kindergarten montana common core standards: …

KINDERGARTEN

Mathematics CURRICULUM & STANDARDS

Montana Mathematics K-12 Content Standards and Practices

From the Montana Office of Public Instruction:

GRADE LEVEL STANDARDS & PRACTICES

CURRICULUM ORGANIZERS

From the Ravalli County Curriculum Consortium Committee:

After each grade level:

Year Long Plan Samples

Unit Organizer Samples

Lesson Plan Samples

Assessment Sample

Resources

Montana Mathematics Kindergarten Content Standards

Montana Common Core Standards for Mathematical Practices and Mathematics Content Page 9

November 2011

Explanations and Examples Grade K Arizona Department of Education: Standards and Assessment Division

Standards for Mathematical Practice: Kindergarten Explanations and Examples Standards Explanations and Examples Students are expected to: The Standards for Mathematical Practice describe ways in which students ought to engage with the subject

matter as they grow in mathematical maturity and expertise. K.MP.1. Make sense of problems and persevere in solving them.

In Kindergarten, students begin to build the understanding that doing mathematics involves solving problems and discussing how they solved them. Students explain to themselves the meaning of a problem and look for ways to solve it. Younger students may use concrete objects or pictures to help them conceptualize and solve problems. They may check their thinking by asking themselves, “Does this make sense?” or they may try another strategy.

K.MP.2. Reason abstractly and quantitatively.

Younger students begin to recognize that a number represents a specific quantity. Then, they connect the quantity to written symbols. Quantitative reasoning entails creating a representation of a problem while attending to the meanings of the quantities.

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

Younger students construct arguments using concrete referents, such as objects, pictures, drawings, and actions. They also begin to develop their mathematical communication skills as they participate in mathematical discussions involving questions like “How did you get that?” and “Why is that true?” They explain their thinking to others and respond to others’ thinking.

K.MP.4. Model with mathematics.

In early grades, students experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures, using objects, acting out, making a chart or list, creating equations, etc. Students need opportunities to connect the different representations and explain the connections. They should be able to use all of these representations as needed.

K.MP.5. Use appropriate tools strategically.

Younger students begin to consider the available tools (including estimation) when solving a mathematical problem and decide when certain tools might be helpful. For instance, kindergarteners may decide that it might be advantageous to use linking cubes to represent two quantities and then compare the two representations side-by-side.

K.MP.6. Attend to precision.

As kindergarteners begin to develop their mathematical communication skills, they try to use clear and precise language in their discussions with others and in their own reasoning.

K.MP.7. Look for and make use of structure.

Younger students begin to discern a pattern or structure. For instance, students recognize the pattern that exists in the teen numbers; every teen number is written with a 1 (representing one ten) and ends with the digit that is first stated. They also recognize that 3 + 2 = 5 and 2 + 3 = 5.

K.MP.8. Look for and express regularity in repeated reasoning.

In the early grades, students notice repetitive actions in counting and computation, etc. For example, they may notice that the next number in a counting sequence is one more. When counting by tens, the next number in the sequence is “ten more” (or one more group of ten). In addition, students continually check their work by asking themselves, “Does this make sense?”



November 2011

Montana Mathematics Kindergarten Content Standards In Kindergarten, instructional time should focus on two critical areas: (1) representing and comparing whole numbers, initially with sets of objects; (2) describing shapes and space. More learning time in Kindergarten should be devoted to number than to other topics.

1. Students use numbers, including written numerals, to represent quantities and to solve quantitative problems, such as counting objects in a set; counting out a given number of objects; comparing sets or numerals; and modeling simple joining and separating situations with sets of objects, or eventually with equations such as 5 + 2 = 7 and 7 – 2 = 5. (Kindergarten students should see addition and subtraction equations, and student writing of equations in kindergarten is encouraged, but it is not required.) Students choose, combine, and apply effective strategies for answering quantitative questions, including quickly recognizing the cardinalities of small sets of objects, counting and producing sets of given sizes, counting the number of objects in combined sets, or counting the number of objects that remain in a set after some are taken away.

2. Students describe their physical world using geometric ideas (e.g., shape, orientation, spatial relations) and vocabulary. They identify, name, and describe basic two-dimensional shapes, such as squares, triangles, circles, rectangles, and hexagons, presented in a variety of ways (e.g., with different sizes and orientations), as well as three-dimensional shapes such as cubes, cones, cylinders, and spheres. They use basic shapes and spatial reasoning to model objects in their environment and to construct more complex shapes.

Mathematical Practices 1. Make sense of problems and

persevere in solving them. 2. Reason abstractly and

quantitatively. 3. Construct viable arguments and

critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools

strategically. 6. Attend to precision. 7. Look for and make use of

structure. 8. Look for and express regularity

in repeated reasoning.

Grade K Overview Counting and Cardinality • Know number names and the

count sequence. • Count to tell the number of

objects. • Compare numbers. Operations and Algebraic Thinking • Understand addition as putting

together and adding to, and understand subtraction as taking apart and taking from.

Number and Operations in Base Ten • Work with numbers 11–19 to

gain foundations for place value.

Measurement and Data • Describe and compare measurable

attributes. • Classify objects and count the

number of objects in categories. Geometry • Identify and describe shapes. • Analyze, compare, create, and

compose shapes.



November 2011

Counting and Cardinality K.CC Know number names and the count sequence. 1. Count to 100 by ones and by tens. 2. Count forward beginning from a given number within the known sequence (instead of having to begin at 1). 3. Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). Count to tell the number of objects. 4. Understand the relationship between numbers and quantities; connect counting to cardinality.

a. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object from a variety of cultural contexts, including those of Montana American Indians.

b. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.

c. Understand that each successive number name refers to a quantity that is one larger. 5. Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many

as 10 things in a scattered configuration; given a number from 1–20, count out that many objects from a variety of cultural contexts, including those of Montana American Indians.

Compare numbers. 6. Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group,

e.g., by using matching and counting strategies.1 7. Compare two numbers between 1 and 10 presented as written numerals. Operations and Algebraic Thinking K.OA Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. 1. Represent addition and subtraction with objects, fingers, mental images, drawings2, sounds (e.g., claps), acting out situations, verbal

explanations, expressions, or equations. 2. Solve addition and subtraction word problems from a variety of cultural contexts, including those of Montana American Indians,

and add and subtract within 10, e.g., by using objects or drawings to represent the problem. 3. Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each

decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). 4. For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings,

and record the answer with a drawing or equation. 5. Fluently add and subtract within 5.



November 2011

Number and Operations in Base Ten K.NBT Work with numbers 11-19 to gain foundations for place value. 1. Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record

each composition or decomposition by a drawing or equation (such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.

Measurement and Data K.MD Describe and compare measurable attributes. 1. Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. 2. Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and

describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter. Classify objects and count the number of objects in each category. 3. Classify objects from a variety of cultural contexts, including those of Montana American Indians, into given categories; count the

numbers of objects in each category and sort the categories by count.3 Geometry K.G Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). 1. Describe objects, including those of Montana American Indians, in the environment using names of shapes, and describe the

relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. 2. Correctly name shapes regardless of their orientations or overall size. 3. Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). Analyze, compare, create, and compose shapes. 4. Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe

their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length).

