1. Mathematics Standard 4.2 Numeral Operations
Today’s workshop is all about New Math Standard 4.2: Numeral Operations – what preschoolers should know and be able to do.
Objectives:
To understand numeral operations, giving teachers a deeper understanding of what different levels of numeral operations mean.
To explore classroom materials and create short activities that demonstrate high quality interactions as they are align to Standard 4.2: Numeral Operations.

2. Five goals…for preschool students to..
become mathematical problem solvers that
communicate mathematically;
reason mathematically;
make mathematical connections; and
use mathematical representations to model and interpret practical situations
What you say:
These are the 5 goals or process skills we want our preschoolers to be actively engaged during math and through out their day; these goals are interwoven throughout each of the Standards.
***Transition to the next ….

3. Five goals….in action Problem solving? Representing? Communicating?
Connecting?
***You will read each process skill, define it and give an example ( provided below) ***
Problem Solving: finding a solution or an answer to a question
Example: It looks like you have used shapes and what made you draw some figures while others you used the real shapes?
Communicating: Sharing thoughts, ideas, and feelings with others through gestures, facial expressions, drawings, writing, and speaking.
Example: It looks like you have used shapes to make columns (rows), what made you draw some figures while others you used the real shapes?
Reasoning: Thinking through a question or a problem to arrive at an answer.
Example: Can you tell me what you have done with of the shapes/colors?
(mathematical reasoning is a key process in learning and developing mathematical knowledge in all areas of mathematics, including number and operations, classification, patterning, measurement, and geometry)
Connecting: Linking new learning to previous experience.
Example: I can see that you have sorted all the shapes that look the same by color, can you remember something else we did in discovery that we sorted by shape or color?
Representing: Showing ones thoughts or ideas in a variety of ways using a variety of tools.
Example: I can see that you have used shapes and have drawn some shapes on your work, can you tell me more about your work?
Reasoning, communicating, and representing lend themselves, specially, to data analysis.
Reasoning?

4. New Jersey’s Revised Preschool Math Standards
4.1: Children begin to demonstrate an understanding of
number and counting.
4.2: Children demonstrate an initial understanding of
numerical operations.
4.3: Children begin to conceptualize measurable attributes
of objects.
4.4: Children develop spatial and geometric sense.
***Take a minute and show audience the Standards, the teacher’s practice and the learning outcomes.***
You will read/say:
Each part of the Standard.
Each of the Standard have Preschool Numbers and “indicators”, we will be discussing these ahead.
The learning outcomes for each of the standards are targeted for the end of the 4 year old experience.
Also emphasize the words “begins to,” explaining to participants that we are helping young children explore and expand their understanding of math content.
Standard 1 is about number sense Common Core Domain Alignment with/ Counting and Cardinality
-children’s understanding of numbers and quantities.
Standard 2 is about number sense Common Core Domain Alignment with/ Counting and Cardinality
-children’s understanding of number relationships and operations.
Standard 3 is about conceptualize measurable attribute Common Core Domain Alignment with/ Measurement and Data
Children’s ability to ….
-compare,
-order; and
-begin to measure.
Standard 4 is about spatial and geometric sense Common Core Domain Alignment with/ Geometry
-children’s ability to identify and use shapes; and
-children’s understanding of position in space.

5. BIG Ideas Content Strand Big Idea Number and Operations
Number names allow us to tell how many are in a set.
Measurement
Comparisons can show which is bigger, but they have to be fair.
Geometry
Two shapes can be combined to make another shape.
Algebra
A single collection of objects can always be sorted in more than one way.
Data Analysis
Collecting and organizing data makes it easier to answer questions.
***This is a handout**
You will say:
In a high-quality preschool classroom, preschoolers are intentionally introduced to and engage in the ‘big ideas’ or (common core goals.)
This is an example of “Big Ideas.” There are many other Big Ideas….
Each of the Big ideas are embedded throughout the preschool Standards/Strands.
Data analysis runs through the teaching practices for each of the 4 strands.

6. Numeral Operations What is Numeral Operations?
When looking at math or numeral operations, consider these levels (reference pg , Engaging Young Children in Mathematics):
Comparing and Ordering
Adding to/Taking away to solve problems
Composing and decomposing
Grouping

7. Comparing
Comparing and Ordering
Ordering

8. Subtracting or taking away
Adding or put together
Adding to/Taking away to solve problems
Subtracting or taking away

9. Composing
Composing and decomposing

10. Decomposing

11. Grouping
pinecones
Grouping
acorns

12. Number and Operations Counting (rote and rational)
Quantity (sense of number)
Comparisons (more/fewer or more/less)
Order (first, second, third last)
Numerals (the written number and what it represents)
Combining Operations (adding)
Separating Operations (subtracting)
Sharing Operations (dividing / fair share)
Set Making Operations (multiplying / equal sets)
When we refer to number and operations we must remember that it involves nine different areas:
4.1 and 4.2 are cross related.
We already discussed about…Counting, Quantify, Comparisons, Order, and Numerals in Standard 4.1
1. Counting: Children must learn three things: the number sequence, one to one correspondence, and that the last number named when counting a set tell how many are in the set. 2. Quantity (Sense of Number): understanding how many are in a set. 3. Comparisons (More and Fewer): children can often tell which has more or less. 4. Order (ordinal numbers): most young children have no problem with first. Second and so forth comes with practice. 5. Numerals: Children need time to investigate numbers. Writing numbers is not an important skill in preschool. It is more important that the children see numbers displayed and begin to understand what the numbers represent.
In Standard 4.2, our focus will be on: 6. Combining Operations (Adding): Children often can put sets of objects together to find out how many in all. 7. Separating Operations (Subtracting): The operation of taking away is a common separating operation and one that young children understand. Note: We don’t focus on sharing and set making operations in preschool math standards.

