Counting and number names
Students learn to count out loud, point to objects one at a time, and write the numbers they say. By the end of this stretch, most can count a small pile of crackers or coins without losing track.
What does a student learn in
This is the year numbers start to mean something. Students learn to count past twenty, match each number they say to one object, and figure out which group has more. They begin adding and taking away with small numbers, often using fingers, blocks, or drawings. By spring, students can count to 100 by ones and tens, write numbers up to 20, and name basic shapes like circles, squares, and triangles.
- Counting
- Adding and subtracting
- Number writing
- Shapes
- Comparing groups
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
Comparing groups of objects
Students figure out which group has more and which has fewer by lining objects up or counting each pile. Expect dinner-table talk about who got more grapes.
- 3
Adding and taking away
Students start putting small groups together and taking some away, using fingers, blocks, or drawings. They work with numbers up to ten and begin to know pairs that make ten without counting every time.
- 4
Shapes and everyday measuring
Students name circles, squares, triangles, cubes, and cones, and notice them in signs, food, and toys. They also compare which pencil is longer or which backpack is heavier.
- 5
Teen numbers and place value
Students see that numbers like 13 and 17 are a ten and some extra ones. Building these numbers with blocks or fingers sets up the addition and subtraction work in first grade.
Mastery Learning Standards
The required skills a student should display by the end of Kindergarten.
Standards for Mathematical Practice
Standards for Mathematical Practice
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Make Sense of Problems
Kindergartners learn to look at a math problem, figure out what it is asking, and keep trying even when the answer does not come right away.
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Reason Abstractly
Students take a real problem, like counting apples, and turn it into numbers they can work with. Then they check that the answer still makes sense in the real world.
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Construct Arguments
Students explain why their math answer makes sense, using shapes, numbers, or drawings as proof. They also listen to a classmate's explanation and say whether they agree or disagree.
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Model with Mathematics
Students use simple math to make sense of real situations, like sharing snacks equally or counting chairs for a group. The idea is that numbers and shapes aren't just for class; they help solve ordinary problems.
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Use Tools Strategically
Students choose the right tool for the job, picking a ruler to measure, fingers to count, or pencil and paper to work out a problem. They start to learn that different tools fit different tasks.
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Attend to Precision
Students choose words and numbers carefully when explaining their thinking. They name shapes, sizes, and counts correctly so their meaning is clear.
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Use Structure
Students notice patterns and shapes in what they see, like how numbers count up in order or how a square always has four equal sides. Spotting that structure helps them solve problems faster.
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Express Regularity
Students notice when the same steps keep working the same way, like adding zero always leaving a number unchanged. They use that pattern as a shortcut instead of starting from scratch each time.
| Standard | Definition | Code |
|---|---|---|
| Make Sense of Problems | Kindergartners learn to look at a math problem, figure out what it is asking, and keep trying even when the answer does not come right away. | VT-MATH.MP.K.1 |
| Reason Abstractly | Students take a real problem, like counting apples, and turn it into numbers they can work with. Then they check that the answer still makes sense in the real world. | VT-MATH.MP.K.2 |
| Construct Arguments | Students explain why their math answer makes sense, using shapes, numbers, or drawings as proof. They also listen to a classmate's explanation and say whether they agree or disagree. | VT-MATH.MP.K.3 |
| Model with Mathematics | Students use simple math to make sense of real situations, like sharing snacks equally or counting chairs for a group. The idea is that numbers and shapes aren't just for class; they help solve ordinary problems. | VT-MATH.MP.K.4 |
| Use Tools Strategically | Students choose the right tool for the job, picking a ruler to measure, fingers to count, or pencil and paper to work out a problem. They start to learn that different tools fit different tasks. | VT-MATH.MP.K.5 |
| Attend to Precision | Students choose words and numbers carefully when explaining their thinking. They name shapes, sizes, and counts correctly so their meaning is clear. | VT-MATH.MP.K.6 |
| Use Structure | Students notice patterns and shapes in what they see, like how numbers count up in order or how a square always has four equal sides. Spotting that structure helps them solve problems faster. | VT-MATH.MP.K.7 |
| Express Regularity | Students notice when the same steps keep working the same way, like adding zero always leaving a number unchanged. They use that pattern as a shortcut instead of starting from scratch each time. | VT-MATH.MP.K.8 |
K-8 Mathematics Content
K-8 Mathematics Content
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Counting and Number
Counting, reading, and comparing whole numbers is the focus at this grade. Students learn to count objects, write numbers, and understand what those numbers mean.
