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Striving toward greater focus and coherence throughContent Standards and Practice Standards

Waterloo Community Unit School District

Kindergarten Mathematics Curriculum Map

Waterloo

School

1

How to Read the Grade Level Content Standards

Standards define what students should understand and be able to do.

Clusters are groups of related standards. Note that standards from different clusters may sometimes be closely related, because mathematics is a connected subject.

Domains are larger groups of related standards. Standards from different domains may sometimes be closely related.

Kindergarten Mathematics Curriculum Map

Waterloo

School

2

Standards for Mathematical PracticeThe Common Core State Standards for Mathematical Practice are expected to be integrated into every mathematics lesson for all students Grades K-12. Below are a few examples of how these Practices may be integrated into tasks students complete.

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

Mathematically proficient students in Kindergarten begin to develop effective dispositions toward problem solving. In richsettings in which informal and formal possibilities for solving problems are numerous, young children develop the ability tofocus attention, test hypotheses, take reasonable risks, remain flexible, try alternatives, exhibit self-regulation, and persevere(Copley, 2010). Using both verbal and nonverbal means, kindergarten students begin to explain to themselves and others themeaning of a problem, look for ways to solve it, and determine if their thinking makes sense or if another strategy is needed.As the teacher uses thoughtful questioning and provides opportunities for students to share thinking, kindergarten studentsbegin to reason as they become more conscious of what they know and how they solve problems.

2. Reason abstractly and quantitatively.

Mathematically proficient students in Kindergarten begin to use numerals to represent specific amount (quantity). Forexample, a student may write the numeral “11” to represent an amount of objects counted, select the correct number card“17” to follow “16” on the calendar, or build a pile of counters depending on the number drawn. In addition, kindergartenstudents begin to draw pictures, manipulate objects, use diagrams or charts, etc. to express quantitative ideas such as ajoining situation (Mary has 3 bears. Juanita gave her 1 more bear. How many bears does Mary have altogether?), or aseparating situation (Mary had 5 bears. She gave some to Juanita. Now she has 3 bears. How many bears did Mary giveJuanita?). Using the language developed through numerous joining and separating scenarios, kindergarten students begin tounderstand how symbols (+, -, =) are used to represent quantitative ideas in a written format.

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

In Kindergarten, mathematically proficient students begin to clearly express, explain, organize and consolidate their maththinking using both verbal and written representations. Through opportunities that encourage exploration, discovery, anddiscussion, kindergarten students begin to learn how to express opinions, become skillful at listening to others, describe theirreasoning and respond to others’ thinking and reasoning. They begin to develop the ability to reason and analyze situationsas they consider questions such as, “Are you sure…?” , “Do you think that would happen all the time…?”, and “I wonderwhy…?”

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4. Model with mathematics.

Mathematically proficient students in Kindergarten begin to experiment with representing real-life problem situations inmultiple ways such as with numbers, words (mathematical language), drawings, objects, acting out, charts, lists, and numbersentences. For example, when making toothpick designs to represent the various combinations of the number “5”, the studentwrites the numerals for the various parts (such as “4” and “1”) or selects a number sentence that represents thatparticular situation (such as 5 = 4 + 1)*.

*According to CCSS, “Kindergarten students should see addition and subtraction equations, and student writing of equations inkindergarten in encouraged, but it is not required”. However, please note that it is not until First Grade when “Understand the meaningof the equal sign” is an expectation (1.OA.7).

5. Use appropriate tools strategically.

In Kindergarten, mathematically proficient students begin to explore various tools and use them to investigate mathematicalconcepts. Through multiple opportunities to examine materials, they experiment and use both concrete materials (e.g. 3-dimensional solids, connecting cubes, ten frames, number balances) and technological materials (e.g., virtual manipulatives,calculators, interactive websites) to explore mathematical concepts. Based on these experiences, they become able to decidewhich tools may be helpful to use depending on the problem or task. For example, when solving the problem, “There are 4dogs in the park. 3 more dogs show up in the park. How many dogs are in the park?”, students may decide to act it outusing counters and a story mat; draw a picture; or use a handful of cubes.

6. Attend to precision.

Mathematically proficient students in Kindergarten begin to express their ideas and reasoning using words. As theirmathematical vocabulary increases due to exposure, modeling, and practice, kindergarteners become more precise in theircommunication, calculations, and measurements. In all types of mathematical tasks, students begin to describe their actionsand strategies more clearly, understand and use grade-level appropriate vocabulary accurately, and begin to give preciseexplanations and reasoning regarding their process of finding solutions. For example, a student may use color words (suchas blue, green, light blue) and descriptive words (such as small, big, rough, smooth) to accurately describe how a collectionof buttons is sorted.

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7. Look for and make use of structure.

Mathematically proficient students in Kindergarten begin to look for patterns and structures in the number system and otherareas of mathematics. For example, when searching for triangles around the room, kindergarteners begin to notice that sometriangles are larger than others or come in different colors- yet they are all triangles. While exploring the part-wholerelationships of a number using a number balance, students begin to realize that 5 can be broken down into sub-parts, suchas 4 and 1 or 4 and 2, and still remain a total of 5.

