USD 305 Kindergarten CCSS Math Curriculum

7/27/2019 USD 305 Kindergarten CCSS Math Curriculum

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USD 305 Kindergarten Math Curriculum

In Kindergarten, instructional time should focus on two critical areas: (1) representing, relating, and operating on whole numbers, initially with setsof 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 aset; 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 answeringquantitative questions, including quickly recognizing the cardinalities of small sets of objects, counting and producing sets of given sizes, countingthe 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 andspatial reasoning to model objects in their environment and to construct more complex shapes.


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MATHEMATICS STANDARDS ARTICULATED BY GRADE LEVEL

Standards for Mathematical Practice

Standards Explanations and Examples

Students are expected

to:

Mathematical Practices are

listed throughout the grade

level document in the 2nd

column to reflect the need

to connect the mathematical

practices to mathematical

content in instruction.

K.MP.1. Make sense ofproblems and persevere

in solving them.

In Kindergarten, students begin to build the understanding that doing mathematicsinvolves 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 studentsmay 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 theymay try another strategy.

K.MP.2. Reasonabstractly andquantitatively.

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 didyou get that? and Why is that true? They explain their thinking to others and respondto others thinking.

K.MP.4. Model with

mathematics.

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


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Standards for Mathematical Practice

Standards Explanations and Examples

Students are expected

to:

Mathematical Practices are

listed throughout the grade

level document in the 2nd

column to reflect the need

to connect the mathematical

practices to mathematical

content in instruction.

K.MP.5. Use

appropriate tools

strategically.

Younger students begin to consider the available tools (including estimation) whensolving a mathematical problem and decide when certain tools might be helpful. Forinstance, kindergarteners may decide that it might be advantageous to use linking cubesto 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 ownreasoning.

K.MP.7. Look for and

make use of structure.

Younger students begin to discern a pattern or structure. For instance, students recognizethe 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 that3 + 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 moregroup of ten). In addition, students continually check their work by asking themselves,

Does this make sense?


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This is the Kindergarten Curriculum for Mathematics. The focus of this document is to provide instructional strategies and resources related to the

standards.

Subject

Grade

Domain

Standard#

Domain Cluster Standard

M K CC 1

Counting and

Cardinality

Know number names and

the count sequence.

Count to 100 by ones and by tens.

M K CC 2

Counting and

Cardinality


the count sequence.

Count forward beginning from a given number within the known sequence

(instead of having to begin at 1).

M K CC 3

Counting and

Cardinality


the count sequence.

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).

M K CC 4

Counting and

Cardinality

Count to tell the number of

objects.

Understand the relationship between numbers and quantities; connect counting

to cardinality.

M K CC 4aCounting andCardinality

Count to tell the number ofobjects.

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.

M K CC 4b

Counting and

Cardinality


objects.

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.


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Subject

Grade

Domain

Standard#


M K CC 4c

Counting and

Cardinality


objects.

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

larger.

M K CC 5

Counting and

Cardinality


objects.

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 .

M K CC 6

Counting and

Cardinality Compare numbers.

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.)

M K CC 7

Counting and

Cardinality Compare numbers. Compare two numbers between 1 and 10 presented as written numerals.

M K OA 1

Operations

and Algebraic

Thinking

Understand addition as

putting together and adding

to, and understand

subtraction as taking apart

and taking from.

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.

M K OA 2

Operations

and Algebraic

Thinking

Understand addition asputting together and adding

to, and understand


and taking from.

Solve addition and subtraction word problems, and add and subtract within 10,

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


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Subject

Grade

Domain

Standard#


M K OA 3

Operations

and Algebraic

Thinking


putting together and addingto, and understand


and taking from.

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).

M K OA 4

Operations

and Algebraic

Thinking



to, and understand


and taking from.

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.

M K OA 5

Operations

and Algebraic

Thinking



to, and understand


and taking from. Fluently add and subtract within 5.

M K NBT 1

Number and

Operations in

Base 10

Work with numbers 11-19

to gain foundations for place

value.

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.

M K MD 1

Measurements

and Data

Describe and compare

measurable attributes.

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

several measurable attributes of a single object.


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Subject

Grade

Domain

Standard#


M K MD 2

Measurements

and Data

Describe and compare

measurable attributes.

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.

M K MD 3

Measurements

and Data

Classify objects and countthe number of objects ineach category.

Classify objects 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.)

M K G 1 Geometry

Identify and describe shapes

(squares, circles, triangles,

rectangles, hexagons, cubes,

cones, cylinders, and

spheres).

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.

M K G 2 Geometry





spheres). Correctly name shapes regardless of their orientations or overall size.

M K G 3 Geometry





spheres).

Identify shapes as two-dimensional (lying in a plane, flat) or three-

dimensional (solid).


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Subject

Grade

Domain

Standard#


M K G 4 Geometry

Analyze, compare, create,

and compose shapes.

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).

M K G 5 Geometry


and compose shapes.

Model shapes in the world by building shapes from components (e.g., sticks

and clay balls) and drawing shapes.

M K G 6 Geometry


and compose shapes.

Compose simple shapes to form larger shapes. For example, "can you join

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

(HOME)

Counting and Cardinality M.K.CC

Know number names and the count sequence.

Instructional Strategies for ClusterThe Counting and Cardinality domain in Kindergarten contains standard statements that are connected to one another. Examine the three samples inthis 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 meaningand mathematize the real world. Help them see patterns, make connections and provide repeated experiences that give students time andopportunities to develop understandings and increase fluency. Encourage students to explain their reasoning by asking probing questions such asHow 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 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 learnhow to count before they understand cardinality, i.e. that the last count word is the amount of the set.


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Counting on or counting from a given number conflicts with the learned strategy of counting from the beginning. In order to be successful incounting on, students must understand cardinality. Students often merge or separate two groups of objects and then re-count from the beginning todetermine the final number of objects represented. For these students, counting is still a rote skill or the benefits of counting on have not beenrealized. Games that require students to add on to a previous count to reach a goal number encourage developing this concept. Frequent and briefopportunities 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 a certain meaning. Numbers have meaning when children can see mental imagesof the number symbols and use those images with which to think. Practice count words and written numerals paired with pictures, representations ofobjects, and objects that represent quantities within the context of life experiences for kindergarteners. For example, dot cards, dominoes and numbercubes 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 seemathematics as something that is alive and that they are involved.

Common MisconceptionsSome students might not see zero as a number. Ask students to write 0 and sayzero to represent the number of items left when all items have beentaken away. Avoid using the wordnone to represent this situation.

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

Quarter Taught: Quarter 1: X Quarter 2: X Quarter 3: X Quarter 4: XTeaching Time: All yearBlooms Level: knowledge

What does this standard mean that a student will know and be able to do?This standard calls for students to rote count by starting at one and count to 100. When students count by tens they are only expected to mastercounting on the decade (0, 10, 20, 30, 40 ). This objective does not require recognition of numerals. It is focused on the rote number sequence.I can count to 10 by ones.I can count to 20 by ones.I can count to 100 by ones.I can count to 100 by tens.


