Counting and number names
Students learn to say numbers in order up to twenty and count small groups of toys or snacks one by one. They start to see that the last number they say tells how many.
What does a student learn in
This is the year numbers start to mean something real. Students learn to count to 20, match each number they say to one object they touch, and notice that the last number tells how many. They begin comparing groups, naming shapes around the room, and sorting toys by size or color. By spring, students can count out ten objects when asked and tell you which pile has more.
- Counting to 20
- Comparing groups
- Shapes
- Sorting
- Patterns
Year at a glance
How the year usually goes. Every school and district set their own curriculum, so treat this as a guide, not official pacing.
- 1
- 2
Shapes and where things are
Students name shapes like circles, squares, and triangles, and use words like above, below, behind, and next to. They build shapes from sticks, blocks, and play dough.
- 3
Comparing and sorting
Students sort buttons, blocks, and other small objects into groups, then count each group. They start saying which pile has more, which has fewer, and when two piles are the same.
- 4
Writing numbers and counting out
Students match written numbers from zero to five with the right number of objects. Given a number up to ten, they can count out that many crackers, crayons, or coins.
- 5
Adding, taking away, and patterns
Students use fingers and objects to act out simple stories about getting more or having some taken away. They copy and extend patterns like red, blue, red, blue.
Mastery Learning Standards
The required skills a student should display by the end of Pre-Kindergarten.
Counting and Cardinality
| Standard | Definition | Code |
|---|---|---|
| Count to 20 | Students say the numbers 1 through 20 out loud, in order, from memory. | NY-PK.CC.1 |
| Writing numerals 0 to 5 | Students count a small group of objects and write the matching number. They also learn that 0 means nothing is there. | NY-PK.CC.2 |
| Counting objects up to 10 | When students count a small group of objects, they point to each one and say one number. The last number they say tells how many there are total, no matter how the objects are arranged. | NY-PK.CC.3 |
| Comparing groups: more, fewer, or equal | Students compare two groups of things and decide which has more, which has fewer, or whether both groups have the same amount. | NY-PK.CC.5 |
| First and last in a line | Students point to the first and last object in a line, like the first crayon in a row or the last child in line. This is the start of understanding order and position. | NY-PK.CC.6 |
| Counting objects up to 10 | Students count up to 10 objects arranged in a row or circle and say how many there are. With scattered objects, they count up to 5 and give the total. | NY-PK.CC.4a |
| Count out objects to match a number | Students hear a number and count out exactly that many blocks, crayons, or other small objects. This is the bridge between knowing a number's name and understanding what it actually means. | NY-PK.CC.4b |
Geometry
| Standard | Definition | Code |
|---|---|---|
| Shapes and where things are | Students name the shapes they see in everyday objects, like a clock or a window, and describe where things are using words like above, below, in front of, and next to. | NY-PK.G.1 |
| Shape names, any size | Students learn the names of basic shapes, like circles, squares, and triangles, no matter how big or small the shape is. | NY-PK.G.2 |
| Shapes: what they look like and how they differ | Students pick up blocks, balls, and flat shapes and talk about what they notice: this one rolls, that one has corners. They use their own words to describe how shapes are alike or different. | NY-PK.G.3 |
| Building shapes from pieces | Students put together triangles, circles, and other shapes using blocks, sticks, or craft materials to build something new. | NY-PK.G.4 |
Measurement and Data
| Standard | Definition | Code |
|---|---|---|
| Describing how heavy or long things are | Students notice that objects can be measured in different ways, like how long, heavy, or tall something is. They practice using words like "longer," "heavier," and "shorter" to describe what they observe. | NY-PK.MD.1 |
| Sorting objects by what they have in common | Students sort a pile of objects (by color, shape, or size) into groups, then count how many belong in each group. | NY-PK.MD.2 |
Operations and Algebraic Thinking
| Standard | Definition | Code |
|---|---|---|
| Adding and taking away with objects | Students practice adding and taking away using toys, fingers, or snacks. They figure out "how many now?" after getting more or losing some. | NY-PK.OA.1 |
| Copying and continuing simple patterns | Students copy a simple pattern (like red, blue, red, blue) using blocks or other objects, then keep it going by adding the next pieces that fit. | NY-PK.OA.2 |
No state assessments at this grade
Students take their next one in Grade 3.
Grade 3 Mathematics Test
All New York public school students take this math test in the spring of grade 3. It covers the Next Generation grade 3 standards, with multiple-choice and constructed-response questions.
- When given:
- Spring of grade 3
- Frequency:
- Annual
NYSAA (New York State Alternate Assessment)
The alternate state test for students with the most significant cognitive disabilities. NYSAA replaces the Grade 3-8 tests and Regents exams in ELA, math, and science for the small group of students whose IEP teams qualify them.
- When given:
- Spring window each year
- Frequency:
- Annual
Common Questions
What math should a four-year-old be doing this year?
Counting to 20 out loud, matching small groups of objects to the numbers 0 through 5, naming shapes, and noticing which pile has more. Most of this happens through play, not worksheets.
How can families practice counting at home?
Count real things together: stairs on the way up, grapes on a plate, socks coming out of the laundry. Touch each object once as the number is said. Five minutes a day builds the habit of one number per object, which is the big skill this year.
What does mastery look like by the end of the year?
Students count to 20, count out up to 10 objects when asked for a number, and write the numerals 0 through 5. They name common shapes, compare two small groups, and copy a simple pattern like red, blue, red, blue.
How should counting be sequenced across the year?
Start with rote counting to 10 and one-to-one touching of objects in a line. Move to cardinality, the idea that the last number said is the total. Then push to 20, add scattered arrangements, and finish the year writing numerals 0 to 5.
Which skills usually need the most reteaching?
One-to-one correspondence and cardinality. Many students can recite numbers to 20 but still double-count objects or forget that the last number said is the total. Plan for daily small-group counting with real objects well into the spring.
What if a child still mixes up numbers past 12?
That is normal at this age. The teens are the hardest part of the count. Keep counting familiar things together and pause at 13, 14, 15 so those words get more practice. Mastery is counting to 20 by the end of the year, not the start.
How are shapes and patterns taught in pre-k?
Through building and sorting, not definitions. Students stack blocks, trace shapes, sort buttons by color or size, and copy patterns with beads or stickers. The goal is informal language: round, flat, pointy, bigger, next to.
How do teachers know students are ready for kindergarten math?
Look for steady one-to-one counting to 10, recognition of written numerals 0 to 5, the ability to compare two small groups, and naming of basic shapes. Students should also be able to extend a simple AB pattern with objects.