Asbury Park School District

Name of Unit: Counting and Cardinality Unit #1 /Duration: 1st Marking Period Content Area: Math Grade Level: Kindergarten Big Idea:

● Counting has a numerical sequence that can be used to determine the quantity of a set of objects and that quantity can be represented by written numerals.

● Compare groups of objects and written numerals using greater than, less than, and equal to. Unit Rationale: Knowing names of numbers, counting, and comparing numbers are areas of major work in Kindergarten. Students build on any prior knowledge they have to begin counting by ones from any number as well as matching number names with the numerals, and comparing the size of numbers.

Focus standards are in bold throughout the unit. Essential Questions: ● Where can I start counting from? ● How can I write how many objects there are? ● How do I know how many objects there are? ● What does a numeral represent? ● How are these groups of objects alike and different? ● What do I know about these two numbers? ● How are these two numbers alike and different?

I Can Statements: ● I can count forward beginning with another number other

than 1.(K.CC.A.2) ● I can count numbers 0 to 20. (K.CC.A.3) ● I can write numerals 0 to 20. (K.CC.A.3) ● I can write the numeral that matches a number of objects 0

to 9. (K.CC.A.3) ● I can write the numeral that matches a number of objects

10 -20.(K.CC.A.3) ● I can match each object with a number when counting.

(K.CC.B.4.a) ● I can tell how many objects are in a group.(K.CC.B.4.b) ● I can tell the number that is one more. (K.CC.B.4.c) ● I can count up to 20 objects that are arranged differently.

(K.CC.B.5) ● I can count objects to match numbers from 1 to 20.

(K.CC.B.5) ● I can describe “equal to”. (K.CC.C.6) ● I can describe “greater than”. (K.CC.C.6) ● I can describe “less than”. (K.CC.C.6) ● I can identify if a group of objects is greater than, less than

or equal to another group.(K.CC.C.6) ● I can tell if a numeral is greater than, less than, or equal to

another number. (K.CC.C.7)

Common Core State Standards: ● K.CC.A.2: Count forward beginning from a given number within the known sequence (instead of having to begin

at 1).

● K.CC.A.3: Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0

representing a count of no objects).

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

● K.CC.B.4.A: When counting objects, say the number names in the standard order, pairing each object with one

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

● K.CC.B.4.B: Understand that the last number name said tells the number of objects counted. The number of

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

● K.CC.B.4.C: Understand that each successive number name refers to a quantity that is one larger.

● K.CC.B.5: Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular

array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that

many objects.

● K.CC.C.6: Identify whether the number of objects in one group is greater than, less than, or equal to the number

of objects in another group, e.g., by using matching and counting strategies.1

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

● 1 Include groups with up to ten objects.

Standards for Mathematical Practices:

● CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.

● CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively. ● CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others. ● CCSS.MATH.PRACTICE.MP4 Model with mathematics. ● CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically. ● CCSS.MATH.PRACTICE.MP6 Attend to precision ● CCSS.MATH.PRACTICE.MP7 Look for and make use of structure ● CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning

Texts Primary Text:

Primary Text: ● envisionMath

Topic 1 Topic 2 Topic 3 Topic 4

Secondary/Supplemental Texts: ●

Suggested Instructional Activities/Strategies Sequence of Daily Activities: enVision Math : Interactive Math Story Daily Common Core Review Problem Based Interactive Learning Guided Practice Independent Practice Quick Check Differentiated Activities & Learning Centers Additional Activities: Journal Writing/Drawing Peer Teaching Math Word Wall Activities Mental Math Activities Open-Ended Problem Solving

Peer Scoring Using Rubrics Self-Reflection Suggested Instructional Activities by Standard (from The Common Core Mathematics Companion: The Standards Decoded by Linda M. Gojak & Ruth Harbin Miles) K.CC.A.2:

● Rote count from a number other than 1 (counting on) without having to go back and start at 1. ● Given the number 3, continue the count (4,5,6) without starting from 1. Complete similar examples within a

range of numbers. Although recognition of written numerals may help students to count on, it is not essential. K.CC.A.3:

● Recognize numerals from 1 to 20. ● Match a collection of items with the appropriate numeral. ● Over time, write the numerals from 1 to 20. Readiness to write the numerals will vary with the development of

eye-hand coordination and small motor skills. ● Represent sets of objects with numerals after they have had experience with CC. Cluster B: Count to tell the

number of objects. ● Use a variety of modalities to trace numerals in the air, in sand, on paper.