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Mathematical Practices:K.MP.7. Look for and make use of structure.

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

Vocabulary: count

Essential Questions: (What provocative questions will foster inquiry, understanding, and transfer learning?)

What does a number represent? How many are there?

Instructional/Learning Activities: (W.H.E.R.E.T.O.)The emphasis of this standard is on the counting sequence.

When counting by ones, students need to understand that the next number in the sequence is one more. When counting by tens, the next number inthe sequence is ten more (or one more group of ten).

Instruction on the counting sequence should be scaffold (e.g., 1-10, then 1-20, etc.).

Counting should be reinforced throughout the day, not in isolation.Examples:

Count the number of chairs of the students who are absent. Count the number of stairs, shoes, etc. Counting groups of ten such as fingers in the classroom (ten fingers per student).

When counting orally, students should recognize the patterns that exist from 1 to 100. They should also recognize the patterns that exist whencounting by 10s.

Assessments: (What will be acceptable evidence thestudent has achieved the desired results?)

Oral assessment

Instructional Resources/Tools:Board games that require countingDot Card and Ten Frame Activities (pp. 1-6, 12-17) Numeracy Project, Winnipeg SchoolDivision, 2005-2006Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity

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M.K.CC.2
http://www.edplus.canterbury.ac.nz/literacy_numeracy/maths/numdocuments/dot_card_and_ten_frame_package2005.pdfhttp://books.nap.edu/openbook.php?record_id=12519&page=1http://books.nap.edu/openbook.php?record_id=12519&page=1http://books.nap.edu/openbook.php?record_id=12519&page=1http://www.edplus.canterbury.ac.nz/literacy_numeracy/maths/numdocuments/dot_card_and_ten_frame_package2005.pdf


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Count forward beginning from a given number within the known sequence (instead of having to begin at 1).

Quarter Taught: Quarter 1: X Quarter 2: X Quarter 3: X Quarter 4: XTeaching Time: All year

Blooms Level: knowledge

What does this standard mean that a student will know and be able to do?This standard includes numbers 0 to 100. This asks for students to begin a rote forward counting sequence from a number other than 1. Thus, giventhe number 4, the student would count, 4, 5, 6 This objective does not require recognition of numerals. It is focused on the rote numbersequence.I can count to 10.I can count to 100.I can count on from a number other than 1 up to 100.

Mathematical Practices:K.MP.7. Look for and make use of structure.

Vocabulary: count



Instructional/Learning Activities: (W.H.E.R.E.T.O.)The emphasis of this standard is on the counting sequence to 100. Students should be able to count forward from any number, 1-99.

Assessments: (What will be acceptable evidence the

student has achieved the desired results?)

Oral assessment

Instructional Resources/Tools:Board games that require countingDot Card and Ten Frame Activities (pp. 1-6, 12-17) Numeracy Project, WinnipegSchool Division, 2005-2006Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity

(HOME)

M.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).

Quarter Taught: Quarter 1: X Quarter 2: X Quarter 3: Quarter 4:


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Teaching Time: 10 minutes/day

Blooms Level: Understanding

What does this standard mean that a student will know and be able to do?This standard addresses the writing of numbers and using the written numerals (0-20) to describe the amount of a set of objects. Due to varieddevelopment of fine motor and visual development, a reversal of numerals is anticipated for a majority of the students. While reversals should bepointed out to students, the emphasis is on the use of numerals to represent quantities rather than the correct handwriting formation of the actualnumeral itself.

This standard asks for students to represent a set of objects with a written numeral. The number of objects being recorded should not be greater than20. Students can record the quantity of a set by writing the numeral. Students can also create a set of objects based on the numeral presented.

Mathematical Practices:K.MP.2. Reason abstractly and quantitatively.

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


Vocabulary: count, number, match



Instructional/Learning Activities: (W.H.E.R.E.T.O.)Students should be given multiple opportunities to count objects and recognize that a number represents a specific quantity. Once this is established,students begin to read and write numerals (numerals are the symbols for the quantities). The emphasis should first be on quantity and then connectingquantities to the written symbols.

A sample unit sequence might include:

1.

Counting up to 20 objects in many settings and situations over several weeks.2. Beginning to recognize, identify, and read the written numerals, and match the numerals to given sets of objects.3. Writing the numerals to represent counted objects.

Since the teen numbers are not written as they are said, teaching the teen numbers as one group of ten and extra ones is foundational tounderstanding both the concept and the symbol that represents each teen number. For example, when focusing on the number 14, studentsshould count out fourteen objects using one-to-one correspondence and then use those objects to make one group of ten and four extra ones.Students should connect the representation to the symbol 14.



Instructional Resources/Tools:Board games that require counting


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Independently writing numbers to 20Counting objects and writing the correct number

Dot Card and Ten Frame Activities (pp. 1-6, 12-17) Numeracy Project, WinnipegSchool Division, 2005-2006Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity

(HOME)


Count to tell the number of objects.

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 and comparing sets or numerals.

Instructional Strategies for ClusterOne of the first major concepts in a students mathematical development is cardinality. Cardinality, knowing that the number word said tells thequantity you have and that the number you end on when counting represents the entire amount counted. The big idea is that number means amountand, 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 countingtasks 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 thereare 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 andcomparing quantities, such as board games, will encourage the development of cardinality. Frequent opportunities to use and discuss counting as ameans of solving problems relevant to kindergarteners is more beneficial than repeating the same routine day after day. For example, ask studentsquestions 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, suchas dot cards and dominoes, become tools for such comparisons. Students can concretely, pictorially or mentally look for similarities and differencesin 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 thatsuccessive numbers name quantities that are one larger. In order to encourage this idea, children need discussion and reflection of pairs of numbersfrom 1 to 10. Activities that utilize anchors of 5 and 10 are helpful in securing understanding of the relationships between numbers. This flexibilitywith 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 willarrive at an understanding of a number when they acquire cardinality and can connect a number with the numerals and the number word for thequantity they all represent.


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Common MisconceptionsSome students might think that the count word used to tag an item is permanently connected to that item. So when the item is used again for countingand should be tagged with a different count word, the student uses the original count word. For example, a student counts four geometric figures:triangle, square, circle and rectangle with the count words: one, two, three, four. If these items are rearranged as rectangle, triangle, circle and squareand counted, the student says these count words: four, one, three, two.

(HOME)

M.K.CC.4Understand the relationship between numbers and quantities; connect counting to cardinality.

Quarter Taught: Quarter 1: Quarter 2: X Quarter 3: X Quarter 4: XTeaching Time: 2 times a week for about 15 mins.

