Skill Descriptor: Describe numbers, ways of representing numbers, relationships among numbers, and number systems.

Global Competencies: CM, CTPS, SGC

Achievement Indicators:

• Name the number that comes before a given number
• Name the number that comes after a given number
• Place benchmarks of five and 10
• Recite a range of number names within the counting sequence
• Match numerals pictorially
• Describe two sets using comparative language such as more, fewer, as many as, the same number, etc.
• Construct sets corresponding to given amounts concretely
• Partition quantities into two parts and name the amount in each part
• Construct sets to show more than, fewer than, or as many as a given set
• Identify patterns that repeat
• Demonstrate consistently the counting sequence stays consistent
• Demonstrate consistently one-to-one correspondence of objects or sets
• Demonstrate consistently sets with respectively different-sized objects can represent the same quantity

Skill Descriptor: Explore strategies for organizing numbers to determine “how many.”

Global Competencies: CTPS

Achievement Indicators:

• Identify quantities to five (without counting) concretely, pictorially, and symbolically
• Explain the process used to determine “how many”
• Demonstrate consistently counting can begin with any object in a set and result in the same total count
• Demonstrate consistently each object in a set being counted is only given one count
• Demonstrate consistently the last count of a set represents the total amount in the set
• Demonstrate consistently the count for a set stays consistent regardless of the distribution (the spacing of objects)

Skill Descriptor: No skill descriptors for kindergarten

Skill Descriptor: Relate life to measurements of time.

Global Competencies: CM, CTPS

Achievement Indicators:

• Describe time as a sequence of events using language like first, next, yesterday, today, tomorrow, longer, shorter, before, after, next, a long time ago
• Name days of the week
• Name months of the year
• Identify the month that comes before, and the month that comes after, a given month
• Order days of the week
• Provide examples of activities that commonly occur during a.m. and commonly occur during p.m.

Skill Descriptor: Compare a single measurement attribute of various shapes and objects.

Global Competencies: CTPS

Achievement Indicators:

• Describe concrete 3D objects using language like big, little, round, like a box, like a can, etc.
• Compare length or height of concrete 3D objects using language like shorter, longer or taller, almost the same, etc.
• Compare mass or weight of concrete 3D objects using language like lighter, heavier, almost the same, etc.
• Compare volume or capacity of concrete 3D objects using language like less, more, bigger, smaller, almost the same, etc.
• Sort familiar concrete 3D objects using a single attribute
• Represent concrete 3D objects concretely

Skill Descriptor: Describe numbers, ways of representing numbers, relationships among numbers, and number systems.

Global Competencies: CM, CTPS, SGC

Achievement Indicators:

• Describe examples of numbers in the environment and other contexts
• Name numerals
• Begin to read and write number words independently (e.g., one, two, three, four, five, six, seven, eight, nine, 10)
• Name numbers that are one more, two more, one less, or two less than a given number
• Place benchmarks zero, five, 10 and 20
• Represent numbers that are one more, two more, one less, or two less than a given number
• Represent numbers to 20 concretely
• Represent a set that has more, fewer, and as many as a given set
• Represent given numbers in a variety of equal groups with and without single leftovers
• Compare sets to referents using language such as more, fewer, as many, etc.
• Recite ranges of number names within the counting sequence
• Skip count by twos, fives, and 10s starting at zero
• Count objects within sets using “counting on”
• Partition quantities into two parts, and name the amount in each part
• Construct equal and unequal sets of concrete 3D objects (same shape and mass)
• Determine if sets are equal or unequal in amount
• Demonstrate consistently that the base 10 number system groups in 10s once the count exceeds nine

Skill Descriptor: Describe strategies for organizing numbers to determine “how many.”

Global Competencies: CM, CTPS

Achievement Indicators:

• Identify quantities to five (without counting) concretely, pictorially, and symbolically
• Identify quantities to 10 concretely, pictorially, and symbolically
• Explain the process used to determine “how many”
• Explain the process used to determine if sets are equal or unequal
• Record different representations of equal quantities

Skill Descriptor: Estimate quantities using benchmarks or referents.

Global Competencies: CM, CTPS

Achievement Indicators:

• Select an estimation from multiple possible estimates
• Estimate quantities up to 20 using benchmarks or referents

Skill Descriptor: Apply foundational addition and subtraction facts with flexibility, efficiency and accuracy to solve problems.

Global Competencies: CL, CM, CTPS, ICE

Achievement Indicators:

• Represent addition and subtraction in numbers to 10
• Represent numbers, and addition and subtraction actions, presented in mathematical problems pictorially or symbolically
• Create problems for addition and subtraction that connect to student experiences

Skill Descriptor: Explore adding and subtracting strategies in-context.

Global Competencies: CTPS, SASM

Achievement Indicators:

• Describe personal strategies used to determine addition facts and corresponding subtraction facts
• Express addition facts for corresponding subtraction facts and vice-versa
• Apply personal adding and subtracting strategies
• Apply foundational adding and subtracting strategies

Skill Descriptor: Relate life to measurements of time.

