1. Number Sense Developed by Carrie Ann Floyd Plainfield School District
Presenter Notes:
This workshop can be presented as a full day presentation that covers the preschool Mathematics Standard in its entirety (4.1.1, 4.1.2, 4.1.3, and 4.1.4). The workshop can also be broken down into two shorter presentations, or delivered as four brief sessions, with each session covering one of the four parts to the Standard. To make your decision, please print out the notes pages for the PowerPoint and thoroughly review the entire workshop, supporting activities, and video materials. Feel free to cut and paste slides and to tailor your activity choices to your needs.
Materials required for the entire workshop:
Chart paper, post it notes, index cards, markers, newspapers and scissors for Application Activity #2, 8 1/2x11 inch signs and masking tape for the Implementation Plan Activity. Handouts: copies of the New Jersey Preschool Mathematics Standards, Counting Song Lesson Plan, Numerals in Newspapers Lesson Plan, Hidden Stars Game, Hiding Game (see Handout Folder). You will want to make certain that your speakers (sound system) have enough volume to be heard by the workshop participants. You will need to be connected to the internet to view the hyperlinked video clips about consistency of quantities and subitizing.
Developed by Carrie Ann Floyd
Plainfield School District

2. 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.
Today we’re going to talk about some key aspects of number sense, an important focus of our preschool teaching and learning standards in New Jersey.
We’ll review the preschool math standards that relate to number sense.
We’ll also define number sense and its importance as a building block for all future mathematical learning. Finally, we will review intentional teaching strategies for number sense.

3. 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.
Ask participants to each write their favorite number from 1-20 on a post it (a number that has personal significance). For example: 4 - I have four children, 2 - I have two golden retrievers. Then, ask participants to get up and mingle with each other, sharing their numbers and the reasons for choosing the numbers. Finally, ask participants to arrange themselves in groups according to their number. Last, ask the groups to order themselves from To summarize, ask participants what math skills they used during the activity. Then go to the next slide to debrief.

4. 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.
This was a simple activity for adults but, in reality, many smaller skills are needed to complete the activity. We used lots of important math skills, including understanding quantity, writing numbers, recognizing numbers, and ordering How do we teach these skills to young children? Let’s take a look.

5. 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”
Number sense is a big idea in early mathematics and one that all mathematical skills build on. For children, number sense is as basic to learning mathematics as phonemic awareness is to learning how to read. Children who have number sense understand what numbers represent and that numbers can be used flexibly and practically in their everyday lives.

6. New Jersey’s Preschool Math Standards and Number Sense
Standard 4.1: Children begin to demonstrate an understanding of number and counting Count to 20 by ones with minimal prompting Recognize and name one digit written numbers up to ten with minimal prompting Know that written numbers are symbols for number quantities and, with support, begin to write numbers from 0 to Understand the relationship between numbers and quantities (i.e., the last word stated when counting tells “how many”).
Ask participants to take out the preschool math standards handout. Point out that standard 4.1 has four parts that focus on number sense:
Count to 20 by ones with minimal prompting, Recognize and name one digit numbers up to ten with minimal prompting, Know that written numbers are symbols for number quantities and with support , begin to write numbers from 0 to 10, and Understand the relationship between numbers and quantities (i.e., the last word stated when counting tells “how many”).

7. 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.
Now let’s look at the Preschool Teaching Practices that are related to number sense. Show participants where the Teaching Practices are located in the Preschool Math Standards document. The Teaching Practices describe the strategies teachers can use to reach the goals of the standard. Teachers help young children develop their number sense by surrounding them with a number rich environment offering many opportunities to work with materials and processes. Here are four examples from the teaching practices. Read the examples to participants. The preschool teacher’s task is to look for opportunities throughout the daily routine to intentionally expose children to the concepts and vocabulary of number sense.

8. 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.
In these three examples of teaching practices, teachers help young children develop their number sense by surrounding them with a number rich environment offering them many opportunities to work with materials. Because early mathematical development depends so much on manipulating objects, it is important that young children have ample opportunities to work with materials relating to numbers and number symbols. Teachers should provide time for children to use these materials in both structured and open-ended ways. By observing children as they engage with the materials, teachers can find out what children already understand and then use specific strategies to build new concepts.

9. 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.
There are three things to think about when it comes to number sense. The first is cardinality. Standard Count to 20 by ones with minimal prompting is about learning the words for cardinal numbers. As children have experience hearing and using the counting words in order they will begin to internalize number order and memorize it. Research suggests that the best strategy is for teachers to model saying the counting numbers for children, instead of pointing out their errors or omissions. Standard Know that written numbers are symbols for number quantities and, with support, begin to write numbers from 0 to 10 also involves cardinality – When we write “4” we are describing a group of 4 things. Standard Understand the relationship between numbers and quantities (i.e., the last word stated when counting tells “how many”) involves cardinality when we help children connect quantities of objects to number words.

