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# Standards - Mathematics

### Knowledge

Students know:
• how to count by ones and tens orally. This includes counting forward and counting backward.

### Skills

Students are able to:
• orally count forward.
• orally count backward.

### Understanding

Students understand that:
• Counting from 0 to 100 is a sequence.

### Vocabulary

• Count forward orally
• Count backwards orally

### Knowledge

Students know:
• how to rote count from 0 to 100 starting with any given number.

### Skills

Students are able to:
• orally count.

### Understanding

Students understand that:
• Counting from 0 to 100 is a sequence and you can begin with any number.

• Count

### Knowledge

Students know:
• how to match numeral name with sets of objects.

### Skills

Students are able to:
• write numerals from 0 to 20.
• Represent numbers from 0 to 20.

### Understanding

Students understand that:
• a written numeral represents a number of objects.

• Numeral
• Number

### Knowledge

Students know:
• Use one to one correspondence when counting objects.
• how to rote count in consecutive order.

### Skills

Students are able to:
• count objects with one to one correspondence.
• Indicate the number of objects.
• Explain one more.

### Understanding

Students understand that:
• a number represents a quantity.

### Vocabulary

• Cardinality
• One to one correspondence
• Hierarchical inclusion

### Knowledge

Students know:
• how to use one-to-one correspondence when counting objects.
• how to demonstrate number word sequence.

### Skills

Students are able to:
• count sequentially.
• Use one to one correspondence.
• Subitize.
• Represent a number of objects within 0 to 20.

### Understanding

Students understand that:
• numbers name quantities regardless of their arrangement.

### Vocabulary

• Rectangular array
• Subitize

### Knowledge

Students know:
• how to identify which number is larger and which number is smaller.
• number word sequence.

### Skills

Students are able to:
• Count sequentially.

### Understanding

Students understand that:
• a set of objects is either greater than, less than, or equal to another set of objects.

• Compare
• Greater than
• More than
• Less than
• Fewer than
• Equal

### Knowledge

Students know:
• how to identify which number is larger and which number is smaller with number 0 - 10.
• number word sequence.

### Skills

Students are able to:
• count sequentially.
• Apply strategies for comparing numbers.

### Understanding

Students understand that:
• successive number names refer to quantities that are larger than the previous numbers in the counting sequence.

### Vocabulary

• Relational thinking
• Inequality symbols

### Knowledge

Students know:
• how to represent addition and subtraction using models, pictures or symbolic representations.
• how to explain representations of quantities.

### Skills

Students are able to:
• Represent quantities and operations physically, pictorially, or symbolically.
• Use informational and mathematical language to communicate the connections among addition and subtraction.

### Understanding

Students understand that:
• both putting together and adding to can be viewed as addition.
• both taking apart and taking from can be viewed as subtraction.

• Expression
• Equation

### Knowledge

Students know:
• Characteristics of addition and subtraction contexts such as putting together, adding to, taking apart, and taking from.

### Skills

Students are able to:
• represent quantities and operations physically, pictorially, or symbolically.
• Strategically use a variety of representations to solve addition and subtraction word problems.
• Use informal and mathematical language to communicate addition and subtraction representations.
• Accurately compute sums and differences.

### Understanding

Students understand that:
• both putting together and adding to can be viewed as addition.
• both taking apart and taking from can be viewed as subtraction.
• Mathematical problems can be solved using a variety of strategies and representations.

### Vocabulary

• Concrete objects
• Drawings

### Knowledge

Students know:
• "equal to" and the concept of equality meaning "the same as."
• Addition is putting together numbers and subtraction is taking apart numbers.

### Skills

Students are able to:
• Represent quantities physically, pictorially, and symbolically.

### Understanding

Students understand that:
• quantities may be named in a variety of ways.

• Decompose
• Equation

### Knowledge

Students know:
• Characteristics of addition and subtraction contexts such as putting together, adding to, taking apart, and taking from.

### Skills

Students are able to:
• Represent quantities and operations physically, pictorially, or symbolically.

### Understanding

Students understand that:
• two smaller quantities join to create a larger target quantity.
• A quantity may be broken into smaller quantities.
• Mathematical tools and representations (ten frames and ten fingers) can be used to solve problems efficiently.

• Compose

### Knowledge

Students know:
• characteristics of addition and subtraction contexts such as putting together, adding to, taking apart, and taking from.
• Strategies for efficiently determining sums and differences within five.

