## primary Block:

# Mathematics

Learners work individually, in partners, or in groups to explore the foundations of numbers, patterns, and measurement, which develops the ability of thinking critically about information. They count, combine, and compare quantities, and investigate patterns, measurement, and data within their environment. Learners develop their understanding through concrete, pictorial, and/or symbolic representations of mathematics. These explorations include the use of physical materials, drawings and words in contextually meaningful languages, and symbols. Learners share their ideas and findings. They ask and consider further questions and apply their understanding to familiar concepts and events. Positive mathematics experiences will build confidence and enjoyment for future learning.

#### CONTEXTS AND CONCEPTS

##### EXPLORATION

**STRATEGIES**

- Familiarizing with and discussing procedures and strategies
- Explaining sorting rules

**PROCESSES**

- Using fingers and manipulatives
- Active situations: the physical joining/separating of sets
- Static situations: the implied joining/separating of sets
- Direct and indirect measurement
- Creating concrete graphs

**FLUENCY**

- Computation skills and representations of numbers
- Subitizing
- Stable order principle
- Order irrelevance principle
- Conservation principle
- Cardinality principle
- Mathematical abstraction
- Part-part-whole relationships
- Unitizing

**COMMUNICATION**

- Representing mathematics concretely, pictorially, symbolically
- Saying number names in a variety of languages
- Using home and community languages that are contextually meaningful
- Becoming familiar with math vocabulary, math symbols and math models
- Numeral writing
- Mathematical expressions

### Strand: Number

#### Big Idea: Number Sense

**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)

#### Big Idea: Operations

**Skill Descriptor:** *No skill descriptors for kindergarten*

### Strand: Shape and Space

#### Big Idea: Measurement

**Skill Descriptor:** Relate life to measurements of time.

**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

### Strand: Number

#### Big Idea: Number Sense

**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.”

**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

#### Big Idea: Operations

**Skill Descriptor:** Estimate quantities using benchmarks or referents.

**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

### Strand: Shape and Space

#### Big Idea: Measurement

**Skill Descriptor:** Relate life to measurements of time.

**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

### Strand: Number

#### Big Idea: Number Sense

**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

#### Big Idea: Operations

**Skill Descriptor:** Estimate quantities using benchmarks or referents.

**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

### Strand: Shape and Space

#### Big Idea: Measurement

**Skill Descriptor:** Relate life to measurements of time.

**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.

**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