K.CC.B.4: ● Say the number name in consecutive order while pointing to each object. Some students may find it helpful to

move the objects as they count. ● Start by counting objects that are in a straight line and then move to organized representations (arrays, circles)

and finally randomly arranged objects. ● Indicate by counting that the last number said tells the number of items. ● Count on to the original number of items in a set, first by adding one item and later by mentally counting up one.

K.CC.B.5: ● Count out a number of items using a variety of concrete objects. ● Match a numeral card with the number of items in a set. ● Given a written numeral, count that number of items from a collection of items. ● Given a drawing of items such as flowers, teddy bears, or cars, circle a number of items and write the numeral. ● Draw a given number of items.

K.CC.C.6: ● Develop vocabulary of greater than (more than ) and less than (fewer than) to compare the number of items in

two sets. ● Use various strategies that make sense to compare items in two sets, including matching, observation, take

away/fair share, counting. ● Explain reasoning to show that one set has more or less than another. ● Identify how many more or how many fewer items one set has than another. ● Recognize two sets that have the same number of items using the description same as.

K.CC.C.7:

● Given two sets of concrete materials, students label each set with the appropriate numeral. ● Compare the number of items in each set using comparison vocabulary and then connect the comparison of

physical objects to the number names in describing the comparison. Suggested Instructional Strategies:

● Communicators ● Connections to Real World Applications ● Cooperative learning groups ● Culturally and Linguistically Responsive Strategies (Dr. Hollie) such as: Pick- a Stick; Roll ‘Em; Give a Shout Out;

Train; Send a Problem; Team; Pair; Solo: Numbered Heads ● Discovery Learning ● Guided Math Instruction ● Math Games ● Partner Talk/Accountable Talk * ● Peer Tutoring ● Quick Writes *

● Read Alouds of Math Literature ● Scaffolding ● Vocabulary Instruction *

* See links or attached items in Appendix Math Manipulatives:

● Connecting cubes ● Five-frame math #7+ ● Number cards #5+ ● Ten-frame mat #8+ ● Two-color counters

Math Literature:

● Bat Jamboree by Kathi Appelt : Lesson using bats to count:http://mathwire.com/themes/themebat.html ● Chicka Chicka 123 by Bill Martin & Michael Sampson: Games and activities:

http://www.makinglearningfun.com/themepages/Apples/ChickaChicka123MathIdeas.htm ● Click, Clack, Splish, Splash by Doreen Cronin ● Five Little Monkeys Jumping on the Bed By Eileen Christelow,: Counting

cards:http://www.makinglearningfun.com/images/Activities/MonkMonkeysOnBedCount.pdf ● How Many Feet in the Bed? by Diane Johnston Hamm : Advanced lesson on patterns: http://mathsolutions.com/wp-

content/uploads/How_Many_Feet.pdf ● Mouse Count by Ellen Stoll Walsh : Lesson on countung:

http://www.floridaearlylearning.com/sites/www/Uploads/files/Oel%20Resources/Sample%20Lessons/MouseCountAdditionandSubtractionLessonPlan.pdf

● Olivia Counts by Ian Falconer

● One Hundred is a Family by Pam Munoz Ryan : Lesson about 100 including video: https://educators.brainpop.com/bp-jr-topic/one-hundred

● One is a Snail, Ten is a Crab - A Counting by Feet Book by April Pulley Sayre and Jeff Sayre: Lesson in which children make animal legs and determine the number of animals: http://nrich.maths.org/136/note.

Printable Math Games:

● http://www.mathematicshed.com/uploads/1/2/5/7/12572836/21funmathgames.pdf: Rules, gameboards, and game cards for games at all levels and all operations.

● http://www.k-5mathteachingresources.com: Printable games and word problems grouped by grade and standard Online Student Math Games:

● http://pbskids.org/curiousgeorge/games/count_your_chickens/count_your_chickens.html ● http://www.topmarks.co.uk/learning-to-count/teddy-numbers ● http://www.sheppardsoftware.com/mathgames/earlymath/fruit_shoot_count.htm ● http://www.sheppardsoftware.com/mathgames/earlymath/Fruit_shoot_SkipCount.htm ● http://www.softschools.com/counting/games/counting_train/ ● http://www.primarygames.com/math/fishycount/