5. Model shapes in the world from a variety of cultural contexts, including those of Montana American Indians, by building shapes from components (e.g., sticks and clay balls) and drawing shapes.

6. Compose simple shapes to form larger shapes. For example, “Can you join these two triangles with full sides touching to make a rectangle?”

_________________ 1 Include groups with up to ten objects. 2 Drawings need not show details, but should show the mathematics in the problem. (This applies wherever drawings are mentioned in the Standards.) 3 Limit category counts to be less than or equal to 10.

KINDERGARTENDomain Cluster Code Common Core State Standard

K.CC.1 Count to 100 by ones and by tens.

K.CC.2Count forward beginning from a given number within the known sequence

(instead of having to begin at 1).

K.CC.3Write numbers from 0 to 20. Represent a number of objects with a written

numeral 0‐20 (with 0 representing a count of no objects).

K.CC.4

Understand the relationship between numbers and quantities; connect counting

to cardinality.

a. When counting objects, say the number names in the standard order,

pairing each object with one and only one number name and each

number name with one and only one object from a variety of cultural

contexts, including those of Montana American Indians.

b. Understand that the last number name said tells the number of objects

counted. The number of objects is the same regardless of their

arrangement or the order in which they were counted.

c. Understand that each successive number name refers to a quantity that

is one larger.

K.CC.5

Count to answer "how many?" questions about as many as 20 things arranged

in a line, a rectangular array, or a circle; or as many as 10 things in a scattered

configuration; given a number from 1‐20, count out that many objects from a

variety of cultural contexts, including those of Montana American Indians.

K.CC.6

Identify whether the number of objects in one group is greater than, less than,

or equal to the number of objects in another group, e.g., by using matching and

counting strategies. (Include groups with up to ten objects.)

K.CC.7 Compare two numbers between 1 and 10 presented as written numerals.

K.OA.1

Represent addition and subtraction with objects, fingers, mental images,

drawings (drawings need not show details, but should show the mathematics in

the problem), sounds (e.g., claps), acting out situations, verbal explanations,

expressions, or equations.

K.OA.2

Solve addition and subtraction word problems from a variety of cultural

contexts, including those of Montana American Indians, and add and subtract

within 10, e.g., by using objects or drawings to represent the problem .

K.OA.3

Decompose numbers less than or equal to 10 into pairs in more than one way,

e.g., by using objects or drawings, and record each decomposition by a drawing

or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).

K.OA.4

For any number from 1 to 9, find the number that makes 10 when added to the

given number, e.g., by using objects or drawings, and record the answer with a

drawing or equation.

K.OA.5 Fluently add and subtract within 5.

Number and

Operations in

Base Ten

Work with numbers

11‐19 to gain

foundations for

place value.

K.NBT.1

Compose and decompose numbers from 11 to 19 into ten ones and some

further ones, e.g., by using objects or drawings, and record each composition or

decomposition by a drawing or equation (such as 18 = 10 + 8); understand that

these numbers are composed of ten ones and one, two, three, four, five, six,

seven, eight, or nine ones.

Operations and

Algebraic

Thinking

Know number

names and the

count sequence.

Counting and

CardinalityCount to tell the

number of objects.

Compare numbers.

Understand

addition as putting

together and

adding to, and

understand

subtraction as

taking apart and

taking from.

KINDERGARTENDomain Cluster Code Common Core State Standard

K.MD.1Describe measurable attributes of objects, such as length or weight. Describe

several measurable attributes of a single object.

K.MD.2

Directly compare two objects with a measurable attribute in common, to see

which object has "more of"/"less of" the attribute, and describe the difference.

For example, directly compare the heights of two children and describe one

child as taller/shorter.

Classify objects and

count the number

of objects in each

category.

K.MD.3

Classify objects from a variety of cultural contexts, including those of Montana

American Indians, into given categories; count the numbers of objects in each

category and sort the categories by count. (Limit category counts to be less than

or equal to 10.)

K.G.1

Describe objects, including those of Montana American Indians, in the

environment using names of shapes, and describe the relative positions of these

objects using terms such as above, below, beside, in front of, behind, and next

to.

K.G.2 Correctly name shapes regardless of their orientations or overall size.

K.G.3Identify shapes as two‐dimensional (lying in a plane, "flat") or three‐dimensional

("solid").

K.G.4

Analyze and compare two‐ and three‐dimensional shapes, in different sizes and

orientations, using informal language to describe their similarities, differences,

parts (e.g., number of sides and vertices/"corners") and other attributes (e.g.,

having sides of equal length).

K.G.5

Model shapes in the world from a variety of cultural contexts, including those of

Montana American Indians, by building shapes from components (e.g., sticks

and clay balls) and drawing shapes.

K.G.6Compose simple shapes to form larger shapes. For example, "can you join these

two triangles with full sides touching to make a rectangle?"

Measurement

and Data

Describe and

compare

measurable

attributes.

Geometry

Identify and

describe shapes

Analyze, compare,

create, and

compose shapes.

November 2012 Materials adapted from Arizona, Delaware and Ohio Departments of Education

Montana Curriculum Organizer

Grade K

Mathematics

Montana Curriculum Organizer: Grade K Mathematics

This document is a curriculum organizer adapted from other states to be used for planning scope and sequence, units, pacing and other materials that support a focused,

coherent, and rigorous study of mathematics K-12.

November 2012 Page 2

TABLE OF CONTENTS

Page 3 How to Use the Montana Curriculum Organizer

Page 4 Introduction to the Math Standards Standards for Mathematical Practice: Grade K Examples and Explanations Critical Areas for Grade K Math

Page 5 Counting & Cardinality K.CC.1, K.CC.2, K.CC.3, K.CC.4a-c, K.CC.5, K.CC.6, K.CC.7 Clusters:

Know number names and the count sequence. Count to tell the number of objects. Compare numbers.

Operations & Algebraic Thinking (Addition & Subtraction) K.OA.1, K.OA.2, K.OA.3, K.OA.4, K.OA.5 Clusters:

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Page 11 Place Value K.NBT.1 Clusters:

Work with numbers 11-19 to gain foundations for place value.

Page 13 Measurement & Data (A strong connection to Number with counting and comparing) K.MD.1, K.MD.2, K.MD.3 Clusters:

Describe and compare measurable attributes. Classify objects and count the number of objects in each category.

Page 15 Geometry (Shapes and Their Attributes) K.G.1, K.G.2, K.G.3, K.G.4, K.G.5, K.G.6 Clusters:

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). Analyze, compare, create, and compose shapes.

Page 18 References





HOW TO USE THE MONTANA CURRICULUM ORGANIZER

The Montana Curriculum Organizer supports curriculum development and instructional planning. The Montana Guide to Curriculum Development, which outlines the curriculum development process, is another resource to assemble a complete curriculum including scope and sequence, units, pacing guides, outline for use of appropriate materials and resources and assessments.

Page 4 of this document is important for planning curriculum, instruction and assessment. It contains the Standards for Mathematical Practice grade-level explanations and examples that describe ways in which students ought to engage with the subject matter as they grow in mathematical maturity and expertise. The Critical Areas indicate two to four content areas of focus for instructional time. Focus, coherence and rigor are critical shifts that require considerable effort for implementation of the Montana Common Core Standards. Therefore, a copy of this page for easy access may help increase rigor by integrating the Mathematical Practices into all planning and instruction and help increase focus of instructional time on the big ideas for that grade level.