13. 4.2: Children demonstrate an initial understanding of numerical operations.
4.2.1: Represent addition and subtraction by manipulating up to 5 objects:
4.2.2: Begin to represent simple word problem data in pictures and drawings.
Let’s take a closer look at each part of 4.2
4.2: Children demonstrate an initial understanding of numerical operations.
Demonstrate 4.2.1: Represent addition and subtraction by manipulating up to 5 objects:
putting together and adding to:
Addition using balls (concrete objects)
(b) taking apart and taking from:
Subtraction using Buttons: (Concrete objects)
Demonstrate 4.2.2: Begin to represent simple word problem data in pictures and drawings.
*****Use dry-erase board to create word problem data in drawing (Example: John has five stickers. He then shared two stickers with Anna. How many stickers does John have left?
This morning I ate four strawberries and one orange. How many fruits did I eat all together? Just an example
*****Use sample pictures to represent simple word problem.
(a) putting together and adding to (e.g., “3 blue pegs, 2 yellow pegs, 5 pegs altogether.”)
(b) taking apart and taking from (“I have four carrot sticks. I’m eating one. Now I have 3.”)

14. 4.2.1: Represent addition and subtraction by manipulating up to 5 objects
putting together and adding to (e.g., “2 red bears and 1 green bear. 3 bears altogether.”)
Quickly discuss each picture as one of many examples that address the standard and its indicators.
**** Addition--Putting together and adding to: Example---There are 2 red bears and 1 green bear. 3 bears all together.
**** Subtraction--Taking apart and taking from: Example---I have four carrot sticks. I’m eating one. How I have 3.
Abacus: Adding and Subtracting
(b) taking apart and taking from (“I have four carrot sticks. I’m eating one. Now I have 3.”)

15. 4.2.2: Begin to represent simple word problem data in pictures and drawings.
Quickly discuss one or two examples that address the standard and its indicators.
***There are three children and a pilot that are ready to ride on this airplane. How many people are there in all?
***I made three little pigs and one big bad wolf. How many animals ?
***One frog is jumping, and three fish are swimming. How many animals do you see?
***I have four people in my family and I made two flowers. I need two more flowers.

16. Numeral Operations….
***Mary has four marbles and her dad gave her one more. How many marbles does she have in all?
***Five Little Monkeys jumping on a bed..One fell of and bumped his head..How many left?
***Old Mother Hubbard
Went to the cupboard
To get her poor doogie a bone
If there were 4 bones in the cupboard,
and Mother Hubbard takes 2,
How many are left?

17. Levels of Numeral or Math Operations
Comparing & Ordering - Can tell which group has more or less
Adding to/Taking away - Solve problems with three to five objects
Composing and Decomposing - Can develop the ability to recognize that three and two are “hiding inside” five
Grouping - Can count groups of objects
Clements, D.H., Engaging Young Children in Mathematics, 2004, pg
One more time let’s review the Levels of Numeral Operations:
Read from the slide..

18. The Teacher’s Role in Promoting Understanding of Numeral Operations:
Throughout the day
Through high-quality teacher-child interactions
Throughout the environment
Preschool teachers will:
• Model addition for children by using counting to combine numbers (e.g., “Maria has two blocks and Justin has three. There are five blocks altogether: 1, 2, 3, 4, 5.”).
• Model subtraction for children by using counting to separate quantities of objects (e.g., “There are five cars on the carpet: 1, 2, 3, 4, 5. I am putting two cars in the basket. There are three cars left on the carpet.”).
• Engage informally with children during center time to explore joining and taking apart small quantities of concrete objects.
• Provide opportunities for children to independently explore addition and subtraction.
• Develop addition and subtraction stories with small groups of children using story mats and flannel board scenes with small quantities of objects and pictures/drawings.
--Pose story problems that involve adding, subtracting.
--Have the children act out the stories themselves or with objects. Then count to solve the problems. Use the numbers 1-5 and remember to emphasize the vocabulary that indicates the actions (e.g., take away).
• Use fingers, chalk, wipe-off markers and/or whiteboard technology to tell and draw addition and subtraction stories with small groups of children.

19. Throughout the Environment
Setting up your classroom environment should include setting the stage for meaningful numeral operations opportunities. We’re going to spend a few minutes thinking about each area of the classroom and what activities might become a part of each learning area.
As a group your job is to brainstorm what activities teachers might embed in various learning areas to incorporate numeral operations – think about opportunities to add, subtract,…; think about how to develop addition and subtraction stories using story mats and flannel board scenes with small quantities of objects and pictures/drawings… Be creative!

20. Teachers are the key! For students to become mathematicians they need
to organize and interpret their world through a
mathematical lens. It is the teacher’s job to keep the
lens in focus…the actions of learning and teaching
are inseparable.
Because teachers are the key, so we need to know the importance of mathematics, and how to provide developmentally appropriate materials, activities and interaction to support ALL learners.

21. Resources The Creative Curriculum Vol 4 Mathematics
Teaching Strategies, Copley, Jones and Dighe
Teaching and Learning Math: The Learning Trajectories Approach by Douglas H. Clements and Julie A. Sarama
The Building Blocks of Math: Lessons from Research, featuring Dr. Doug Clements