Blooms Level: Applying Level 3

What does this standard mean that a student will know and be able to do?

This standard asks students to count a set of objects and see sets and numerals in relationship to one another, rather than as isolated numbers or sets.These connections are higher-level skills that require students to analyze, to reason about, and to explain relationships between numbers and sets ofobjects. This standard should first be addressed using numbers 1-5 with teachers building to the numbers 1-10 later in the year. The expectation isthat students are comfortable with these skills with the numbers 1-10 by the end of Kindergarten.



K.MP.8. Look for and express regularity in repeated re atoning.

Vocabulary: number, group, set, greater than, less than, equal, more, fewer, same, most, least

Essential Questions: (What provocative questions will foster inquiry, understanding, and transfer learning?

o Can students identify the numeric symbol and word form of a given amount of objects in a set?

o Can students accurately name the quantity of a set of objects regardless of their physical arrangement?

o When given a number, can students draw the amount of objects that accurately depict that numeric value?

o Are students able to match the word form or numeric symbol with a set of objects?


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Instructional/Learning Activities: (W.H.E.R.E.T.O.)This standard focuses on one-to-one correspondence and how cardinality connects with quantity.

For example, when counting three bears, the student should use the counting sequence, 1-2-3, to count the bears and recognize that threerepresents the group of bears, not just the third bear. A student may use an interactive whiteboard to count objects, cluster the objects, andstate, This is three.

Students need opportunities to connect number words (orally) and the quantities they represent.

Students should have opportunities to arrange a set of objects in a variety of ways and be shown that the arrangement of those objects does not

change its quantity, numeric symbol or name in word form.

Students need a variety of games and activities which will provide ample opportunities for matching a set of objects with its corresponding numeric

symbol and its word form.

The use of a variety of manipulatives and technologies is useful as well.

Students should be encouraged to draw their own examples of number sets.

In order to understand that each successive number name refers to a quantity that is one larger, students should have experience counting objects,placing one more object in the group at a time.

For example, using cubes, the student should count the existing group, and then place another cube in the set. Some students may need to re-

count from one, but the goal is that they would count on from the existing number of cubes. S/he should continue placing one more cube at atime and identify the total number in order to see that the counting sequence results in a quantity that is one larger each time one more cube isplaced in the group.

A student may use a clicker (electronic response system) to communicate his/her count to the teacher.

Assessments: (What will be acceptable evidence

the student has achieved the desired results?)One on one demonstrates manipulating objects toshow 2 different numbers. (e.g. Roll dice, studentshows number using manipulatives) Then, stateswhich is more, fewer,

Instructional Resources/Tools:Dot Card and Ten Frame Activities (pp. 1-6, 12-17) Numeracy Project, Winnipeg SchoolDivision, 2005-2006http://teachers.net/lessons/posts/1417.html*Above can be modified using a variety of manipulatives.Kim Sutton materials

(HOME)

M.K.CC.4aWhen counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number namewith one and only one object.

Quarter Taught: Quarter 1: X Quarter 2: X Quarter 3: X Quarter 4: X
http://www.edplus.canterbury.ac.nz/literacy_numeracy/maths/numdocuments/dot_card_and_ten_frame_package2005.pdfhttp://teachers.net/lessons/posts/1417.htmlhttp://teachers.net/lessons/posts/1417.htmlhttp://teachers.net/lessons/posts/1417.htmlhttp://www.edplus.canterbury.ac.nz/literacy_numeracy/maths/numdocuments/dot_card_and_ten_frame_package2005.pdf


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Teaching Time: 2 times a week for 15 mins.

Blooms Level: Application Level 3

What does this standard mean that a student will know and be able to do?This standard reflects the ideas that students implement correct counting procedures by pointing to one object at a time (one-to-one correspondence)using one counting word for every object (one-to-one tagging/synchrony), while keeping track of objects that have and have not been counted.. Thisis the foundation of counting.

Vocabulary: counting by 1s, one to one number touch, object

Essential Questions: (What provocative questions will foster inquiry, understanding, and transfer learning?)What would happen if I said a number and did not touch the object?

Instructional/Learning Activities: (W.H.E.R.E.T.O.)


Students should have opportunities to arrange a set of objects in a variety of ways and be shown that the arrangement of those objects does

not change its quantity, numeric symbol or name in word form.

Students need a variety of games and activities which will provide ample opportunities for matching a set of objects with its correspondingnumeric symbol and its word form.



Assessments: (What will be acceptable evidence

the student has achieved the desired results?)One on one, student counts aloud while touchingobjects

Instructional Resources/Tools:Dot Card and Ten Frame Activities (pp. 1-6, 12-17) Numeracy Project, Winnipeg SchoolDivision, 2005-2006http://teachers.net/lessons/posts/1315.htmlKim Sutton materials

(HOME)

M.K.CC.4bUnderstand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement orthe order in which they were counted.
http://www.edplus.canterbury.ac.nz/literacy_numeracy/maths/numdocuments/dot_card_and_ten_frame_package2005.pdfhttp://teachers.net/lessons/posts/1315.htmlhttp://teachers.net/lessons/posts/1315.htmlhttp://teachers.net/lessons/posts/1315.htmlhttp://www.edplus.canterbury.ac.nz/literacy_numeracy/maths/numdocuments/dot_card_and_ten_frame_package2005.pdf


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Quarter Taught: Quarter 1: X Quarter 2: X Quarter 3: X Quarter 4: Teaching Time: Two times a week for 15-20 mins.

Bloos Level: Application

What does this standard mean that a student will know and be able to do?This standard calls for students to answer the question How many are there? by counting objects in a set and understanding that the last numberstated when counting a set (8, 9, 10) represents the total amount of objects: There are 10bears in this pile. (Cardinality). It also requires studentsto understand that the same set counted three different times will end up being the same amount each time. Thus, a purpose of keeping track of

objects is developed. Therefore, a student who moves each object as it is counted recognizes that there is a need to keep track in order to figure outthe amount of objects present. While it appears that this standard calls for students to have conservation of number, (regardless of the arrangement ofobjects, the quantity remains the same), conservation of number is a developmental milestone of which some Kindergarten children will not havemastered. The goal of this objective is for students to be able to count a set of objects; regardless of the formation those objects are placed.

Vocabulary: counting, groups, sets, How many are there?, total, in all, number of object


o What is a number?

o

Why is it important to count objects?o How many would there be if we added one more object?

o Can students identify the numeric symbol and word form of a given amount of objects in a set?

o Can students accurately name the quantity of a set of objects regardless of their physical arrangement?

o When given a number, can students draw the amount of objects that accurately depict that numeric value?

o Are students able to match the word form or numeric symbol with a set of objects?



Students should have opportunities to arrange a set of objects in a variety of ways and be shown that the arrangement of those objects does

not change its quantity, numeric symbol or name in word form.