Online Student Practice: Includes videos and games

● www.khanacademy.org ● www.adaptedmind.com ● www.learnzillion.com

Teacher Resources

Teacher Resources: Better Lessons: Detailed lessons listed by grade and Common Core Standards

http://betterlesson.com Common Core State Standards: Mathhttp://www.corestandards.org/Math envision MATH: www.pearsonsuccessnet.com Illuminations NCTM: Activities and lessons endorsed by the national; Council for Teachers of Mathematics https://illuminations.nctm.org Illustrative Mathematics: Activities and lessons listed by Common Core Standards https://www.illustrativemathematics.org/ Plickers: An online tool for formative assessment https://plickers.com Resource Area for Teaching: Free, downloadable games and hands-on activities by standard http://www.raftbayarea.org/idea-grid Teaching Channel: A video showcase of innovative and effective teaching practices. www.teachingchannel.org The Quantile Framework for Mathematics: Resources by Grade and Standard https://www.quantiles.com/tools/math-skills-database/ The Common Core Mathematics Companions: The Standards Decoded by Linda M. Gojak & Ruth Harbin Miles

Vocabulary

Domain Specific Academic Vocabulary (Tier 3) ● ● 1 fewer than ● 2 fewer than ● 1 more than ● 2 more than ● As many ● Benchmark number ● Column ● Count ● Eight ● Fewer than ● Fewest ● Fifth ● First ● Five ● Four ● Fourth

● Greater ● Growing patterns ● Less

General Academic Vocabulary (Tier 2) ● Backward ● Compare ● Forward ● Symbol ● Unique

● More than ● Most ● None ● Nine ● Number ● One ● Order ● Row ● Same as ● Same number as ● Second ● Seven ● Sixth ● Ten ● Third ● Three ● Two ● Zero

Assessments Formative Assessments:

● envision Math Daily Quick Check Masters ● envision Math Topic Readiness tests ● Center Activities ● Student Participation ● Classroom Practice & Homework Review ● Student Response Journals/Self-Reflections ● Teacher Made Assessments ● First in Math Reports ● Teacher Observation ● Teacher/Student Conferences

●

Summative Assessment: ● enVision math Topic Tests ● enVision Math Benchmark Assessments ● envision Math Performance Assessments ● enVision MATH; Basic Fact Tests ● Link-It tests

●

Type Differentiation/Scaffolding (for example ELL, students who are classified, struggling learners, etc.)

Visual ● Create flashcards on index cards or on the computer

.http://www.timeforkids.com/homework-helper/study-helper/addition#next

● Use visual images to associate information. Anything that encourages the student

to develop a mental image will be beneficial.

● Organize diagrams, charts, and graphic organizers into statements. ● Model taking notes in pictures or diagrams rather than in sentences

● Allow students to construct, draw, or create visual representations of concepts.

● Use computers so that material can be presented visually.

● Let students draw pictures of the material they are learning (e.g.

● Representing numbers into pictures, drawing images of their Math problems,)

● Schedule brief ”visual thinking” breaks for students which might

● involve solving visual-spatial puzzles, playing visual-spatial

● games (e.g. Pictionary, or doing imagination exercises like

● imagining what their ideal school would look like).

● Reduce the reading level of the assignment (reword, paraphrase, etc.)

● Incorporate writing activities like math journals.

● Make sure there are visual clues around the room to prompt appropriate behavior and

academic activities. ● Anchor charts for new concepts/process.

● Preferential seating

● Video lessons ie learnzillion or Khan academy www.learnzillion.com ,

https://www.khanacademy.org/math

● Practice and review with board games or instructional software are effective ways to develop conceptual number readiness

Auditory ● Think, Pair Share (first read problem independently, work to solve problem with peer and

then share information with teacher) http://ell.stanford.edu/sites/default/files/math_learnmore_files/4.Language%20of%20Math%20Task%20Templates%20

10-4-13.pdf ● Create songs or Mnemonics to aid in memorization.

● Buddy Buzz or Talk it out

.http://www.ascd.org/publications/books/108035/chapters/Procedures-for-Classroom-Talk.aspx ● In small groups take turns talking through the problems, each person gets a chance to both speak

and listen to their peers ● Actually hearing the problem-solving process will help to solidify it.

● Give instructions through several methods (written, oral, demonstration, etc.)