Pages 5 through 17 consist of tables organized into learning progressions that can function as units. The table for each learning progression, unit, includes: 1) domains, clusters and standards organized to describe what students will Know, Understand, and Do (KUD), 2) key terms or academic vocabulary, 3) instructional strategies and resources by cluster to address instruction for all students, 4) connections to provide coherence, and 5) the specific standards for mathematical practice as a reminder of the importance to include them in daily instruction.

Description of each table:

LEARNING PROGRESSION STANDARDS IN LEARNING PROGRESSION

Name of this learning progression, often this correlates with a domain, however in some cases domains are split or combined.

Standards covered in this learning progression.

UNDERSTAND:

What students need to understand by the end of this learning progression.

KNOW: DO:

What students need to know by the end of this learning progression.

What students need to be able to do by the end of this learning progression, organized by cluster and standard.

KEY TERMS FOR THIS PROGRESSION:

Mathematically proficient students acquire precision in the use of mathematical language by engaging in discussion with others and by giving voice to their own reasoning. By the time they reach high school they have learned to examine claims, formulate definitions, and make explicit use of those definitions. The terms students should learn to use with increasing precision in this unit are listed here.

INSTRUCTIONAL STRATEGIES AND RESOURCES:

Cluster: Title Strategies for this cluster

Instructional Resources/Tools Resources and tools for this cluster

Cluster: Title Strategies for this cluster

Instructional Resources/Tools Resources and tools for this cluster

CONNECTIONS TO OTHER DOMAINS AND/OR CLUSTERS:

Standards that connect to this learning progression are listed here, organized by cluster.

STANDARDS FOR MATHEMATICAL PRACTICE:

A quick reference guide to the eight standards for mathematical practice is listed here.

http://opi.mt.gov/Curriculum/Curriculum-Development-Guide/index.php#gpm1_1

http://opi.mt.gov/Curriculum/Curriculum-Development-Guide/index.php#gpm1_1





Mathematics is a human endeavor with scientific, social, and cultural relevance. Relevant context creates an opportunity

for student ownership of the study of mathematics. In Montana, the Constitution pursuant to Article X Sect 1(2) and

statutes §20-1-501 and §20-9-309 2(c) MCA, calls for mathematics instruction that incorporates the distinct and unique

cultural heritage of Montana American Indians. Cultural context and the Standards for Mathematical Practices together

provide opportunities to engage students in culturally relevant learning of mathematics and create criteria to increase

accuracy and authenticity of resources. Both mathematics and culture are found everywhere, therefore, the incorporation

of contextually relevant mathematics allows for the application of mathematical skills and understandings that makes

sense for all students.

Standards for Mathematical Practice: Kindergarten Explanations and Examples

Standards Explanations and Examples

Students are expected to: The Standards for Mathematical Practice describe ways in which students ought to engage with the subject matter as they

grow in mathematical maturity and expertise.

K.MP.1. Make sense of

problems and persevere in

solving them.

In Kindergarten, students begin to build the understanding that doing mathematics involves solving problems and discussing

how they solved them. Students explain to themselves the meaning of a problem and look for ways to solve it. Younger

students may use concrete objects or pictures to help them conceptualize and solve problems. They may check their

thinking by asking themselves, “Does this make sense?” or they may try another strategy.

K.MP.2. Reason abstractly

and quantitatively. Younger students begin to recognize that a number represents a specific quantity. Then, they connect the quantity to written

symbols. Quantitative reasoning entails creating a representation of a problem while attending to the meanings of the

quantities. K.MP.3. Construct viable

arguments and critique the

reasoning of others.

Younger students construct arguments using concrete referents, such as objects, pictures, drawings, and actions. They also

begin to develop their mathematical communication skills as they participate in mathematical discussions involving

questions like “How did you get that?” and “Why is that true?” They explain their thinking to others and respond to others’

thinking.

K.MP.4. Model with

mathematics. In early grades, students experiment with representing problem situations in multiple ways including numbers, words

(mathematical language), drawing pictures, using objects, acting out, making a chart or list, creating equations, etc.

Students need opportunities to connect the different representations and explain the connections. They should be able to

use all of these representations as needed.

K.MP.5. Use appropriate

tools strategically. Younger students begin to consider the available tools (including estimation) when solving a mathematical problem and

decide when certain tools might be helpful. For instance, kindergarteners may decide that it might be advantageous to use

linking cubes to represent two quantities and then compare the two representations side-by-side.

K.MP.6. Attend to

precision.

As kindergarteners begin to develop their mathematical communication skills, they try to use clear and precise language in

their discussions with others and in their own reasoning.

K.MP.7. Look for and make

use of structure. Younger students begin to discern a pattern or structure. For instance, students recognize the pattern that exists in the teen

numbers; every teen number is written with a 1 (representing one ten) and ends with the digit that is first stated. They also

recognize that 3 + 2 = 5 and 2 + 3 = 5.

K.MP.8. Look for and

express regularity in

repeated reasoning.

In the early grades, students notice repetitive actions in counting and computation, etc. For example, they may notice that the

next number in a counting sequence is one more. When counting by tens, the next number in the sequence is “ten more”

(or one more group of ten). In addition, students continually check their work by asking themselves, “Does this make

sense?”

CRITICAL AREAS FOR GRADE K MATH In Kindergarten, instructional time should focus on two critical areas:

(1) representing and comparing whole numbers, initially with sets of objects; and

(2) describing shapes and space.

More learning time in Kindergarten should be devoted to number than to other topics.






Counting & Cardinality K.CC.1, K.CC.2, K.CC.3, K.CC.4a-c, K.CC.5, K.CC.6, K.CC.7

UNDERSTAND:

Counting strategies can be used to determine the number of objects. Understand the relationship between numbers and quantities.

KNOW: DO:

The number-word sequence, combined with the order inherent in the natural numbers, can be used as a foundation for counting.

The counting sequence by ones and tens.

Ten different digits can be used and sequenced to express any whole number (In K, write numbers 0-20).

The last number named when counting said tells the number of objects counted (cardinality).

The number of objects is the same regardless of their arrangement or the order in which they were counted.

When comparing two sets of objects or numbers, the one with the largest quantity is more or smallest quantity is less.

Know number names and the count sequence. K.CC.1 Count to 100 by ones and by tens. K.CC.2 Count forward beginning from a given number within the

known sequence (instead of having to begin at 1). K.CC.3 Write numbers from 0 to 20. Represent a number of objects

with a written numeral 0-20 (with 0 representing a count of no objects).

Count to tell the number of objects K.CC.4 Understand the relationship between numbers and quantities;

connect counting to cardinality. a. When counting objects, say the number names in the standard

order, pairing each object with one, and only one, number name and each number name with one, and only one, object from a variety of cultural contexts, including those of Montana American Indians.

b. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.

c. Understand that each successive number name refers to a quantity that is one larger.

K.CC.5 Count to answer "How many?" questions about as many as 20 things arranged in a line, a rectangular array, or a circle; or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects from a variety of cultural contexts, including those of Montana American Indians.

