Standards are the floor. Mastery and understanding are the goal.

Explore how each subject becomes a coherent sequence of knowledge, reasoning, practice, and transfer—not a disconnected checklist.

Kindergarten Math

22 curriculum outcomes with explicit teaching progressions

Select a record to inspect its progression

Counting Cardinality · K.CC.A.1

Count to 100 by ones and tens

Independently count to 100 by ones and by tens. across representations and contexts.

Component progression

  1. 1I can count aloud from 1 to 100 by ones without skipping or repeating a number.
  2. 2I can count aloud by tens (10, 20, 30, ...) up to 100.
  3. 3I can count by ones correctly across a decade boundary, such as from 29 to 30 or 59 to 60.
Counting Cardinality · K.CC.A.2

Count forward from a given number

Independently count forward beginning from a given number within the known sequence, instead of having to begin at one. across representations and contexts.

Component progression

  1. 1I can begin counting aloud from a stated number rather than from 1.
  2. 2I can continue counting forward accurately for several numbers after the given starting point.
  3. 3I can count forward from a given number anywhere within the range up to 100.
Counting Cardinality · K.CC.A.3

Write and match numerals zero through twenty

Independently write numerals from 0 to 20, and represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). across representations and contexts.

Component progression

  1. 1I can write each numeral from 0 to 20 correctly.
  2. 2I can match a written numeral from 0 to 20 to a group of objects with that many items.
  3. 3I can count a group of objects (up to 20) and write the numeral representing that quantity.
Counting Cardinality · K.CC.B.4

Connect counting to cardinality

Independently understand the relationship between numbers and quantities: connect counting to cardinality by pairing each object with one and only one number name and each number name with one and only one object, understanding the last number counted tells the total regardless of the objects' arrangement or the order in which they were counted, and understanding each successive number refers to a quantity one larger. across representations and contexts.

Component progression

  1. 1I can count a group of objects by pairing each object with exactly one number name, without skipping or double-counting.
  2. 2I can state that the last number said when counting a group tells how many objects are in the group, and that this total does not change when the same objects are rearranged or counted in a different order.
  3. 3I can explain that each successive counting number represents a quantity that is one more than the number before it.
Counting Cardinality · K.CC.B.5

Count to answer how-many questions

Independently count to answer 'how many?' questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. across representations and contexts.

Component progression

  1. 1I can count up to 20 objects arranged in a line, array, or circle to answer 'how many?'.
  2. 2I can count up to 10 objects in a scattered arrangement to answer 'how many?', keeping track of which have been counted.
  3. 3I can given a number from 1 to 20, count out that many objects from a larger group.
Counting Cardinality · K.CC.C.6

Compare groups by quantity

Independently identify whether the number of objects in one group (up to 10 objects) is greater than, less than, or equal to the number of objects in another group, using matching and counting strategies. across representations and contexts.

Component progression

  1. 1I can compare two groups of objects by matching them one-to-one to determine which has more, fewer, or the same number.
  2. 2I can count each of two groups of objects and compare the counts to determine which is greater, less, or equal.
  3. 3I can state correctly whether one group has a greater, lesser, or equal number of objects compared to another.
Counting Cardinality · K.CC.C.7

Compare written numerals

Independently compare two numbers between 1 and 10 presented as written numerals, identifying which is greater and which is less. across representations and contexts.

Component progression

  1. 1I can correctly identify each numeral from 1 to 10 by name.
  2. 2I can compare two written numerals between 1 and 10 and state which represents a greater quantity.
  3. 3I can given several numerals between 1 and 10, order them from least to greatest.
Operations Algebraic Thinking · K.OA.A.1

Represent addition and subtraction

Independently represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations. across representations and contexts.

Component progression

  1. 1I can represent an addition situation using objects, fingers, drawings, or acting it out.
  2. 2I can represent a subtraction situation using objects, fingers, drawings, or acting it out.
  3. 3I can connect a concrete addition or subtraction representation to its matching expression or equation.
Operations Algebraic Thinking · K.OA.A.2

Solve addition and subtraction word problems within ten

Independently solve addition and subtraction word problems within 10, using objects or drawings to represent the problem. across representations and contexts.

Component progression

  1. 1I can represent an addition or subtraction word problem within 10 using objects or a drawing.
  2. 2I can solve an addition word problem within 10 by combining the represented quantities.
  3. 3I can solve a subtraction word problem within 10 by removing the represented quantity.
Operations Algebraic Thinking · K.OA.A.3

Decompose numbers into pairs

Independently decompose numbers less than or equal to 10 into pairs in more than one way, recording each decomposition with a drawing or equation. across representations and contexts.

Component progression

  1. 1I can break a number less than or equal to 10 into two parts using objects or a drawing.
  2. 2I can find more than one way to decompose the same number into two parts.
  3. 3I can record each decomposition of a number as an equation.
Operations Algebraic Thinking · K.OA.A.4

Find the number that makes ten

Independently for any number from 1 to 9, find the number that makes 10 when added to the given number, using objects or drawings, and record the answer with a drawing or equation. across representations and contexts.

