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Number Sense Developed by Carrie Ann Floyd Plainfield School District

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Objectives : During this workshop we will: Review the revised Preschool Math Standards that relate to number sense. Define number sense and its importance as a building block for all future mathematical learning. Review teaching strategies for number sense.

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Opening Activity Write your favorite number from 1-20 that has personal significance to you on the post it. For example: 4 - I have four children, 2 - I have two golden retrievers. Mingle with each other, sharing your number and why you chose it. Then, form groups based on the number you have. After getting into your groups line up in order from 1-20.

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What math skills did you use? Number recognition: “We both have the number 3.” Writing numbers: “I wrote down the number 3.” Saying counting words in order: Getting into the order 1-10. Understanding that written numbers are symbols for number quantities. Understanding the relationship between numbers and quantities. These skills all relate to number sense.

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Number sense is defined as an intuitive feel for numbers and a common sense approach to using them. It is a comfort with what numbers represent, coming from investigating their characteristics and using them in diverse situations. Number sense is an attribute of all successful users of mathematics. Preschoolers are beginning to develop number sense when they construct a notion of oneness, twoness, and so on… Young children also have a emerging concept of number when they see the relationship of one number to another. Number Sense *HighScope Preschool Mathematics Curriculum, 2012, p. 31”

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New Jersey’s Preschool Math Standards and Number Sense Standard 4.1: Children begin to demonstrate an understanding of number and counting. 4.1.1 Count to 20 by ones with minimal prompting. 4.1.2 Recognize and name one digit written numbers up to ten with minimal prompting. 4.1.3 Know that written numbers are symbols for number quantities and, with support, begin to write numbers from 0 to 10. 4.1.4 Understand the relationship between numbers and quantities (i.e., the last word stated when counting tells “how many”).

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Preschool Teaching Practices to Promote Number Sense Encourage and support individual attempts to learn to count to 20 or higher. Include and refer by name to written numbers in the classroom environment during daily routines and in the context of large and small group experiences. Intentionally refer to the symbol and number name when discussing numbers (quantities) of objects. Make materials and books that promote exploration of number quantities.

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Preschool Teaching Practices to Promote Number Sense (cont.) Encourage children to compare numbers frequently through questions (e.g., “Are there more people riding in the bus or in the airplane?”) and graphing (e.g., favorite colors, pets). Provide manipulative and materials (e.g., print and digital material, sand molds, tactile numeral cards, puzzles, counting books, hand-held devices such as tablets, interactive whiteboards) and activities (e.g., tracing numbers in sand, forming numbers with clay, recording data) that feature number names and number quantities. Provide a wide variety of writing materials for children to informally explore writing numbers along with meaningful contexts for children to write numbers on charts and graphs.

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Thinking About Number Sense 1. Cardinality Recognizing that things come in quantities begins around 2 years old. Children grasp the association between numbers and quantities by connecting concrete objects with more abstract number words and symbols. (The idea of “oneness” and “twoness.”) Preschoolers learn cardinal number words by rote and can count up to 20 by kindergarten. At first they often say them in any order. They may omit some numbers and repeat others. Preschoolers will become familiar with numerical order if exposed to numbers in counting songs, number books and natural opportunities.

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Thinking About Number Sense (cont.) 2.Recognizing Number Symbols Learning to read numbers symbols depends on how often children are exposed to them. Children need adults to explicitly identify and name numerals when they are in the environment.

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Thinking About Number Sense (cont.) 3. Writing Numerals Writing numerals is a more difficult task then reading them. Children begin with the numbers that are the easies to draw or write. (1,3,4,7) and then progress to more complex ones (2,5,6,8,9). Perception and motor development may limit their ability. Children may reverse numbers such as 2,3, 5. When adults model standard numeral writing children will learn how to write them on their own. There is no need to correct such errors.

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Recommended Materials for Number Sense

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Books About Numbers

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Puzzles and Manipulatives

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Materials for Making and Writing Numerals

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Using the Daily Routine

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Taking A Closer Look at the Parts of Standard 4.1

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Scaffolding Number Sense Scaffolding is a term developed by the theorist Lev Vygotsy. It means to provide children with support on their current level of development while occasionally offering a gentle extension to the next level. As you carry out these activities reflect on your experiences with children and the developmental range of these skills seen in preschoolers. How might children, at varying levels of development, respond to the content and the materials? * HighScope Scaffolding Group Times For Early Learners