Compare numbers. K.CC.6 Identify whether the number of objects in one group is greater

than, less than, or equal to the number of objects in another group (by using matching and counting strategies).

1

K.CC.7 Compare two numbers between 1 and 10 presented as written

numerals.


Add, Compare, Count, Equal to, Greater than, Less, Less than, More, Number, Subtract


Cluster: Know number names and the count sequence. The Counting and Cardinality domain in Kindergarten contains standard statements that are connected to one another. Examine the three samples in this domain at the same time to obtain a more holistic view of the content.

Provide settings that connect mathematical language and symbols to the everyday lives of kindergarteners. Support students’ ability to make meaning and mathematize the real world. Help them see patterns, make connections and provide repeated experiences that give students time and opportunities to develop understandings and increase fluency. Encourage students to explain their reasoning by asking probing questions such as “How do you know?”

Students view counting as a mechanism used to land on a number. Young students mimic counting often with initial lack of purpose or meaning. Coordinating the number words, touching or moving objects in a one-to-one correspondence may

1 Include groups with up to 10 objects.





be little more than a matching activity. However, saying number words as a chant or a rote procedure plays a part in students constructing meaning for the conceptual idea of counting. They will learn how to count before they understand cardinality (i.e. that the last count word is the amount of the set).

Counting on or counting from a given number conflicts with the learned strategy of counting from the beginning. In order to be successful in counting on, students must understand cardinality. Students often merge or separate two groups of objects and then re-count from the beginning to determine the final number of objects represented. For these students, counting is still a rote skill or the benefits of counting on have not been realized. Games that require students to add on to a previous count to reach a goal number encourage developing this concept. Frequent and brief opportunities utilizing counting on and counting back are recommended. These concepts emerge over time and cannot be forced.

Like counting to 100 by either ones or tens, writing numbers from 0 to 20 is a rote process. Initially, students mimic the actual formation of the written numerals while also assigning it a name. Over time, children create the understanding that number symbols signify the meaning of counting. Numerals are used to communicate across cultures, and through time, or a certain meaning. Numbers have meaning when children can see mental images of the number symbols and use those images with which to think. Practice count words and written numerals paired with pictures, representations of objects, and objects that represent quantities within the context of life experiences for kindergarteners. For example, dot cards, dominoes and number cubes all create different mental images for relating quantity to number words and numerals. One way students can learn the left to right orientation of numbers is to use a finger to write numbers in air (sky writing). Children will see mathematics as something that is alive and that they are involved.

Students should study and write numbers 0 to 20 in this order: numbers 1 to 9, the number 0, then numbers 10 to 20. They need to know that 0 is the number items left after all items in a set are taken away. Do not accept “none” as the answer to “How many items are left?” for this situation.

Instructional Resources/Tools Board games that require counting

National Research Council. Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity. Washington,

DC: The National Academies Press, 2009.

Winnipeg School Division. 2005-2006. Numeracy Project: Dot Card and Ten Frame Activities. (pp. 1-6, 12-17).

Cluster: Count to tell the number of objects. One of the first major concepts in a student’s mathematical development is cardinality. Cardinality, knowing that the number word said tells the quantity you have and that the number you end on when counting, represents the entire amount counted. The big idea is that number means amount and, no matter how you arrange and rearrange the items, the amount is the same. Until this concept is developed, counting is merely a routine procedure done when a number is needed. To determine if students have the cardinality rule, listen to their responses when you discuss counting tasks with them. For example, ask, “How many are here?” The student counts correctly and says that there are seven. Then ask, “Are there seven?” Students may count or hesitate if they have not developed cardinality. Students with cardinality may emphasize the last count or explain that there are seven because they counted them. These students can now use counting to find a matching set.

Students develop the understanding of counting and cardinality from experience. Almost any activity or game that engages children in counting and comparing quantities, such as board games, will encourage the development of cardinality. Frequent opportunities to use and discuss counting as a means of solving problems relevant to kindergarteners is more beneficial than repeating the same routine day after day. For example, ask students questions that can be answered by counting up to 20 items before they change and as they change locations throughout the school building.

As students develop meaning for numerals, they also compare numerals to the quantities they represent. The models that can represent numbers, such as dot cards and dominoes, become tools for such comparisons. Students can concretely, pictorially or mentally look for similarities and differences in the representations of numbers. They begin to “see” the relationship of one more, one less, two more and two less, thus landing on the concept that successive numbers name quantities that are one larger. In order to encourage this idea, children need discussion and reflection of pairs of numbers

http://books.nap.edu/openbook.php?record_id=12519&page=1

http://www.edplus.canterbury.ac.nz/literacy_numeracy/maths/numdocuments/dot_card_and_ten_frame_package2005.pdf





from 1 to 10. Activities that utilize anchors of 5 and 10 are helpful in securing understanding of the relationships between numbers. This flexibility with numbers will build students’ ability to break numbers into parts. Provide a variety of experiences in which students connect count words or number words to the numerals that represent the quantities. Students will arrive at an understanding of a number when they acquire cardinality and can connect a number with the numerals and the number word for the quantity they all represent. Instructional Resources/Tools Winnipeg School Division. 2005-2006. Numeracy Project: Dot Card and Ten Frame Activities. (pp. 1-6, 12-17).

Cluster: Compare numbers. As children develop meaning for numerals, they also compare these numerals to the quantities represented and their number words. The modeling numbers with manipulatives such as dot cards and five- and ten-frames become tools for such comparisons. Children can look for similarities and differences in these different representations of numbers. They begin to “see” the relationship of one more, one less, two more and two less, thus landing on the concept that successive numbers name quantities where one is larger. In order to encourage this idea, children need discussion and reflection of pairs of numbers from 1 to 10. Activities that utilize anchors of 5 and 10 are helpful in securing understanding of the relationships between numbers. This flexibility with numbers will greatly impact children’s ability to break numbers into parts.

Children demonstrate their understanding of the meaning of numbers when they can justify why their answer represents a quantity just counted. This justification could merely be the expression that the number said is the total because it was just counted, or a “proof” by demonstrating a one-to-one match, by counting again or other similar means (concretely or pictorially) that makes sense. An ultimate level of understanding is reached when children can compare two numbers from 1 to10 represented as written numerals without counting.

Students need to explain their reasoning when they determine whether a number is greater than, less than, or equal to another number. Teachers need to ask probing questions such as “How do you know?” to elicit their thinking. For students, these comparisons increase in difficulty, from greater than to less than to equal. It is easier for students to identify differences than to find similarities.

Instructional Resources/Tools Board games Winnipeg School Division. 2005-2006. Numeracy Project: Dot Card and Ten Frame Activities.


Describe and compare measurable attributes. (K.MD.1, K.MD.2) Classify objects and count the number of objects in each category. (K.MD.3) Analyze, compare, create, and compose shapes. (K.G.4)


1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the


4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.








Operations & Algebraic Thinking (Addition & Subtraction) K.OA.1, K.OA.2, K.OA.3, K.OA.4, K.OA.5

UNDERSTAND:

Understand addition as putting together and adding to. Understand subtraction as taking apart and taking from. Numbers can be decomposed into place value parts and represented in multiple ways.

KNOW: DO:

There are different ways to show addition and subtraction solutions.

Objects or drawings can be used to solve addition and subtraction word problems.