Component progression

  1. 1I can use objects or a drawing to find how many more are needed to make 10 when starting from a given number.
  2. 2I can record a make-ten fact found concretely as an equation.
  3. 3I can state the number that makes 10 for a given number from 1 to 9 without needing to count out objects.
Operations Algebraic Thinking · K.OA.A.5

Fluently add and subtract within five

Independently fluently add and subtract within 5. across representations and contexts.

Component progression

  1. 1I can add two numbers with a sum of 5 or less without needing to count out objects.
  2. 2I can subtract within 5 without needing to count out objects.
  3. 3I can recall a family of related addition and subtraction facts within 5.
Number Operations Base Ten · K.NBT.A.1

Compose and decompose eleven through nineteen

Independently compose and decompose numbers from 11 to 19 into ten ones and some further ones, using objects or drawings, and record each composition or decomposition with a drawing or equation, understanding these numbers are composed of ten ones and one, two, three, ... nine ones. across representations and contexts.

Component progression

  1. 1I can use objects or a drawing to decompose a number from 11-19 into one group of ten and some ones.
  2. 2I can combine one group of ten ones and a given number of extra ones to form and name the resulting teen number.
  3. 3I can record a teen number's decomposition into ten ones and further ones as an equation, such as 14 = 10 + 4.
Measurement Data · K.MD.A.1

Describe measurable attributes

Independently describe measurable attributes of objects, such as length or weight, and describe several measurable attributes of a single object. across representations and contexts.

Component progression

  1. 1I can identify a measurable attribute of an object, such as its length, height, or weight.
  2. 2I can describe an object using appropriate language for a specific measurable attribute, such as 'long' or 'heavy'.
  3. 3I can describe more than one measurable attribute of the same object.
Measurement Data · K.MD.A.2

Compare two objects by a shared attribute

Independently 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. across representations and contexts.

Component progression

  1. 1I can identify the measurable attribute shared by two objects that will be compared.
  2. 2I can directly compare two objects by the shared attribute, such as lining them up to compare length.
  3. 3I can describe which object has more or less of the attribute and explain how the comparison was made.
Measurement Data · K.MD.B.3

Classify and count objects by category

Independently classify objects into given categories, count the number of objects in each category (category counts of 10 or fewer), and sort the categories by count. across representations and contexts.

Component progression

  1. 1I can sort a group of objects into given categories based on a shared characteristic.
  2. 2I can count the number of objects in each sorted category.
  3. 3I can order the categories from least to greatest (or greatest to least) based on their counts.
Geometry · K.G.A.1

Describe objects using shape names and positions

Independently 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. across representations and contexts.

Component progression

  1. 1I can identify an everyday object in the environment and name its shape, such as square, circle, rectangle, or triangle.
  2. 2I can describe the position of an object relative to another object using a correct spatial word such as above, below, beside, in front of, or behind.
  3. 3I can describe an object in the environment using both its shape name and its position relative to another object.
Geometry · K.G.A.2

Name shapes regardless of orientation or size

Independently correctly name shapes regardless of their orientation or overall size. across representations and contexts.

Component progression

  1. 1I can correctly name common two-dimensional shapes, such as circle, triangle, square, and rectangle, shown in their typical orientation.
  2. 2I can correctly name a shape when it is rotated or turned from its typical orientation.
  3. 3I can correctly name examples of the same shape shown in different sizes.
Geometry · K.G.A.3

Identify shapes as two- or three-dimensional

Independently identify shapes as two-dimensional ('flat') or three-dimensional ('solid'). across representations and contexts.

Component progression

  1. 1I can identify a shape as two-dimensional (flat) and name examples such as circle, square, and triangle.
  2. 2I can identify a shape as three-dimensional (solid) and name examples such as sphere, cube, and cylinder.
  3. 3I can sort a group of shapes and objects into two-dimensional and three-dimensional categories.
Geometry · K.G.B.4

Analyze and compare shapes by attributes

Independently analyze and compare two- and three-dimensional shapes of different sizes and orientations, using informal language to describe their similarities, differences, parts, and attributes such as number of sides or corners. across representations and contexts.

Component progression

  1. 1I can describe a shape's attributes, such as its number of sides or corners.
  2. 2I can compare two shapes and describe their similarities and differences using their attributes.
  3. 3I can compare shapes presented in different sizes and orientations, focusing on their defining attributes rather than appearance.
Geometry · K.G.B.5

Model shapes by building and drawing

Independently model shapes in the world by building shapes from components, such as sticks and clay balls, and by drawing shapes. across representations and contexts.

Component progression

  1. 1I can build a given two-dimensional shape using components such as sticks, with the correct number of sides.
  2. 2I can draw a given two-dimensional shape with its correct defining attributes.
  3. 3I can identify the shape modeled by an everyday object in the environment.
Geometry · K.G.B.6

Compose simple shapes into larger shapes

Independently compose simple shapes to form larger shapes, such as joining two triangles to form a rectangle. across representations and contexts.

Component progression

  1. 1I can join two simple shapes together edge-to-edge without gaps or overlaps.
  2. 2I can name the larger shape formed by composing two or more simple shapes.
  3. 3I can use given simple shapes to compose a specified larger target shape.
Request Academy Access