kindergarten mathematics curriculum document 2014-2015

Kindergarten

Mathematics Curriculum Document

2014-2015

Trouble Shooting Guide *The 2014-15 Mathematics Curriculum Document for Grade K includes the following features:

A.) The NISD Curriculum Document is a TEKS-Based Curriculum B.) YAG detailing the Curriculum Bundles, Suggested Days of Instruction, & TEKS C.) Color Coding: Yellow=Supporting Standards, Green=Readiness Standards, & Blue=Process

Standards, Italic Red=Teacher Note, Purple Text=ELPS, BOLD=Notations of TEKS Standard Change, Cognitive Change, and Content Change to Bridge Understanding of New TEKS

D.) TEKS, Understanding, Rigor Questions, Instructional Strategies/Resources, Questions & Stems and Teacher Notes/Resources are Detailed with each Curriculum Bundle. Focus on STAAR Alignment & Supporting of Readiness Connections.

E.) The expectation is that teachers will share additional effective resources with their campus Curriculum Specialist(s) for inclusion in the document.

F.) Since this is Year 1 of a New Mathematics Resource Adoption, inclusion of references to the resource will be included at a later time.

G.) Performance Tasks have been purposefully omitted; however, performance tasks are highly encouraged. The following resource offers tasks and corresponding directive cards (English and Spanish) and rubrics: http://www.rda.aps.edu/MathTaskBank/fi_html/k2tasks.htm. (See example, Pg 7) These activities ARE NOT to be thought of as projects. Project-Based Learning Projects will be included in the document at a later time after further professional development into PBL. Please follow up with your Campus Curriculum Specialists if you need assistance with selecting applicable performance tasks from the Mathematics Performance Task Bank.

Table of Contents Cover Page………………………………………………………………………………Page 1

Trouble Shooting Guide…………..…………………………………………………….Page 2

Table of Contents………………………………………………………………………..Page 3

Year At A Glance………………………………………………………………………..Page 4

Process Standards……………………………………………………………………….Page 5

First Six Weeks…………………………………………………………………………..Page 6

Second Six Weeks………………………………………………………………………..Page 14

Third Six Weeks……………………………………………………………………….…Page 23

Fourth Six Weeks…………………………………………………………………….…..Page 33

Fifth Six Weeks…………………………………………………………………………...Page 38

Sixth Six Weeks…………………………………………………………………………...Page 42

Year at a Glance By Six Weeks/Bundle/TEKS

First Semester Second Semester 1st Six Weeks 4th Six Weeks • Bundle #1= 14 Days: K.2A (Supporting); K.2B (Readiness); K.2C

(Supporting); K.5 (Supporting)

• Bundle #2= 14 Days: K.8A (Supporting); K.2A (Supporting); K.2B (Readiness); K.2C (Supporting);

• Bundle #7=19 Days: K.6 A (Supporting); K.6D (Supporting); K.6E (Readiness); K.6F (Supporting);

• Bundle #8=14 Days: K.5 (Supporting); K.6B (Supporting); K.6C (Supporting); K.6 E (Readiness)

2nd Six Weeks 5th Six Weeks • Bundle #3=15 Days: K.2A (Supporting); K.2B (Readiness); K.2C

(Supporting); K.2D (Supporting); K.2G (Supporting); K.5 (Supporting); K.2I (Readiness)

• Bundle #4= 10 Days: K.2E (Supporting); K.2G (Supporting); K.2I (Readiness); K.2D (Supporting); K.2B (Readiness); K.2C (Supporting);

Bundle #9=14 Days: K.7A (Supporting); K.7B (Readiness)

• Bundle #10=19 Days: K.3A (Supporting); K.3B (Readiness); K.3C (Supporting);

3rd Six Weeks 6th Six Weeks • Bundle #5=10 Days: K.2F (Supporting); K.2H (Readiness); K.8B

(Readiness); K.8C (Readiness); K.8A (Supporting); K.2B (Readiness); K.2C (Supporting);

• Bundle #6= 15 Days: K.2C (Supporting); K.2A (Supporting); K.4 (Supporting); K.9A (Supporting); K.9B (Supporting); K.9C (Supporting); K.9D (Supporting); K.2B (Readiness);

• Bundle #11=15 Days: K.3A (Supporting); K.3B (Readiness); K.3C

(Supporting);

• Bundle #12=17 Days: K.3A (Supporting); K.3B (Readiness); K.3C (Supporting);

Process Standards K.1A K.1B K.1C K.1D K.1E K.1F K.1G

Apply mathematics to problems arising in everyday life, society, 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.

*Process Standards MUST be integrated within EACH Bundle to ensure the success of students.

Course: Kindergarten Math

Bundle 1: Counting and Naming Number Quantities August 25 – September 12 (14 days)

Understandings • Objects and numbers can be counted in a sequence. • Objects can be represented with a number. • Develop strategies for accurately counting a set of objects by ones. • Count and connect number words, numerals, and quantities.

Rigor Questions 1. How many do I have? 2. How can I use counting to help myself in everyday life? 3. What do I count and why? 4. How do I count?

Vocabulary: Cognitive Complexity Verbs for TEKS: Apply; Write

count; sequence; whole numbers (0-‐20); forward; backward; cardinality; whole numbers (0-‐100); ones; tens

TEKS/Student Expectations TEKS/ELPS Integration Instructional Strategies/Resources Clarifications and Examples

The student is expected to: K.2.A-count forward and backward to at least 20 with and without objects; (Supporting Standard)

Current Standard: K.6B count by ones to 100 (Patterns, Relationships, and Algebraic Thinking Strand.)

Cognitive Change: N/A

Content Change: Changed strand from “Patterns, Relationships, and Algebraic Thinking” to “Number and Operations:”; Added the counting of numbers forward and backward; Changed counting to 100 to “at least” to 20; Added counting with and without the use of objects.

K.2.A Supports Readiness Standard By: 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. ELPS.1.E - internalize new basic and academic language by using and reusing it in meaningful ways in speaking and writing activities that build concept and language attainment; ELPS.1.F - use accessible language and learn new and essential language in the process

ELPS.2.C - learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions;

ELPS.2.D - monitor understanding of spoken language during classroom instruction and interactions and seek clarification as need.

K.2.A Instructional Implications: 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.

Focus Students count forward to 10 without objects. Questions and Stems •Count to 10 for me. •When you count, what number comes after ___? (0-9) Teacher Notes This skill will also be addressed in daily calendar routines. Will be extending counting forward and backward to 20 in future bundles. Mastery of TEKS (0-10) is expected in bundle 3, and (11-20) is expected in bundle 6.


The student is expected to: K.2.B-read, write, and represent whole numbers from 0 to at least 20 with and without objects or pictures; (Readiness Standard)

Current Standard: K.1B Use sets of concrete objects to represent quantities given in verbal or written form (through 20); K.1C Use numbers to describe how many objects are in a set) through 20 using verbal and symbolic descriptions.