10. 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.
The next part of number sense is recognizing the number symbols. Standard is about recognizing and naming one digit numbers up to ten with minimal prompting. Learning to read written number symbols depends on how often children encounter them in their environment and to the extent that adults point out number symbols. It is important for teachers to provide children with materials that show numerals, and for teachers to talk about them in meaningful contexts throughout the daily routine.

11. 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.
And last, writing numerals. Standard addresses, “Know that written numbers are symbols for number quantities and with support begin to write numbers from 0 to 10.”
Writing numerals parallels reading and writing alphabet letters in literacy. As with letter writing , children often begin with making numeral-like marks on paper. Teachers need to respond positively to all children’s attempts to write numerals, and can support children by providing materials and time for children to experiment with writing them. Adults should look for opportunities to model numeral writing throughout the day.

12. Recommended Materials for Number Sense
As highlighted in the Preschool Teaching Practices, it is important to expose children to numerals in the classroom environment. Things with numerals on them, such as calculators, playing cards, thermometers, and simple board games with spinners and dice help children recognize numerals. Teachers should provide children with time during the day for children to use these kinds of materials in open-ended ways.

13. Books About Numbers
The preschool classroom should have many examples of counting books and books with numbers in them. The table toy, math, discovery, and block areas are good places to have a basket full of counting books, and books relating to other math concepts. Teachers can also help children make their own counting books.

14. Puzzles and Manipulatives
Puzzles, games, and other manipulatives can be used by children in open-ended ways. Children can hold them, explore quantity, and use them as models when writing numerals. Teachers should observe children using manipulatives, support their ideas and gently extend those emerging ideas about number sense.

15. Materials for Making and Writing Numerals
Numerals made of wood, plastic, or heavy cardboard are optimal so children can sort, copy, and trace them. The larger the object is, the easier it will be for children to use it. Either store bought or teacher made materials will do the job. Again, children need time to explore these materials in open-ended ways, but also benefit from adult interactions. Teachers should encourage children to use these materials and support the unique ways children choose to use them.

16. Using the Daily Routine
The daily routine offers many opportunities to expose children to numerals. The examples here show ways for teachers to plan both large and small group activities, such as children adding scoops on to their ice cream cones and writing the numerals, making a graph of the number of letters in their name, and using number beanbags at large group time.

17. Taking A Closer Look at the Parts of Standard 4.1
Presenter Notes: The following slides include activities, discussions, and video material for Standards 4.1.1, 4.1.2, 4.1.3, and , followed by a culminating activity.  You should choose which standards and activities to cover based on the allotted time for your workshop.

18. 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
For the remainder of the workshop, we’re going to practice and discuss strategies that illustrate how teachers can scaffold number sense with their students. Scaffolding, the term developed by Lev Vygotsy, means providing children with support at their current level of development while occasionally offering a gentle extension to the next level.

19. Counting to Twenty by Ones
Standard 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
“Counting Song” Activity (20 minutes)
This exercise demonstrates how to scaffold children’s ability to count to 20 during a large group time. As you do the activity, use your own experiences with children to think about three basic levels of development: Earlier, Middle, Later. How might children respond to the content and the materials? As a teacher, how would you support each developmental level?
Remember to think in terms of three broad categories of development: Earlier, Middle, and Later.
Presenter Notes:
Hand out the lesson plan “Counting Song” needed for this activity, Ask participants to form groups (5-8 people per group) Say: “Your group will now role play the lesson. Some of you as children, others as teachers. Each group should have one or two teachers. The rest of the group should role play as the children.” After groups complete the role play, say: “Now lets review the part of the lesson plan handout that shows the three basic levels of development (earlier, middle and later ) for this activity. In your group, come up with ideas for supporting each developmental level, and chart it on paper.” Circulate around the room to see if participants need assistance and refer them to the Lesson Plan Handout “Counting Song ” where examples are listed. After 5 to 10 minutes, draw them back by moving to the next slide.
Presenters should review the lesson plan and the strategies ahead of time so they are familiar with the lesson and the developmental levels.

20. “Counting Song” Large Group Lesson
Standard 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
Presenter asks the groups to post their chart and to report out the strategies they came up with for supporting each developmental level.

21. “Counting Song ” Video Clip
Let’s watch a short video clip of this activity being done in a preschool classroom. Pay particular attention to the three levels and the strategies the adults use. You may want to write them down and compare them to the ones your group came up with. The “Counting Song” video clip is located in the materials folder . It is not embedded here and must be played separately.