● Accompany oral directions with written pictorial directions for future reference

● Repeat directions, then have the student explain the directions to you Kinesthetic ● Use Circle Map, in which you place the main topic in a small circle and add student ideas

in a bigger circle around the topic. Students may use their native language with peers to brainstorm. ● Incorporate many opportunities for students to move.

o Dance and body movement ● Have students use puppets to explain concept. ● Have students act out a math problem or concept incorporate guest speakers Readers Theater ● http://tips-for-teachers.com/readers_theater.htm· ● Incorporate hands on activities

o Play Dough Number Mats: Students make numbers on the mats with play dough o Linker Cube Numbers: Students form numbers out of linker cubes o Roll and Write: Roll a number with a die and write it o Monthly Calendars: Write the numbers on the calendar

http://www.scholastic.com/teachers/top-teaching/2013/03/counting-and-cardinality-kindergarten-meeting-common-core

● Corners Cooperative learning strategy. http://cooperativelearningstrategies.pbworks.com/w/page/28234420/Corners ● Explain concepts in terms of how to do it, how it functions or how it might feel. ● Incorporate multisensory activities (i.e. math us food, writing use different textiles) ● Utilize pictures and photographs that illustrate your idea. ● Gather information about the unit and design a bulletin board that illustrates what was learned (small group, surveys, interviews etc…)

● Create a three panel board KWL chart to display what was learned in the unit (small group or individual) ● Use independent study experiences

● Utilize peer tutoring

● Use calculators and computers to solve complex math problems.

● Find educational computer games that require a great deal of mouse movement

● Interactive notebooks see Teachers pay Teachers /www.teacherspayteachers.com or

pinterest for ideas.

Language Development ● Gallery Walk with a peer. Use vocabulary to explain how you will solve the

problem..http://literacy.kent.edu/eureka/strategies/gallery_walk.pdf

● Master word cards to learn new vocabulary -Frayer model

● Have students share problem-solving strategies.

● Math word riddles,play snap,use word sorts http://dspearmath.weebly.com/uploads/5/1/1/3/5113576/strategies_for_understanding_math_vocabulary.pdf ● Think, Pair Share (first read problem independently, work to solve problem with peer and

then share information with teacher) http://ell.stanford.edu/sites/default/files/math_learnmore_files/4.Language%20of%20Math%20Task%20Templates%20

10-4-13.pdf ● Develop sentence frames to help use and understand math problems.

● Create a three panel board KWL chart to display what was learned in the unit (small group

or individual)

● Previewing Content Vocabulary is a strategy that would be used to assess your students’

knowledge of the words and concepts in a specific text. (page 15 explains strategy) http://steinhardt.nyu.edu/scmsAdmin/uploads/004/740/NYU_PTE_SocialStudies_for_ELLS_Oct2009.pdf ● Encourage students to offer bilingual support to each other.

● Have review time with peers weekly using Self-Assessment strategy. (explained on pg.19) http://steinhardt.nyu.edu/scmsAdmin/uploads/004/740/NYU_PTE_SocialStudies_for_ELLS_Oct2009.pdf

● Give instructions using gestures and facial expressions. For some students,mathematics readiness instruction may need to include the development of language number concepts such as big and small and smallest to largest; and attributes such as color, size, or shape. Instruction, review, and practice of these concepts must be provided for longer time periods for students with mathematics disabilities than for other students. Practice and review with board games or instructional software are effective ways to develop conceptual number readiness for students with mathematics disabilities. Manipulatives, such as Cuisenaire rods and Unifix math materials (e.g.,100 block trays) allow students with math disabilities to visualize numerical concepts and engage in age-appropriate readiness skills

Appendix 1 (graphic organizers, rubrics, websites, activities, manipulatives, sample assessments, etc.)

1. Accountable Math Talk Resources: https://www.teacherspayteachers.com/Product/Mathematical-Accountable-Talk-Bookmark-1670330 2. Frayer Vocabulary Model 3. Common Core State Standards Mathematics Glossary table 1 4. Quick Writes and Other Writing Strategies for Math http://www.michigan.gov/documents/mde/Writing_to_Learn_Mathematics_306722_7.pdf 5. Addition and Subtraction Situations Table 1 6. Addition and Subtraction Fact Strategies Table 2 7. Scaffolding Addition and Subtraction Table 3 8. Sample Addition and Subtraction Strategies Table 4 9. Standards for Mathematical Practice Table 5 10. Effective Teaching Practices Table 6 11. Sample Activities by Standard:

● K.CC.A.2: Whole class lesson using a classroom number line. https://s3.amazonaws.com/quantile-resources/resources/downloads/QuantileResource32152.pdf

