different types of triangles) and a variety of orientations, color, and size should be used to ensure that students use the geometric attributes to identify a shape. Instruction should clearly identify a square as a rectangle because it has four sides and four vertices. Students need to view a square as a special rectangle because all of its sides are of equal length. As students begin to recognize how circles are curved and triangles, rectangles, and squares have straight sides, instruction can begin modeling the term polygon for those two- dimensional shapes that are enclosed with straight sides.

The ability to identify two-dimensional shapes based on their geometric attributes and properties supports the future classification and sorting of such figures. K.6E: classify and sort a variety of regular and irregular two- and three-dimensional figures regardless of orientation or size

This SE pairs with K.6D. Students identify two-dimensional shapes based on attributes using informal and formal language such as the number of sides or the number of corners (vertices). When paired with SE k.1D, K.1F, and K.1G, the expectation is that students may describe and compare the identified figures to justify their identifications.

K.6B: identify three-dimensional solids, including cylinders, cones, spheres, and cubes, in the real world

Students should use the attributes of a given sold to correctly identify a related real world example (i.e. a rectangular prism has six faces, eight vertices, and 12 edges and so does a cereal box). A variety of real world three-dimensional solids should be provided (i.e. cone: ice cream cone, party hat, megaphone, water dispensing cup, etc.).

Being able to identify three-dimensional figures in the real world provides a concrete visual to students of the geometric attributes and properties. K.6E: classify and sort a variety of regular and irregular two- and three-dimensional figures regardless of orientation or size

Students identify three-dimensional solids based on attributes using informal and formal language such as curved, flat, surface, corners (vertices), edges, and faces.

K.6C: identify two-dimensional components of three-dimensional objects

Students need to understand that three-dimensional solids are made up of two-dimensional shapes/polygons. Providing students opportunities where they stamp out the various sides of three-dimensional solids (i.e.

Identifying how three-dimensional solids consist of two-dimensional shapes will allow students to focus on the various attributes. This understanding will support the sorting and classification of various figures.

To align with this SE, the two-dimensional components include circles, triangles, rectangles, and squares. For example, the face of a tissue box is a rectangle.

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taking a cube and making six square face imprints in clay) will demonstrate how the two are related to each other. During such activities, students should identify polygons and how many of each type of two-dimensional shapes make up a given solid (i.e. a triangular prism is made up of five polygons; two triangles, and three rectangles). Instruction should introduce how the two-dimensional shapes represent the faces of a three-dimensional solid, the sides of a polygon create the edges of a solid, and the vertices of the polygon relate to the number of vertices on a solid. Students should analyze how the number of vertices/sides of a polygon compares to that of a solid (i.e. a square has four sides and four vertices. A cube is comprised of six square faces. However, a cube does not have 24 sides and 24 vertices because some of the vertices and sides of the square overlap in creating the solid).

K.6E: classify and sort a variety of regular and irregular two- and three-dimensional figures regardless of orientation or size K.7B compare two objects with a common measurable attribute to see which object has more of/less of the attribute and describe the differences

K.6D: identify attributes of two-dimensional shapes using informal and formal geometric language interchangeably

Students may describe a given two-dimensional shape as having “three lines” and/or “three pointy corners.” Teachers should then paraphrase those responses using the correct formal vocabulary, such as “three sides and three vertices.” With exposure, students will begin to use the appropriate academic terms.

As students begin discovering attributes of various two-dimensional shapes, they need to translate their informal descriptions to more formal geometric vocabulary. This foundational understanding will support their ability to sort and classify two-dimensional figures. K.6E: classify and sort a variety of regular and irregular two- and three-dimensional figures regardless of orientation or size

Students are expected to use formal geometric language such as “vertex” or “vertices” for corners and “side” to identify circles, triangles, rectangles, and squares.

K.6E: classify and sort a variety of regular and irregular two- and three-dimensional figures regardless of orientation or size

In order to adhere to the standard, students must sort and classify a group of two-dimensional shapes, a group of three-dimensional

* Students may interchange the term side, referencing two-dimensional shapes, and edge, referencing a three-

A variety of regular and irregular two-dimensional figures may include a regular hexagon and a hexagon where

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solids, and a group of two- and three-dimensional figures combined. Orientation, color, or size cannot be a geometric attribute for sorting/classifying of these objects. Allowing students to engage in all three types of sorts allows them to focus on what attributes distinguish between a two-dimensional and three-dimensional object in support of K.6C. Students need to be exposed to both regular (i.e. and equilateral triangle) and irregular (i.e. right, scalene, and isosceles types of triangles) two-dimensional figures.

dimensional shape. * Students may not view a square as a rectangle. * Students may confuse the identification of a three-dimensional shape by its two-dimensional attribute (i.e. a cube is mistakenly identified as a square).

all sides are not the same.