### Skills

Students are able to:

### Understanding

Students understand that:
• Fluency involves a mixture of "just knowing" answers, knowing answers from patterns, and knowing answers from the use of strategies. The word fluently is used in the standards to mean accurately, efficiently, and flexibly.

• Fluently

### Knowledge

Students know:
• the number sequence to 19.
• Strategies to decompose a number into tens and ones.

### Skills

Students are able to:
• Use objects to compose and decompose numbers.

### Understanding

Students understand that:
• ten things can be represented as one ten or as ten ones.

• Compose
• Decompose

### Knowledge

Students know:
• how to count.
• Sort objects.
• Category descriptors (e.g. triangles, rectangles, round, curved sides, color, etc).

### Skills

Students are able to:
• sort objects.
• Effectively use strategies to count groups of objects.

### Understanding

Students understand that:
• objects can be grouped into categories based on like characteristics.
• They can gain information from graphs.

### Vocabulary

• Classify
• Venn diagrams
• Pictographs
• Yes/no charts
• Bar graphs
• Symbolic representations
• Pictorial representations

### Knowledge

Students know:
• how to describe similarities and differences in objects.

### Skills

Students are able to:
• Describe measurable attributes of objects using informal language.

### Understanding

Students understand that:
• objects can be described by using measurable attributes.

• Attribute

### Knowledge

Students know:
• how to describe similarities and differences in objects.

### Skills

Students are able to:
• Directly compare two objects and explain which object has more of or less of the attribute.

### Understanding

Students understand that:
• objects and geometric figures have measurable attributes that allow them to be compared.

• Attribute

### Knowledge

Students know:
• 2D and 3D shapes.

### Skills

Students are able to:
• Describe objects in the environment using names of shapes.
• Describe the relative position of objects.

### Understanding

Students understand that:
• the world is made up of geometric shapes.

### Vocabulary

• Two dimensional
• Three dimensional

### Knowledge

Students know:
• 2D and 3D shapes.

### Skills

Students are able to:
• Use geometric reasoning and visual characteristics of shapes to name shapes in a variety of sizes and orientations.

### Understanding

Students understand that:
• geometric shapes can be sorted based on like characteristics.

### Vocabulary

• Two dimensional
• Three dimensional

### Knowledge

Students know:
• Characteristics of 2D and 3D shapes.

### Skills

Students are able to:
• Use geometric reasoning and visual characteristics of shapes to designate shapes as 2D or 3D.

### Understanding

Students understand that:
• geometrics shapes can be grouped into classes of 2D or 3D shapes based on their physical characteristics.

### Vocabulary

• Two dimensional
• Three dimensional

### Knowledge

Students know:
• attributes of shapes (sides, corners, vertices, faces, edges, etc.).
• Informal language to describe these components.

### Skills

Students are able to:
• Use geometric reasoning and attributes to compare and contrast a variety of shapes.

### Understanding

Students understand that:
• geometric shapes can be grouped into classes of shapes that all seem to be alike based on their visual characteristics.

• Attributes

### Knowledge

Students know:
• 2D and 3D shapes (triangle, square, rectangle, hexagon, rhombus, circle, cube, cylinder, sphere, cone).

### Skills

Students are able to:
• Compose shapes with known attributes using a variety of materials (pipe cleaners, marshmallows/toothpicks, etc.).

### Understanding

Students understand that:
• geometric shapes can be constructed and represented using a variety of physical materials.

### Knowledge

Students know:
• 2D and 3D shapes (triangle, square, rectangle, hexagon, rhombus, circle, cube, cylinder, sphere, cone).

### Skills

Students are able to:
• Combine simple shapes to form larger shapes.

### Understanding

Students understand that:
• geometric shapes can be composed of and decomposed into smaller shapes.

### Knowledge

Students know:
• addition and subtraction strategies and models.
• how to form an equation.

### Skills

Students are able to:
• represent quantities and operations (addition & subtraction) with concrete objects, pictorially, or symbolically.
• Use informal and mathematical language to communicate the representations.
• Accurately compute sums and differences.

### Understanding

Students understand that:
• addition is both putting together and adding to. subtraction is taking apart, taking from, and comparisons.
• Mathematical problems can be solved using a variety of strategies. models, and representations.
• variables in the form of blanks, boxes, or letters, represent unknown quantities when representing mathematical situations algebraically.

### Vocabulary

• Change unknown
• Put together
• Take apart
• Compare