● K.CC.A.3: Whole class lesson exploring the concept of zero. http://betterlesson.com/lesson/514475/zero-my-hero-exploring-the-number-zero

● K.CC.B.4: Counting game http://www.raftbayarea.org/readpdf?isid=115

● K.CC.B.4.A: Lesson making a class book of student names and using names to count letters. http://illuminations.nctm.org/Lesson.aspx?id=3263

● K.CC.B.4.B: Activity counting to twenty. https://www.illustrativemathematics.org/content-standards/tasks/447

● K.CC.B.4.C Whole class lesson comparing numbers. http://betterlesson.com/lesson/524469/greedy-gordy-goes-on-a-diet-learning-about-less

● K.CC.B.5: Monthly whole class lessons to reinforce counting. https://s3.amazonaws.com/quantile-resources/resources/downloads/QuantileResource32053.pdf

● K.CC.C.7: “Fishing” game comparing numbers. http://www.raftbayarea.org/readpdf?isid=157

Mathematics Glossary » Table 1 PRINT THIS PAGE

Common addition and subtraction.1

RESULT UNKNOWN CHANGE UNKNOWN START UNKNOWN

ADD TO

Two bunnies sat on the

grass. Three more

bunnies hopped there.

How many bunnies are

on the grass now? 2 + 3 =

?

Two bunnies were sitting

on the grass. Some more

bunnies hopped there.

Then there were five

bunnies. How many

bunnies hopped over to

the first two? 2 + ? = 5

Some bunnies were

sitting on the grass. Three

more bunnies hopped

there. Then there were

five bunnies. How many

bunnies were on the grass

before? ? + 3 =5

TAKE FROM

Five apples were on the

table. I ate two apples.

How many apples are on

the table now?5-2 = ?

Five apples were on the

table. I ate some apples.

Then there were three

apples. How many apples

did I eat?5 – ? = 3

Some apples were on the

table. I ate two apples.

Then there were three

apples. How many apples

were on the table before??

-2 = 3

TOTAL UNKNOWN ADDEND UNKNOWN BOTH ADDENDS

UNKNOWN2

PUT TOGETHER

/ TAKE APART3

Three red apples and two

green apples are on the

table. How many apples

are on the table? 3 + 2 = ?

Five apples are on the

table. Three are red and

the rest are green. How

many apples are green? 3

+ ? = 5, 5-3 = ?

Grandma has five

flowers. How many can

she put in the red vase

and how many in her blue

vase? 5 = 0 + 5, 5 + 0 5 =

1 +4, 5 = 4 +1 5 = 2 + 3, 5

= 3 + 2

COMPARE DIFFERENCE

UKNOWN

BIGGER UNKNOWN SMALLER UNKNOWN

(“How many more?”

version):Lucy has two

apples. Julie has five

apples. How many more

apples does Julie have

than Lucy?(“How many

(Version with “more”):

Julie has three more

apples than Lucy. Lucy

has two apples. How

many apples does Julie

have? (Version with

(Version with

“more”):Julie has three

more apples than Lucy.

Julie has five apples. How

many apples does Lucy

have?(Version with

fewer?” version): Lucy

has two apples. Julie has

five apples. How many

fewer apples does Lucy

have then Julie? 2 + ? =

5, 5 – 2 = ?

“fewer”): Lucy has 3

fewer apples than Julie.

Lucy has two apples.

How many apples does

Julie have? 2 + 3 = ?, 3 +

2 = ?

“fewer”): Lucy has 3

fewer apples than Julie.

Julie has five apples. How

many apples does Lucy

have? 5 – 3 = ?, ? + 3 = 5

1 Adapted from Box 2-4 of Mathematics Learning in Early Childhood, National Research Council (2009, pp. 32, 33). 2 These take apart situations can be used to show all the decompositions of a given number. The associated equations, which have

the total on the left of the equal sign, help children understand that the = sign does not always mean, makes or results in but

always does mean is the same number as.

3 Either addend can be unknown, so there are three variations of these problem situations. Both addends Unknown is a productive

extension of the basic situation, especially for small numbers less than or equal to 10. 4 For the Bigger Unknown or Smaller Unknown situations, one version directs the correct operation (the version using more for

the bigger unknown and using less for the smaller unknown). The other versions are more difficult.

Appendix 2 (Quad D Exemplar Lesson Plan)