Colorado Academic Standards Online

Supportive Teaching Practices/Adults May:

1. Count and use numbers as they play with children.
2. Take advantage of every opportunity to count with children in a practical and authentic setting.

Examples of Learning/Children May:

1. Read stories, sing songs, and act out poems and finger plays that involve counting, numerals, and shapes.
2. Practice saying a sequence of number words.
3. Respond to the question, "What comes after four?" with "One, two, three, four … five!"

Coherence Connections:

1. This expectation represents major work of the grade.
2. Between \(24\)–\(36\) months, children say or sign some number words in sequence, starting with one, and understand that counting words are separate words, such as "one," "two," "three," versus "onetwothree."
3. In preschool, learning the counting sequence is part of learning progressions that go (a) from saying the counting words to counting out objects and (b) from speaking number words to writing base-ten numerals.
4. In kindergarten, students count to \(100\) by ones and tens and count forward from a given number.

Supportive Teaching Practices/Adults May:

1. Hold five or fewer objects in a closed hand, then open it briefly for the child, close it again, and ask, "How many did you see?"
2. Quickly show children a card with five or fewer dots, then hide it and ask who can say how many dots they saw.
3. Ask children to place their hands where they can't see them, then show a small number on their fingers, then have the children check their work by looking at their hands.

Examples of Learning/Children May:

1. Play with a friend and say without counting, "I have five big rocks and you have five little rocks. We have the same."
2. Find fewer objects or objects in patterns (like two rows of \(2\) to make four) easier to subitize.

Coherence Connections:

1. This expectation supports the major work of the grade.
2. Between \(36\)–\(60\) months, children develop an understanding of what whole numbers mean and become increasingly able to quickly recognize the number of objects in a small set (known as subitizing).
3. In preschool, subitizing facilitates efficient counting.
4. In kindergarten, students count to determine the number of up to \(20\) arranged or up to \(10\) scattered objects.

Supportive Teaching Practices/Adults May:

1. Play age-appropriate games that involve counting spaces or objects.
2. Count to five from thumb to pinky on an open hand, then close the hand except for the pinky and ask, "How many fingers are still showing?" to see if a child answers one or five.
3. Help children count by pointing to objects or drawings of objects, then confirming the total by asking, "So how many are there altogether?"
4. Provide opportunities to count objects for lunch, such as plates, napkins, and cups.

Examples of Learning/Children May:

1. Match a group of \(1\) to \(10\) objects with written and spoken numbers.
2. Play simple games that match numbers to a movement of spaces on a game board.
3. Take a specified number of crackers from a bowl during snack time.

Coherence Connections:

1. This expectation represents major work of the grade.
2. Between \(36\)–\(60\) months, children coordinate verbal counting with objects by pointing at each object for each number word (known as one-to-one correspondence) and develop an understanding that the last number in the sequence represents how many in the group (known as cardinality).
3. In preschool, students connect the process of counting to a conceptual understanding of cardinality.
4. In kindergarten, students count to determine the number of objects using one-to-one correspondence and cardinality for up to \(20\) objects in a line or \(10\) scattered objects.

Supportive Teaching Practices/Adults May:

1. Have children group and order materials when cleaning up.
2. Describe quantities using vocabulary including more than, less than, and equal to.
3. Provide opportunities for children to count, group, and order objects and materials.
4. Put four counting chips inside a circle and one chip outside the circle, then ask, "Which has more, inside or outside? Which has fewer chips?"

Examples of Learning/Children May:

1. Count, group, and sort objects and materials.
2. Be able to express a preference for greater numbers of things (such as candy or toys) when comparing groups of different sizes.
3. Say phrases like, "There are more cookies in this box," or "There are fewer pencils on that table than on this one."
4. Identify which item is first, second, third, etc., when pointing to items or talking about events that are ordered.

Coherence Connections:

1. This expectation represents major work of the grade.
2. Between \(36\)–\(60\) months, children begin to count and compare same-size objects (with adult assistance) and begin to understand that the number of objects is independent of the size of the objects.
3. In kindergarten, students identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group for up to \(10\) objects. Students also compare two numbers between \(1\) and \(10\) presented as written numerals.

Supportive Teaching Practices/Adults May:

1. Play games with children where spinning a wheel with numbers or the number written on a card is associated with the need to count that number of objects or spaces.
2. Help a child write or trace using any writing tool the numeral corresponding to his or her age.
3. Support the use of a numeral by connecting it to a group of objects or a picture of objects to help students associate the numeral to a quantity.

Examples of Learning/Children May:

1. Match a group of \(1\) to \(5\) objects with written and spoken numbers.
2. Copy a printed numeral using their own handwriting.
3. Play games that involve matching numerals to numbers of objects, such as dots on cards.

Coherence Connections:

1. This expectation supports the major work of the grade.
2. Between \(36\)–\(60\) months, children develop an understanding that a written numeral represents a quantity and uses symbols, like tally marks, to represent numerals.
3. In preschool, work with numerals is still in its early stages. Writing numerals does not become a focus until kindergarten, but it can be done in preschool to support other work in mathematics and writing.
4. In kindergarten, students write numbers from \(0\) to \(20\) and associate a number of objects with the written numerals \(0\)–\(20\).