8. Look for and express regularity in repeated reasoning.

In Kindergarten, mathematically proficient students begin to notice repetitive actions in geometry, counting, comparing, etc.For example, a kindergartener may notice that as the number of sides increase on a shape, a new shape is created (trianglehas 3 sides, a rectangle has 4 sides, a pentagon has 5 sides, a hexagon has 6 sides). When counting out loud to 100,kindergartners may recognize the pattern 1-9 being repeated for each decade (e.g., Seventy-ONE, Seventy-TWO, Seventy-THREE… Eighty-ONE, Eighty-TWO, Eighty-THREE…). When joining one more cube to a pile, the child may realize that the new amount is the next number in the count sequence.

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Kindergarten Mathematics Curriculum MapWaterloo School District Scope and Sequence Overview

Unit of StudyEveryday

Math Alignment

Domain and Standards

Daily Routines

Routines

Domain: Standards:

1

2

3

4

5

6

7

8

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KindergartenInstruction and Assessment Schedule

2013-2014

It is expected that the units will be taught consecutively. The table below reflects which units are assessed on each benchmark. It is possible to begin a new unit prior to the quarter in which it is being assessed.

Approx. Number of

Days of Instruction

B

ench

mar

k 1

?? ?? ??

Com

mon

Ass

essm

ent A

?? ?? ??

C

omm

on A

sses

smen

t B

Ben

chm

ark

2

?? ?? ??

C

omm

on A

sses

smen

t C

?? ?? ??

C

omm

on A

sses

smen

t D

Ben

chm

ark

3

End ofYear

InstructionalContent

Unit ofStudy

1

Unit ofStudy

2

Unit ofStudy

3

Unit ofStudy

4

Unit ofStudy

5

Unit ofStudy

6

Unit ofStudy

7

Unit ofStudy

8

Unit ofStudy

9

Unit ofStudy

10

Unit ofStudy

11

Unit ofStudy

12

Getting Ready for Gr.1 Unit

Assessment Ch. 1Test

Ch. 2Test

Ch. 3Test

Ch. 4Test

Ch. 5Test

Ch. 6Test

Ch. 7 Test

Ch. 8Test

Ch. 9Test

Ch. 10Test

Ch. 11Test

Ch. 12Test

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Kindergarten Mathematics Curriculum Map - Overview Waterloo School District policy requires elementary mathematics instruction to be 60 minutes per day.

Unit of Study The mathematical content is sequenced in Units of Study that will take approximately 2-3 weeks each to teach.The sequence of Units of Study provides a coherent flow to mathematics instruction throughout the year.

Everyday Math The primary textbook adopted in Waterloo School District for Grades K-6

Teacher’sResources and Notes

Teachers are encouraged to make notes of their own lesson ideas and resources that align with each Unit ofStudy.

AdditionalResources

Assessment

There are many formative and summative assessment options:

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Daily Routines Kindergarten Quarter 1 Approx. 10 days

Domain: CCCluster(s): 1,2,3, 4a,4b,4c,5,6,7

Domain: MDCluster(s): 3

Domain: OACluster(s): 4

Domain: NBTCluster(s): 1

Math Content Objectives Vocabulary Teacher’s Resources and Notes

I can:

K.CC.1Count to 100 by 1’s and 10’s.

K.CC.2Count starting with any number.

K.CC.3Write the numeral for the number of objects I counted.

K.CC.4aSay the number as I count each object.

AllAll togetherGraphPatternMonthDayDateWeekYearCalendarTodayYesterday

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Daily Routines (continued)Math Content Objectives Vocabulary Teacher’s Resources and Notes

I can:

K.CC.4bUnderstand the last number I said is the total number of objects I counted.

K.CC.4cUnderstand that each number name is one more than the last number name.

K.CC.5Count objects to answer questions.

K.CC.6Compare objects to decide which is greater than, less than, or equal to.

K.CC.7Compare two written numerals to decide which is greater than, less than, or equal to.

K.MD.3Sort and count objects.

K. OA.4Find the number that makes ten when added to the given number.

K. NBT.1Show how the numbers 11-19 are made of ten ones and more ones.

TomorrowWeekendSameMostLeastThermometerTemperatureHotColdWarmCoolCountEqual toGreater thanLess thanNumberOnesTensAddDays of the weekMonths of the year

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Everyday MathCommon Core Alignment

Unit of Study 1 – Additional Resources

Routine 1:K.CC.1K.CC.2K.CC.3K.CC.4aK.CC.4bK.CC.4cK.NBT.1K.OA.4

Routine 2:K.CC.4aK.CC.4bK.CC.5

Routine 4:K.CC.3

Routine 6:K.CC.5K.CC.6K.MD.3

Routine 7:K.MD.3

Routine 8:K.MD.3

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Unit of Study 1 Kindergarten Quarter 1 Approx. ?? daysDomain: MDCluster(s): 1, 2, 3

Domain:GCluster(s): 1,2,4,6

Domain:OACluster(s): 3, 4

Domain: CCCluster(s): 1,2,3,4a,4b,4c,5,6


I can:





CountNumberAbout the sameAboveBelowBiggerCompareDataGraphHexagonLengthLessLongerMatch

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Unit of Study 1 (continued)Math Content Objectives Vocabulary Teacher’s Resources and Notes

K.CC.4b

Understand the last number I said is the total number of objects I

counted.