Record equations to represent addition or subtraction problems. Addition and subtraction facts to 5.

Quantities represented by numbers can be composed and decomposed into part/whole relationships (by place value up to 20 in K).

Kindergarten students should see addition and subtraction equations, and student writing of equations in kindergarten is encouraged, but it is not required.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. K.OA.1 Represent addition and subtraction with objects, fingers,

mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

K.OA.2 Solve addition and subtraction word problems from a variety of cultural contexts, including those of Montana American Indians, and add and subtract within 10 (e.g., by using objects or drawings to represent the problem).

K.OA.3 Decompose numbers less than or equal to 10 into pairs in more than one way (e.g., by using objects or drawings), and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).

K.OA.4 For any number from 1 to 9, find the number that makes 10 when added to the given number (e.g., by using objects or drawings), and record the answer with a drawing or equation.

K.OA.5 Fluently add and subtract within 5.


Add, Addition, Equation, Subtract, Subtraction


Cluster: Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. Provide contextual situations for addition and subtraction that relate to the everyday lives of kindergarteners. A variety of situations can be found in children’s literature books. Students then model the addition and subtraction using a variety of representations such as drawings, sounds, acting out situations, verbal explanations and numerical expressions. Manipulatives, like two-color counters, clothespins on hangers, connecting cubes and stickers can also be used for modeling these operations. Kindergarten students should see addition and subtraction equations written by the teacher. Although students might struggle at first, teachers should encourage them to try writing the equations. Students’ writing of equations in Kindergarten is encouraged, but it is not required.

Create written addition or subtraction problems with sums and differences less than or equal to 10 using the numbers 0 to 10 and Table 1 on page 72 in the Montana Common Core Standards for School Mathematics Grade-Band for guidance. It is important to use a problem context that is relevant to kindergarteners. After the teacher reads the problem, students choose their own method to model the problem and find a solution. Students discuss their solution strategies while the teacher represents the situation with an equation written under the problem. The equation should be written by listing the numbers and symbols for the unknown quantities in the order that follows the meaning of the situation. The teacher and students should use the words equal and is the same as interchangeably.

Have students decompose numbers less than or equal to 5 during a variety of experiences to promote their fluency with sums and differences less than or equal to 5 that result from using the numbers 0 to 5. For example, ask students to use different models to decompose 5 and record their work with drawings or equations. Next, have students decompose 6, 7, 8, 9, and 10 in a similar fashion. As they come to understand the role and meaning of arithmetic operations in number systems, students gain computational fluency, using efficient and accurate methods for computing.

The teacher can use back mapping and scaffolding to teach students who show a need for more help with counting. For instance, ask students to build a tower of 5 using 2 green and 3 blue linking cubes while you discuss composing and

http://opi.mt.gov/Curriculum/montCAS/MCCS/index.php#gpm1_4





decomposing 5. Have them identify and compare other ways to make a tower of 5. Repeat the activity for towers of 7 and 9. Help students use counting as they explore ways to compose 7 and 9.

Instructional Resources/Tools Colored cubes Linking cubes Part-Part-Whole Mat and objects to model problem situations and find solutions. (The mat is divided into three sections and the labels for the sections in order are Part, Part, and Whole.) Montana Office of Public Instruction. 2011. Montana Common Core Standards for School Mathematics Grade-Band: Table 1 on page 72 illustrates 12 addition and subtraction problem situations.

National Council of Teachers of Mathematics. 2000-2012.

Exploring adding with sets: This lesson builds on the previous two lessons in the unit Do It with Dominoes and

encourages students to explore another model for addition, the set model.

Links Away: In this unit (lessons 2, 4, 5, and 7), students explore models of subtraction (counting, sets, balanced

equations, and inverse of addition) and the relation between addition and subtraction using links. Students also write story problems in which subtraction is required.

More and More Buttons: In this lesson, students use buttons to create, model, and record addition sentences.

Winnipeg School Division. 2005-2006. Numeracy Project: Dot Card and Ten Frame Activities


Work with numbers 11-19 to gain foundations for place value. (K.NBT.1)






http://opi.mt.gov/Curriculum/montCAS/MCCS/index.php#gpm1_4

http://illuminations.nctm.org/LessonDetail.aspx?ID=L54









Place Value K.NBT.1

UNDERSTAND:

Teen numbers can be decomposed into place value parts and represented in multiple ways.

KNOW: DO:

Quantities represented by numbers can be composed and decomposed into part/whole relationships (by place value up to 20 in K).

The base-ten number system allows for a new place-value unit by grouping ten of the previous place-value units (and this process can be iterated to obtain larger and larger place-value units).

The value of a digit in a written numeral depends on its place, or position, in a number.

Each composition or decomposition can be recorded by a drawing or equation (e.g., 18 = 10 + 8).

Kindergarten students should see addition and subtraction equations, and student writing of equations in kindergarten is encouraged, but it is not required.

Work with numbers 11-19 to gain foundations for place value. K.NBT.1 Compose and decompose numbers from 11 to 19 into ten

ones and some further ones (e.g., by using objects or drawings), and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.


Add, Subtract, Ones, Tens, Eleven, Twelve, Thirteen, Fourteen, Fifteen, Sixteen, Seventeen, Eighteen, Nineteen


Cluster: Work with numbers 11–19 to gain foundations for place value. Kindergarteners need to understand the idea of a ten so they can develop the strategy of adding onto 10 to add within 20 in Grade 1. Students need to construct their own base-ten ideas about quantities and their symbols by connecting to counting by ones. They should use a variety of manipulatives to model and connect equivalent representations for the numbers 11 to19. For instance, to represent 13, students can count by ones and show 13 beans. They can anchor to five and show one group of 5 beans and 8 beans or anchor to ten and show one group of 10 beans and 3 beans. Students need to eventually see a ten as different from 10 ones.

After the students are familiar with counting up to 19 objects by ones, have them explore different ways to group the objects that will make counting easier. Have them estimate before they count and group. Discuss their groupings and lead students to conclude that grouping by ten is desirable. 10 ones make 1 ten makes students wonder how something that means a lot of things can be one thing. They do not see that there are 10 single objects represented on the item for ten in pre-grouped materials, such as the rod in base-ten blocks. Students then attach words to materials and groups without knowing what they represent. Eventually they need to see the rod as a ten that they did not group themselves. Students need to first use groupable materials to represent numbers 11 to 19 because a group of ten such as a bundle of 10 straws or a cup of 10 beans makes more sense than a ten in pre-grouped materials. Kindergarteners should use proportional base-ten models, where a group of ten is physically 10 times larger than the model for a one. Non-proportional models such as an abacus and money should not be used at this grade level. Students should impose their base-ten concepts on a model made from groupable and pre-groupable materials (see Resources/Tools). Students can transition from groupable to pre-groupable materials by leaving a group of ten intact to be reused as a pre-grouped item. When using pre-grouped materials, students should reflect on the ten-to-one relationships in the materials, such as the “tenness” of the rod in base-ten blocks. After many experiences with pre-grouped materials, students can use dots and a stick (one tally mark) to record singles and a ten.





