Focus Areas for Kindergarten
- Understanding numbers, names, and the count sequence
- Counting to tell the number of objects
- Understanding addition as putting together and subtraction as taking apart
- Working with numbers 11-19 to gain foundations for place value
- Describing and comparing measurable attributes
Math Standards by Domain
Counting and Cardinality (K.CC)
What Students Learn:
Students learn the foundation of counting: saying number names in order, recognizing that numbers follow a pattern, and writing numerals. They practice counting to 100 by ones and by tens, and learn to start counting from any given number.
Key Skills:
- Count to 100 by ones: 1, 2, 3, 4... 100
- Count to 100 by tens: 10, 20, 30... 100
- Count forward from any number less than 100 (e.g., start at 47 and count to 52)
- Write numbers from 0 to 20
- Recognize and name numbers 0-20
- Understand that each number name has a fixed position in the sequence
Count by ones: 1, 2, 3, 4, 5... 20
Count by tens: 10, 20, 30, 40, 50
Start at 14 and count forward: 14, 15, 16, 17, 18
Write the number fifteen: 15
What Students Learn:
Students connect counting to quantity by learning that the last number counted tells "how many." They learn to count objects systematically, match one number to each object, and understand that the order of counting doesn't change the total.
Key Skills:
- Count objects up to 20, touching or moving each as you count
- Understand that the last number said tells how many objects total (cardinality)
- Answer "how many?" by counting a set of objects
- Understand that counting order doesn't matter (can start anywhere in a group)
- Count out a specific number of objects from a larger group
- Recognize that each object gets exactly one number
Count 8 blocks: 1, 2, 3, 4, 5, 6, 7, 8 → There are 8 blocks
"Give me 5 crayons" → Student counts out 1, 2, 3, 4, 5 crayons
No matter which block you start with, there are still 8 blocks total
What Students Learn:
Students learn to compare groups of objects to determine which has more, which has fewer, or if they have the same amount. They use strategies like matching, counting, or visual comparison, and learn comparison vocabulary.
Key Skills:
- Compare two groups of objects and identify which has more or fewer
- Use matching to compare (line up objects one-to-one)
- Use counting to compare groups
- Understand and use vocabulary: greater than, less than, equal to, more, fewer, same
- Compare written numerals 1-10
- Identify when two groups have an equal number
Group A has 7 apples, Group B has 5 apples → Group A has more
Match objects: ●●●●● and ●●●●●●● → The second group has more (2 extra)
Compare numbers: 8 is greater than 3, 4 is less than 9
Are there the same? 6 blocks and 6 cubes → Yes, equal amounts
Operations and Algebraic Thinking (K.OA)
What Students Learn:
Students develop a concrete understanding of addition as "putting together" or "adding to" and subtraction as "taking apart" or "taking from." They use hands-on materials, drawings, and actions to show these operations before using numbers and symbols.
Key Skills:
- Represent addition by combining groups of objects
- Represent subtraction by removing objects from a group
- Act out addition and subtraction situations
- Use fingers, counters, or drawings to show adding and subtracting
- Solve addition and subtraction word problems within 10
- Begin to use + and - symbols and write simple equations
There are 3 birds. 2 more birds come. How many birds now? (3 + 2 = 5)
Show with objects: ●●● and ●● → ●●●●●
Example (Subtraction):You have 5 cookies. You eat 2. How many left? (5 - 2 = 3)
Show: ●●●●● cross out ●● → ●●● remain
What Students Learn:
Students learn that numbers can be broken apart (decomposed) into smaller numbers in multiple ways. They practice breaking apart and putting together numbers, and develop fluency with simple addition and subtraction within 5.
Key Skills:
- Decompose numbers into pairs (e.g., 7 = 3 + 4, 7 = 5 + 2, 7 = 6 + 1)
- Find all the ways to make a number (e.g., 5 = 0+5, 1+4, 2+3, 3+2, 4+1, 5+0)
- For any number 1-9, find the number that makes 10 when added
- Fluently (quickly and accurately) add and subtract within 5
- Use drawings or objects to show different decompositions
Ways to make 6: 1+5, 2+4, 3+3, 4+2, 5+1
What makes 10? 6 + ? = 10 → 6 + 4 = 10
Decompose 8: 8 = 3 + 5, or 8 = 2 + 6, or 8 = 7 + 1
Fluently: 2 + 3 = 5, 4 - 1 = 3, 5 - 2 = 3
Number and Operations in Base Ten (K.NBT)
What Students Learn:
Students learn that teen numbers (11-19) are composed of one ten and some extra ones. This is their first introduction to place value concepts, building a foundation for understanding tens and ones in first grade.