Students need a variety of games and activities which will provide ample opportunities for matching a set of objects with its corresponding

numeric symbol and its word form.



Assessments: (What will be acceptable evidence Instructional Resources/Tools:


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the student has achieved the desired results?) Dot Card and Ten Frame Activities (pp. 1-6, 12-17) Numeracy Project, Winnipeg SchoolDivision, 2005-2006http://teachers.net/lessons/posts/1289.htmlKim Sutton materials

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M.K.CC.4cUnderstand that each successive number name refers to a quantity that is one larger.

Quarter Taught: Quarter 1: Quarter 2: Quarter 3: X Quarter 4: XTeaching Time: Two times a week for 15-20 mins.

Blooms Level: Creating

What does this standard mean that a student will know and be able to do?This standard represents the concept of one more while counting a set of objects. Students are to make the connection that if a set of objects was

increased by one more object then the number name for that set is to be increased by one as well. Students are asked to understand this concept withand without objects. For example, after counting a set of 8 objects, students should be able to answer the question, How many would there be if weadded one more object?; and answer a similar question when not using objects, by asking hypothetically, What if we have 5 cubes and added onemore. How many cubes would there be then? This concept should be first taught with numbers 1-5 before building to numbers 1-10. Studentsshould be expected to be comfortable with this skill with numbers to 10 by the end of Kindergarten.

Vocabulary: counting, objects, groups, one more

Essential Questions: (What provocative questions will foster inquiry, understanding, and transfer learning?)How many would there be if we added one more object?; and answer a similar question when not using objects, by asking hypothetically, What if

we have 5 cubes and added one more. How many cubes would there be then?

Instructional/Learning Activities: (W.H.E.R.E.T.O.)http://www.teacherspayteachers.com/Product/Counting-Practice-Game-Using-Common-Core-Standards-for-Promethean(This page will direct you todownload, once you download you will need to sign in to get the flipchart. This site has some free material.)

Assessments: (What will be acceptable evidence the student has achieved the desired results?)One on One settingComplete the assessment page found on share portal or click on the link below

Instructional Resources/Tools:Dot Card and Ten Frame Activities (pp.1-6, 12-17) Numeracy Project, Winnipeg
http://www.edplus.canterbury.ac.nz/literacy_numeracy/maths/numdocuments/dot_card_and_ten_frame_package2005.pdfhttp://teachers.net/lessons/posts/1289.htmlhttp://teachers.net/lessons/posts/1289.htmlhttp://www.teacherspayteachers.com/Product/Counting-Practice-Game-Using-Common-Core-Standards-for-Prometheanhttp://www.teacherspayteachers.com/Product/Counting-Practice-Game-Using-Common-Core-Standards-for-Prometheanhttp://www.edplus.canterbury.ac.nz/literacy_numeracy/maths/numdocuments/dot_card_and_ten_frame_package2005.pdfhttp://www.edplus.canterbury.ac.nz/literacy_numeracy/maths/numdocuments/dot_card_and_ten_frame_package2005.pdfhttp://www.teacherspayteachers.com/Product/Counting-Practice-Game-Using-Common-Core-Standards-for-Prometheanhttp://teachers.net/lessons/posts/1289.htmlhttp://www.edplus.canterbury.ac.nz/literacy_numeracy/maths/numdocuments/dot_card_and_ten_frame_package2005.pdf


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https://shareportal.usd305.com/elementary/kindergarten/Shared%20Documents/Standard%20MKCC.4c.docx

School Division, 2005-2006http://teachers.net/lessons/posts/3981.html(Dice Toss)

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M.K.CC.5Count 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 ascattered configuration; given a number from 120, count out that many objects.

Quarter Taught: Quarter 1: X Quarter 2: X Quarter 3: X Quarter 4: XTeaching Time: 25 minutes a week

Blooms Level: remembering

What does this standard mean that a student will know and be able to do?This standard asks students to count a set of objects and see sets and numerals in relationship to one another, rather than as isolated numbers or sets.

These connections are higher-level skills that require students to analyze, to reason about, and to explain relationships between numbers and sets ofobjects. This standard should first be addressed using numbers 1-5 with teachers building to the numbers 1-10 later in the year. The expectation isthat students are comfortable with these skills with the numbers 1-10 by the end of Kindergarten.




Vocabulary: count, number, numeral, match, how many


What does this number represent? How many are there?

Instructional/Learning Activities: (W.H.E.R.E.T.O.)Students should develop counting strategies to help them organize the counting process to avoid re-counting or skipping objects.

Examples:
https://shareportal.usd305.com/elementary/kindergarten/Shared%20Documents/Standard%20MKCC.4c.docxhttps://shareportal.usd305.com/elementary/kindergarten/Shared%20Documents/Standard%20MKCC.4c.docxhttps://shareportal.usd305.com/elementary/kindergarten/Shared%20Documents/Standard%20MKCC.4c.docxhttp://teachers.net/lessons/posts/3981.htmlhttp://teachers.net/lessons/posts/3981.htmlhttp://teachers.net/lessons/posts/3981.htmlhttp://teachers.net/lessons/posts/3981.htmlhttp://teachers.net/lessons/posts/3981.htmlhttps://shareportal.usd305.com/elementary/kindergarten/Shared%20Documents/Standard%20MKCC.4c.docxhttps://shareportal.usd305.com/elementary/kindergarten/Shared%20Documents/Standard%20MKCC.4c.docx


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If items are placed in a circle, the student may mark or identify the starting object. If items are in a scattered configuration, the student may move the objects into an organized pattern.

Some students may choose to use grouping strategies such as placing objects in twos, fives, or tens (note: this is not a kindergartenexpectation).

Counting up to20 objects should be reinforced when collecting data to create charts and graphs.A student may use a clicker (electronic response system) to communicate his/her count to the teacher.



ClickersInteractive white boardsUsing manipulatives, students will count a group ofobjects. After being mixed around, students can stillidentify how many.

Instructional Resources/Tools:

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

Clickers and interactive boards

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Compare numbers.

Instructional Strategies for ClusterAs children develop meaning for numerals, they also compare these numerals to the quantities represented and their number words. The modelingnumbers with manipulatives such as dot cards and five- and ten-frames become tools for such comparisons. Children can look for similarities anddifferences in these different representations of numbers. They begin to see the relationship of one more, one less, two more and two less, thuslanding on the concept that successive numbers name quantities where one is larger. In order to encourage this idea, children need discussion andreflection of pairs of numbers from 1 to 10. Activities that utilize anchors of 5 and 10 are helpful in securing understanding of the relationshipsbetween numbers. This flexibility with numbers will greatly impact childrens 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. Thisjustification 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-onematch, by counting again or other similar means (concretely or pictorially) that makes sense. An ultimate level of understanding is reached whenchildren 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
http://www.edplus.canterbury.ac.nz/literacy_numeracy/maths/numdocuments/dot_card_and_ten_frame_package2005.pdfhttp://www.edplus.canterbury.ac.nz/literacy_numeracy/maths/numdocuments/dot_card_and_ten_frame_package2005.pdf


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to ask probing questions such as How do you know? to elicit their thinking. For students, these comparisons increase in difficulty, from greaterthan to less than to equal. It is easier for students to identify differences than to find similarities.