Content Change: Added reading and writing of numbers to “at least 20”; Added reading and writing of whole numbers with and “without” the use of objects or pictures.

K.2.B STAAR Grade 3 Scaffold: 3.2 A compose and decompose numbers up to 100,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens, and so many ones using objects, pictorial models, and numbers, including expanded notation as appropriate (R)

K.2.B Instructional Implications 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.). While 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.

Focus

Students recognize numbers 0-10. Questions and Stems

What number is this? (0-10) Teacher Notes Will be extending expectations for writing and representing numbers to 20 in future bundles. Mastery of TEKS (0-10) is expected in bundle 3, and (11-20) is expected in bundle 6.

K.2.B Distractor Factor: 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 10 or 1 through 20, without associating the number name with the appropriate number or value; Students may confuse number names that are homophones (one/won, two/to/too, four/for, eight/ate); Students may not consider zero a number.

The student is expected to: K.2.C-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; (Supporting Standard)

Current Standard: K.1 Use numbers to describe how many objects are in a set (through 20) using verbal and symbolic descriptions.


Content Change: Added the understanding of cardinality; Added counting to “at least” 20.

K.2.C Supports Readiness Standard By: Applying one-‐to-‐one correspondence to counting a set of objects up to 20 and understanding the cardinality rule will support student’s ability to develop strategies to recall basic facts to solve addition/subtraction problems.

K.2.C Instructional Implications: 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

Focus Students count a set of objects up to 10 in various arrangements.

Questions and Stems

•How many objects are there? •Show students a set of manipulatives 0-10 and ask student to count them. •Show same number in a different arrangement (such as a 10 frame, pile, group, etc) and ask

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).

students to count them.

Teacher Notes This skill will continued to be addressed through bundle 3. This is also checking for 1 to 1 correspondence. Will be extending expectations for counting sets of objects to 20 in future bundles. Mastery of TEKS (0-10) is expected by bundle 3, and (11-20) is expected in bundle 6.

K.5-Algebraic reasoning. 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. (Supporting Standard)

Current Standard: K.6B Count by ones to 100.


Content Change: Added counting by ones and tens to “at least” 100.

K.5- Supports Readiness Standard By: 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 value in order to solve addition/subtraction problems.

K.5-Instructional Implications: 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 100’s 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 as well. 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”).

Focus

Students count by 10s up to 100 with or without real world objects. Questions and Stems

•Count by 10s up to 100 beginning with 10. •Use real-world objects in groups of 10 to demonstrate skip counting as a relevant strategy for counting. Teacher Notes

Student is expected to be able to count to 100 by 10s by the end of bundle 3, and by 1s by the end of bundle 6.


Bundle 2: Naming number quantities and sorting objects. September 15 – October 2 (14 days)

Understandings • Objects can be sorted and organized by their attributes. • Use manipulatives, drawings, tools, and notations to show strategies. • Count and connect number words, numerals, and quantities.

Rigor Questions

1. How are groups alike/different? 2. How do I know where this object belongs? 3. How can I record my quantity? 4. How do I compare two or more groups to each other? 5. What attributes can I use to identify, compare, and sort objects?

Vocabulary: Cognitive Complexity Verbs for TEKS: Apply; Organize; Write;

collect; sort; categories; data; numbers (1-‐100); ones; tens; whole numbers (0-‐20); forward; backward


K.8.A-collect, sort, and organize data into two or three categories; (Supporting Standard)

Current Standard: K.12A Construct graphs using real objects or pictures in order to answers questions.

Cognitive Change: Added “collecting, sorting, and organizing” of data.

Content Change: Added two or three categories.

K.8.A Supports Readiness Standard By: Having students collect, sort, and organize their own data facilitates students as they draw reasonable conclusions and make reasonable predictions more reasonably. Representing student collected data on a real-‐object graphs and picture graphs enables students to interpret the information more accurately.

ELPS.1.C - use strategic learning techniques such as concept mapping, drawing, memorizing, comparing, contrasting, and reviewing to acquire basic and grade-level vocabulary.

K.8.AInstructional Implications: 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?” yield too many different categories; “Do you like to play football, basketball, or baseball” limits the categories to no more than 3).

Focus Students sort objects using a variety of manipulatives by attributes (size, color, shape, etc) and explain their thinking. Questions and Stems How did you sort your groups? -How are your groups alike? -How are your groups different? -Where does this object belong? Teacher Notes Students will begin sorting objects to gain a foundation for categorization before sorting data. (i.e. graphing)





K.2.A Supports Readiness Standard By: 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.

K.2.A Instructional Implications: 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

Focus Students count forward and backward to 10 without objects. Questions and Stems Count to 10 for me. Count backward from 10. When you count, what number comes before ___? (0-9) Teacher Notes Will be extending counting forward and backward to 20 in future bundles. Mastery of TEKS is expected in bundle 6








Focus Students recognize and write numbers 0-10. Students create representations of numbers 0-10 with objects and pictures. Questions and Stems Draw a picture to show ___. (0-10) "Show me ___ objects." (0-10) - verbal cue Teacher provides student with a number (non-verbal cue), and student creates a group of manipulatives that matches. Teacher provides student with a set of objects and student records the number showing the quantity of the set. Teacher Notes This skill can also be addressed with daily calendar routines. Expectations for writing and representing numbers to 20 will be extended in future bundles. Mastery of TEKS is expected in bundle 6 K.2.B Distractor Factor: 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 10 or 1 through 20, without associating the number name with the appropriate number or value; Students may confuse number names that are homophones (one/won, two/to/too, four/for, eight/ate); Students may not consider zero a number.







ELPS.2.F - listen to and derive meaning from a variety of media such as audio tape, video, DVD, and CD ROM to build and reinforce concept and language attainment.

K.2.C Instructional Implications: 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).

Focus Students count a set of objects up to 10 in various arrangements. Questions and Stems

How many objects are there? -Show students a set of manipulatives 0-10 and ask student to count them. -Show same number in a different arrangement (such as a 10 frame, pile, group, etc) and ask students to count them.

Teacher Notes

This is a continuation from bundle 1. This is also checking for 1 to 1 correspondence. Will be extending expectations for counting sets of objects to 20 in future bundles. Mastery of TEKS is expected in bundle 6

Course: Kindergarten Math Bundle 3: Counting and Comparing October 6–October 24 (15 days)

Understandings • Develop the idea of equivalence, more and fewer. • Develop an understanding of the magnitude of numbers. • Develop instant recognition of small groups of objects.

Rigor Questions

1. Does order matter when I count? 2. How did I compare? 3. Which has more or fewer?

Vocabulary: Cognitive Complexity Verbs for TEKS: Apply; Organize; Write; Recognize; Compare

numbers (1-‐100); ones; tens; whole numbers (0-‐20); backward; compose; decompose; more; less; as many (equal)








Focus Students count forward and backward to 10 with and without objects.

