Maria Locuniak and Nancy Jordan (2008) found that children who understood basic addition and subtraction in kindergarten had better mathematical fluency in second grade. Early numbers are important for setting the foundation for mathematical learning throughout the rest of students’ academic careers. We have included resources for teachers to help students gain fluency with early number concepts. First, we have included the National Council of Teachers of Mathematics standards for kindergarten through second grade, followed by the Utah State Core Curriculum for math in kindergarten through second grade.

The following is a link to the Overview of K-2 Standards from National Council of Teachers of Mathematics. It discusses the concepts students in Kindergarten through second grade need to understand. http://standards.nctm.org/document/chapter4/index.htm

This is a link for the Utah State Core Curriculum. There is a link to the mathematic standards for all grades part way down the page where you can select the grade you are interested in. Early numbers are covered in Kindergarten through second grade. K-12 Core Curriculum – UEN

This link will show you many sites when excellent activities and fun games can be found. It uses effective ways of encouraging the children to expand their learning and get in some extra practice. These may be used when there is spare time throughout the day or as a great and effective fast finisher. These are value based and amide at broadening the fundamental principles and providing quality practice. http://www.teachingideas.co.uk/earlyyears/contents.htm

Teaching and Learning Early Numbers, Edited by Ian Thompson – This is a book that you can look at free online. It gives educators a brush up on early numbers and mathematical understanding. It can be used as a brief overview of a specific topic or a detailed outline of early numbers and the strategies that go with it. http://www.amazon.co.uk/gp/reader/0335198511/ref=sib_dp_pt/277-2546284-9095548#reader-link

#### References

#### Illuminations NCTM. (2008). Retrieved Dec. 12, 2008, from http://illuminations.nctm.org/LESSONDETAIL.aspx?ID=U147

#### K-12 core curriculum. Retrieved Dec. 12, 2008, from http://www.uen.org/core/

#### Locuniak, M. N., & Jordan, N. C. (2008). Using kindergarten number sense to predict calculation fluency in second grade. Journal of Learning Disabilities, 41(5; 5), 451-459.

#### Principles and standards for school mathematics. (2004). Retrieved Dec. 12, 2008, from http://standards.nctm.org/document/chapter4/index.htm

#### Teaching and learning early number(2003). In Thompson I. (Ed.), . Berkshire, Great Britain: McGraw-Hill Education.

#### Teaching ideas for primary teachers. (2008). Retrieved Dec. 12, 2008, from

#### Thinkfininty lesson plans. [Video/DVD] Retrieved from http://www.uen.org/curriculumsearch/SearchResults.do

####
**Early Number Skills-** are the foundational skills for all other math concepts and assist a student to begin to move from concrete thinking to abstract thinking. As a teacher, A teacher should provide many opportunities for whole class and small group discussion about how the students see groups and then connect writing number sentences with the groups.

**Big Ideas-**

- Counting tells how many items there are altogether. When counting, the last number tells the total number of items; it is a cumulative count (Charles 2005, 12).
- There is a number word and a matching symbol that tell exactly how many items are in a group (Charles 2005, 12).
- The distance between any two consecutive counting numbers on a given number line is the same. Numbers can also be used to tell the position of objects in a sequence (Charles 2005, 12).
- The numbers are related to each other through a variety of number relationships (Van de wall 2004, 115).

Children begin constructing early number concepts in Kindergarten and it continues throughout the grades. There are 6 Developmental Phases for numbers.

**Phase**

**Description**

**Typical Grade in which Instruction is Found in U.S. Curriculum**

Emergent

Emerging skills with numeracy and realizing that numbers signify quantity.

- Know numbers signify quantity
- Rote count to 10 with words in order
- Identify by sight 1-5 objects
- Know numerals are different from letters
- Know more, less and same and that a change results in either bigger or smaller (but not know by how much)

Prekindergarten and kindergarten

Matching

One-to-one correspondence for sharing and counting.

**Counting**

- Rote count to double digits
- Count lots of collections
- Know one-to-one correspondence
- Count all or use direct modeling in problem solving
- Know the cardinality principle (last number counted stands for total amount; it is not just a label)
- Know what things can be discretely counted vs. continually counted

**Number Relationships**

· Know more, less and same

· Figure out how many more or less or how many to make the same amount

· Know one more and one les without counting

· Know Spatial relationships and beginning estimation

· Relate one number to another (when changing numbers).