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Operations and Algebraic Thinking
Adding and subtracting small numbers to solve simple word problems. Students figure out how many there are in all, how many are left, or how many more one group has than another.
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Measurement and Data
Students sort objects into groups and show what they found using a simple picture graph or tally chart. They answer basic questions about the data, like which group has more.
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Geometry
Students sort and describe flat shapes like circles and squares, and solid shapes like cubes and spheres. They notice how shapes are alike and different by counting sides, corners, and faces.
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Ratios and Proportional Relationships
Kindergarten ratio work means students use simple comparisons to solve everyday problems, like figuring out if there are enough cups for every student or whether one group has more than another. The focus is on noticing "how many" and "how many more."
| Standard | Definition | Code |
|---|---|---|
| Counting and Number | Counting, reading, and comparing whole numbers is the focus at this grade. Students learn to count objects, write numbers, and understand what those numbers mean. | VT-MATH.K8.K.1 |
| Operations and Algebraic Thinking | Adding and subtracting small numbers to solve simple word problems. Students figure out how many there are in all, how many are left, or how many more one group has than another. | VT-MATH.K8.K.2 |
| Measurement and Data | Students sort objects into groups and show what they found using a simple picture graph or tally chart. They answer basic questions about the data, like which group has more. | VT-MATH.K8.K.3 |
| Geometry | Students sort and describe flat shapes like circles and squares, and solid shapes like cubes and spheres. They notice how shapes are alike and different by counting sides, corners, and faces. | VT-MATH.K8.K.4 |
| Ratios and Proportional Relationships | Kindergarten ratio work means students use simple comparisons to solve everyday problems, like figuring out if there are enough cups for every student or whether one group has more than another. The focus is on noticing "how many" and "how many more." | VT-MATH.K8.K.5 |
No state assessments at this grade
Students take their next one in Grade 3.
VTCAP: Mathematics (Grades 3-9)
Vermont's spring summative math test for grades 3 through 9, aligned to Vermont's Common Core-based math standards.
- When given:
- spring
- Frequency:
- annual
Common Questions
What math should a kindergartner know by the end of the year?
Most students leave kindergarten counting to 100, writing numbers to 20, and adding and subtracting small amounts up to 10. They should also name basic shapes, compare which group has more, and sort objects by size or color.
How can I practice counting at home in just a few minutes?
Count real things during the day. Count steps to the car, grapes on a plate, or socks in the laundry. Ask which pile has more and which has fewer. Five minutes a day builds the number sense kindergarten asks for.
My child can say the numbers but miscounts objects. Is that normal?
Yes, and it is the most important thing to practice. Have students touch each object as they say the number, and stop when they run out of objects. This one-to-one match is the skill behind almost everything else this year.
How should I sequence number work across the year?
Start with counting and matching numbers to objects up to 10, then build to 20 by midyear and 100 by spring. Add and subtract within 5 in the fall, then within 10 by spring. Shapes, measurement, and sorting can run alongside the number work all year.
Which skills usually need the most reteaching?
Counting on from a number other than one, the teen numbers as ten and some more, and reliable one-to-one counting past 20. Plan short daily warm-ups on these rather than long single lessons. Most students need many short exposures.
Do students need to memorize addition facts in kindergarten?
Not yet. Students should be fluent with sums and differences within 5 by the end of the year, but the rest of small addition is still about counting and grouping objects. Speed drills are not the goal here.
How do I know a student is ready for first grade math?
A ready student counts to 100, reads and writes numbers to 20, solves small story problems with objects or fingers, names common shapes, and can say which of two numbers is bigger. If those are steady, first grade work will land.
What is the best way to help with math homework if a child gets stuck?
Pull out objects. Buttons, cereal, or coins turn an abstract problem into something students can move and count. Ask them to show the problem before they try to answer it, and let them count out loud.