Encourage students to use base-ten language to describe quantities between 11 and 19. At the beginning, students do not need to use ones for the singles. Some of the base-ten language that is acceptable for describing quantities such as18 includes one ten and eight, a bundle and eight, a rod and 8 singles and ten and eight more. Write the horizontal equation 18 = 10 + 8 and connect it to base-ten language. Encourage, but do not require, students to write equations to represent quantities.

Instructional Resources/Tools Groupable models

Dried beans and small cups for holding groups of 10 dried beans Linking cubes Plastic chain links

Pre-grouped materials Base-ten blocks Dried beans and bean sticks (10 dried beans glued on a craft stick)

Pearson Education, Inc. 2012: Five-frame and Ten-frame Place-value mat with ten-frames Strips (ten connected squares) and squares (singles)


None



2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning

of others.


http://www.ablongman.com/vandewalleseries/Vol_1_BLM_PDFs/BLM1-2.pdf

http://www.ablongman.com/vandewalleseries/Vol_1_BLM_PDFs/BLM15.pdf







Measurement & Data (A strong connection to Number with counting and comparing)

K.MD.1, K.MD.2, K.MD.3

UNDERSTAND:

Objects can be sorted/classified by their attributes. Objects can be described and compared by their attributes.

KNOW: DO:

Objects have different attributes that can be measured or compared.

Describe and compare measurable attributes. K.MD.1 Describe measurable attributes of objects, such as length or

weight. Describe several measurable attributes of a single object. K.MD.2 Directly compare two objects with a measurable attribute in

common, to see which object has "more of"/"less of" the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter.

Classify objects and count the number of objects in each category. K.MD.3 Classify objects from a variety of cultural contexts, including

those of Montana American Indians, into given categories; count the numbers of objects in each category and sort the categories by count. (Limit category counts to be less than or equal to 10).

3


Attribute, Classify, Compare, Less than, Measure, More than, Sort


Cluster: Describe and compare measurable attributes. It is critical for students to be able to identify and describe measureable attributes of objects. An object has different attributes that can be measured, like the height and weight of a can of food. When students compare shapes directly, the attribute becomes the focus. For example, when comparing the volume of two different boxes, ask students to discuss and justify their answers to these questions: “Which box will hold the most?”, “Which box will hold least?”, and “Will they hold the same amount?” Students can decide to fill one box with dried beans then pour the beans into the other box to determine the answers to these questions.

Have students work in pairs to compare their arm spans. As they stand back-to-back with outstretched arms, compare the lengths of their spans, then determine who has the smallest arm span. Ask students to explain their reasoning. Then ask students to suggest other measureable attributes of their bodies that they could directly compare, such as their height or the length of their feet.

Connect to other subject areas. For example, suppose that the students have been collecting rocks for classroom observation and they wanted to know if they have collected typical or unusual rocks. Ask students to discuss the measurable attributes of rocks. Lead them to first comparing the weights of the rocks. Have the class chose a rock that seems to be a “typical” rock. Provide the categories: Lighter Than Our Typical Rock and Heavier Than Our Typical Rock. Students can take turns holding a different rock from the collection and directly comparing its weight to the weight of the typical rock and placing it in the appropriate category. Some rocks will be left over because they have about the same weight as the typical rock. As a class, they count the number of rocks in each category and use these counts to order the categories and discuss whether they collected “typical” rocks.

Instructional Resources/Tools Dried beans Rice Two- and three-dimensional real-world objects

3 Limit category counts to be less than or equal to 10.





National Council of Teachers of Mathematics. 2000-2012. Magnificent Measurement: The Weight of Things: This lesson introduces and provides practice with the measurable attribute of weight.

Cluster: Classify objects and count the number of objects in each category. Provide categories for students to use to sort a collection of objects. Each category can relate to only one attribute, like Red and Not Red or Hexagon and Not Hexagon, and contain up to ten objects. Students count how many objects are in each category and then order the categories by the number of objects they contain.

Ask questions to initiate discussion about the attributes of shapes. Then have students sort a collection of two-dimensional and three-dimensional shapes by their attributes. Provide categories like Circles and Not Circles or Flat and Not Flat. Have students count the objects in each category and order the categories by the number of objects they contain.

Have students infer the classification of objects by guessing the rule for a sort. First, the teacher uses one attribute to sort objects into two loops or regions without labels. Then the students determine how the objects were sorted, suggest labels for the two categories and explain their reasoning.

Instructional Resources/Tools Attribute blocks Large paper to draw loops Variety of objects to sort Yarn for loops


Count to tell the number of objects. (K.CC.4, K.CC.5) Compare numbers. (K.CC.6, K.CC.7) Analyze, compare, create, and compose shapes. (K.G.4)












Geometry (Shapes and Their Attributes) K.G.1, K.G.2, K.G.3, K.G.4, K.G.5, K.G.6

UNDERSTAND:

Shapes can be described, compared, and sorted by their attributes. Shapes can be joined together to make larger shapes.

KNOW: DO:

A shape has the same name regardless of orientation or size.

Shapes have attributes that allow them to be analyzed and compared.

Shapes can be combined to form larger shapes.

2-D is "lying flat".

3-D is "solid".

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). K.G.1 Describe objects in the environment using names of shapes, and describe

the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.

K.G.2 Correctly name shapes regardless of their orientations or overall size. K.G.3 Identify shapes as two-dimensional ("flat") or three-dimensional ("solid").

Analyze, compare, create, and compose shapes. K.G.4 Analyze and compare two- and three-dimensional shapes, in different

sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/corners) and other attributes (e.g., having sides of equal length).

K.G.5 Model shapes in the world from a variety of cultural contexts, including those of Montana American Indians, by building shapes from components (e.g., sticks and clay balls) and drawing shapes.

K.G.6 Compose simple shapes to form larger shapes. For example, "Can you join these two triangles with full sides touching to make a rectangle?"


Above, Attributes, Below, Behind, Corner (vertices), Equal, Next to, Side Shape names: 2D:, 3D:, Circles, Cones, Cubes, Cylinders, Hexagons, Rectangles, Spheres, Squares, Triangles


Cluster: Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). Develop spatial sense by connecting geometric shapes to students’ everyday lives. Initiate natural conversations about shapes in the environment. Have students identify and name two- and three-dimensional shapes in and outside of the classroom and describe their relative position.

Ask students to find rectangles in the classroom and describe the relative positions of the rectangles they see (e.g., This rectangle (a poster) is over the sphere (globe)). Teachers can use a digital camera to record these relationships. Hide shapes around the room. Have students say where they found the shape using positional words (e.g., I found a triangle UNDER the chair.)

Have students create drawings involving shapes and positional words: (e.g., Draw a window ON the door or Draw an apple UNDER a tree.). Some students may be able to follow two- or three-step instructions to create their drawings.

Use a shape in different orientations and sizes along with non-examples of the shape so students can learn to focus on defining attributes of the shape.

Manipulatives used for shape identification actually have three dimensions. However, kindergartners need to think of these shapes as two-dimensional or “flat” and typical three-dimensional shapes as “solid.” Students will identify two-dimensional shapes that form surfaces on three-dimensional objects. Students need to focus on noticing two and three dimensions, not on the words two-dimensional and three-dimensional.

