# 1.1 - Counting 0-110

The student will

a)  count forward orally by ones to 110, starting at any number between 0 and 110;

b)  write the numerals 0 to 110 in sequence and out-of-sequence;

c)  count backward orally by ones when given any number between 1 and 30; and

d)  count forward orally by ones, twos, fives, and tens to determine the total number of objects to 110.

### BIG IDEAS

• So that by understanding counting to 110 and 1:1 correspondence,I will begin to understanding place value
• So that I can count things in everyday life (collections, materials for school, etc)
• So that by learning skip counting, I can count groups faster.

### UNDERSTANDING THE STANDARD

• There are three developmental levels of counting:
•     rote sequence;
•     one-to-one correspondence; and
•     the cardinality of numbers.
• Counting involves two separate skills: verbalizing the list (rote sequence counting) of standard number words in order (“one, two, three,¼”) and connecting this sequence with the items 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.
• The last number stated represents the number of objects in the set. The total number of objects in the set is known as the cardinality of the set.  After having a student count a collection of objects, the teacher may be able to assess whether the student has cardinality of number by asking the question, “How many are there?”  Students who do not yet have cardinality of number are often unable to tell you how many objects there were without recounting them.
• Rote counting is a prerequisite skill for the understanding of addition (one more), subtraction (one less), and the ten-to-one concept of place value.
• Conservation of number is applied when students understand that a group of 10 objects is still 10 objects regardless of whether they are arranged in a cup, group, stack, etc.
• Unitizing is the concept that a group of objects can be counted as one unit (e.g., 10 ones can be counted as 1 ten.)
• Using objects and asking the questions such as “How many are in each group?” or “How many groups are there?” and” What is the total number you have?” supports students as they learn to skip count and helps to solidify their understanding of cardinality and assists in developing multiplicative reasoning.
• The patterns developed as a result of skip counting are precursors for recognizing numeric patterns, functional relationships, and concepts underlying money, time, and multiplication.
• Powerful models for developing these concepts include counters, number paths, and hundred charts.

Example of a Number Path

 1 2 3 4 5 6 7 8 9 10

• A number path is a counting model where each number is represented within a square and the squares can be clearly counted.
• A number line is a length model with each number being represented by its length from zero.  When young children use a number line as a counting tool, they often confuse what should be counted, the numbers or the spaces between the numbers.  A number path is more appropriate for students at this age.
• Counting backward by rote lays the foundation for subtraction.
• Skip counting by twos supports the development of the concept of even numbers and the development of multiplication facts for two
• Skip counting by fives lays the foundation for telling time to the nearest five minutes, counting money, and developing the multiplication facts for five.
• Skip counting by tens is a precursor for place value, addition (10 more), subtraction (10 less), counting money, and developing the multiplication facts for ten.
• Manipulatives that can be physically connected and separated into groups of tens and leftover ones, such as connecting or snap cubes, beans on craft sticks, pennies in cups, bundle of sticks, or beads on pipe cleaners should be used.
• Ten-to-one trading activities with manipulatives on place value mats and base ten blocks are more appropriate in grade two.

### ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

• Count forward orally, by ones, from 0 to 110 starting at any number between 0 and 110. (a)
• Use the oral counting sequence to tell how many objects are in a set. (a)
• Write numerals 0-110 in sequence and out of sequence. (b)
• Count backward orally by ones when given any number between 1 and 30. (c)
• Count forward orally by ones, twos, fives, and tens to determine the total number of objects to 110. (d)

### KEY VOCABULARY

Updated: Aug 22, 2018