Questions and Stems

Count these objects for me. Count these objects backwards. (uncount) When you count, what number comes before/after ___? (0-10) Assessment Methods Use objects to assess for mastery for 0-10 in this bundle. Teacher Notes

Will be extending counting forward and backward to 20 in future bundles. Mastery of TEKS is expected in bundle 6


The student is expected to: K.2.B-read, write, and represent whole numbers from 0 to at least 20 with and without objects or pictures. (Readiness Standard)




K.2.B STAAR Grade 3 Scaffold: 3.2 A compose and decompose numbers up to 100,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens, and so many ones using objects, pictorial models, and numbers, including expanded notation as appropriate (R) ELPS.3.B expand and internalize initial English vocabulary by learning and using high-frequency English words necessary for identifying and describing people, placed, and objects, by retelling simple stories and basic information represented or supported by pictures, and by learning and using routine language for classroom communication. ELPS.3.F 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. LPS.3.H narrate, describe, and explain with increasing specificity and detail as more English is acquired.


Focus

Students recognize and write numbers 0-10. Students create representations of numbers 0-10 with objects and pictures. Questions and Stems

Draw a picture to show ___. (0-10) "Show me ___ objects." (0-10) - verbal cue Teacher provides student with a number (non-verbal cue), and student creates a group of manipulatives that matches. Teacher provides student with a set of objects and student records the number showing the quantity of the set. Assessment Methods Use flashcards or written numbers in random order for students to identify. (0-10) Teacher Notes

This skill can also be addressed with daily calendar routines.Expectations for writing and representing numbers to 20 will be extended in future bundles. Mastery of TEKS is expected in bundle 6.


TEKS/Student Expectations TEKS/ELPS Integration Instructional Clarifications and Examples

Strategies/Resources The student is expected to: K.2.D-recognize instantly the quantity of a small group of objects in organized and random arrangements; (Supporting Standard-NEW STANDARD!!!)

K.2.D Supports Readiness Standard By: Being able to recognize the quantity of structured and random arrangements will support students in visually comparing two numbers.

K.2.D Instructional Implications: 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, five/tens 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.

Focus Student instantly recognize the numbers (0-6) of objects in random and arranged order.

Questions and Stems

How many objects are there? -using dice or Quick Images from Investigations (for organized arrangements). -using pictures or objects (for random arrangements) Teacher Notes

This is considered subitizing. This is also checking for 1 to 1 correspondence. Expectations for counting sets of objects to 20 will be extended in future bundles. Mastery of TEKS is expected in bundle 6.

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Strategies/Resources The student is expected to: K.2.G-compare sets of objects up to at least 20 in each set using comparative language; (Supporting Standard)

Current Standard: K.1A use one-to-one correspondence and language such as more than, same number as, or two less than to describe relative sizes of sets of concrete objects.


Content Change: Added representations to “at least” 20; Deleted one-to-one correspondence.

K.2.G Supports Readiness Standard By: 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 ( <, >, or =).

ELPS.2.H - understand implicit ideas and information in increasingly complex spoken language commensurate with grade-level learning expectations;

K.2.G Instructional Implications: 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 student that are developmentally ready.

Focus Students compare sets of objects up to 10 using comparative language, such as "more than" or "less than" or "equal/the same". Questions and Stems

Which group has more? Which group has less? Are any groups equal/the same? Teacher Notes Will be extending expectations for counting sets of objects to 20 in future bundles. Mastery of TEKS is expected in bundle 6





K.5- Supports Readiness Standard By: 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 value in order to solve addition/subtraction problems. .


Focus Students count by 10s to 100, and by 1s to 20.

Questions and Stems

Count by 10s to 100. Count by 1s to 20. "Starting with __ (0-19), count to 20." Teacher Notes Mastery of TEKS is expected in bundle 9.


Strategies/Resources The student is expected to: K.2.I-compose and decompose numbers up to 10 with objects and pictures. (Readiness Standard-NEW STANDARD!!!)

K.2.I STAAR Grade 3 Scaffold:3.4A- solve with fluency one-‐step and two-‐step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction (R)

K.2.I Instructional Implications: 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 as many different combinations for four cubes (i.e. 4 blue; 4 yellow; 3 blue and 1 yellow, three yellow and 1 blue, 2 blue 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).

Focus Students use objects to compose and decompose numbers up to 10.

Questions and Stems

How many do you have? Given a set of objects, how many more do you need to make ___? (0-10) How many objects are there all together? Teacher Notes

Students will revisit this skill when addressing number sentences in bundles 10-12.

K.2.I Distractor Factor: 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).

Course: Kindergarten Math Bundle 4: Creating and Comparing Sets October 27 – November 7 (10 Days)

Understandings • Quantities can be recognized. • Numbers can be compared. • Sets of objects can be created for comparison.

Rigor Questions

1. Can I make a set with more/less/as many (equal) objects? 2. How do you know which set has more/less? 3. How is recognizing quantities instantly helpful?

Vocabulary: Cognitive Complexity Verbs for TEKS: Generate; Analyze; Recognize; Write; Use

numbers (1-‐100); ones; tens; whole numbers (0-‐20); forward; backward; compose; decompose; more than; less than; as many (equal)


The student is expected to: K.2.E-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; (Supporting Standard)

Current Standard: K.1A Use one-to-one correspondence and language such as more than, same number as, or two less than to describe relative sizes of sets of concrete objects.

Cognitive Change: Added “generating” numbers that are more than/less than/equal to.

Content Change: Added the use of pictorial models.

K.2.E Supports Readiness Standard By: 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. The student is expected to

K.2.E Instructional Implications: Students counting forward and backward from a given number or given set of objects (see K.2A) begin the foundational an 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 less, 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 given 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 = ___).

Focus Students create sets of objects up to 20, as well as sets that contain more than, less than, or equal amounts.

Questions and Stems

Make a set of ___ (0-20) objects. Make a set with more/less/equal amounts.

Teacher Notes

Mastery of TEKS is expected in bundle 6.


The student is expected to: K.2.G-compare sets of objects up to at least 20 in each set using comparative language; (Supporting Standard)

Current Standard: K.1A use one-to-one correspondence and language such as more than, same number as, or two less than to describe relative sizes of sets of concrete objects.


Content Change: Added representations to “at least” 20; Deleted one-to-one correspondence.

K.2.G Supports Readiness Standard By: 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 ( <, >, or =).

The student is expected to

K.2.G Instructional Implications: 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 student that are developmentally ready.

Focus

Students compare sets of objects up to 20, using comparative language, such as "more than", "less than", or "equal amount". Questions and Stems

Which set has more/less? Teacher Notes

This is a continuation from bundle 3.

The student is expected to: K.2.I-compose and decompose numbers up to 10 with objects and pictures. . (Readiness Standard-NEW STANDARD!!!)

