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 \(0\)–\(20\).

Supportive Teaching Practices/Adults May:

1. Use fingers on both hands to represent addition.
2. Ask a child with five crackers, “If you eat three of your crackers, how many will you have left?”
3. Ask "How many more?" questions, such as, "We have three children in this group. How many more children do we need to make a group of five?"

Examples of Learning/Children May:

1. Add a group of three and a group of two, counting “One, two three … ” and then counting on “Four, five!” while keeping track using their fingers.
2. Take three away from five, counting “Five, four, three … two!” while keeping track using their fingers.
3. Say after receiving more crackers at snack time, “I had two and now I have four.”
4. Predict what will happen when one more object is taken away from a group of five or fewer objects, and then verify their prediction by taking the object away and counting the remaining objects.

Coherence Connections:

1. This expectation represents major work of the grade.
2. Between \(36\)–\(60\) months, children develop beginning understandings of adding and subtracting with the help of objects and adult support.
3. In preschool, students should work with small numbers and simpler problem subtypes (see Appendix, Table 1).
4. In kindergarten, students add and subtract within \(10\) using objects or drawings to represent problems and fluently add and subtract within \(5\).

Supportive Teaching Practices/Adults May:

1. Provide everyday opportunities to explore numbers and patterns, such as setting the table with a cup, plate, and fork for each person.
2. Provide opportunities to observe naturally occurring patterns within the indoor and outdoor environments, such as looking at patterns in the bricks of a building or patterns in art and design.
3. Introduce songs and movement patterns where children can extend and grow the pattern.

Examples of Learning/Children May:

1. Use art materials and other objects to create or replicate patterns (e.g., weaving, stringing beads, stacking blocks, or drawing repeating pictures).
2. Recognize patterns in a story or song.
3. Identify two blocks, one red and one blue, as the core unit of a longer pattern using alternating red and blue blocks.
4. Sequence story cards to show beginning, middle, and end.

Coherence Connections:

1. This expectation supports the major work of the grade.
2. Between \(36\)–\(60\) months, children recognize and work with simple patterns (like ABAB) in different forms, such as patterns of objects, numbers, sounds, and movements.
3. In preschool, students may recognize and duplicate more complicated patterns, such as ABC, ABB, and AABB.
4. In kindergarten, pattern recognition is embedded in and focused on early numeracy, such as counting by tens, number composition/decomposition, making tens, describing attributes of objects, and classifying objects into categories.

Supportive Teaching Practices/Adults May:

1. Follow a pictorial recipe and let children measure, pour, and stir the ingredients while asking questions like, “How many cups of flour does the recipe show we need to put in the bowl?”
2. Provide opportunities for children to sort, classify and group household objects and materials.
3. Ask questions of measurement (e.g., “How many steps does it take to walk from the front door to your cubby?” or “How many blocks long is your arm?”).
4. Offer a variety of measuring tools and models, such as rulers, yardsticks, measuring tapes, measuring cups, scales, and thermometers. (Children may not use each of these correctly, but they are developing early understandings of how tools measure things.)
5. Provide opportunities for children to use non-standard measuring tools such as cubes, paperclips, blocks, etc.

Examples of Learning/Children May:

1. Sort objects by physical characteristics such as a color or size.
2. Group objects according to their size, using standard and nonstandard forms of measurement (e.g., height, weight, length, color, or brightness).
3. Explore various processes and units for measurement and begin to notice different results of one method or another.

Coherence Connections:

1. This expectation is in addition to the major work of the grade.
2. Between \(36\)–\(60\) months, children develop an understanding that attributes can be described and compared in simple ways, such as one child being taller than another.
3. In preschool, this expectation connects with counting, comparing numbers, and comparing shapes.
4. In kindergarten, students describe multiple measurable attributes of an object and make direct comparisons of two objects with a measurable attribute in common.

Supportive Teaching Practices/Adults May:

1. Use a sensory table with various bowls, cups, or other containers to encourage activities with shapes and sorting.
2. Provide children with puzzles made of simple geometric shapes and encourage saying the names of shapes as they play.
3. Discuss geometric shapes in terms of their attributes, such as “This is a circle. It’s perfectly round with no bumps or corners. This is a triangle. It has three sides and three angles.”
4. Use a variety of lengths and angles in their shapes (such as scalene triangles, long and thin rectangles) as well as more common configurations of shapes (such as equilateral triangles).

Examples of Learning/Children May:

1. Match, sort, group, and name basic shapes found outside or in the classroom.
2. Use pattern tiles to make shapes out of other shapes, such as putting two squares side-by-side to make a non-square rectangle.
3. Put away blocks and/or tiles into different containers based on the number or length of sides.

Coherence Connections:

1. This expectation is in addition to the major work of the grade.
2. Between \(36\)–\(60\) months, children start by recognizing circles and squares and then add triangles and other shapes. As understanding of shape develops, children identify sides and angles as distinct parts of shapes.
3. In preschool, this expectation connects with measuring and comparing objects by their attributes.
4. In kindergarten, students identify and describe squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres.

Supportive Teaching Practices/Adults May:

1. Provide opportunities for conversation using everyday words to indicate space location, shape, and size of objects, saying things like, "You crawled under the picnic table, over the tree stump, and now you are in the tunnel slide!"
2. Help children organize toys, pointing out concepts such as “in,” “on,” and “beside.”

Examples of Learning/Children May:

1. Use the vocabulary of geometry and position to describe shapes within the room and surrounding environment.
2. Understand relational directions, such as “Please put a mat under each plate.”

Coherence Connections:

1. This expectation is in addition to the major work of the grade.
2. Between \(36\)–\(60\) months, students develop spatial vocabulary and become able to follow directions involving their own position in space.
3. In preschool and early elementary, students work with shapes and their attributes in increasingly sophisticated ways over time.
4. In kindergarten, students describe objects in the environment using names of shapes and describe the relative positions of these objects using terms such as above, below, in front of, behind, and next to.