Counting and number names
Students learn to count out loud, point to objects one at a time, and write the numbers they say. They start to see that the last number counted tells how many are in the group.
What does a student learn in
This is the year numbers become real. Students learn to count objects up to 20, match each number to one item, and figure out which group has more. They start adding and taking away small amounts using fingers, cubes, or drawings, and they name everyday shapes like circles and squares. By spring, students can count out a small handful of pennies and tell you how many.
- Counting to 20
- Adding and subtracting
- Comparing numbers
- Shapes
- Sorting
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 and numbers
Students put two groups side by side and decide which has more, which has fewer, and which are the same. They begin to compare written numbers, not just piles of things.
- 3
Adding and taking away
Students act out simple stories with fingers, blocks, and drawings to join groups or take some away. They start to recognize the pairs of numbers that make ten.
- 4
Shapes and the world around them
Students name circles, squares, triangles, and rectangles, and find them in real objects like signs, books, and snacks. They also describe boxes, balls, and cans as three-dimensional shapes.
- 5
Measuring and sorting
Students compare two objects by length, height, or weight using words like longer, shorter, and heavier. They sort items into groups and count how many are in each.
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
Students look at a math problem, think about what it's asking, and keep trying even when it gets hard. They check their work to see if the answer makes sense.
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Reason Abstractly
Students take a word problem about real things, like apples or blocks, 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 objects or pictures as proof. They also listen to a classmate's reasoning and say whether they agree or disagree.
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Model with Mathematics
Students use drawings, numbers, or simple objects to make sense of everyday situations, like figuring out how many apples are left after sharing some.
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Use Tools Strategically
Students learn which tool fits the job: a ruler for length, fingers for counting, or paper and pencil for working something out. They practice choosing, not just using.
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Attend to Precision
Students use the right words and careful counting when they talk and work through math problems. Saying "three apples" instead of "some" or writing a number clearly enough to read are both part of this.
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Use Structure
Students notice patterns and shapes that repeat or fit together, then use what they see to solve a problem. Spotting a pattern in a row of blocks or a number sequence counts as using structure.
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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 solving each problem from scratch.
| Standard | Definition | Code |
|---|---|---|
| Make Sense of Problems | Students look at a math problem, think about what it's asking, and keep trying even when it gets hard. They check their work to see if the answer makes sense. | MA-MATH.MP.K.1 |
| Reason Abstractly | Students take a word problem about real things, like apples or blocks, and turn it into numbers they can work with. Then they check that the answer still makes sense in the real world. | MA-MATH.MP.K.2 |
| Construct Arguments | Students explain why their math answer makes sense, using objects or pictures as proof. They also listen to a classmate's reasoning and say whether they agree or disagree. | MA-MATH.MP.K.3 |
| Model with Mathematics | Students use drawings, numbers, or simple objects to make sense of everyday situations, like figuring out how many apples are left after sharing some. | MA-MATH.MP.K.4 |
| Use Tools Strategically | Students learn which tool fits the job: a ruler for length, fingers for counting, or paper and pencil for working something out. They practice choosing, not just using. | MA-MATH.MP.K.5 |
| Attend to Precision | Students use the right words and careful counting when they talk and work through math problems. Saying "three apples" instead of "some" or writing a number clearly enough to read are both part of this. | MA-MATH.MP.K.6 |
| Use Structure | Students notice patterns and shapes that repeat or fit together, then use what they see to solve a problem. Spotting a pattern in a row of blocks or a number sequence counts as using structure. | MA-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 solving each problem from scratch. | MA-MATH.MP.K.8 |
K-8 Mathematics Content
K-8 Mathematics Content
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Counting and Number
Counting and understanding numbers is the foundation of kindergarten math. Students count objects, compare small groups, and learn that numbers represent real quantities like five blocks or ten fingers.
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Operations and Algebraic Thinking
Adding and subtracting small groups of objects is the focus here. Students count, combine, and take away to solve simple number problems.
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Measurement and Data
Students sort objects into groups and show the results in a simple chart or picture graph. They practice reading those charts to answer basic questions, like which group has more.
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Geometry
Students sort and describe flat shapes like circles and triangles, and solid shapes like cubes and spheres. They use words like "corner," "side," and "flat" to explain what makes each shape different.
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Ratios and Proportional Relationships
Students use simple comparisons, like noticing there are twice as many apples as oranges, to solve everyday number problems. They practice matching quantities and figuring out how many of something they need.
| Standard | Definition | Code |
|---|---|---|
| Counting and Number | Counting and understanding numbers is the foundation of kindergarten math. Students count objects, compare small groups, and learn that numbers represent real quantities like five blocks or ten fingers. | MA-MATH.K8.K.1 |
| Operations and Algebraic Thinking | Adding and subtracting small groups of objects is the focus here. Students count, combine, and take away to solve simple number problems. | MA-MATH.K8.K.2 |
| Measurement and Data | Students sort objects into groups and show the results in a simple chart or picture graph. They practice reading those charts to answer basic questions, like which group has more. | MA-MATH.K8.K.3 |
| Geometry | Students sort and describe flat shapes like circles and triangles, and solid shapes like cubes and spheres. They use words like "corner," "side," and "flat" to explain what makes each shape different. | MA-MATH.K8.K.4 |
| Ratios and Proportional Relationships | Students use simple comparisons, like noticing there are twice as many apples as oranges, to solve everyday number problems. They practice matching quantities and figuring out how many of something they need. | MA-MATH.K8.K.5 |
No state assessments at this grade
Students take their next one in Grade 3.
MCAS: Mathematics (Grades 3-8)
Massachusetts's spring summative math test for grades 3 through 8, aligned to the Massachusetts Curriculum Framework for Mathematics.
- When given:
- spring
- Frequency:
- annual
Common Questions
What math should students know by the end of the year?
Students count objects accurately, usually to 20 and beyond, and know which group has more or less. They recognize and write numbers, put small groups together, take some away, and name common shapes like circles, squares, and triangles.
How can families practice counting at home?
Count real things during normal routines. Steps on the stairs, grapes on a plate, socks in the laundry, cars in the parking lot. Ask questions like how many are left after eating two, or which pile has more.
Does a student need to write numbers neatly this year?
Students learn to write numbers 0 through 20, but reversed or wobbly numbers are normal at this age. Focus on recognizing numbers and matching them to a count of objects. Neat handwriting comes with time and practice.
How should counting and number sense be sequenced across the year?
Start with counting to 10 with one-to-one matching, then build to 20 by midyear and past 100 by spring. Layer in comparing groups, then composing and decomposing numbers within 10. Save written equations for later in the year once the meaning is solid.
Which skills usually need the most reteaching?
One-to-one correspondence past 12, the teen numbers, and the idea that the last number counted tells how many. Many students also need extra time pulling apart numbers within 10 in more than one way. Build these into daily warm-ups all year.
What can families do if a student gets stuck on a math problem?
Hand over real objects to count. Buttons, blocks, cereal pieces, or fingers all work. Ask the student to show the problem with the objects and say the count out loud. Pictures and acting it out help more than worksheets at this age.
How do teachers know students are ready for first grade math?
Ready students count past 20 with accuracy, instantly see small groups without counting, and can break 10 into pairs like 7 and 3 or 6 and 4. They also solve simple add and take-away stories with objects or fingers and name basic shapes.
Are flashcards and memorizing math facts a good idea?
Not yet. Memorizing sums comes later. Right now students need to build the meaning of numbers by counting real objects, comparing groups, and breaking small numbers apart. Quick games with dice, dominoes, or playing cards do more than flashcards.