K.2.I STAAR Grade 3 Scaffold:3.4A- solve with fluency one-‐step and two-‐step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction (R)

K.2.I Instructional Implications: 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 as many different combinations for four cubes (i.e. 4 blue; 4 yellow; 3 blue and 1 yellow, three yellow and 1 blue, 2 blue 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).

Focus

Students use objects to compose and decompose numbers up to 10.

Questions and Stems

How many do you have? Given a set of objects, how many more do you need to make ___? (0-10) How many objects are there all together?

Teacher Notes

Students will revisit this skill when addressing number sentences in bundles 10-12

K.2.I Distractor Factor: 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).


The student is expected to: K.2.D-recognize instantly the quantity of a small group of objects in organized and random arrangements; (Supporting Standard-NEW STANDARD!!!)

K.2.D Supports Readiness Standard By: Being able to recognize the quantity of structured and random arrangements will support students in visually comparing two numbers.

K.2.D Instructional Implications: 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, five/tens 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.

Focus

Student instantly recognize the numbers (0-6) of objects in random and arranged order.

Questions and Stems

How many objects are there? -using dice or Quick Images from Investigations (for organized arrangements). -using pictures or objects (for random arrangements)

Teacher Notes

This is considered subitizing. This is also checking for 1 to 1 correspondence. Expectations for counting sets of objects to 20 will be extended in future bundles. Mastery of TEKS is expected in bundle 6






ELPS.2.E - use visual, contextual, and linguistic support to enhance and confirm understanding of increasingly complex and elaborated spoken language


Focus Students recognize and write numbers 1-20. Students create representations of numbers 0-10 with objects and pictures.

Questions and Stems

Draw a picture to show ___. (0-‐20) "Show me ___ objects." (0-‐20) -‐ verbal cue Teacher provides student with a number (non-‐verbal cue), and student creates a group of manipulatives that matches. Teacher provides student with a set of objects and student records the number showing the quantity of the set.

Assessment Methods

Use flashcards or written numbers in random order for students to identify. (0-20)

Teacher Notes

This skill can also be addressed with daily calendar routines. Expectations for writing and representing numbers to 20 will be extended in future bundles. Mastery of TEKS is expected in bundle 6.



The student is expected to: K.2.C-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; ; (Supporting Standard)





ELPS.1.H - develop and expand repertoire of learning strategies such as reasoning inductively or deductively, looking for patterns in language, and analyzing sayings and expressions commensurate with grade-level learning expectations.

K.2.C Instructional Implications: 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).

Focus Students count a set of objects up to 20 in various arrangements. Questions and Stems

How many objects are there? Show students a set of manipulatives 0-20 and ask student to count them. Show same number in a different arrangement (such as a 10 frame, pile, group, etc) and ask students to count them.

Assessment Methods Use manipulatives to assess for mastery in this bundle.

Teacher Notes

This is a continuation from bundle 1. This is also checking for 1 to 1 correspondence. Will be extending expectations for counting sets of objects to 20 in future bundles. Mastery of TEKS (0-10) is expected in bundle 3, and (11-20) is expected in bundle 6


Bundle 5: Creating Graphs and Using Numbers to Compare Quantities November 10 – 21 (10 days)

Understandings • Graphs help us compare and analyze data. • Groups can be identified by quantities. • Quantities can be compared.

Rigor Questions

1. What information does this graph tell me? 2. How does making a graph or table help me to solve problems? 3. How can I tell if a group is greater/less than/equal to another group. 4. How do I compare two or more groups to each other? 5. What number is more/less than (any number up to 10)?

Vocabulary: Cognitive Complexity Verbs for TEKS: Generate; Use; Analyze; Organize; Write

numbers (1-‐100); whole numbers (0-‐20); more than; less than; as many (equal); data; real-‐object graph; picture graph; collect; sort


The student is expected to: K.2.F-generate a number that is one more than or one less than another number up to at least 20; (Supporting Standard)

Current Standard: K.1A use one-to-correspondence and language such as more than, same number as, or two less than to describe relative sizes of sets of concrete objects.

Cognitive Change: Added “generating” of number that are more than/less than/equal to.

Content Change: Limited to “one” more or less; deleted “two less”; Added representations to “at least” 20

K.2.F Supports Readiness Standard By: In generating a number greater than, less than, or equal to a given whole number, students will develop the understanding of the magnitude of whole numbers which will support their ability to compare/order numbers. The student is expected to:

K.2.F Instructional Implications: 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.

Focus Given a number, students generate a number that is one more or one less than the given number (0-20).

Questions and Stems

What is one more/less than ___ (0-20). Show me a set that has one more/less than ___. (0-20)

Teacher Notes

Students can demonstrate this skill orally as well as with manipulatives.


The student is expected to: K.2.H-use comparative language to describe two numbers up to 20 presented as written numerals;

Current Standard: K.1A Use one-to-one correspondence and language such as more than, same number as, or two less than to describe relative sizes of sets of concrete objects.


Content Change: Added the comparison of written representation of numbers up to 20.

K.2.H STAAR Grade 3 Scaffold: 3.3D compose and decompose a fraction a/b with a numerator greater than zero and less than or equal to b as a sum of parts 1/b. The student is expected to ELPS.3.D - speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency;

ELPS.3.J - respond orally to information presented in a wide variety of print, electronic, audio, and visual media to build and reinforce concept and language attainment.

K.2.H Instructional Implications: 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).

Focus Given two numerals, students describe them with comparative language. Questions and Stems

What can you tell me about these two numbers? (Teacher shows student two written numerals.) Teacher Notes

Students are expected to generate their own comparative language for this skill.

K.2.H Distractor Factor: Due to developmental reasons, students may not be able to compare written representation 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).

The student is expected to: K.8.B-use data to create real-object and picture graphs; (Readiness Standard)

Current Standard: K.12A Construct graphs using real objects or pictures in order to answer questions.

Cognitive Change: Added the “collecting, sorting, and organizing” of data .


K.8.B STAAR Grade 3 Scaffold:3.8A- summarize a data se t with multiple categories using a frequency table, dot plot, pictograph, or bar graph with scaled intervals (R)

K.8.B Instructional Implications: 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.

Focus

Students create graphs using data.

Questions and Stems How can you organize your information? What does your information tell you?

K.8.B Distractor Factor: 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 the 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 moreking size than snack size candy bars).

The student is expected to: K.8.C-draw conclusions from real-object and picture graphs. (Readiness Standard)

K.8.C STAAR Grade 3 Scaffold:3.8B- solve one-‐ and two-‐step problems using categorical data represented with a frequency table, dot plot, pictograph, or bar graph with scaled

K.8.C Instructional Implications: In alignment with K.8A/B, once students have collected their own data and displayed their data on either a real-‐object graph or

Focus

Students use graphs to answer questions and gain

Current Standard: K.12B Use information from a graph of real objects or pictures in order to answer questions.

