*The
curriculum framework offers an explanation of the specific STRAND and
detailed expectations of the material that should be covered by the
teacher and learned by the students (according to the Virginia
Department of Education Standards of Learning).*

**K.1 The student, given two sets, each containing 10 or fewer concrete objects, will identify and describe one set as having more, fewer, or the same number of members as the other set, using the concept of one-to-one correspondence.**

UNDERSTANDING THE STANDARD

· A set is a collection of distinct elements or items.

· A one-to-one correspondence exists when two sets have an equal number of items.

· Strategies for developing the concept of one-to-one matching involve set comparisons without counting. Hands-on experiences in matching items between two sets by moving, touching, and aligning objects, using one-to-one correspondence, enable visual as well as kinesthetic comparisons of the number of items in the two sets.

· Students can also count to make comparisons between two sets without matching the sets, using one-to-one correspondence.

· Students are generally familiar with the concept of *more*, but have had little experience with the term *less*. It is important to use the terms together to build an understanding of their relationship. For example, when asking which group has more, follow with which group has less and vice versa.

**K.2 The student, given a set containing 15 or fewer concrete objects, will**

a) tell how many are in the set by counting the number of objects orally;

b) write the numeral to tell how many are in the set; and

* c) select the corresponding numeral from a given set of numerals.*

UNDERSTANDING THE STANDARD

· Counting involves two separate skills: verbalizing the list of standard number words in order (“one, two, three, ¼”) and connecting this sequence with the objects in the set being counted, using one-to-one correspondence. Association of number words with collections of objects is achieved by moving, touching, or pointing to objects as the number words are spoken. Objects may be presented in random order or arranged for easy counting.

· Kinesthetic involvement (e.g., tracing the numbers, using tactile materials, such as sand, sandpaper, carpeting, or finger paint) facilitates the writing of numerals.

· Articulating the characteristics of each numeral when writing numbers has been found to reduce the amount of time it takes to learn to write numerals.

· Zero (0) is both a number and a digit. As a number, it plays a central role in mathematics as the additive identity of the integers, real numbers, and many other algebraic structures. As a digit, zero is used as a placeholder in systems.

· *Conservation of number* and *cardinality principle* are two important milestones in development to attaching meaning to counting.

· The cardinality principle refers to the concept that the last counted number describes the total amount of the counted set. It is an extension of one-to-one correspondence.

· Conservation of number is the understanding that the number of objects remains the same when they are rearranged spatially.

*K.3 The student, given an ordered set of ten objects and/or pictures, will indicate the ordinal position of each object, first through tenth, and the ordered position of each object.*

UNDERSTANDING THE STANDARD

· Understanding the cardinal and ordinal meanings of numbers are necessary to quantify, measure, and identify the order of objects.

· An ordinal number is a number that names the place or position of an object in a sequence or set (e.g., first, third). *Ordered position*, *ordinal position*, and *ordinality* are terms that refer to the place or position of an object in a sequence or set.

· The ordinal position is determined by where one starts in an ordered set of objects or sequence of objects.

· The ordinal meaning of numbers is developed by identifying and verbalizing the place or position of objects in a set or sequence (e.g., the student’s position in line when students are lined up alphabetically by first name).

**K.4 The student will**

a) count forward to 100 and backward from 10;

b) identify one more than a number and one less than a number; and

c) count by fives and tens to 100.

UNDERSTANDING THE STANDARD

· Counting skills are essential components of the development of number ideas; however, they are only one of the indicators of the understanding of numbers.

· Counting forward by rote advances the child’s development of sequencing. The natural numbers are 1, 2, 3, 4…. The whole numbers are 0, 1, 2, 3, 4…. Students should count the whole numbers 0, 1, 2, 3, 4,...

· Counting backward by rote lays the foundation for subtraction. Students should count backward beginning with 10, 9, 8,through 3, 2, 1, 0.

· Counting forward and backward leads to the development of counting on and counting back.

· The patterns developed as a result of skip counting are precursors for recognizing numeric patterns, functional relationships, and concepts underlying money, time telling, and multiplication. Powerful models for developing these concepts include, but are not limited to, counters, hundred chart, and calculators.

· Skip counting by fives lays the foundation for reading a clock effectively and telling time to the nearest five minutes, counting money, and developing the multiplication facts for five.

· Skip counting by tens is a precursor for use of place value, addition, counting money, and multiplying by multiples of 10.

· Calculators can be used to display the numeric patterns that result from skip counting.

**K.5 The student will identify the parts of a set and/or region that represent fractions for halves and fourths. **

UNDERSTANDING THE STANDARD .

A fraction is a way of representing part of a whole (as in a region/area model) or part of a group (as in a set model).

. In each fraction model, the parts must have the same area.

. The fractional parts of a set model are subsets of an equal number. For example, in a set of ten cubes, each half would have a subset of five cubes.. Informal, integrated experiences with fractions at this level will help students develop a foundation for deeper learning at later grades. Understanding the language of fractions furthers this development (e.g., *fourths *means "four equal parts of a whole" or 1/4 represents one of four parts of equal size when a pizza is shared among four students).

** **

**K.2 The student, given a set containing 15 or fewer concrete objects, will**

a) tell how many are in the set by counting the number of objects orally;

b) write the numeral to tell how many are in the set; and

*K.3 The student, given an ordered set of ten objects and/or pictures, will indicate the ordinal position of each object, first through tenth, and the ordered position of each object.*