#### Math - 2018-19

# 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.

*Adopted: 2016*

### 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*