Standards - Mathematics

MA19.K.1

Count forward orally from 0 to 100 by ones and by tens. Count backward orally from 10 to 0 by ones.

Unpacked Content

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

MA19.K.2

Count to 100 by ones beginning with any given number between 0 and 99.

Unpacked Content

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.

Vocabulary

  • Count

MA19.K.3

Write numerals from 0 to 20.

Unpacked Content

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.

Vocabulary

  • Numeral
  • Number

MA19.K.3a

Represent 0 to 20 using concrete objects when given a written numeral from 0 to 20 (with 0 representing a count of no objects).

MA19.K.4

Connect counting to cardinality using a variety of concrete objects.

Unpacked Content

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

MA19.K.4c

Indicate that the number of objects in a set is the same regardless of their arrangement or the order in which they were counted.

MA19.K.5

Count to answer “how many?” questions.

Unpacked Content

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

MA19.K.6

Orally identify whether the number of objects in one group is greater/more than, less/fewer than, or equal/the same as the number of objects in another group, in groups containing up to 10 objects, by using matching, counting, or other strategies.

Unpacked Content

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.

Vocabulary

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

MA19.K.7

Compare two numbers between 0 and 10 presented as written numerals (without using inequality symbols).

Unpacked Content

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

MA19.K.8

Represent addition and subtraction up to 10 with concrete objects, fingers, pennies, mental images, drawings, claps or other sounds, acting out situations, verbal explanations, expressions, or equations.

Unpacked Content

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.

Vocabulary

  • Expression
  • Equation

MA19.K.9

Solve addition and subtraction word problems, and add and subtract within 10, by using concrete objects or drawings to represent the problem.

Unpacked Content

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

MA19.K.10

Decompose numbers less than or equal to 10 into pairs of smaller numbers in more than one way, by using concrete objects or drawings, and record each decomposition by a drawing or equation.

COS Examples

Example: 5 = 2 + 3 and 5 = 4 + 1

Unpacked Content

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.

Vocabulary

  • Decompose
  • Equation

MA19.K.11

For any number from 0 to 10, find the number that makes 10 when added to the given number, by using concrete objects or drawings, and record the answer with a drawing or equation.

Unpacked Content

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.

Vocabulary

  • Compose

MA19.K.12

Fluently add and subtract within 5.

Unpacked Content

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:
  • Use addition strategies efficiently.

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.

Vocabulary

  • Fluently

MA19.K.13

Duplicate and extend simple patterns using concrete objects.

Unpacked Content

Knowledge

Students know:
  • how to sort and group objects before being able to duplicate and extend simple patterns.

Skills

Students are able to:
  • Duplicate and extend simple patterns.

Understanding

Students should understand that:
  • looking for, describing, and extending patterns helps them develop the skills in all mathematical situations.

Vocabulary

  • Simple pattern
  • Sequence

MA19.K.14

Compose and decompose numbers from 11 to 19 by using concrete objects or drawings to demonstrate understanding that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.

Unpacked Content

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.

Vocabulary

  • Compose
  • Decompose

MA19.K.15

Classify objects into given categories of 10 or fewer; count the number of objects in each category and sort the categories by count.

Unpacked Content

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.
  • Read and understand graphs.

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

MA19.K.15a

Categorize data on Venn diagrams, pictographs, and “yes-no” charts using real objects symbolic representations or pictorial representations.

MA19.K.16

Identify and describe measurable attributes (length, weight, height) of a single object using vocabulary such as long/short, heavy/light, or tall/short.

Unpacked Content

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.

Vocabulary

  • Attribute

MA19.K.17

Directly compare two objects with a measurable attribute in common to see which object has more of“ or “less of” the attribute and describe the difference.“

COS Examples

Example: Directly compare the heights of two children and describe one child as taller“ or “shorter.”

Unpacked Content

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.

Vocabulary

  • Attribute

MA19.K.18

Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.

Unpacked Content

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

MA19.K.19

Correctly name shapes regardless of their orientations or overall sizes.

Unpacked Content

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

MA19.K.20

Identify shapes as two-dimensional (lying in a plane, flat“) or three-dimensional (“solid”).“

Unpacked Content

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

MA19.K.21

Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (number of sides and vertices or corners“) and other attributes.“

COS Examples

Example: having sides of equal length

Unpacked Content

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.

Vocabulary

  • Attributes

MA19.K.22

Model shapes in the world by building them from sticks, clay balls, or other components and by drawing them.

Unpacked Content

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.

MA19.K.23

Use simple shapes to compose larger shapes.

COS Examples

Example: Join two triangles with full sides touching to make a rectangle.

Unpacked Content

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.
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