Orientation and size should not be attributes which students use to sort or classify figures as these are not related to attributes of 2D and 3D figures. Comparing two objects based on their attributes becomes subsumed within the sorting of a variety of figures. For example, students may sort a collection of 2D and 3D figures based on dimension. They might compare a triangle and a triangular pyramid while sorting.

K.6F: create two-dimensional shapes using a variety of materials and drawings

This standard requires students to apply their ability to identify attributes of two dimensional shapes (K.6A/C/D) to creating them. Instruction should vary the materials (i.e. spaghetti, straws, toothpicks, pennies, string, etc.). It is important to observe student selection of appropriate materials (i.e. will students recognize that three straws would be easier to demonstrate a triangle than three pennies). Instruction should extend the study of attributes by taking an already created shape and ask to modify it to create a new shape (i.e. students made a rectangle out of clay; student is now asked to modify the rectangle to make it a square and explain how the attributes/properties of the two shapes were similar yet different).

Creating two-dimensional shapes of given attributes (i.e. the number of sides and vertices) and properties (i.e. all sides are of different lengths) allows students to focus on the geometric attributes of a figure. This attention to specific attributes and properties supports the classification of various figures. K.6E: classify and sort a variety of regular and irregular two- and three-dimensional figures regardless of orientation or size

Students may create two-dimensional figures by using materials, sketching figures, cutting figures out of paper, etc. This builds to 1.6C and 1.6F.

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Course: Kinder Math Bundle 5: Measurement and Expanded Addition and Subtraction

Dates: February 27th- April 21st (33 days)

TEKS K.7A: give an example of a measurable attribute of a given object, including length, capacity, and weight K.7B: compare two objects with a common measurable attribute to see which object has more of/less of the attribute and describe the difference K.3A: model the action of joining to represent addition and the action of separating to represent subtraction K.3B: solve word problems using objects and drawings to find sums up to 10 and differences within 10 K.3C: explain the strategies used to solve problems involving adding and subtracting within 10 using spoken words, concrete and pictorial models, and number sentences

ELPS Learning Strategies 1A: use prior knowledge and experiences to understand meanings in English Listening 2E: use visual, contextual, and linguistic support to enhance and confirm understanding of increasingly complex and elaborated spoken language 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 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 Reading 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 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

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Vocabulary

Unit Vocabulary Add Equal sign Less than More than Subtract Addition Heavier Lighter Number sentence Subtraction Capacity Joining Longer than Separating Sum Combining Length Measureable attribute Shorter than Weight Difference

Cognitive Complexity Verbs: give, compare, describe, model, solve, explain Academic Vocabulary by Standard: K.7A: capacity, length, weight, measureable attribute K.7B: attribute, capacity, difference, heavier, lighter, length, longer than, shorter than, more than, less than, weight K.3A: joining/ combining (addition), separating (subtraction) K.3B: addition, add, difference, subtraction, subtract, sum K.3C: addition (joining/ combining), equal sign, number sentence, subtraction (separating)

Suggested Math Manipulatives Balance Scales Snap Cubes Capacity Containers Non-Standard Measurement Tools Color Tiles Water Tables

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K.7A: give an example of a measurable attribute of a given object, including length, capacity, and weight

1.7A use measuring tools to measure the length of objects to reinforce the continuous nature of linear measurement 2.9D determine the length of an object to the nearest marked unit using rulers, yardsticks, meter sticks, or measuring tapes 3.7D determine when it is appropriate to use measurements of liquid volume (capacity) or weight 3.7E determine liquid volume (capacity) or weight using appropriate units and tools

K.7B: compare two objects with a common measurable attribute to see which object has more of/less of the attribute and describe the difference

4.8C solve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate


1.3B use objects and pictorial models to solve word problems involving joining, separating, and comparing sets within 20 and unknowns as any one of the terms in the problem such as 2 + 4 = [ ]; 3 + [ ] = 7; and 5 = [ ] - 3.


1.3C compose 10 with two or more addends with and without concrete objects


1.3E explain strategies used to solve addition and subtraction problems up to 20 using spoken words, objects, pictorial models, and number sentences 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

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TEKS/Student Expectations Instructional Implications Distractor Factors Supporting Readiness Standards


K.7A: give an example of a measurable attribute of a given object, including length, capacity, and weight

Students are given an object (i.e. box of cereal) and asked to identify a measureable attribute (i.e. student responds “we could measure how long it is, how much cereal it holds, or how much it weighs”). According to the TEKS, students are to use comparative language to describe their findings (i.e. student responds, “This cereal box is longer/shorter than this one. This cereal box holds more/less cereal than this one. This cereal box weighs more/less than this one”). The use of this comparative language also supports K.2G. Encourage students to articulate two statements for each comparison (i.e. Cereal Box A held more cereal than Cereal Box B; Cereal Box B held less cereal than Cereal Box A).