22. 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)
To summarize the activity, the presenter should read this slide to the audience, and add: The strategies listed here will help you to support and extend children’s counting to 20 by ones. After observing children at a particular level of development adults can scaffold children’s learning to move them to the next level. Remember we are thinking of three broad levels of development related to this skill.

23. 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, )
The presenter should read this slide to the audience and add: Teachers should become familiar with the strategies and use them flexibly, meaning the teacher can choose from the list, and might not use every strategy during the activity. I like to think of it as a bag of tools they carry and can use according to their judgment. Which levels did we see in the video clip? Which strategies did the teacher use?
These same teaching strategies can and should be used for individual instruction as children move throughout the daily routine.
Presenter should review the clip before the workshop to become familiar with the levels and strategies seen in the clip.

24. Standard 4.1.2 Recognizing and Naming Numbers
Math Standard 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
“Numerals in Newspapers” Activity (20 minutes)
Standard calls for children to recognize and name one digit numbers. Let’s take a look at one way to support this ability during a small group time. As you do this activity, use your experiences with children to think about the three basic levels of development -- Earlier, Middle, Later. How might children respond to the content and the materials? As a teacher, how would you support each developmental level?
Presenter Notes:
Hand out the lesson plan “Numerals in Newspapers,” the newspaper, and scissors for this activity, Ask participants to form groups ( 5-8 people per group). Say, “Your group will now role play this lesson, some of you as children, others as teachers. Again, each group should have 1 or 2 teachers. The rest of the group should role play as children.” After a few minutes of role playing, say: “Now lets review the part of the lesson plan that shows the basic three developmental levels (earlier, middle, and later ) for this activity. As a group, come up with ideas for supporting each developmental level, and chart it on paper. Circulate around the room to see if participants need assistance and refer them to the Lesson Plan Handout “Numerals in Newspapers” where examples are listed. After 5 to 10 minutes, draw them back by moving to the next slide.
Presenters should review the lesson plan and the strategies ahead of time so they are familiar with the lesson and the developmental levels.

25. “Numerals In Newspapers” Small Group Lesson
Math Standard 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
Presenter asks each group to post their chart and report out their strategies for supporting each developmental level.

26. “Numerals in Newspapers” Video Clip
Let’s look at a short video clip of the Numerals in Newspapers activity happening in a preschool classroom. Pay close attention to the three levels and the strategies the adults use. Jot down what you see and hear so we can compare it to the ideas our groups came up with. The “Numerals in Newspapers” video clip is located in the materials folder . It is not embedded here and must be played separately.

27. 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
To summarize the activity, the presenter should read this slide to the audience and add: The strategies listed here will help you to support and gently extend children’s ability to recognize and name one digit numbers. Again after observing children on a particular level of development, adults can scaffold children’s learning to move them to the next level.

28. 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
The presenter should read this slide to the audience and add: It is important to remember that during early childhood it is common to see wide ranges in child development. It is possible that the children in any given classroom may be on a wide range of developmental levels.” Teachers need to recognize and support a wide range of developmental levels. What levels of development did you see in the video clip? What strategies did the teacher use?
These same teaching strategies may be used for individual instruction as children move throughout the daily routine and use open-ended materials.
Presenter Note: Presenter should review the clip before the workshop to become familiar with the levels and strategies seen in the clip.

29. Standard 4.1.3 Writing Numbers from 0-10
Standard Know that written numbers are symbols for number quantities and, with support, begin to write numbers from 0 to 10.
Standard is about writing numerals, a task that involves perceptual and motor development. A child who can read numerals may still have difficulty writing them. Reversals are common and not a cause for concern – the standard says “begin to…” The key to this standard is lots of teacher modeling during everyday activities and lots of opportunities for children to practice with tactile materials as well as using writing implements (crayons, markers, pencils) during play and for a purpose. Rote activity, such as repeatedly tracing and writing rows of numerals is not a recommended practice in our preschool standards.

30. Standard 4.1.3 Written Numbers and Number Quantities (cont.)
Standard Know that written numbers are symbols for number quantities and, with support, begin to write numbers from 0 to 10.
The best way to talk about and model written numbers is in authentic contexts– activities that connect written numbers to number quantities. Here, you see a child filling in a chart with a very practical purpose – lunch! Also pictured is an illustration from Donald Crews book, 10 Black Dots – such a great literacy connection to math that helps children understand that written numbers are symbols for number quantities: “2 dots can make the eyes of a fox.”

31. 4.1.3 . Writing Numbers from 0-10 Developmental Range:
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)
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
To summarize the activity, the presenter should read this slide to the audience and add: The strategies listed here will help you to support and gently extend children’s ability to write numerals . Again after observing children on a particular level of development, adults can scaffold children’s learning to move them to the next level.