Cognitive Change: Replaced “answering” questions to “drawing” conclusions.

Content Change: N/A

intervals (S) 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.

information.

Questions and Stems What information does this graph show you? Which one has more/less? Are any equal/the same?

K.8.C Distractor Factor: Due to developmental reasons, students may have more difficulty interpreting data from a picture graph than a real-‐object graph


The student is expected to: K.8.A-collect, sort, and organize data into two or three categories; (Supporting Standard)

Current Standard: K.12A Construct graphs using real objects or pictures in order to answers questions.

Cognitive Change: Added “collecting, sorting, and organizing” of data.


K.8.A Supports Readiness Standard By: Having students collect, sort, and organize their own data facilitates students as they draw reasonable conclusions and make reasonable predictions more reasonably. Representing student collected data on a real-‐object graphs and picture graphs enables students to interpret the information more accurately.

K.8.AInstructional Implications: 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?” yield too many different categories; “Do you like to play football, basketball, or baseball” limits the categories to no more than 3).

Focus Students organize data to gain information.

Questions and Stems

What did you learn from this information? Which group has more/less? Which group has the most/least?






ELPS.2.E - use visual, contextual, and linguistic support to enhance and confirm understanding of increasingly complex and elaborated spoken language;


Focus

Students recognize and write numbers 1-20. Students create representations of numbers 0-10 with objects and pictures. Questions and Stems

Draw a picture to show ___. (0-‐20) "Show me ___ objects." (0-‐20) -‐ verbal cue Teacher provides student with a number (non-‐verbal cue), and student creates a group of manipulatives that matches. Teacher provides student with a set of objects and student records the number showing the quantity of the set. Assessment Methods Use flashcards or written numbers in random order for students to identify. (0-‐20)

Teacher Notes

This skill can also be addressed with daily calendar routines. Expectations for writing and representing numbers to 20 will be extended in future bundles. Mastery of TEKS is expected in bundle 6.









K.2.C Instructional Implications: 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


Questions and Stems

How many objects are there?

Show students a set of manipulatives 0-20 and ask student to count them.

Show same number in a different arrangement (such as a 10 frame, pile, group, etc) and ask students to count them.


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).

Teacher Notes

This is a continuation from bundle 1. This is also checking for 1 to 1 correspondence. Will be extending expectations for counting sets of objects to 20 in future bundles. Mastery of TEKS (0-10) is expected in bundle 3, and (11-20) is expected in bundle 6.

Course: Kindergarten Math Bundle 6: Financial Literacy December 1 -19 (15 days)

Understandings • Distinguish between needs and wants. • Identify ways to earn income. • Identify coins

Rigor Questions

1. What is the difference between needs and wants? 2. How do I earn income? 3. What skills are required for jobs? 4. What is a penny/nickel/dime/quarter?

Vocabulary: Cognitive Complexity Verbs for TEKS: Apply; Identify; Write

whole numbers (0-‐20); forward; backward; coins; penny(ies); nickel(s); dime(s); quarter(s); income; earn; wants; needs;


The student is expected to: K.2.C-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. (Supporting Standard)






K.2.C Instructional Implications: 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


Questions and Stems

How many objects are there?

Show students a set of manipulatives 0-20 and ask student to count them.

Show same number in a different arrangement (such as a 10 frame, pile, group, etc) and ask students to count them.

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).


Teacher Notes

This is a continuation from bundle 1. This is also checking for 1 to 1 correspondence.







Focus Students count forward and backward to 20 with and without objects.

Questions and Stems

Count to 20 for me. Count backward from 20. When you count, what number comes before/after ___? (0-20)

Assessment Methods By this bundle, students should have mastery of K.2 TEKS (EXCEPT K.2I). Teacher Notes: *Previously addressed in Bundles 1-3. Assess for mastery at this time.


K.4-Number and operations. The student applies mathematical process standards to identify coins in order to recognize the need for monetary transactions. The student is expected to identify U.S. coins by name, including pennies, nickels, dimes, and quarters. (Supporting Standard)

Current Standard: 1.1C Identify individual coins by name and value and describe relationships among them.


Content Change: Moved the identification of coins from grade 1 to Kindergarten.

K.4- Supports Readiness Standard By: Being able to identify U.S. coins is critical in solving monetary transactions.

K.4-Instructional Implications: 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 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.

Focus

Students identify US Coins by name. Questions and Stems Can you name this coin? (Teacher shows student picture/model of coin.)

The student is expected to: K.9.A-identify ways to earn income; (Supporting Standard-NEW STANDARD!!!)

K.9.A Supports Readiness Standard By: Identifying ways to earn income will support one’s ability to manage financial resources more effectively for a lifetime of financial security.

ELPS.1.E - internalize new basic and academic language by using and reusing it in meaningful ways in speaking and writing activities that build concept and language attainment; ELPS.1.F - use accessible language and learn new and essential language in the process

ELPS.2.C - learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions;

ELPS.2.D - monitor understanding of spoken language during classroom instruction and interactions and seek clarification as needed;

K.9.A Instructional Implications: 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 could be incorporated into the Number and Operations strand (see K.2H and K.3A/B/C).

Focus Students learn various ways to earn income.

Questions and Stems

What are some ways people earn money? What can you do to earn money? Teacher Notes:

This is integrated with Social Studies TEKS.


The student is expected to: K.9.B-differentiate between money received as income and money received as gifts

K.9B Supports Readiness Standard By: 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. The student is expected to

K.9B Instructional Implications: 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 could be incorporated into the Number and Operations strand (see K.2H and K.3A/B/C).

Focus

Students differentiate between earned income and monetary gifts. Questioning and Stems What are ways for you to receive money? What makes money you earn different from money you receive as a gift? Teacher Notes:

This is integrated with Social Studies TEKS

The student is expected to: K.9.C-list simple skills required for jobs; (Supporting Standard-NEW STANDARD!!!)

K.9.C Supports Readiness Standard By: Identifying ways to earn income will support one’s ability to manage financial resources more effectively for a lifetime of financial security.

K.9.C Instructional Implications: Instruction should allow students to investigate different job choices and participate in discussions about what skills are needed to do such jobs.

Focus

Students learn skills needed to obtain a job. Questioning and Stems What skills do you need to be able to be a ______________? (profession) Are the same skills required for each job? Teacher Notes:

This is integrated with Social Studies TEKS The student is expected to: K.9.D-distinguish between wants and needs and identify income as a source to meet one's wants and needs. (Supporting Standard-NEW STANDARD!!!)

K.9.D- Supports Readiness Standard By: 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 more effectively for a lifetime of financial security.

K.9.D-Instructional Implications: 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 could be incorporated into the Number and Operations strand (see K.2H and K.3A/B/C).