Common Misconceptions

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M.K.CC.6Identify 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 usingmatching and counting strategies.1

1Include groups with up to ten objects.

Quarter Taught: Quarter 1: Quarter 2: X Quarter 3: Quarter 4: Teaching Time: 25 minutes a weekBlooms Level: remembering

What does this standard mean that a student will know and be able to do?This standard expects mastery of up to ten objects. Students can use matching strategies (Student 1), counting strategies or equal shares (Student 3) todetermine whether one group is greater than, less than, orequal to the number of objects in another group (Student 2).



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Vocabulary: greater than, less than, equal, larger, smaller



Instructional/Learning Activities: (W.H.E.R.E.T.O.)Students should develop a strong sense of the relationship between quantities and numerals before they begin comparing numbers.

Other strategies:

Matching: Students use one-to-one correspondence, repeatedly matching one object from one set with one object from the other set todetermine which set has more objects.

Counting: Students count the objects in each set, and then identify which set has more, less, or an equal number of objects.

Observation: Students may use observation to compare two quantities (e.g., by looking at two sets of objects, they may be able to tell which

set has more or less without counting). Observations in comparing two quantities can be accomplished through daily routines of collecting and organizing data in displays. Students

create object graphs and pictographs using data relevant to their lives (e.g., favorite ice cream, eye color, pets, etc.). Graphs may beconstructed by groups of students as well as by individual students.

Benchmark Numbers: This would be the appropriate time to introduce the use of 0, 5 and 10 as benchmark numbers to help students furtherdevelop their sense of quantity as well as their ability to compare numbers.

Students state whether the number of objects in a set is more, less, or equal to a set that has 0, 5, or 10 objects.



Clickers/interactive white boardsTeacher observation

Instructional Resources/Tools:Board gamesDot Card and Ten Frame Activities (pp. 1-6, 12-17) Numeracy Project, Winnipeg

School Division, 2005-2006ManipulativesGraphing paper

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

Quarter Taught: Quarter 1: Quarter 2: X Quarter 3: Quarter 4: Teaching Time: 25 minutes a week

Blooms Level: remembering

What does this standard mean that a student will know and be able to do?This standard calls for students to apply their understanding of numerals 1-10 to compare one from another. Thus, looking at the numerals 8 and 10,

a student must be able to recognize that the numeral 10 represents a larger amount than the numeral 8. Students should begin this standard by havingample experiences with sets of objects (K.CC.3 and K.CC.6) before completing this standard with just numerals. Based on early childhood research,students should not be expected to be comfortable with this skill until the end of Kindergarten.


Vocabulary: greater than, less than, equal, larger, smaller



Instructional/Learning Activities: (W.H.E.R.E.T.O.)Given two numerals, students should determine which is greater or less than the other.

Using a number line, students will find the two numbers and identify which is greater/less than.

Students can draw a picture to check and see if their number is greater.

Using dice, students can compare and find the number that is greater or less than.



Teacher observationClickers/Interactive whiteboards

Instructional Resources/Tools:Board gamesDot Card and Ten Frame Activities (pp. 1-6, 12-17) Numeracy Project, WinnipegSchool Division, 2005-2006DiceNumber line

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Operations and Algebraic Thinking M.K.OA


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If students progress from working with manipulatives to writing numerical expressions and equations, they skip using pictorial thinking. Studentswill then be more likely to use finger counting and rote memorization for work with addition and subtraction. Counting forward builds to the conceptof addition while counting back leads to the concept of subtraction. However, counting is an inefficient strategy. Teachers need to provideinstructional experiences so that students progress from the concrete level, to the pictorial level, then to the abstract level when learning mathematicalconcepts.

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M.K.OA.1Represent addition and subtraction with objects, fingers, mental images, drawings2, sounds (e.g., claps), acting out situations, verbal explanations,expressions, or equations.

2Drawings need not show details, but should show the mathematics in the problem. (This applies wherever drawings are mentioned in the Standards.)

Quarter Taught: Quarter 1: Quarter 2: Quarter 3: Quarter 4: Teaching Time:Blooms Level:


Students understand the concepts of addition and subtraction by manipulating concrete objects, drawing depictions of objects, making sounds torepresent objects (such as with rhythm sticks), expressing situations verbally, or acting out story problems.

Mathematical Practices:K.MP.1. Make sense of problems and persevere in solving them.

K.MP.2. Reason abstractly and quantitatively.

K.MP.4. Model with mathematics.

K.MP.5. Use appropriate tools strategically.

Vocabulary:joining, separating, addition, subtraction, equal, equation, same amount as, mental picture, less, more



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Stranger in the Woodsby Dana IslasOriginally featured in Math Solutions Online Newsletter, Issue 38This lesson is anchored to the award-winning book, Stranger in the Woods by Carl Sams and Jean Stoick. The book features photographs of a seriesof forest animals coming forward to explore a snowman (the stranger) that has appeared in the woods. After reading the story, children will be askedto solve three key questions:

Which animals visited the snowman? How many visited the snowman in our problem? How could you represent the animals to share your thinking with others?Students use a combination of pictures, words, and numbers to describe their problem. Samples of student work are included along with the teacherschart for their formative assessment. (Source: Math Solutions)

Comparing Connecting Cubesby Grace M. BurtonIn this five-part unit, students use connecting cubes and counting stories, such as Ten Black Dots by Donald Crews, to build an understanding ofsubtraction. There are five different presentations to explore subtraction. Lesson One uses counting back/counting on to help children generatesimple subtraction models. In Lesson Two children write subtraction problems and model them with cubes. The results are recorded in a table so that

the two sets can be compared. Hopping on a number line is the central activity for Lesson Three as children find another way to understandsubtraction. Lesson Four uses cubes and a balance beam to illustrate concepts of more and less. Lesson Five focuses on fact families. A briefbibliography of counting stories that work well in a kindergarten classroom is included. (Source: Illuminations, Comparing Connecting Cubes)

Dragon Feet

Excerpt posted on website for www.mathsolutions.com Math for All: Differentiating Instruction, Grades K2 by Linda Dacey and Rebeka Eston

Salemi

This lesson uses the picture book, Dragon Feet by Marjorie Jackson as the anchor for this math lesson. The teacher uses this story about two children

who are celebrating the Chinese Lunar New Year by being part of a dragon costume. The story prompts students to figure out questions such as how

many children are in the costume and how many feet the dragon has. Through a combination of acting out the story and drawings, the children

explore the math involved in this story and the concepts of one-to-one correspondence and one-to-two correspondence of objects. Additionally, the

author provides teaching strategies to build differentiation into the lessons to meet her students varied developmental needs. (Source: Math