Key Skills:
- Understand that 11-19 are made of one group of ten and some ones
- Compose teen numbers: 10 + 3 = 13, 10 + 7 = 17
- Decompose teen numbers: 15 = 10 + 5, 18 = 10 + 8
- Use objects to show ten ones and additional ones
- Record compositions using drawings or equations
- Build foundation for place value understanding
Show 14 with blocks: Make one group of 10 and a group of 4
14 = 10 + 4 (one ten and four ones)
Show 17: ●●●●●●●●●● and ●●●●●●● (10 + 7)
What is 10 + 6? It's 16 (one ten and six ones)
Measurement and Data (K.MD)
What Students Learn:
Students learn to identify and describe attributes that can be measured, such as length, height, weight, and capacity. They use comparison language to describe differences between objects and understand that different attributes can be measured differently.
Key Skills:
- Identify measurable attributes: length, height, weight, capacity (how much it holds)
- Describe attributes using vocabulary: long/short, tall/short, heavy/light, full/empty
- Directly compare two objects by matching or placing side by side
- Use comparative language: longer than, shorter than, taller than, heavier than
- Understand that objects can be compared in multiple ways
Compare two pencils: "This pencil is longer than that one"
Compare height: "I am taller than my friend"
Compare weight: "This book is heavier than this paper"
Compare capacity: "This cup holds more water than this small cup"
What Students Learn:
Students learn to sort and classify objects into groups based on common attributes (color, size, shape, type). They practice counting how many objects are in each category, building early data organization skills.
Key Skills:
- Sort objects into categories based on attributes (color, shape, size, type)
- Count how many objects are in each category
- Identify the category with more or fewer objects
- Sort up to 10 objects into categories
- Explain the sorting rule used
- Organize and represent simple data
Sort buttons by color: Red (4 buttons), Blue (6 buttons), Green (3 buttons)
Sort shapes: Circles (5), Squares (4), Triangles (7)
Which category has the most? Triangles (7)
Sort animals: Farm animals (3), Pets (5), Wild animals (2)
Geometry (K.G)
What Students Learn:
Students learn to recognize and name basic 2D and 3D shapes. They identify shapes in their environment and understand that shapes keep their name even when rotated, resized, or positioned differently.
Key Skills:
- Identify and name 2D shapes: circles, triangles, squares, rectangles
- Identify and name 3D shapes: spheres, cubes, cones, cylinders
- Describe shapes in the environment (e.g., "The clock is a circle")
- Recognize shapes regardless of orientation (a triangle is still a triangle even upside down)
- Recognize shapes regardless of size (big and small circles are both circles)
- Describe position: above, below, beside, in front of, behind, next to
Find shapes around you: "The door is a rectangle, the ball is a sphere"
All of these are triangles: △ ▽ ◁ ▷
Name 3D shapes: A can is a cylinder, dice are cubes, an ice cream cone is a cone
Position: "The book is on top of the desk, next to the pencil"
What Students Learn:
Students learn to analyze shapes by examining their parts and comparing different shapes. They build and draw shapes, and discover that simple shapes can be combined to create more complex shapes, developing spatial reasoning skills.
Key Skills:
- Analyze shapes by describing their parts (sides, corners/vertices)
- Compare and classify shapes (e.g., all triangles have 3 sides)
- Draw shapes using straight and curved lines
- Build shapes with materials (blocks, clay, sticks)
- Combine simple shapes to make new shapes (two triangles make a square)
- Use shapes to create pictures and designs
Describe: "A square has 4 sides and 4 corners"
Build with blocks: Stack cubes to make a tower
Combine shapes: Put two triangles together to make a square or rectangle
Draw a house using shapes: square for the base, triangle for the roof, rectangle for the door