Colorado Academic Standards Online

Colorado Essential Skills and Mathematical Practices:

1. Recognize that the number sequence from \(1\) to \(9\) repeats between the decade numbers, except in the spoken numbers between \(10\) and \(20\). (MP7)
2. Reason that counting to \(100\) by tens reaches the same number as can be counted repeatedly by ones. (MP8)

Inquiry Questions:

1. When might you want to count by tens instead of ones?
2. When might you want to start counting from a number other than one?
3. What number can we use to show we have nothing to count?

Coherence Connections:

1. This expectation represents major work of the grade.
2. In preschool, students understand that number words have a sequence and that the words are separate (not "onetwothree").
3. In kindergarten, this expectation is key to several progressions of learning: (a) from saying the counting words to counting out objects, (b) from counting to counting on, and (c) from spoken number words to written base-ten numerals to base-ten system understanding.
4. In Grade 1, students extend the counting sequence to \(120\).

Colorado Essential Skills and Mathematical Practices:

1. Progress from thinking about numbers as the result of the process of counting to abstractly thinking about numbers as mental objects of their own—especially the quantity \(10\). (MP2)
2. Explain how the number reached when counting on is a relationship between the quantity started from and the quantity added. (MP3)
3. Make counting efficient by following rows, columns, or other patterns in a group of arranged objects. (MP7)

Inquiry Questions:

1. How is counting to five different from the number five?
2. What number is one larger than four? What number is one larger than seven?

Coherence Connections:

1. This expectation represents major work of the grade.
2. In preschool, students build conceptions of what whole numbers mean, of subitizing, of one-to-one correspondence between verbal counting and objects, and of cardinality.
3. In kindergarten, this expectation is key to several progressions of learning: (a) from saying the counting words to counting out objects, (b) from counting to counting on, and (c) from spoken number words to written base-ten numerals to base-ten understanding.
4. In Grade 1, students use their understanding of counting and cardinality to add and subtract within \(20\).

Colorado Essential Skills and Mathematical Practices:

1. Make reasoned arguments about the relative sizes of groups, such as by matching objects of two groups and seeing which has extra objects, or by counting the objects in each group and seeing which has the number further in the counting sequence. (MP3)
2. Use precise language to describe why one quantity is less than, greater than, or equal to another, and avoid mixing and misusing different ways of quantifying such as dimension, weight, or magnitude. (MP6)

Inquiry Questions:

1. Other than counting, how might you decide whether one set has more objects than another?
2. Which is more, \(3\) small cookies or \(2\) big cookies? What makes this difficult to answer?

Coherence Connections:

1. This expectation represents major work of the grade.
2. In preschool, students build an understanding of same versus different numbers of items, numbers of objects versus their size, and ordering from first to fifth.
3. In kindergarten, this expectation is key to several progressions of learning: (a) from counting to counting on and (b) from comparison by matching to comparison by numbers to comparison involving adding and subtracting.
4. In Grade 1, students build an understanding of ten and place value with two-digit numbers. Students also organize data into categories and compare how many more or less are in one category than in another.

Colorado Essential Skills and Mathematical Practices:

1. Be precise in drawings, diagrams, and numerical recordings about objects or symbols that represent ones and objects or symbols that represent tens. (MP6)
2. See the structure of a number as composed of its base-ten units. (MP7)
3. Repeat the reasoning afforded by the uniformity of the base-ten system, where \(10\) copies compose 1 base-ten unit of the next highest value. (MP8)

Inquiry Questions:

1. Can you show the number \(13\) as ten ones and some more ones? How many more ones than tens are there?
2. In the number \(11\), what makes the "\(1\)" on the left different from the "\(1\)" on the right? Could you show this with objects or a diagram?
3. What would a number called "ten four" look like? What word do we usually say for this number?
4. Why might someone call the number \(17\) “ten seven?”

Coherence Connections:

1. This expectation represents major work of the grade.
2. In preschool, students develop conceptions of addition and subtraction when adding to and taking away from small collections of objects.
3. In kindergarten, this expectation is part of a progression from comparison by spoken number words to written base-ten numerals to base-ten system understanding.
4. In Grade 1, students build an understanding of ten and place value with two-digit numbers.