Solutions)



Performance assessment


Growing Mathematical Ideas in KindergartenThis article talks about strategies to help teachers frame meaningful math questions for
http://mathsolutions.com/index.cfm?page=wp9&crid=56http://mathsolutions.com/index.cfm?page=wp9&crid=56http://illuminations.nctm.org/LessonDetail.aspx?ID=L41http://illuminations.nctm.org/LessonDetail.aspx?ID=L41http://www.mathsolutions.com/documents/9780941355773CH4.pdfhttp://www.mathsolutions.com/documents/9780941355773CH4.pdfhttp://www.mathsolutions.com/documents/0-941355-22-5_L.pdfhttp://www.mathsolutions.com/documents/0-941355-22-5_L.pdfhttp://www.mathsolutions.com/documents/0-941355-22-5_L.pdfhttp://www.mathsolutions.com/documents/9780941355773CH4.pdfhttp://illuminations.nctm.org/LessonDetail.aspx?ID=L41http://mathsolutions.com/index.cfm?page=wp9&crid=56


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student exploration and provides a sample counting activity in which children comparethe lengths of their names using connecting cubes and letters. (Source: Math Solutions)

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

Quarter Taught: Quarter 1: Quarter 2: Quarter 3: Quarter 4: Teaching Time:

Blooms Level:


Students will solve problems in a story format with a specific emphasis on using objects or drawings to determine the solution using numbers 1-10.

Teachers need to be aware of the three types of problems for addition and subtraction: Result Unknown, Change Unknown, and Start Unknown.

*Result Unknown: There are 3 students on the playground. 4 more students show up. How many students are there now?*Change Unknown: There are 3 students on the playground. Some more students show up. There are now 7 students. How many students came?*Start Unknown: There are some students on the playground. 4 more students come. There are now 7 students. How many students were on theplayground at the beginning?



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


K.MP.5. Use appropriate tools strategically.

Vocabulary:joining, separating, addition, subtraction, equal, equation, same amount as, mental picture, less, more


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o Teach the concept of fact families.

o When adding, students can look for ways to make 10 in order to make computing sums and differences easier.

o Activities that allow for number exploration is critical. One such way to do this is to give students a set of objects that total no more than

10. Have students find multiple ways to separate those objects into two sets and then rationalizing that although the original set is split,

they still have the same amount that they started with. From here, they can make addition sentences to represent their findings.

o The use of manipulatives and technologies has a strong influence on their understanding of this skill .




Instructional Resources/Tools:Colored cubesLinking cubesStudents can use a Part-Part-Whole Mat and objects to model problem situations andfind solutions. This mat is divided into three sections and the labels for the sections in

order are Part, Part, and Whole.Dot Card and Ten Frame Activities (pp. 1-6, 12-17) Numeracy Project, WinnipegSchool Division, 2005-2006Common Core State Standards for Mathematics: Common addition and subtractionsituationsTable 1 on page 88 in the Common Core State Standards for School Mathematicsillustrates 12 addition and subtraction problem situations.ORC # 1129 From the National Council of Teachers of Mathematics:Exploring addingwith setsThis lesson builds on the previous two lessons in the unitDo It with Dominoes andencourages students to explore another model for addition, the set model.ORC # 4319 From the National Council of Teachers of Mathematics:Links AwayIn the unitLinks Away (lessons 2, 4, 5, and 7) students explore models of subtraction(counting, sets, balanced equations, and inverse of addition) and the relation betweenaddition and subtraction using links. Students also write story problems in whichsubtraction is required.ORC # 4269 From the National Council of Teachers of Mathematics:More and MoreButtonsIn this lesson, students use buttons to create, model, and record addition sentences. Inthis lesson, students use buttons to create, model, and record addition sentences.
http://www.edplus.canterbury.ac.nz/literacy_numeracy/maths/numdocuments/dot_card_and_ten_frame_package2005.pdfhttp://illuminations.nctm.org/LessonDetail.aspx?ID=L54http://illuminations.nctm.org/LessonDetail.aspx?ID=L54http://illuminations.nctm.org/LessonDetail.aspx?ID=L54http://illuminations.nctm.org/LessonDetail.aspx?ID=L104http://illuminations.nctm.org/LessonDetail.aspx?ID=L104http://illuminations.nctm.org/LessonDetail.aspx?ID=L26http://illuminations.nctm.org/LessonDetail.aspx?ID=L26http://illuminations.nctm.org/LessonDetail.aspx?ID=L26http://illuminations.nctm.org/LessonDetail.aspx?ID=L26http://illuminations.nctm.org/LessonDetail.aspx?ID=L26http://illuminations.nctm.org/LessonDetail.aspx?ID=L104http://illuminations.nctm.org/LessonDetail.aspx?ID=L54http://illuminations.nctm.org/LessonDetail.aspx?ID=L54http://www.edplus.canterbury.ac.nz/literacy_numeracy/maths/numdocuments/dot_card_and_ten_frame_package2005.pdf


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M.K.OA.3Decompose 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 adrawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).

Quarter Taught: Quarter 1:

Quarter 2:

Quarter 3:

Quarter 4:

Teaching Time:

Blooms Level:


This objective asks students to realize that a set of objects can be broken in multiple ways. When breaking apart a set, students use the understandingthat a smaller set of objects exists within that a larger set.Every whole number can be broken in to parts.

Mathematical Practices:

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





Vocabulary:



**Teach the concept of fact families.

**When adding, students can look for ways to make 10 in order to make computing sums and differences easier.


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**Activities that allow for number exploration is critical. One such way to do this is to give students a set of objects that total no more than 10. Have

students find multiple ways to separate those objects into two sets and then rationalizing that although the original set is split, they still have the same

amount that they started with. From here, they can make addition sentences to represent their findings.

**The use of manipulatives and technologies has a strong influence on their understanding of this skill.





Colored cubesLinking cubesStudents can use a Part-Part-Whole Mat and objects to model problem situations andfind solutions. This mat is divided into three sections and the labels for the sections inorder are Part, Part, and Whole.Dot Card and Ten Frame Activities (pp. 1-6, 12-17) Numeracy Project, WinnipegSchool Division, 2005-2006Common Core State Standards for Mathematics: Common addition and subtractionsituationsTable 1 on page 88 in the Common Core State Standards for School Mathematics

illustrates 12 addition and subtraction problem situations.ORC # 1129 From the National Council of Teachers of Mathematics:Exploring addingwith setsThis lesson builds on the previous two lessons in the unitDo It with Dominoes andencourages students to explore another model for addition, the set model.ORC # 4319 From the National Council of Teachers of Mathematics:Links AwayIn the unitLinks Away (lessons 2, 4, 5, and 7) students explore models of subtraction(counting, sets, balanced equations, and inverse of addition) and the relation betweenaddition and subtraction using links. Students also write story problems in whichsubtraction is required.