Prekindergarten and kindergarten

Quantifying

Using part-part-whole relations for numerical quantities.

**Counting**

- Count on, count back
- Skip count (in groups)
- Know ordinal numbers

**Number Relationships**

· Develop a sense of quantity and reasonableness

· Understand part-part-whole relationships

· Combine by using relationships, using doubles and near doubles, and just knowing

· Use benchmarks of 5 and 10

· Know how many to add or subtract (to change a number)

· Relate one number to another

· Have conservation of number

· Write number sentences (equations)

· Understand greater than, less than, and equal to

· Understand that when dealing all groups are the same

· Use concrete materials to model tens and ones and to add tens

Kindergarten and first grade

Partitioning

Using additive thinking or thinking in tens and ones.

**Counting**

- Count by tens starting with any number
- Skip count while keeping track of number of groups counted.

**Number Relationships**

- Use part-part-whole relationships without seeing objects
- Know any number is made with other numbers
- Understand and use inverse operations for addition and subtraction
- Compare whole numbers using patterns that do not concretely represent amounts (100 charts)

**Number as Tens and Ones**

- Recognize numbers as tens and ones
- Combine and separate tens and ones
- Know 10 more or less for any two-digit number
- Know place value for two-digit numbers
- Know and use expanded notation

**Fractional Understanding**

· Believe equal halves can look different

· Divide numbers into fractions

· Know 1/3 is greater than ¼

Late first and second grades

Factoring

Thinking additively and multiplicatively about quantities

**Numbers as Hundreds, Tens, and Ones**

- Know place value for three-digit numbers and larger
- Read, write, and say whole numbers beyond thousands

**Multiplication and Division**

- Use arrays to represent multiplication
- Understand inverse operation for multiplication and division
- Decompose and recompose factors without changing quantity
- Understand and use the commutative property of multiplication
- Think additively and multiplicatively
- Understand different models for division
- Use other language to interpret multiplication and division signs (groups of, shared by etc.)

**Fractional Understanding**

· Represent fractions with models and pictures and compare their like and unlike denominators

· Split fractions and decimals into whole and parts

· Relate fractions to division

Late second and third grades

Operating

Thinking of multiplication and division in terms of operators with whole, fractional, and decimal numbers

**Counting, Place Value, and Number Relationships**

- Count by tenths, hundredths, and thousandths over the whole
- Use understanding of relationships between successive places to order decimal numbers

**Multiplication and Division**

- Make multiplicative comparisons and deal with proportional situations
- Understand that when multiplying by a factor less than one, the product is smaller.
- Understand that when dividing by a divisor less than one, the quotient is larger

**Fractional Understanding**

· See any number can be thought of as a unit that can be repeated or split up a number of times

· Represent common and decimal fractions on a number line

· Partition decimal numbers

· Understand that two fractions are being compared to same whole

· Compose and decompose fractions visually or mentally

· Write number sentences (equations) for multiplication and division of whole numbers, fractions and decimals

Fourth, fifth, and sixth grades

It is important that children have plenty of concrete experiences as they move through the phases of number senses development to assist them in creating generalizations and developing the ability to think abstractly about early number concepts ( Bahr, Damon L. and de Garcia, Lisa Ann Elementary Mathematics Is Anything but Elementary: 2010, Wadsworth, Cengage Learning)

In order to give students sufficient concrete experiences it is necessary to teach them explicitly how to use manipulative and then give them meaningful activities, in which students can use the manipulative to help them explore an early number concept. Manipulative need to be organized in the classroom in a way that they are easily accessible to students.

Games:

**Building Trains or Towers:**

Students will work in groups with 2 colors of unifix cubes and make trains or towers for example:

3+2=5

2+3+5

**Snap it:**

Make a train of a number ie 5

Show the train

Put train behind back, snap of part of blocks

Show blocks that are left on train (keeping the rest of blocks behind back)

Other student says how many are behind back

**Daily Routine:**

**Days in School-**

Using 10 Frames have students color in 1 square per day.

Have a tub with snap cubes. Have students snap one cube onto train per day up to 10 days.

Match it to the 10 frames.

Keep 10’s trains and compute to day and count 10 frames to day.