Focus

Students differentiate between wants and needs and how to obtain them. Questions and Stems

What is the difference between something you want and something you need? How can you get the things you want/need? Teacher Notes:

This is integrated with Social Studies TEKS






K.2.B STAAR Grade 3 Scaffold: 3.2 A compose and decompose numbers up to 100,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens, and so many ones using objects, pictorial models, and numbers, including expanded notation as appropriate (R) The student is expected to

ELPS.2.E - use visual, contextual, and linguistic support to enhance and confirm understanding of increasingly complex and elaborated spoken language;


Focus Students recognize and write numbers 1-20. Students create representations of numbers 0-10 with objects and pictures.

Questions and Stems

Draw a picture to show ___. (0-20)

"Show me ___ objects." (0-20) - verbal cue

Teacher provides student with a number (non-verbal cue), and student creates a group of manipulatives that matches.

Teacher provides student with a set of objects and student records the number showing the quantity of the set.

Assessment Methods

Use flashcards or written numbers in random order for students to identify. (0-20)

Teacher Notes

This skill can also be addressed with daily calendar routines.



Bundle 7: Identifying, Classifying, and Sorting 2D Shapes January 5 – 30 (19 Days)

Understandings • Objects can be sorted and described according to their attributes. • Shapes can be created using a variety of items.

Rigor Questions

1. What attributes help me identify a shape? 2. What attributes help me to sort shapes? 3. How can I create 2D shapes? 4. What number is more/less than (any number up to 20)?

Vocabulary: Cognitive Complexity Verbs for TEKS: Identify

two-‐dimensional shape; circle(s); triangle(s); rectangle(s); square(s); attributes; classify; sort;


The student is expected to: K.6.A-identify two-dimensional shapes, including circles, triangles, rectangles, and squares as special rectangles; (Supporting Standard)

Current Standard: K.8A Describe and identify and object by its attributes using informal language.

Cognitive Change: Deleted “describing/comparing”; however, applied in “analyzing/generalizing” geometric properties as outlines by the TEKS K.6.

Content Change: Added the use of formal and informal geometric vocabulary.

K.6.A Supports Readiness Standard By: The ability to identify two-‐dimensional shapes based on their geometric attributes and properties supports the future classification and sorting of such figures.

ELPS.1.C - use strategic learning techniques such as concept mapping, drawing, memorizing, comparing, contrasting, and reviewing to acquire basic and grade-level vocabulary

ELPS.3.E - share information in cooperative learning interactions;

K.6.A Instructional Implications: Students should use the attributes of given shapes (K.6D) to correctly identify a shape. A variety of shapes (i.e. equilateral triangle, scalene triangle, right triangle, etc.) 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, squares have straight sides, instruction can begin modeling the term polygon for those two-‐dimensional shapes that are enclosed with straight sides.

Focus

Students identify 2D shapes. Questioning and Stems What shape is this? (Teacher provides student a picture/model of shape.) Teacher Notes Teachers should expose students to shapes in different orientations, colors, sizes, etc to ensure understanding of 2D shapes.


The student is expected to: K.6.D-identify attributes of two-dimensional shapes using informal and formal geometric language interchangeably; (Supporting Standard)

Current Standard: K.9C Describe, identify, and compare circles, triangles, rectangles, and squares.

Cognitive Change: Deleted “describing/comparing”; however, applied in “analyzing/generalizing” geometric properties as outlines by the TEKS K.6.

Content Change: Added the use of formal and informal geometric vocabulary.

K.6.D Supports Readiness Standard By: 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.

ELPS.1.C - use strategic learning techniques such as concept mapping, drawing, memorizing, comparing, contrasting, and reviewing to acquire basic and grade-level vocabulary

K.6.D Instructional Implications: 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.

Focus Students identify attribute of 2D shapes with formal and informal language.

Questioning and Stems

What makes this shape a __________? (name shape) Tell me about this shape. Teacher Notes

Teachers should make note of formal/informal language students use to describe shapes.

The student is expected to: K.6.E-classify and sort a variety of regular and irregular two- and three-dimensional figures regardless of orientation or size. (Readiness Standard)

Current Standard: K.8B Compare two objects based on their attributes; K.8C Sort a variety of objects including two- and three-dimensional geometric figures according to their attributes and describe how the objects are sorted.

Cognitive Change: Added “classifying” of two-dimensional and three-dimensional figures.

Content Change: Added the use of “irregular” shapes; Focused on Geometrical attributes that define a figure not orientation or size; Deleted the use of concrete objects; however, it can be applied within the process standards (K.1C). K.6F Create two-dimensional shapes using a variety of materials and drawings. (Supporting Standard-NEW STANDARD!!!)

K.6.E STAAR Grade 3 Scaffold:3.6A- classify and sort two-‐ and three-‐dimensional figures, including cones, cylinders, spheres, triangular and rectangular prisms, and cubes, based on attributes using formal geometric language (R) K.6F Supports Readiness Standard By: 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 and sorting of various figures.

K.6.E Instructional Implications: In order to adhere to the standard, students must sort and classify a group of two-‐dimensional shapes, a group of three-‐dimensional 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. equilateral triangle) and irregular (i.e. right, scalene, isosceles type of triangles) two-‐dimensional figures. K.6F Instructional Implications: 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 asked to modify it to create a new shape (i.e. students made a rectangle out of clay;

Students create 2D shapes.


How can you make a ___________? (name shape) Teacher Notes

Teachers should provide students with a variety of materials for them the create shapes.

K.6.E Distractor Factor: Students may interchange the term side, referencing two-‐dimensional shapes, and edge, referencing a three-‐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).

student is now asked to now modify the rectangle to make it a square and explain how the attributes/properties of the two shapes were similar yet different).


Bundle 8: Identifying, Classifying, and Sorting 2D and 3D Shapes February 2 – 20 (14 days)

Understandings • 2D shapes are components of 3D shapes.

Rigor Questions

1. How do 2D shapes relate to 3D shapes?

Vocabulary: Cognitive Complexity Verbs for TEKS: Apply; Identify

whole numbers 0-‐100; ones; tens; two dimensional; three dimensional; solids; cylinder(s); cone(s); sphere(s); cube(s); sort; classify






K.5- Supports Readiness Standard By: 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 value in order to solve addition/subtraction problems.


Focus Students identify 3D shapes.


What shape is this? (Teacher provides student a picture/model of shape.)

Teacher Notes

Teachers should expose students to shapes in different orientations, colors, sizes, etc to ensure understanding of 3D shapes.


The student is expected to:

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

Current Standard: K.9A describe and compare the attributes of real-lie objects such as balls, boxes, cans, and cones or models of three-dimensional figures; K.9B recognize shapes in real-life three-dimensional geometric figures or models of three-dimensional geometric figures.


Content Change: identified the specific types of solids (i.e. cylinders, cones, spheres, and cubes) K.6.C-identify two-dimensional components of three-dimensional objects;

Current Standard: K.9B recognize shapes in real-life three-dimensional geometric figures or models of three dimensional figures.


Content Change: Added the specific connection of two-dimensional to three-dimensional.