ORC # 4269 From the National Council of Teachers of Mathematics:More and MoreButtonsIn this lesson, students use buttons to create, model, and record addition sentences.

(HOME)

M.K.OA.4
http://www.edplus.canterbury.ac.nz/literacy_numeracy/maths/numdocuments/dot_card_and_ten_frame_package2005.pdfhttp://illuminations.nctm.org/LessonDetail.aspx?ID=L54http://illuminations.nctm.org/LessonDetail.aspx?ID=L54http://illuminations.nctm.org/LessonDetail.aspx?ID=L54http://illuminations.nctm.org/LessonDetail.aspx?ID=L104http://illuminations.nctm.org/LessonDetail.aspx?ID=L104http://illuminations.nctm.org/LessonDetail.aspx?ID=L26http://illuminations.nctm.org/LessonDetail.aspx?ID=L26http://illuminations.nctm.org/LessonDetail.aspx?ID=L26http://illuminations.nctm.org/LessonDetail.aspx?ID=L26http://illuminations.nctm.org/LessonDetail.aspx?ID=L26http://illuminations.nctm.org/LessonDetail.aspx?ID=L104http://illuminations.nctm.org/LessonDetail.aspx?ID=L54http://illuminations.nctm.org/LessonDetail.aspx?ID=L54http://www.edplus.canterbury.ac.nz/literacy_numeracy/maths/numdocuments/dot_card_and_ten_frame_package2005.pdf


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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 theanswer with a drawing or equation.

Quarter Taught: Quarter 1: Quarter 2: Quarter 3: X Quarter 4: Teaching Time: 150-180 minutes weekly including center time

Blooms Level: Level 3-Application/Level 4-Analysis

What does this standard mean that a student will know and be able to do?This standard builds upon the understanding that a number can be decomposed into parts (K.OA.3). Once students have had experiences breaking

apart ten into various combinations, this asks students to find a missing part of 10.

Example:A full case of juice boxes has 10 boxes. There are only 6 boxes in this case. How many juice boxes are missing?






Vocabulary: total, add, equals, missing, number sentenceIntroduce and use: addend, sum, equation, combination



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What are the different combinations to make 10?

Instructional/Learning Activities: (W.H.E.R.E.T.O.)The number pairs that total ten are foundational for students ability to work fluently within base-ten numbers and operations. Different models, suchas ten-frames, cubes, two-color counters, etc., assist students in visualizing these number pairs for ten.

Example 1:Students place three objects on a ten frame and then determine how many more are needed to make a ten.Students may use electronic versions of ten frames to develop this skill.

Example 2:

The student snaps ten cubes together to make a train. Student breaks the train into two parts. S/he counts how many are in each part and record the associated equation (10 = ___ + ___).

Student breaks the train into two parts. S/he counts how many are in one part and determines how many are in the other part without directlycounting that part. Then s/he records the associated equation (if the counted part has 4 cubes, the equation would be 10 = 4 + ___).

Student covers up part of the train, without counting the covered part. S/he counts the cubes that are showing and determines how many arecovered up. Then s/he records the associated equation (if the counted part has 7 cubes, the equation would be 10 = 7 + ___).

Example 3:The student tosses ten two-color counters on the table and records how many of each color are facing up.



Students will be able to find the different combinationsfrom 1-9 to find the sum of ten.


Colored cubesLinking cubesStudents can use a Part-Part-Whole Mat and objects to model problem situations andfind solutions. This mat is divided into three sections and the labels for the sections inorder are Part, Part, and Whole.Dot Card and Ten Frame Activities (pp. 1-6, 12-17) Numeracy Project, WinnipegSchool Division, 2005-2006Common Core State Standards for Mathematics: Common addition and subtractionsituations


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Table 1 on page 88 in the Common Core State Standards for School Mathematicsillustrates 12 addition and subtraction problem situations.ORC # 1129 From the National Council of Teachers of Mathematics:Exploring addingwith setsThis lesson builds on the previous two lessons in the unitDo It with Dominoes andencourages students to explore another model for addition, the set model.ORC # 4319 From the National Council of Teachers of Mathematics:Links Away

In the unitLinks Away (lessons 2, 4, 5, and 7) students explore models of subtraction(counting, sets, balanced equations, and inverse of addition) and the relation betweenaddition and subtraction using links. Students also write story problems in whichsubtraction is required.ORC # 4269 From the National Council of Teachers of Mathematics:More and MoreButtons

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

(HOME)

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

Quarter Taught: Quarter 1: Quarter 2: Quarter 3: X Quarter 4: Teaching Time: 150-180 including center time

Blooms Level: Level 3-Application

What does this standard mean that a student will know and be able to do?This standard uses the word fluently, which means accuracy (correct answer), efficiency (a reasonable amount of steps), and flexibility (using

strategies such as the distributive property). Fluency is developed by working with many different kinds of objects over an extended amount of time.This objective does not require students to instantly know the answer. Traditional flash cards or timed tests have not been proven as effectiveinstructional strategies for developing fluency.



http://illuminations.nctm.org/LessonDetail.aspx?ID=L54http://illuminations.nctm.org/LessonDetail.aspx?ID=L54http://illuminations.nctm.org/LessonDetail.aspx?ID=L54http://illuminations.nctm.org/LessonDetail.aspx?ID=L104http://illuminations.nctm.org/LessonDetail.aspx?ID=L104http://illuminations.nctm.org/LessonDetail.aspx?ID=L26http://illuminations.nctm.org/LessonDetail.aspx?ID=L26http://illuminations.nctm.org/LessonDetail.aspx?ID=L26http://illuminations.nctm.org/LessonDetail.aspx?ID=L26http://illuminations.nctm.org/LessonDetail.aspx?ID=L26http://illuminations.nctm.org/LessonDetail.aspx?ID=L104http://illuminations.nctm.org/LessonDetail.aspx?ID=L54http://illuminations.nctm.org/LessonDetail.aspx?ID=L54


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Vocabulary: add, subtract, equals,Introduce and use: addend, sum, equation, subtrahend, difference


Why is it important to add and subtract quickly?

Instructional/Learning Activities: (W.H.E.R.E.T.O.)This standard focuses on students being able to add and subtract numbers within 5. Adding and subtracting fluently refers to knowledge ofprocedures, knowledge of when and how to use them appropriately, and skill in performing them flexibly, accurately, and efficiently.