Instructional Resources/Tools Common two- and three-dimensional items Pattern blocks Die-cut shapes





Digital camera Three-dimensional models

International Reading Association and the National Council of Teachers of English. 2012. Going on a Shape Hunt: Integrating Math and Literacy: In this unit, students are introduced to the idea of shapes through a read-aloud session with an appropriate book. They then use models to learn the names of shapes, work together and individually to locate shapes in their real-world environment. Pearson Education, Inc. 2012:

Assorted shapes Tangrams

Cluster: Analyze, compare, create and compose shapes. Use shapes collected from students to begin the investigation into basic properties and characteristics of two- and three-dimensional shapes. Have students analyze and compare each shape with other objects in the classroom and describe the similarities and differences between the shapes. Ask students to describe the shapes while the teacher records key descriptive words in common student language. Students need to use the word flat to describe two-dimensional shapes and the word solid to describe three-dimensional shapes.

Use the sides, faces and vertices of shapes to practice counting and reinforce the concept of one-to-one correspondence.

The teacher and students orally describe and name the shapes found on a Shape Hunt. Students draw a shape and build it using materials regularly kept in the classroom such as construction paper, clay, wooden sticks or straws.

Students can use a variety of manipulatives and real-world objects to build larger shapes with these and other smaller shapes: squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres. Kindergarteners can manipulate cardboard shapes, paper plates, pattern blocks, tiles, canned food, and other common items.

Have students compose (build) a larger shape using only smaller shapes that have the same size and shape. The sides of the smaller shapes should touch and there should be no gaps or overlaps within the larger shape. For example, use one-inch squares to build a larger square with no gaps or overlaps. Have students also use different shapes to form a larger shape where the sides of the smaller shapes are touching and there are no gaps or overlaps. Ask students to describe the larger shape and the shapes that formed it.

Instructional Resources/Tools Balls Boxes that are cubes Cans of food Carpet squares or rectangles Clay Colored tiles Construction paper Cubes Floor tiles Paper plates Pattern blocks Straws Tangrams Three-dimensional models Wooden sticks National Council of Teachers of Mathematics. 2000-2012. What can you build with triangles?: The first lesson in this unit includes the Just Two Triangles activity worksheet where students are asked to form different larger shapes with two triangles.

http://www.readwritethink.org/classroom-resources/lesson-plans/going-shape-hunt-integrating-776.html?tab=4#session1

http://www.readwritethink.org/classroom-resources/lesson-plans/going-shape-hunt-integrating-776.html?tab=4#session1


http://www.ablongman.com/vandewalleseries/Vol_1_BLM_PDFs/BLM27.pdf







Describe and compare measurable attributes. (K.MD.1) Describe several measurable attributes of a single object. (K.MD.2) Classify objects and count the number of objects in each category. (K.MD.3) Count to tell the number of objects. (K.CC.4, K.CC.5) Compare numbers. (K.CC.6, K.CC.7)










This Curriculum Organizer was created using the following materials:

ARIZONA - STANDARDS FOR MATHEMATICAL PRACTICE EXPLANATIONS AND EXAMPLES

http://www.azed.gov/standards-practices/mathematics-standards/

DELAWARE – LEARNING PROGRESSIONS

http://www.doe.k12.de.us/infosuites/staff/ci/content_areas/math.shtml

OHIO – INSTRUCTIONAL STRATEGIES AND RESOURCES (FROM MODEL CURRICULUM)

http://education.ohio.gov/GD/Templates/Pages/ODE/ODEDetail.aspx?Page=3&TopicRelationID=1704&Content=134773

http://www.azed.gov/standards-practices/mathematics-standards/

http://www.doe.k12.de.us/infosuites/staff/ci/content_areas/math.shtml

http://education.ohio.gov/GD/Templates/Pages/ODE/ODEDetail.aspx?Page=3&TopicRelationID=1704&Content=134773

SAMPLE YEAR LONG PLANCOURSE: KINDERGARTEN MATH

Unit

Knows number names

& count sequence

numbers 0‐50

Count to tell the

number of objects

Compare

numbers & sets

of objects 1‐10

Describe and

compare

measurable

attributes

Classifies &

counts objects

in categories

Identify &

Describe Shapes

Analyze,

compare,create, &

compose shapes

(Time) (10 days) (10 days) (10 days) (5 days) (5 days) (10 days) (10 days)

STANDARDS K.CC.1 K.CC.4a K.CC.6 K.MD.1 K.MD.2 K.G.1 K.G.4

K.CC.2 K.CC.4b K.CC.7 K.G.2 K.G.5

K.CC.3 K.CC.4c K.G.3 K.G.6

K.CC.5

Major

Supporting

Additional

KINDERGARTEN MATH P.2

Count numbers 51‐100

Count to tell the

number of objects

Compare numbers

& sets of objects 1‐

10

Understands addition

to 5

Understands

subtraction to 5

Decomposing

Numbers less than or

equal to 10

Work with numbers 11‐

19 for place value

(10 days) (10 days) (10 days) (30 days) (20 days) (20 days) (20 days)

K.CC.1 K.CC.4a K.CC.6 K.OA.1 K.OA.1 K.OA.3 K.NBT.1

K.CC.2 K.CC.4b K.CC.7 K.OA.2 K.OA.2 K.OA.4

K.CC.4c K.OA.5 K.OA.5

K.CC.5

is about…

TEACHER: _______________________________________________ SCHOOL DISTRICT/BUILDING: ______________________________________________

COURSE: Math GRADE LEVEL(S): Kindergarten

LAST UNIT Compare numbers & sets of objects

CURRENT UNIT Addition

NEXT UNIT Subtraction

UNIT SCHEDULE UNIT MAP Show examples using

manipulatives

Introduce symbols +,=

I do, we do using manipulatives

Manipulatives on own

Picture worksheet w/help

Do several similar picture worksheets whole group

Picture worksheet on own

Word problems together

Word problems on own

Equations whole group

Equations on own

Review concepts

End of unit assessment

UN

IT S

ELF

TEST

Q

UES

TIO

NS

Use manipulatives and drawings to demonstrate an understanding of addition MATH STANDARDS

Solve addition word problems K.OA.1

Solve addition equations up to five

K.OA.2

K.OA.5

Addition

Manipulatives:

K.OA.1 Represent addition

using a variety of objects

Picture Worksheets:

K.OA.1 Represent addition

using a variety of objects

Word Problems: K.OA.2 Solve

addition using work problems

from a variety of cultural

contexts

Equations:

K.OA.5 Fluently add

16

Lesson 2: Birds on the Tree Overview and Background Information

Mathematical Goals

By the end of the lesson students will: • Join two groups of objects • Find the total quantity after joining two groups of objects • Explain their process of joining two groups of objects to find the quantity

Common Core State Standards

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

K.OA.1 Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

K.OA.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

K.OA.5 Fluently add and subtract within 5. Count to tell the number of objects. K.CC.5 Count to answer “how many?” questions about as many as 20 things

arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects.