Lesson Plans/Activities

http://http://www2.scholastic.com/browse/article.jsp?id=2951

http://http://www.hummingbirded.com/number-sense.html

http://http://www.teachingideas.co.uk/maths/numberhat.htm

http://http://illuminations.nctm.org/Lessons.aspx

Online Games/Manipulative

http://nlvm.usu.edu/en/nav/grade_g_1.html

**Early Number Skills-**are the foundational skills for all other math concepts and assist a student to begin to move from concrete thinking to abstract thinking. As a teacher, A teacher should provide many opportunities for whole class and small group discussion about how the students see groups and then connect writing number sentences with the groups.

**Big Ideas-**

**Phase**

**Description**

**Typical Grade in which Instruction is Found in U.S. Curriculum**

Emergent

Emerging skills with numeracy and realizing that numbers signify quantity.

- Know numbers signify quantity
- Rote count to 10 with words in order
- Identify by sight 1-5 objects
- Know numerals are different from letters
- Know more, less and same and that a change results in either bigger or smaller (but not know by how much)

Prekindergarten and kindergarten

Matching

One-to-one correspondence for sharing and counting.

**Counting**

- Rote count to double digits
- Count lots of collections
- Know one-to-one correspondence
- Count all or use direct modeling in problem solving
- Know the cardinality principle (last number counted stands for total amount; it is not just a label)
- Know what things can be discretely counted vs. continually counted

**Number Relationships**

· Know more, less and same

· Figure out how many more or less or how many to make the same amount

· Know one more and one les without counting

· Know Spatial relationships and beginning estimation

· Relate one number to another (when changing numbers).

Prekindergarten and kindergarten

Quantifying

Using part-part-whole relations for numerical quantities.

**Counting**

- Count on, count back
- Skip count (in groups)
- Know ordinal numbers

**Number Relationships**

· Develop a sense of quantity and reasonableness

· Understand part-part-whole relationships

· Combine by using relationships, using doubles and near doubles, and just knowing

· Use benchmarks of 5 and 10

· Know how many to add or subtract (to change a number)

· Relate one number to another

· Have conservation of number

· Write number sentences (equations)

· Understand greater than, less than, and equal to

· Understand that when dealing all groups are the same

· Use concrete materials to model tens and ones and to add tens

Kindergarten and first grade

Partitioning

Using additive thinking or thinking in tens and ones.

**Counting**

- Count by tens starting with any number
- Skip count while keeping track of number of groups counted.

**Number Relationships**

- Use part-part-whole relationships without seeing objects
- Know any number is made with other numbers
- Understand and use inverse operations for addition and subtraction
- Compare whole numbers using patterns that do not concretely represent amounts (100 charts)

**Number as Tens and Ones**

- Recognize numbers as tens and ones
- Combine and separate tens and ones
- Know 10 more or less for any two-digit number
- Know place value for two-digit numbers
- Know and use expanded notation

**Fractional Understanding**

· Believe equal halves can look different

· Divide numbers into fractions

· Know 1/3 is greater than ¼

Late first and second grades

Factoring

Thinking additively and multiplicatively about quantities

**Numbers as Hundreds, Tens, and Ones**

- Know place value for three-digit numbers and larger
- Read, write, and say whole numbers beyond thousands

**Multiplication and Division**

- Use arrays to represent multiplication
- Understand inverse operation for multiplication and division
- Decompose and recompose factors without changing quantity
- Understand and use the commutative property of multiplication
- Think additively and multiplicatively
- Understand different models for division
- Use other language to interpret multiplication and division signs (groups of, shared by etc.)

**Fractional Understanding**

· Represent fractions with models and pictures and compare their like and unlike denominators

· Split fractions and decimals into whole and parts

· Relate fractions to division

Late second and third grades

Operating

Thinking of multiplication and division in terms of operators with whole, fractional, and decimal numbers

**Counting, Place Value, and Number Relationships**

- Count by tenths, hundredths, and thousandths over the whole
- Use understanding of relationships between successive places to order decimal numbers

**Multiplication and Division**

- Make multiplicative comparisons and deal with proportional situations
- Understand that when multiplying by a factor less than one, the product is smaller.
- Understand that when dividing by a divisor less than one, the quotient is larger

**Fractional Understanding**

· See any number can be thought of as a unit that can be repeated or split up a number of times

· Represent common and decimal fractions on a number line

· Partition decimal numbers

· Understand that two fractions are being compared to same whole

· Compose and decompose fractions visually or mentally

· Write number sentences (equations) for multiplication and division of whole numbers, fractions and decimals

Fourth, fifth, and sixth grades

**Building Trains or Towers:**

**Snap it:**

**Daily Routine:**

**Days in School-**