Strategies students may use to attain fluency include:

Counting on (e.g., for 3+2, students will state, 3, and then count on two more, 4, 5, and state the solution is 5)

Counting back (e.g., for 4-3, students will state, 4, and then count back three, 3, 2, 1 and state the solution is 1)

Counting up to subtract (e.g., for 5-3, students will say, 3, and then count up until they get to 5, keeping track of how many they countedup, stating that the solution is 2)

Using doubles (e.g., for 2+3, students may say, I know that 2+2 is 4, and 1 more is 5)

Using commutative property (e.g., students may say, I know that 2+1=3, so 1+2=3) Using fact families (e.g., students may say, I know that 2+3=5, so 5-3=2)

Students may use electronic versions of five frames to develop fluency of these facts.



Students will be able to fluently add and subtract within 5.

Instructional Resources/Tools:Colored cubesLinking cubesStudents can use a Part-Part-Whole Mat and objects to model problem situations andfind solutions. This mat is divided into three sections and the labels for the sections inorder are Part, Part, and Whole.

Dot Card and Ten Frame Activities (pp. 1-6, 12-17) Numeracy Project, WinnipegSchool Division, 2005-2006Common Core State Standards for Mathematics: Common addition and subtractionsituationsTable 1 on page 88 in the Common Core State Standards for School Mathematicsillustrates 12 addition and subtraction problem situations.ORC # 1129 From the National Council of Teachers of Mathematics:Exploring addingwith setsThis lesson builds on the previous two lessons in the unitDo It with Dominoes and
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encourages students to explore another model for addition, the set model.ORC # 4319 From the National Council of Teachers of Mathematics:Links AwayIn the unitLinks Away (lessons 2, 4, 5, and 7) students explore models of subtraction(counting, sets, balanced equations, and inverse of addition) and the relation betweenaddition and subtraction using links. Students also write story problems in whichsubtraction is required.ORC # 4269 From the National Council of Teachers of Mathematics:More and More

ButtonsIn this lesson, students use buttons to create, model, and record addition sentences.

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Number and Operations in Base Ten

Work with numbers 1119 to gain foundations for place value.

Instructional Strategies for ClusterKindergarteners need to understand the idea ofa ten so they can develop the strategy of adding onto 10 to add within 20 in Grade 1. Students need toconstruct their own base-ten ideas about quantities and their symbols by connecting to counting by ones. They should use a variety of manipulativesto model and connect equivalent representations for the numbers 11 to19. For instance, to represent 13, students can count by ones and show 13beans. 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. Studentsneed 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 countingeasier. Have them estimate before they count and group. Discuss their groupings and lead students to conclude that grouping by ten is desirable. 10ones 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 objectsrepresented on the item for ten in pregrouped 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 usegroupable 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 aten in pregrouped materials.

Kindergarteners should use proportional base-ten models, where a group of ten is physically 10 times larger than the model for a one.Nonproportional 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 pregroupable materials (see Resources/Tools). Students cantransition from groupable to pregroupable materials by leaving a group of ten intact to be reused as a pregrouped item. When using pregrouped
http://illuminations.nctm.org/LessonDetail.aspx?ID=L104http://illuminations.nctm.org/LessonDetail.aspx?ID=L104http://illuminations.nctm.org/LessonDetail.aspx?ID=L26http://illuminations.nctm.org/LessonDetail.aspx?ID=L26http://illuminations.nctm.org/LessonDetail.aspx?ID=L26http://illuminations.nctm.org/LessonDetail.aspx?ID=L26http://illuminations.nctm.org/LessonDetail.aspx?ID=L26http://illuminations.nctm.org/LessonDetail.aspx?ID=L104


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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 manyexperiences with pregrouped 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 thesingles. Some of the base-ten language that is acceptable for describing quantities such as18 includes one ten and eight, a bundle and eight, a rodand 8 singles andten 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.

Common MisconceptionsStudents have difficulty with ten as a singular word that means 10 things. For many students, the understanding that a group of 10 things can bereplaced by a single object and they both represent 10 is confusing. Help students develop the sense of 10 by first using groupable materials thenreplacing the group with an object or representing 10. Watch for and address the issue of attaching words to materials and groups without knowingwhat they represent. If this misconception is not addressed early on it can cause additional issues when working with numbers 11-19 and beyond

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M.K.NBT.1Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record eachcomposition 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.

Quarter Taught: Quarter 1: Quarter 2: Quarter 3: X Quarter 4: XTeaching Time: 3

rdand 4

thquarters

Blooms Level: application


This standard is the first time that students move beyond the number 10 with representations, such as objects (manipulatives) or drawings. The spiritof this standard is that students separate out a set of 11-19 objects into a group of ten objects with leftovers. This ability is a pre-cursor to later gradeswhen they need to understand the complex concept that a group of 10 objects is also one ten (unitizing). Ample experiences with ten frames will helpsolidify this concept. Research states that students are not ready to unitize until the end of first grade. Therefore, this work in Kindergarten lays thefoundation of composing tens and recognizing leftovers.

Example:Teacher: Please count out 15 chips.Student: Student counts 15 counters (chips or cubes).Teacher: Do you think there is enough to make a group of ten chips? Do you think there might be some chips leftover?


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Student: Student answers.Teacher: Use your counters to find out.Student: Student can either fill a ten frame or make a stick of ten connecting cubes. They answer, There is enough to make a group of ten.

Teacher: How many leftovers do you have?Student: Students say, I have 5 left over.Teacher: How could we use words and/or numbers to show this?Student: Students might say Ten and five is the same amount as 15, 15 = 10 + 5






Vocabulary: compose, decompose, equation, base ten


How does a digits position affect its value?

Instructional/Learning Activities: (W.H.E.R.E.T.O.)Special attention needs to be paid to this set of numbers as they do not follow a consistent pattern in the verbal counting sequence.

Eleven and twelve are special number words.

Teen means one ten plus ones.

The verbal counting sequence for teen numbers is backwards we say the ones digit before the tens digit. For example 27 reads tens toones (twenty-seven), but 17 reads ones to tens (seven-teen).

In order for students to interpret the meaning of written teen numbers, they should read the number as well as describe the quantity. For


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example, for 15, the students should read fifteen and state that it is one group of ten andfive ones and record that 15 = 10 + 5.

Teaching the teen numbers as one group of ten and extra ones is foundational to understanding both the concept and the symbol that represent eachteen number. For example, when focusing on the number 14, students should count out fourteen objects using one-to-one correspondence and thenuse those objects to make one group of ten ones and four additional ones. Students should connect the representation to the symbol 14. Studentsshould 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 thatis first stated.

Assessments: (What will be acceptable evidence thestudent has achieved the desired results?)

Visual assessment with the instructor

Instructional Resources/Tools:Groupable modelsDried beans and small cups for holding groups of 10 dried beansLinking cubesPlastic chain links

Pregrouped materialsStrips (ten connected squares) and squares (singles)Base-ten blocksDried beans and bean sticks (10 dried beans glued on a craft stick)

Five-frame and Ten-framePlace-value mat with ten-frames

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Measurement and Data

Describe and compare measurable att