Being able to ascertain a measureable attribute will support students in understanding the difference between length, capacity, and weight. Distinguishing among those three types of measurements is foundational to selecting appropriate tools, applying appropriate units of measure, and solving measurement problems. K.7B: compare two objects with a common measurable attribute to see which object has more of/less of the attribute and describe the difference

While students may give many examples of measureable attributes, the attributes of length, capacity, and weight build vertically to measurement in later grades.

K.7B: compare two objects with a common measurable attribute to see which object has more of/less of the attribute and describe the difference

In alignment with K.7A, as students begin identifying a measurable attribute such as length, capacity, or weight, instruction can extend to comparing the differences (i.e. comparing the length, capacity, and weight of a trial size cereal box versus a full size cereal box). Instruction is limited to direct comparison (i.e. laying two cereal boxes next to each other to compare length). In alignment withK.2G/H, students should use appropriate comparative language in describing the differences (i.e. the full size cereal box is longer than the trial size cereal box; the full size cereal box holds more than the trial size cereal box; the full size cereal box is heavier than the trial size cereal box). Encourage students to articulate two comparison statements (i.e. the full size cereal box is longer

* Students may view a comparison statement and its inverse as two different comparison statements (i.e. the full size cereal box is longer than the trial size cereal box is the same thing as stating that the trial size cereal box is shorter than the full size cereal box).

Common measurable attributes include length. To describe the difference in length, students may use language such as “longer,” “shorter,” or “the same.” Common measureable attributes include capacity. To describe a difference in capacity, students may use language such as “holds more,” “holds less,” or “holds the same.” Common measureable attributes include weight. To describe a difference in weight, students may use language such as “heavier than,” “lighter than,” or “equal to.”

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than the trial size cereal box is the same as stating that the trial size cereal box is shorter than the full size cereal box).


Instruction should focus on the meaning of addition and subtraction through the lens of the terms joining and separating. Instruction should provide multiple opportunities for students to use manipulatives to act out their understanding of joining and separating to distinguish between the two operations. Instruction should include both prepared story problems for students to act out and student generated story problems to model their understanding of the difference between the two operations. Joining and separating word problems should include a variety of contexts: Joining: Sarah had 7 pencils. Juan gave her 3 more pencils. How many pencils does Sarah have now? Sarah had 7 pencils. Juan gave her some more pencils. Now Sarah has 10 pencils. How many pencils did Juan giver her? Sarah had some pencils. Juan gave her 3 pencils. Now Sarah has a total of 10 pencils. How many pencils did Sarah have to begin with? Separating: Sarah had 10 pencils. She gave 3 pencils to Juan. How many pencils does Sarah have now? Sarah had a total of 10 pencils. She gave some to Juan. Now she only has 3 pencils. How many pencils did she give to Juan? Sarah had some pencils. She gave 3 to Juan. Now Sarah has 7 pencils left. How many pencils did Sarah have before?

The use of concrete objects and pictorial models to demonstrate joining and separating situations will support students’ understanding of the context of addition and subtraction problems. Connecting such actions to their corresponding number sentence will support students to move from concrete to the abstract understanding. K.3B: solve word problems using objects and drawings to find sums up to 10 and differences within 10 1.3F generate and solve problem situations when given a number sentence involving addition or subtraction of numbers within 20

This SE focuses on the action of joining and separating in which the result is unknown. Therefore, addition would be the more appropriate operation to solve a joining problem, and subtraction would be the more appropriate operation to solve the separation problem.

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In alignment with K.3A, students begin modeling the actions of joining and separating. Students should be provided with multiple opportunities to solve problems in order to build their understanding of addition and subtraction. The use of drawings and/or objects will be critical for developing the conceptual understanding of joining and separating. It is important that instruction begin with acting out addition/ subtraction problems with manipulatives and then associating those actions to a pictorial model. This will support students with moving from the concrete to the abstract.

* Students may not recognize a number sentence and its inverse as being equivalent (i.e. 10 – 4 = ___ is the same thing as 4 + ___ = 10).

Modeling includes the result from joining to determine sums and separating to determine differences. When paired with K.1A, students may use objects and drawings to solve problems related to real-world situations.