Global Competencies: CM, CTPS

Achievement Indicators:

• Order months of the year
• Read dates on calendars
• Relate duration to measurements of time
• Identify activities that can or cannot be accomplished in minutes, hours, days, months, and years
• Explain time in relation to cycles (daily routine, nature, seasons, culture, etc.)

Skill Descriptor: Compare measurement attributes of various shapes and objects.

Global Competencies: CTPS

Achievement Indicators:

• Sort familiar 2D shapes
• Sort familiar concrete 3D objects
• Identify common attributes to compare objects
• Determine longest and shortest by ordering 2D shapes and concrete 3D objects
• Determine heaviest and lightest by comparing concrete 3D objects
• Determine most and least capacity by filling concrete 3D objects
• Determine greatest and least area by covering concrete 3D objects

Skill Descriptor: Describe numbers, ways of representing numbers, relationships among numbers, and number systems.

Global Competencies: CM, CTPS, SGC

Achievement Indicators:

• Describe examples of repeating patterns in the environment and other contexts
• Name numerals
• Read and write number words from zero to 20
• Identify the position of numerals or objects in sequences by using ordinal numbers up to and including tenth
• Identify even and odd numbers in sequences
• Represent place value of numbers concretely
• Represent numbers and place value to 100
• Place benchmarks zero, five, 10, 20, 50, 100
• Skip count by twos and fives starting at multiples of two and five
• Skip count by 10s starting at any digit
• Apply “counting on” for groups of two, five, or 10
• Order sets of numbers in ascending and descending order
• Sort sets of numbers by even and odd
• Compare ordinal position of specific numerals or concrete 3D objects in two different sequences
• Explain the place value of each digit of given numbers
• Predict elements or extend repeating patterns
• Create or explain repeating pattern rules

Skill Descriptor: Justify choices to determine “how many” using personal strategies.

Global Competencies: CTPS

Achievement Indicators:

• Identify quantities to 20 using groups concretely, pictorially, and symbolically
• Explain the process used to determine “how many”
• Sort sets as equal or unequal
• Verify the equality of quantities of concrete 3D objects (same shape and mass) using a scale
• Justify whether sides of number sentences are equal (=) or not equal (≠)
• Record equalities and inequalities

Skill Descriptor: Estimate quantities using benchmarks or referents.

Global Competencies: CM, CTPS

Achievement Indicators:

• Select an estimation from multiple possible estimates
• Estimate quantities up to 100 using benchmarks or referents
• Estimate the number of groups of 10 in quantities

Skill Descriptor: Apply foundational and derived addition and subtraction facts with flexibility, efficiency, and accuracy to solve problems.

Global Competencies: CM, CTPS, SASM

Achievement Indicators:

• Represent addition and subtraction derived facts with answers to 20 concretely and pictorially
• Record addition and subtraction symbolically
• Create addition or subtraction number sentences and story problems
• Describe strategies used to solve problems missing addends and/or subtrahends
• Explain why the order in which numbers are added does not affect the sum
• Explain why the order in which numbers are subtracted will affect finding the difference
• Explain why the sum and difference is the same as the addend and minuend when adding and subtracting zero

Skill Descriptor: Explore adding and subtracting strategies in-context

Global Competencies: CTPS, SASM

Achievement Indicators:

• Apply personal strategies for addition and subtraction to solve problems
• Explain personal or foundational strategies used to solve problems
• Justify choice of adding and subtracting strategies for efficiency
• Apply strategies to demonstrate mathematical flexibility

Skill Descriptor: Relate life to measurements of time.

Global Competencies: CM, CTPS

Achievement Indicators:

• Describe intervals between events using units of time such as seconds, minutes, hours, weeks, months, years, decades, etc.
• Describe time using language such as minutes to, minutes after the hour, etc.
• Match dates in a written format to dates on a calendar
• Record dates in a variety of formats
• Express significant events using calendar dates
• Explain personal referents for minutes and hours
• Measure time using standard and non-standard units

Skill Descriptor: Compare measurement attributes of shapes and objects using non-standard units.

Global Competencies: CM, CTPS

Achievement Indicators:

• Sort regular and irregular 2D shapes using two attributes
• Sort concrete 3D objects using two attributes
• Estimate number of non-standard units in measurements of concrete 3D objects
• Estimate lengths that are not straight lines
• Select non-standard units for measuring length/mass
• Measure concrete 3D objects using non-standard units many times
• Measure lengths that are not straight lines
• Estimate number of non-standard units needed for measurements
• Explain results of measuring, changing the orientation of 2D shapes or concrete 3D objects, and remeasuring
• Explain which given non-standard units may be better choices for measuring length and for measuring mass
• Explain why number of units of measure will vary depending upon units of measure used
• Explain why overlapping or leaving gaps does not result in accurate measures