K.CC.4c

Understand that each number name is one more than the last number

name.

K.CC.5

Count objects to answer questions.

K.CC.6

Compare objects to decide which is greater than, less than, or equal to.

K.MD.1

Describe objects.

K.MD.2

Compare two objects.

K.MD.3

Sort and count objects.

K.G.1

Describe objects around me by their shape and where they are found.

K.G.2

Name shapes.

K.G.4

Describe how shapes are alike and different. K.G.6 Put shapes together to make another shape. K.OA.3 Break apart numbers into pairs many ways. K. OA.4

Find the number that makes ten when added to the given number.

MoreNext toNonePatternRectangleRepeatRhombusRotateSameSame lengthSetShapeShorterSmallerSortSquareTallerTen FrameTotalTrapezoidTriangleVolumeZero

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Activities Unit 1:1.11.21.32.71.51.61.81.111.121.131.141.151.16

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Everyday Math Common Core Alignment


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Unit of Study 2 Kindergarten Quarter 1 Approx. ?? daysDomain: CCCluster(s): 1,2,3,4a,4b,4c,5,6

Domain: MDCluster(s): 1,2,3

Domain:OACluster(s): 1,2,3,4

Domain: GCluster(s): 1,2,3,4,6Domain: NBTCluster(s): 1


I can:





AddAll togetherAroundBehindBesideBetweenCircleCornerCurveCurvedDigitDownEqualEstimate

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K.CC.4b

Understand the last number I said is the total number of objects I counted.

K.CC.4c

Understand that each number name is one more than the last number name.

K.CC.5


K.CC.6


K.MD.1

Describe objects.

K.MD.2


K.MD.3


K.G.1


K.G.2

Name shapes.

K.G.3

Tell if a shape is flat or solid.

K.G.4

Describe how shapes are alike and different.

K.G.6

Put shapes together to make another shape.

K.NBT. 1

Show how the numbers 11-19 are made of ten ones and more ones.

K.OA.1

Show subtraction and addition.

KOA/2

Add and subtract to solve word problems. K.OA.3 Break apart numbers into pairs many ways. K. OA.4

Find the number that makes ten when added to the given number.

FlatIn front ofInsideJoinLeftLineNumber storyOutsideOverRemoveRightRoundSideStraightSubtractTake awayTeenTopTwo-dimensionalUnderUp

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Activities Unit 2:

2.12.22.32.42.62.72.82.92.102.112.122.14

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Unit of Study 3 Kindergarten Quarter ? Approx. ?? daysDomain: CCCluster(s): 1,2,3, 4a,4b,4c,5,6,7

Domain: MDCluster(s):1,2,3

Domain: OACluster(s):1,2,4,5

Domain: NBTCluster(s):1

Domain: GCluster(s): 1,2,4,6


I can:





1s,10sAllApproximateBalanceBar GraphCertainChanceColumnCount BackCount OnCounting by 10s

20


K.CC.4b

Understand the last number I said is the total number of objects I

counted.

K.CC.4c

Understand that each number name is one more than the last number

name.

K.CC.5


K.CC.6


K.C.C.7

Compare two written numerals to decide which is greater than, less

than, or equal to.

K.MD.1

Describe objects.

K.MD.2


K.MD.3


K.G.1


K.G.2

Name shapes.

K.G.4

Describe how shapes are alike and different.

K.G.6

Put shapes together to make another shape.

K.NBT. 1

Show how the numbers 11-19 are made of ten ones and more ones.

ForwardHalfHeavyHighHow manyImpossibleLeastLevelLighterLikelyLowMaybeMeasureMight happenMostNumber lineOrderPan BalancePossiblePredictProbablyRowSkip countingSomeTenUnlikelyWeight

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K.OA.1Show subtraction and addition.KOA/2Add and subtract to solve word problems.

K. OA.4Find the number that makes ten when added to the given number.K.OA.5Quickly add numbers up to five.

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Activities Unit 3: 3.13.33.43.53.63.73.83.93.123.133.143.153.16

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Unit of Study 4 Kindergarten Quarter ? Approx. ?? daysDomain: Cluster(s):

Domain: Cluster(s):


I can:

24


25



26



27


Domain: Cluster(s):


I can:

28


29



30



31


Domain: Cluster(s):


I can:

32


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34



35


Domain: Cluster(s):


I can:

36


37



38



39


Domain: Cluster(s):


I can:

40


41



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Domain: Cluster(s):


I can:

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