In conjunction with K.6A/F, as students begin solving joining and separating problems, they should explain their thought processes orally, using objects/pictures, and with number sentences. Students should orally explain how his/her picture relates to the given number sentence (i.e. in the number sentences 2 + 3 + 5 and 5 = 2 + 3; these two blue birds in the picture stand for the 2 in the number sentence. These three red birds in the pictures joined the blue birds which is the +3 in my number sentence. There is now a total of 5 birds sitting in the tree which is the same as 5 in the number sentence). Real world situations should be extended beyond two addends (i.e. There are two blue birds, one red robin, and one hummingbird in the tree. How many birds are in the tree?).

Being able to relate the manipulation of concrete objects to pictorial models to a number sentence is a critical transition to move students from the concrete to the abstract understanding of addition and subtraction. K.3B: solve word problems using objects and drawings to find sums up to 10 and differences within 10 1.3F generate and solve problem situations when given a number sentence involving addition or subtraction of numbers within 20 1.5G apply properties of operations to add and subtract two or three numbers

By pairing this SE with K.1E, students can be expected to explain and record observations which may include strategies. Students are expected to explain their thinking using spoken words, pictorial models, and number sentences.

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Course: Kinder Math Bundle 6: Data and Personal Financial Literacy Dates: April 24th-June 1st (28 days) TEKS

K.8A: collect, sort, and organize data into two or three categories K.8B: use data to create real-object and picture graphs K.8C: draw conclusions from real-object and picture graphs K.4: The student is expected to identify U.S. coins by name, including pennies, nickels, dimes, and quarters. K.9A: identify ways to earn income K.9B: differentiate between money received as income and money received as gifts K.9C: list simple skills required for jobs K.9D: distinguish between wants and needs and identify income as a source to meet one's wants and needs

ELPS Learning Strategies 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) Listening 2D: monitor understanding of spoken language during classroom instruction and interactions and seek clarification as needed Speaking 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 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 Reading 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 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

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Vocabulary

Unit Vocabulary Categories Earned Labels Picture graphs Cent Gift Money Quarter Coin Given Needs Real-object graphs Conclusions Graph title Nickel Skills Data Income Penny Wants Dime Jobs

Cognitive Complexity Verbs: collect, sort, organize, use, create, draw conclusions, identify, differentiate, list, distinguish Academic Vocabulary by Standard: K.8A: categories, data K.8B: data, graph title, labels, picture graphs, real-object graphs K.8C: conclusions, real-object graphs, picture graphs K.4: cent, coin, dime, nickel, penny, quarter K.9A: income, money K.9B: gift, given, earned, income, money K.9C: jobs, skills K.9D: income, needs, wants

Suggested Math Manipulatives Coins Snap Cubes Chart Paper 2 Color Counters Sticky Notes Graph Paper

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K.8A: collect, sort, and organize data into two or three categories 1.8A collect, sort, and organize data in up to three categories using models/representations such as tally marks or T-charts

K.8B: use data to create real-object and picture graphs 1.8B use data to create picture and bar-type graphs 2.10B organize a collection of data with up to four categories using pictographs and bar graphs with intervals of one or more

K.8C: draw conclusions from real-object and picture graphs 1.8C draw conclusions and generate and answer questions using information from picture and bar-type graphs 2.10D draw conclusions and make predictions from information in a graph

K.4: The student is expected to identify U.S. coins by name, including pennies, nickels, dimes, and quarters.

1.4A identify U.S. coins, including pennies, nickels, dimes, and quarters, by value and describe the relationships among them

K.9A: identify ways to earn income 1.9A define money earned as income K.9B: differentiate between money received as income and money received as gifts

K.9C: list simple skills required for jobs K.9D: distinguish between wants and needs and identify income as a source to meet one's wants and needs

1.9B identify income as a means of obtaining goods and services, oftentimes making choices between wants and needs

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K.8A: collect, sort, and organize data into two or three categories

In order to adhere to the standard, students should be the ones to collect, sort, and organize the data. Instruction should only prompt the actions (i.e. the teacher says: “I wonder how many of us own a dog or a cat? What could we do to collect that data? How could you organize the data collected?”). Data categories can extend to no more than three categories (i.e. “What is your favorite sport?” could yield too many different categories; “Do you like to play football, basketball, or baseball?” limits the categories to no more than 3).

Having students collect, sort, and organize their own data facilitates students as they draw reasonable conclusions and make reasonable predictions. Representing student collected data on a real-object graph and picture graph enables students to interpret the information more accurately. K.8B: use data to create real-object and picture graphs K.8C: draw conclusions from real-object and picture graphs

The data collection takes place in response to a question. The data collected is to be sorted into two or three categories. To build to 1.8A, data may be organized using T-charts and tally marks. When paired with K.8B, the student is expected to use the organized data to create real-object or picture graphs.