K.6.B- Supports Readiness Standard By: Being able to identify three-‐dimensional figures in the real world provides a concrete visual to future students of the geometric attributes and properties.

K.6.C- Supports Readiness Standard By: 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.

ELPS.3.G - 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;

K.6.B-Instuctional Implications: Students should use the attributes of given solid 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.) K.6.C-Instructional Implications: 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. taking a cube and making six square face imprints on 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).

Focus

Students identify 2D shapes within 3D shapes (faces).


What shape is this? (Teacher provides student a picture/model of shape.) What 2D shape do you see? (Teacher shows student a 3D shape) Teacher Notes

Teachers should address the concept of 2D shapes as faces on 3D shapes..

The student is expected to: K.6.E-classify and sort a variety of regular and irregular two- and three-dimensional figures regardless of orientation or size; (Readiness Standard)

Current Standard: K.8B Compare two objects based on their attributes; K.8C Sort a variety of objects including two- and three-dimensional geometric figures according to their attributes and describe how the objects are sorted.

K.6.E STAAR Grade 3 Scaffold:3.6A- classify and sort two-‐ and three-‐dimensional figures, including cones, cylinders, spheres, triangular and rectangular prisms, and cubes, based on attributes using formal geometric language (R)

K.6.E Instructional Implications: In order to adhere to the standard, students must sort and classify a group of two-‐dimensional shapes, a group of three-‐dimensional 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

Focus

Students classify and sort 2D and 3D shapes.


How are these shapes the same/different? How did you sort your objects? Can you sort these objects in a different way?

Cognitive Change: Added “classifying” of two-dimensional and three-dimensional figures.

Content Change: Added the use of “irregular” shapes; Focused on Geometrical attributes that define a figure not orientation or size; Deleted the use of concrete objects; however, it can be applied within the process standards (K.1C).

support of K.6C. Students need to be exposed to both regular (i.e. equilateral triangle) and irregular (i.e. right, scalene, isosceles type of triangles) two-‐dimensional figures.

Teacher Notes

Students are working with both 2D and 3D shapes at this time.

K.6.E Distractor Factor: Students may interchange the term side, referencing two-‐dimensional shapes, and edge, referencing a three-‐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).


Bundle 9: Describing and Comparing Attributes of Length, Capacity, & Weight February 23 – March 13 (14 Days)

Understandings • Objects can be compared by length, mass, and capacity.

Rigor Questions 1. What words do I use to describe and compare length/mass/capacity? 2. How can you tell if an object is longer or shorter than another? 3. How can you compare the weights of different objects? 4. How can you tell if a container holds same, more, or less than another?

Vocabulary: Cognitive Complexity Verbs for TEKS: Compare

length; weight/mass; capacity; attributes; temperature; more than; less than; same as; shorter; longer


The student is expected to: K.7.A-give an example of a measurable attribute of a given object, including length, capacity, and weight; (Supporting Standard-NEWSTANDARD!!!)

K.7.A- Supports Readiness Standard By: 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.7.A-Instructional Implications: 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 that Cereal Box B; Cereal Box B held less cereal than Cereal Box A).

Focus

Students identify ways to measure objects. Questioning and Stems

How can you measure this object? Is there another attribute of this object that you can measure? What tool can I use to measure?

Teacher Notes

Make sure students understand that objects can have more than one measurable attribute.


The student is expected to: K.7.B-compare two objects with a common measurable attribute to see which object has more of/less of the attribute and describe the difference. (Readiness Standard)

K.7.B STAAR Grade 3 Scaffold:3.6C-determine the area of rectangles with whole number side lengths in problems using multiplication related to the number of rows times the number of unit squares in each row (R)

K.7.B Instructional Implications: In alignment with K.7A, as students begin identifying a measureable attribute such as length, capacity, or weight instruction can extend to comparing the differences (i.e.

Focus Students compare objects by their common attributes.

Current Standard: K.10A-D; K.11A-B; 1.7C-G, 1.8A

Cognitive Change: Added “describing” the difference in the measurable attributes.

Content Change: Limited comparison of measurable attributes to two objects; Deleted the examples of measurable attributes (i.e. length, area, capacity, weight/mass, temperature, time) from Grade 1 Curriculum; only addressed in K.7B

ELPS.1.E - internalize new basic and academic language by using and reusing it in meaningful ways in speaking and writing activities that build concept and language attainment; ELPS.3.G - 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;

comparing the length, capacity, and weight of a 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 with K.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 than the trial size cereal box is the same as stating the trial size cereal box is shorter than the full size cereal box).


How can we measure these objects? Which object is heavier/lighter? Which object weighs more/less? Which object holds more/less? What is the best attribute to compare these objects?

K.7.B Distractor Factor: 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 as stating the trial size cereal box is shorter than the full size cereal box).


Bundle 10: Understanding Addition and Subtraction March 23 – April 17 (19 Days)

Understandings • Quantities are determined by joining or separating sets.

Rigor Questions 1. What is the relationship between joining and separating? 2. How do you show joining and separating? 3. How can you show a separating story as a subtraction sentence? 4. How can you show a joining story as an addition sentence?

Vocabulary: Cognitive Complexity Verbs for TEKS: Analyze; Determine; Write

joining (addition); separating (subtraction); problem solving; reasonableness; mental math; number sense; sums (0-10); differences (0-10); strategies; number sentence; mathematical ideas; symbols; diagrams; graphs


The student is expected to: K.3.A-model the action of joining to represent addition and the action of separating to represent subtraction; (Supporting Standard)

Current Standard: K.4 Model and create addition and subtraction problems in real situations with concrete objects.

Cognitive Change: Added “explaining” the strategies used to solve (K.3C)

Content Change: Added the understanding of “joining” for addition and “separating” for subtraction; Added the use of drawing (K.3C); Limited the sums and differences to 10 (K.3B-C); Combined process standard K.14A with content standard K.3C

K.3.A Supports Readiness Standard By: The use of concrete objects and pictorial models to demonstrate joining and separation situations will support a student’s 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. ELPS.3.J - respond orally to information presented in a wide variety of print, electronic, audio, and visual media to build and reinforce concept and language attainment.

ELPS.2.G - understand the general meaning, main points, and important details of spoken language ranging from situations in which topics, language, and contexts are familiar to unfamiliar;

K.3.A Instructional Implications: 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 give 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.

Focus Students model the act of joining and separating objects.


Are you joining or separating? What happens when you join? What happens when you separate? Teacher Notes

Students learn the concept of joining and separating BEFORE addition and subtraction. (+ and -) This skill will be readdressed throughout bundles 11 and 12 as well

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 student is expected to: K.3.B-solve word problems using objects and drawings to find sums up to 10 and differences within 10; (Readiness Standard)

Current Standard: K.14 communicate mathematical ideas using objects, words, pictures, numbers and technology (Process Standard)



K.3.B STAAR Grade 3 Scaffold:3.4A- solve with fluency one-‐step and two-‐step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction (R)



K.3.B Instructional Implications: In alignment with K.3A, as students will begin modeling the actions of joining and separating. Students should be provided 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.