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Counting to Twenty by Ones Standard 4.1.1 Count to 20 by ones with minimal prompting “Counting Song” Activity At your table, you will be role playing this lesson as children while one or two people will be the teacher. After a few minutes, review the lesson plan that shows the basic three developmental levels for this activity: Earlier, Middle, and Later. As a group come up with ideas for supporting each developmental level, and chart it on paper. *HighScope Scaffolding Small Group Times for Early Learners

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“Counting Song” Large Group Lesson Standard 4.1.1 Count to 20 by ones with minimal prompting Children sing a counting song to a familiar tune while tapping a body part a corresponding number of times during large group music and movement time. *HighScope Numbers Plus

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“Counting Song ” Video Clip

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4.1.1 Count to 20 by Ones with Minimal Prompting Developmental Range: Children may… Earlier Sing random number words or pat but do not do both at the same time Middle Recognize when numbers 1-5 are not said in the correct order Sing numbers 1-5 in the correct order Adults can… use these strategies Encourage children to sing the number words with them Slow down the singing and patting to help children hear Count correctly and incorrectly, each time asking Is this the right order Make a mistake in counting, (skip and number and see if children spot the error)

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4.1.1 Count to 20 by Ones with Minimal Prompting Developmental Range: (cont.) Children may… Later Say which numbers come next in sequence Fill in a missed number Say a number sequence up to 10 Adults can… use these strategies While singing, stop counting and ask, What number comes next? Extend the song up to 20 Ask a child to suggest a number to count to and to lead the next round using the next round Count backwards, beginning with small numbers (e.g., 3, 2, 1, )

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Standard 4.1.2 Recognizing and Naming Numbers Math Standard 4.1.2 Recognize and name one digit numbers up to ten with minimal prompting “Numerals in Newspapers” Activity At your table, you will be role playing the lesson as children while one or two people will be the teacher. After a few minutes, review the lesson plan that shows the basic three developmental levels for this activity: Earlier, Middle, and Later. As a group come up ideas for supporting each developmental level, and chart it on paper. * HighScope Scaffolding Small Group Times

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“Numerals In Newspapers” Small Group Lesson Math Standard 4.1.2 Recognize and name one digit numbers up to ten with minimal prompting Children search for large numbers in magazines and cut them out to make number collections during small group time. *HighScope 50 Small Group Times to Scaffold Early Learning

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“Numerals in Newspapers” Video Clip

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4.1.2. Recognize and Name One Digit Numbers Developmental Range: Children may… Earlier Point to a letter and call it a number Look at or point to numerals and identify them as numerals e.g., “Here is a number.” Middle Identity numerals but make errors Search for and finds a specific numeral Relate numerals to familiar objects and events e.g., “That’s a four, I’m four years old.” Adults can… use these strategies Point out letters and numbers e.g., “This is the letter in your name, this is a number it says how many there are of something.” Point to a number in the room and the same number in the magazine Supply numeral names but not correct children Cut out a specific numeral and ask children to find more of that numeral Ask children to find specific numerals Ask children to find numerals related to objects and events

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4.1.2. Recognize and Name One Digit Numbers Developmental Range (cont.) Children may… Later Line up numerals in order (example: I found a 1,2, and 3. I need a 4.) Identify missing numerals Say by how much one numeral is more or less than another (example: I found a 3. It’s one more than a 2.) Adults can… use these strategies Cut out numerals 0-9 and ask, Can you help me glue mine in order? Ask: What number comes after or before...? Line up numerals with a space for a missing numeral and ask what else goes there (example:1,2,4,5, What number is missing?) Ask many how many one numeral is bigger or smaller than another

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Standard 4.1.3 Writing Numbers from 0-10 Standard 4.1.3 Know that written numbers are symbols for number quantities and, with support, begin to write numbers from 0 to 10.

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Standard 4.1.3 Written Numbers and Number Quantities (cont.) Standard 4.1.3 Know that written numbers are symbols for number quantities and, with support, begin to write numbers from 0 to 10.

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4.1.3. Writing Numbers from 0-10 Developmental Range: Children may… Earlier Write squiggles to represent numerals Middle Write numeral like forms (example: 1 and 0 backward 3) Later Write 3 or more recognizable numerals Adults can… use these strategies Acknowledge children’s interest in writing numerals Provide materials for children to make numerals (example: play dough, sand crayons) Ask children to read the numerals they write. Write numerals during play (example: Write a 2 and say, “I want 2 pieces of pizza”) Encourage writing numerals in play. Provide opportunities to write numerals. (example: As part of messages on message board)

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Standard 4.1.4: Numbers and Quantities 4.1.4 Understand the relationship between numbers and quantities (i.e., the last word stated when counting tells “how many”). (a)Accurately count quantities of objects up to 10, using one-to one- correspondence, and accurately count as many as 5 objects in a scattered configuration. (b)Arrange and count different kinds of objects to demonstrate understanding of the consistency of quantities (i.e., “5” is constant, whether it is a group of 5 people, 5 blocks or 5 pencils). (c)Instantly recognize, without counting, small quantities of up to 3 or 4 objects (i.e., subitize).