K.8B: use data to create real-object and picture graphs

In alignment with K.8A, once students have collected and sorted their own data, they will need to represent the data on a real-object graph and/or picture graph. Picture graphs are limited to representing one piece of data (i.e. a smiley face can only represent one person not five). Instruction should emphasize the importance of a title and labeling the categories of the graph. Students should be exposed to both vertical and horizontal graphs.

* Due to developmental reasons, students may have difficulty moving from a real-object graph to a picture graph. * When representing the same set of data vertically and horizontally, students may interpret the data as different because of the difference in visual representations. * When using real-objects to represent data, students may associate the larger the object the more data it represents (i.e. two king size candy bars aligned next to four snack size candy bars appears as if there are more king size than snack size candy bars).

The real-object graphs and picture graphs build to 1.8B where students use data to create picture and bar-type graphs. Arrangements of objects and pictures should be linear. The limitations of two or three categories found in K.8A apply to this SE.

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K.8C: draw conclusions from real-object and picture graphs

In alignment with K.8A/B, once students have collected their own data and displayed their data on either a real-object or pictograph, they are to draw their own conclusions (i.e. there are a lot more students that own dogs than cats in our class. We have four people in our class that own a cat because there are four pictures of cats, etc.). As students are the creators of the data and representation, they will be able to more accurately interpret the data.

* Due to developmental reasons, students may have more difficulty interpreting data from a picture graph than a real-object graph.

Students should draw conclusions related to the question that led to the data collection. Students may also draw conclusions about the data related to the number concepts and operations in the Number and Operations strand for kindergarten.

K.4: The student is expected to identify U.S. coins by name, including pennies, nickels, dimes, and quarters.

In adherence to the standard, students only have to identify coins in Kindergarten. The value of the coin is introduced in grade 1 (see 1.4A). Describing the attributes of the coins may support students with identifying them correctly (i.e. color, size, smooth vs. rough edges, etc.). Students need to identify the coin whether the heads or tails side of the coin is visible. Focusing on the attributes of the coin will support students in appropriately identifying all versions of coins. The standard also requires that the students recognize the need for coins in monetary transactions which would be a connection to the personal financial literacy strand (K.9).

Being able to identify U.S. coins is critical in solving monetary transactions. 1.4C use relationships to count by twos, fives, and tens and determine the value of a collection of pennies, nickels, and/or dimes

This SE builds to 1.4A where students are expected to describe the relationship among these coins, 1.4B where students are expected to write a number with the cent symbol to describe the value of the coin, and 1.4C where students may determine the value of a collection of pennies, nickels, and/or dimes.

K.9A: identify ways to earn income

Instruction should allow students the opportunity to discuss how their parents earn income and how students can earn income. Teachers could incorporate story problems involving real world situations of money being earned to incorporate K.2H and K.3A/B/C.

Identifying ways to earn income will support one’s ability to manage financial resources more effectively for a lifetime of financial security.

This SE builds to 1.9A.

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K.9B: differentiate between money received as income and money received as gifts

Instruction should allow students the opportunity to discuss the difference between working for money as income compared to money given as a gift. Doing chores to earn money is income; money received from family/ friends for birthdays/ holidays is a gift. Teachers could incorporate story problems involving real world situations of money being earned as income and/or gifts.

Understanding the difference between money earned vs. money received as a gift supports one’s ability to manage financial resources more effectively for a lifetime of financial security.

This SE builds to 1.9A and 1.9B.

K.9C: list simple skills required for jobs

Instruction should allow students to investigate different job choices and participate in discussions about what skills are needed to do such jobs.

Identifying ways to earn income will support one’s ability to manage financial resources more effectively for a lifetime of financial security.

Jobs describe work that is completed for the purpose of receiving income. This SE builds to 3.9A and 6.14H.

K.9D: distinguish between wants and needs and identify income as a source to meet one's wants and needs

Instruction should provide students with a variety of suggested wants and needs to sort (i.e. water, food, shelter, clothes, video games, cell phones, etc.). Students should defend the category they choose and debate among their classmates. In alignment with K.9A, students need to recognize that earning an income is a source for meeting those wants and needs. Teachers could incorporate story problems involving real world situations of wants and needs.

Understanding the difference between wants and needs and how income serves as a way to obtain such measures will support one’s ability to manage financial resources effectively for a lifetime of financial security.

This SE can build to 1.9D or 2.11B.

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Kindergarten Mathematics Curriculum Document 2016-2017

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