Emphasized Standards for Mathematical Practice

1. Make Sense and Persevering while Solving Problems 2. Reason Abstractly and Quantitatively 4. Use Appropriate Tools Strategically 8. Look for and Express Regularity in Repeated Reasoning

Prior Knowledge Needed

making sets of objects (within 5), counting sets of objects consistently with accuracy (within 5)

Vocabulary join Materials Whole class: tree work mats, counters, number cubes marked 1, 2 and 3, large picture

cards Station 1: number cards, counters, ten frame Station 2: small picture cards, number cubes (1-3), tree work mat, counters Station 3: pom-poms, hoops Station 4: cubes Station 5: paper plate with a line drawn down the center, counters Recording sheets for Stations 3, 4, and 5

tlysons

Typewritten Text

tlysons

Typewritten Text

Kindergarten Lesson Example, from North Carolina Department of Public Instruction, www.ncdpi.wikispaces.net, retrieved 6/2013.

tlysons

Typewritten Text

17

Tasks in the Lesson Engage 3-5 minutes During whole group time, read the following story off Picture Card A and show it to students: There were 2 birds sitting in the tree. The teacher will roll a number cube marked 1, 2, and 3 Suddenly __ more birds flew onto the tree. How many birds are on the tree now? Ask students to come act out the story. The teacher might say: Let’s think about this problem. We have a tree. Here is our tree (points to the ground). We need two birds (calls 2 students to come and stand in front of the class. The teacher continues by asking __ more students to stand up but in a separate group from the first two students.) The teacher can then ask the class, “How many students are on the tree now?” As students give their solutions, it is acceptable to allow many students to share their solution, even if they all say the same solution. The teacher might say: How many birds are in the tree? Does anyone have a different solution? Regardless of the solution, the teacher should not lead students to think whether their solution is correct or incorrect. The teacher then asks students: How can we find out how many birds are in the tree? Possible responses: We can count the number of students (birds). I know that I start at 2 and then count on __ more. I know that 2 and __ is __. Explore and Explain 10-12 minutes Pass out counters and tree work mats to every student. I’m going to tell you a story. Use your counters and tree mat to solve the story problem. Read the following story off Picture Card B: There were 3 birds on the tree. The teacher rolls the number cube. __ more birds flew on the tree. How many birds are on the tree now? Allow students to use their counters and tree mat however they want in order to represent the problem. As students are working, observe:

• Do students place the correct number of counters on the tree? • Can students tell you the total number of counters? • Could any students immediately put counters out without modeling the problem?

After students have had a few minutes to model the problem, ask students: How many birds are on the tree? As students share their solution, ask students to share their strategies. Possible responses: I put 2 counters on the tree and then I put __ counter(s) on the tree. Then I counted them. There were 2 counters on the tree. I knew that __ more is __. I knew that 2 and __ is __.

18

Ask students to clear their work mat to get ready for a new story problem. Read the following story off Picture Card C and show the card to students: 3 birds are on the tree. The teacher rolls the number cube. __ more birds flew on the tree. How many birds are on the tree now? Allow students to use their counters and tree mat however they want in order to represent the problem. As students are working, observe:

• Do students place the correct number of counters on the tree? • Can students tell you the total number of counters? • Could any students immediately put counters out without modeling the problem?

After students have had a few minutes to model the problem, ask students: How many birds are on the tree? As students share their solution, follow up with students to share their strategies. Possible responses: I put 3 counters on the tree and I counted. I put 3 counters on a tree and then counted on. I knew that 3 and __ is __. Tell students to clear their work mat and get ready for another story problem. This time, choose a student to read the story card to the class. Follow the process above to have students act out and solve the problem. Do this with Picture Cards D, E, and F. Elaborate 30-35 minutes Students will spend the remainder of the lesson in independent work stations practicing concepts related to joining and number sense. The teacher’s role is to scaffold and extend students’ learning by interacting with students at each of the stations. The teacher should not be fixed at one station the entire time. These stations are intended to focus on combinations of 3, 4, and 5 only. Each day a student should only be working on combinations of either 3, 4, or 5. This is determined by the teacher or the student. Stations 2, 3, 4, and 5 should be introduced prior to this lesson. Here is an overview of the five stations: Station 1: One or Two More Animals Students will select a number card (0-5) and use that number as the start number in their story problem. Students make that number using counters. From the start number, students will determine how many there will be if there will be one more animal came. Students can also find “two more” if they need enrichment. No recording is needed at this station. Students continue to select different number cards. Station 2: Adding to a Picture Students will select a Picture Card and make the picture with counters. Students will roll a number cube marked 1, 2, and 3. Students will add that many counters to their picture. Students will determine how many total counters they have. No recording is needed at this station. Students continue to select different story cards. Station 3: Pom-pom Toss Students will toss pom-poms at a hoop on the floor. Students will count how many landed inside the hoop and how many landed outside the hoop. Students record their solutions on the sheet. Station 4: Snap It Students make a tower of cubes and place it behind their back. While their tower is behind their back, they snap it and bring one part of the tower in front so they can see it. Students determine how many cubes are still behind their back and record their results. Station 5: Walk the line Students will spill beans or counters onto a paper plate that has a line drawn down the center. Students will count the number of counters on the left and on the right and record their results.

19

Evaluation of Students Formative: As students are working at Station 1: Do students accurately place the correct number of counters out? Are students able to join two sets and correctly identify the total? At Stations 2-5: Can students accurately determine the various parts and the whole while working? What strategies are students using to determine the various parts? (e.g., counting all, counting on, fluently identifying parts) Plans for Individual Differences Intervention: For struggling students, only work with combinations to 3 and 4. Extension: The number of objects at each station can be increased.

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Howard County Public School System • Draft 2011/2012 Adapted from Van de Walle, J. (2004) Elementary and Middle School Mathematics: Teaching Developmentally. Boston: Pearson Education, 65

Example: Kindergarten Formative Instructional and Assessment Tasks

NC DEPARTMENT OF PUBLIC INSTRUCTION KINDERGARTEN

OA Task 1a

Domain Operations and Algebraic Thinking

Cluster Understand addition as putting together and adding to, and understand subtraction as taking

apart and taking from.

Standard(s) K.OA.1 Represent addition and subtraction with objects, fingers, mental images, drawings,

sounds (e.g., claps), acting out situations, expressions, or equations.

K.OA.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g.,

by using objects or drawings to represent the problem.

Add to- Result Unknown

Materials Manipulatives such as chips/cubes, pencil, dice, picture cards that teacher will create

Task Provide materials to the student. Read the problem to the student: Sam saw two birds sitting

in the tree. Suddenly, ___ more birds flew onto the tree How many birds are on the tree

now? Show your thinking with objects, words, pictures or numbers. (Dok3) Ask students to

create his/her own problem and solve it.

Continuum of Understanding

Developing

Understanding

• Incorrectly solves the problem.

• Includes an answer without an explanation of how the

problem was solved.

Strategies Used:

Counting All

Counting On

Knows Basic Fact

Other

Explained Thinking:

Objects

Pictures

Numbers

Words

Other

Complete

Understanding

• Correctly solves the problem:

• Uses objects, words, pictures, and/or numbers to show

how the problem was solved.

Standards for Mathematical Practice

1. Makes sense and perseveres in solving problems.

2. Reasons abstractly and quantitatively.

3. Constructs viable arguments and critiques the reasoning of others.

4. Models with mathematics.

5. Uses appropriate tools strategically.

6. Attends to precision.

7. Looks for and makes use of structure.

8. Looks for and expresses regularity in repeated reasoning.

Available from www.ncpublicschools.org , Retrieved 6/2013.

http://www.ncpublicschools.org/

kindergarten montana common core standards: …

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