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Standard 4.1.4(a) Accurately Counting Quantities 4.1.4 Understand the relationship between numbers and quantities (i.e., the last word stated when counting tells “how many”). (a)Accurately count quantities of objects up to 10, using one-to one-correspondence, and accurately count as many as 5 objects in a scattered configuration.

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Standard 4.1.4(b) Consistency of Quantities 4.1.4 Understand the relationship between numbers and quantities (i.e., the last word stated when counting tells “how many”). (b)Arrange and count different kinds of objects to demonstrate understanding of the consistency of quantities (i.e., “5” is constant, whether it is a group of 5 people, 5 blocks or 5 pencils).

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Standard 4.1.4(b) Consistency of Quantities (cont.) Arranging and Counting Quantities http://earlymath.erikson.edu/number-arrangements/

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Standard 4.1.4(c) Subitizing 4.1.4 Understand the relationship between numbers and quantities (i.e., the last word stated when counting tells “how many”). (c)Instantly recognize, without counting, small quantities of up to 3 or 4 objects (i.e., subitize).

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Standard 4.1.4(c) Subitizing (cont.) http://earlymath.erikson.edu/matching-quantity-with-child-3/

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4.1.4. Understand the relationship between numbers and quantities Developmental Range Children may… Earlier Count objects by saying numbers in random order. (example: “2,8,3”) Recount from beginning when asked “how many objects” Use general quantity words (example: lots,whole lot, many) rather than words that compare quantity Middle Count up to 10 objects, may double count or skip numbers Say a different number than the last one counted when saying “how many” Count or eyeball two sets of objects and say which one has more, fewer, less Adults can… use these strategies Give children opportunities to count objects and model counting objects slowly Acknowledge when children recount from the beginning Introduce quantity words to compare (example: more, fewer less, same) Recount with children by touching or moving objects while counting Label the last number as how many (example: “You counted six. There are six bears.”) Ask children how many more objects there are when they compare two sets of objects

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Children may… Later Count objects accurately using one to one correspondence Say the last numbers of objects tells “how many” Count or eye ball two sets of objects and say by how many one is more or fewer less than the other * HighScope Numbers Plus Curriculum Adults can… use these strategies Acknowledge when children count objects correctly Provide collections of more than 10 items for use in play Ask genuine “how many” questions Provide larger sets of objects to compare how many more or fewer a set has or if they are the same Encourage children to explain how they figured out how many more or less when comparing sets 4.1.4. Understand the relationship between numbers and quantities Developmental Range

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Implementation Plan With your table, brain storm authentic opportunities for children to develop number sense throughout the daily routine. Write your ideas on index cards- include the activity and the part of the day. Post each index card by the sign that corresponds to your activity’s when, during the day, your activity would take place.

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New Jersey’s Preschool Math Standards and Number Sense Standard 4.1: Children begin to demonstrate an understanding of number and counting. 4.1.1 Count to 20 by ones with minimal prompting. 4.1.2 Recognize and name one digit written numbers up to ten with minimal prompting. 4.1.3 Know that written numbers are symbols for number quantities and, with support, begin to write numbers from 0 to 10. 4.1.4 Understand the relationship between numbers and quantities (i.e., the last word stated when counting tells “how many”).

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Resources NJ DOE Preschool Math Standards http://www.nj.gov/education/ece/guide/standards/math/master/standards.pdf Number Sense Educational Leadership Article http://www.ascd.org/ASCD/pdf/journals/ed_lead/el200402_griffin.pdf Young Children and Math http://membership.highscope.org/app/issues/54.pdf NAEYC Math Position Statement http://www.naeyc.org/store/files/store/TOC/167.pdf Early Math the Next New Thing Article http://highscope.org/file/NewsandInformation/ReSourceReprints/EarlyMath.pdf 50 Small Group Times to Scaffold Early Learning High/Scope Press http://secure.highscope.org/productcart/pc/viewPrd.asp?idproduct=1026 Numbers Plus Math Curriculum High Scope Press http://secure.highscope.org/productcart/pc/viewPrd.asp?idproduct=1066 Teaching Math to Young Children NCEE 2014-4005 U.S. Department of Education http://ies.ed.gov/ncee/wwc/practiceguide.aspx?sid=18

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