32. Standard 4.1.4: Numbers and Quantities
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).
Standard asks children to understand that, when counting, the last word stated tells “how many.” There are three ideas here to think about: counting accurately to 10; understanding that a quantity is the same, whether it is 5 people or 5 elephants; and the ability to instantly recognize how many are in a small group of objects without having to stop and count each object. Let’s take a look at each of these ideas.

33. Standard 4.1.4(a) Accurately Counting Quantities
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.
Sometimes children will say the number sequence out of order, skip numbers, or use the same number more than once. To help children at this stage, teachers can recite or sing the sequence with children.
Some children might not count one-to-one at all, just skimming over using a rote sequence of numbers. Teachers can model counting the objects, slowly demonstrating one-to one counting.
Sometimes children will count the same object two times or skip over and not count an object. In this case, teachers can verbally encourage children to slow down. Teachers can slowly touch and count with children. It’s important to remember that is always more difficult to count objects in a scattered configuration.
Some children might be able to do all of the above but still not realize that the last number word used in the counting process indicates the total. In this case, teachers should use small collections of one to three items first, then progress toward larger collections. Here’s a game that you can play with children to help them more fully understand the cardinality rule: The last word stated when counting tells how many. Using cards with stars (made beforehand), presenter should demonstrate the Hidden Stars game for participants. Presenter should then direct participants to the Hidden Star game handout for use in their classrooms.

34. Standard 4.1.4(b) Consistency of Quantities
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).
Children also need experiences counting objects that are not all the same type, size, or color so that they can understand that 5 is always whether it is 5 animals, 5 vehicles, or five apples. Or, in the case of the photos on the slide, 2 penguins, 2 keys, two plants is 2. That’s why a wide variety of objects should be available for use as math manipulatives.

35. Standard 4.1.4(b) Consistency of Quantities (cont.)
Arranging and Counting Quantities
Here’s slightly different example of arranging and counting. The teacher in this video clip helps children to create visual representations of a small quantity in different ways.
Presenter Note: You must be connected to the internet to view this clip. Right click on the hyperlink and choose open hyperlink from the drop down menu.

36. Standard 4.1.4(c) Subitizing
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).
Children need many chances to practice recognizing the total number of objects in small collections and labeling them with a number word without needing to count them. This is called subitizing – small-number recognition. It means being able to answer the question, “How many do you see?” Being able to correctly determine the number of objects in a small collection is a critical skill that children must develop. Being able to subitize helps children learn more complex skills, including counting larger collections and eventually, adding and subtracting.
One way to help children learn to subitize is to make a contrast. For example, in addition to labeling a collection of four toys as “four” the teacher can label a collection of two toys as “not four” by saying, “That’s two toys, not four toys.” Once children are used to hearing examples and non-examples, teachers can ask children to find their own examples – “Can someone find four toys? Now can someone find a group of something that is not four?”
In your packet is a handout called The Hiding Game. You can use this game to help your children become subitizers!

37. Standard 4.1.4(c) Subitizing (cont.)
Here’s a clip that demonstrates what subitizing is and how teachers can scaffold children’s emerging abilities in this area.
Presenter Note: You must be connected to the internet to view this clip. Right click on the hyperlink and choose open hyperlink from the drop down menu.

38. 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

39. 4.1.4. Understand the relationship between numbers and quantities Developmental Range
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

40. 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.
Closing Activity: Hang signs around the room (made before the workshop) that depict the typical segments of a preschool daily routine. Ask each table group to brainstorm authentic opportunities for children to use and write numerals during different segments of the day. Give groups index cards to write their ideas on. Tell groups to be certain to write both the activity and the intended segment of the day on each card. Groups report out and then post their index card ideas next to the appropriate segment of the day signs. If time allows, invite some participants to elaborate on their ideas.
If possible, compile the list of ideas and, as a workshop follow-up, it to participants .

41. New Jersey’s Preschool Math Standards and Number Sense
Standard 4.1: Children begin to demonstrate an understanding of number and counting Count to 20 by ones with minimal prompting Recognize and name one digit written numbers up to ten with minimal prompting Know that written numbers are symbols for number quantities and, with support, begin to write numbers from 0 to Understand the relationship between numbers and quantities (i.e., the last word stated when counting tells “how many”).
An understanding of number sense is a critical math concept and one that depends on teachers intentionally embedding opportunities for learning all, day every day in our preschool classrooms. And because learning about number sense is not as simple as 1-2-3, young children need their teachers to provide lots of hands-on experiences that are engaging and meet the developmental needs of every child in the class.

42. Resources NJ DOE Preschool Math Standards
Number Sense Educational Leadership Article
Young Children and Math
NAEYC Math Position Statement
Early Math the Next New Thing Article
50 Small Group Times to Scaffold Early Learning High/Scope Press
Numbers Plus Math Curriculum High Scope Press
Teaching Math to Young Children NCEE U.S. Department of Education