Focus

Students find sums and differences up to 10 using objects or drawing. Questioning and Stems What is the problem asking? Is it a joining or separating problem? How can you use drawings or objects to help you solve your problems. Teacher Notes Math journals can be used to address this skill. This skill will be readdressed throughout bundles 11 and 12 as well.

K.3.B Distractor Factor: Students may not recognize a number sentence and its inverse as being equivalent (i.e. 10 -‐ 4 = ___ is the same things as 4 + ___ = 10).

The student is expected to: K.3.C-explain the strategies used to solve problems involving adding and subtracting within 10 using spoken words, concrete and pictorial models, and number sentences. (Supporting Standard)

Current Standard: N/A



K.3.C Supports Readiness Standard By: Being able to relate the manipulation of concrete objects to pictorials to a number sentence is a critical transition to move students from the concrete to the abstract understanding of addition and subtraction. ELPS.3.J - respond orally to information presented in a wide variety of print, electronic, audio, and visual media to build and reinforce concept and language attainment.


K.3.C Instructional Implications: 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 picture 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?).

Focus

Students explain their thinking when solving word problems. Questioning and Stems

How did you know to join or separate? What strategy did you use to solve your problem? (drawing/manipulatives/number sentences) How would you write a number sentence to show how you solved your problem. Teacher Notes

This skill will be readdressed throughout bundles 11 and 12 as well.


Bundle 11: Addition and Subtraction: Explaining Our Thinking April 20 – May 8 (15 days)

Understandings • Number sentences can be used to explain our thinking.

Rigor Questions 1. What is the relationship between joining and separating? 2. How do you show joining and separating? 3. How can you show a separating story as a subtraction sentence? 4. How can you show a joining story as an addition sentence?

Vocabulary: Cognitive Complexity Verbs for TEKS: Analyze; Determine; Write



The student is expected to: K.3.A-model the action of joining to represent addition and the action of separating to represent subtraction. (Supporting Standard)




K.3.A Supports Readiness Standard By: The use of concrete objects and pictorial models to demonstrate joining and separation situations will support a student’s 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. ELPS.3.J - respond orally to information presented in a wide variety of print, electronic, audio, and visual media to build and reinforce concept and language attainment.


K.3.A Instructional Implications: 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 give 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

Focus

Students model the act of joining and separating objects. Questioning and Stems

Are you joining or separating? What happens when you join? What happens when you separate?

Teacher Notes

This skill will be readdressed throughout bundle 12 as well.

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 student is expected to: K.3.B-solve word problems using objects and drawings to find sums up to 10 and differences within 10. (Readiness Standard)



Content Change: Added the understanding of “joining” for addition and “separating” for subtraction; Added the use of drawing (K.3C); Limited the sums and differences to 10 (K.3B-C); Combined process standard K.14A with content standard K.3C The student is expected to: K.3.C-explain the strategies used to solve problems involving adding and subtracting within 10 using spoken words, concrete and pictorial models, and number sentences. (Supporting Standard)




K.3.B STAAR Grade 3 Scaffold:3.4A- solve with fluency one-‐step and two-‐step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction (R) K.3.C Supports Readiness Standard By: Being able to relate the manipulation of concrete objects to pictorials to a number sentence is a critical transition to move students from the concrete to the abstract understanding of addition and subtraction.

Cognitive Change: Changed the “using” of tools to the “selecting” of tools

Content Change: Added the tool of paper/pencil; Added the use of techniques included mental math, estimation, and number sense. ELPS.3.J - respond orally to information presented in a wide variety of print, electronic, audio, and visual media to build and reinforce concept and language attainment.




Focus Students explain their thinking when solving word problems.


How did you know to join or separate? What strategy did you use to solve your problem? (drawing/manipulatives/number sentences) How would you write a number sentence to show how you solved your problem.

Teacher Notes

This skill will be readdressed throughout bundle 12 as well.


Course: Kindergarten Math Bundle 12: Problem Solving May 11- June 3 (17 days)

Understandings • Mathematics can be applied in everyday situations.

Rigor Questions 1. What is the relationship between joining and separating? 2. How do you show joining and separating? 3. How can you show a separating story as a subtraction sentence? 4. How can you show a joining story as an addition sentence? 5. What tools can you use to solve a problem? 6. How do you explain the strategies you used to solve a problem? 7. How can you use addition and subtraction to solve real world problems? Vocabulary: Cognitive Complexity Verbs for TEKS: Analyze; Determine; Write



The student is expected to: K.3.A-model the action of joining to represent addition and the action of separating to represent subtraction; (Supporting Standard)




K.3.A Supports Readiness Standard By: The use of concrete objects and pictorial models to demonstrate joining and separation situations will support a student’s 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.


ELPS.2.G - understand the general meaning, main points, and important details of spoken language ranging from situations in which topics,

K.3.A Instructional Implications: 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 give her?

Focus Students model the act of joining and separating objects.


Are you joining or separating? What happens when you join? What happens when you separate?

language, and contexts are familiar to unfamiliar;

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 student is expected to: K.3.B-solve word problems using objects and drawings to find sums up to 10 and differences within 10. (Readiness Standard)




K.3.B STAAR Grade 3 Scaffold:3.4A- solve with fluency one-‐step and two-‐step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction (R) ELPS.3.J - respond orally to information presented in a wide variety of print, electronic, audio, and visual media to build and reinforce concept and language attainment.



Focus

Students find sums and differences up to 10 using objects or drawing.


What is the problem asking? Is it a joining or separating problem? How can you use drawings or objects to help you solve your problems


The student is expected to: K.3.C-explain the strategies used to solve problems involving adding and subtracting within 10 using spoken words, concrete and pictorial models, and number sentences. (Supporting Standard)




K.3.C Supports Readiness Standard By: Being able to relate the manipulation of concrete objects to pictorials to a number sentence is a critical transition to move students from the concrete to the abstract understanding of addition and subtraction. ELPS.3.J - respond orally to information presented in a wide variety of print, electronic, audio, and visual media to build and reinforce concept and language attainment.



Focus Students explain their thinking when solving word problems.


How did you know to join or separate? What strategy did you use to solve your problem? (drawing/manipulatives/number sentences) How would you write a number sentence to show how you solved your problem.

Resource Categories The resources included here provide teaching examples and/or meaningful learning experiences to address the District Curriculum. In order to address the TEKS to the proper depth and complexity, teachers are encouraged to use resources to the degree that they are congruent with the TEKS and research-based best practices. Teaching using only the suggested resources does not guarantee student mastery of all standards. Teachers must use professional judgment to select among these and/or other resources to teach the district curriculum.

kindergarten mathematics curriculum document 2014-2015

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