Counting and naming numbers
Students learn to count out loud, write numbers, and match a number to a group of objects. By the end of this stretch, counting to 20 and beyond feels steady instead of shaky.
What does a student learn in
This is the year numbers start to mean something. Students learn to count out loud, count objects one by one up to about 20, and match a number to how many things are in a group. They start adding and taking away small amounts using fingers, blocks, or drawings, and they name shapes like circles, squares, and triangles. By spring, they can count a small pile of objects, tell you how many, and figure out simple problems like three crackers plus two more.
- Counting
- Adding and subtracting
- Number sense
- Shapes
- Sorting and comparing
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 amounts
Students figure out which group has more, which has fewer, and which are the same. They start using words like greater than and less than when looking at small sets of objects.
- 3
Adding and taking away
Students put small groups together and take some away, often using fingers, counters, or drawings. Story problems with numbers up to 10 become familiar territory.
- 4
Shapes and the world around them
Students name circles, squares, triangles, cubes, and spheres, and notice them in everyday objects. They also describe size, length, and weight using words a parent would recognize.
- 5
Making ten and beyond
Students see numbers from 11 to 19 as a ten and some extra ones. This sets up the place value work that comes 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
Students figure out what a math problem is asking before they start solving it, and keep trying even when it gets hard.
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Reason Quantitatively
Students take a real problem (like counting five apples) and turn it into numbers they can work with, then check that the answer still makes sense in real life.
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Construct Arguments
Students explain why their answer makes sense and listen to how classmates solved the same problem. They practice saying "I think this because..." and pointing out when a different answer doesn't add up.
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Model with Mathematics
Students use drawings, objects, or simple number sentences to show a math idea, like sketching a group of apples to figure out how many are left after eating a few.
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Use Tools Strategically
Students learn which tools help with a math problem and which don't. A ruler measures length, a counter helps with counting, and choosing the right one is part of doing the math.
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Attend to Precision
Students use the right words and careful counting to describe math ideas clearly. When measuring, sorting, or adding, they say exactly what they mean instead of guessing.
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Use Structure
Students notice patterns and rules in math, like how numbers follow an order or shapes fit together in a certain way, and use those patterns to solve problems.
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Express Regularity
Students notice when the same steps keep working the same way. They use that pattern as a shortcut instead of starting from scratch each time.
| Standard | Definition | Code |
|---|---|---|
| Make Sense of Problems | Students figure out what a math problem is asking before they start solving it, and keep trying even when it gets hard. | OH-MATH.MP.K.1 |
| Reason Quantitatively | Students take a real problem (like counting five apples) and turn it into numbers they can work with, then check that the answer still makes sense in real life. | OH-MATH.MP.K.2 |
| Construct Arguments | Students explain why their answer makes sense and listen to how classmates solved the same problem. They practice saying "I think this because..." and pointing out when a different answer doesn't add up. | OH-MATH.MP.K.3 |
| Model with Mathematics | Students use drawings, objects, or simple number sentences to show a math idea, like sketching a group of apples to figure out how many are left after eating a few. | OH-MATH.MP.K.4 |
| Use Tools Strategically | Students learn which tools help with a math problem and which don't. A ruler measures length, a counter helps with counting, and choosing the right one is part of doing the math. | OH-MATH.MP.K.5 |
| Attend to Precision | Students use the right words and careful counting to describe math ideas clearly. When measuring, sorting, or adding, they say exactly what they mean instead of guessing. | OH-MATH.MP.K.6 |
| Use Structure | Students notice patterns and rules in math, like how numbers follow an order or shapes fit together in a certain way, and use those patterns to solve problems. | OH-MATH.MP.K.7 |
| Express Regularity | Students notice when the same steps keep working the same way. They use that pattern as a shortcut instead of starting from scratch each time. | OH-MATH.MP.K.8 |
K-8 Mathematics Content
K-8 Mathematics Content
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Counting and Number
Students count objects, compare small numbers, and learn that each number means one more than the one before. This is the foundation for all the addition and subtraction work ahead.
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Operations and Algebraic Thinking
Adding and subtracting small numbers to solve simple word problems. Students use objects, drawings, or equations to show how numbers go together or come apart.
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Measurement and Data
Students sort objects into groups and count each group, then show what they found in a simple picture or chart. They practice reading those charts to answer basic questions like "which group has more?"
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Geometry
Students sort and describe everyday shapes like circles, squares, and cubes by counting their sides, corners, and faces. They also compare shapes by size and figure out which ones match or fit together.
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Ratios and Proportional Relationships
Students use ratio reasoning to solve everyday problems, like figuring out how many apples each person gets if there are 12 apples and 4 people. They practice thinking about how two amounts relate to each other.
| Standard | Definition | Code |
|---|---|---|
| Counting and Number | Students count objects, compare small numbers, and learn that each number means one more than the one before. This is the foundation for all the addition and subtraction work ahead. | OH-MATH.K8.K.1 |
| Operations and Algebraic Thinking | Adding and subtracting small numbers to solve simple word problems. Students use objects, drawings, or equations to show how numbers go together or come apart. | OH-MATH.K8.K.2 |
| Measurement and Data | Students sort objects into groups and count each group, then show what they found in a simple picture or chart. They practice reading those charts to answer basic questions like "which group has more?" | OH-MATH.K8.K.3 |
| Geometry | Students sort and describe everyday shapes like circles, squares, and cubes by counting their sides, corners, and faces. They also compare shapes by size and figure out which ones match or fit together. | OH-MATH.K8.K.4 |
| Ratios and Proportional Relationships | Students use ratio reasoning to solve everyday problems, like figuring out how many apples each person gets if there are 12 apples and 4 people. They practice thinking about how two amounts relate to each other. | OH-MATH.K8.K.5 |
No state assessments at this grade
Students take their next one in Grade 3.
Ohio's State Test Mathematics (Grades 3-8)
OST Mathematics is the spring summative math test for grades 3 through 8, aligned to Ohio's Learning Standards for Mathematics.
- When given:
- spring
- Frequency:
- annual
Common Questions
What math should students know by the end of the year?
Students should count to 100 by ones and tens, count groups of up to 20 objects, and write numbers from 0 to 20. They should also add and subtract within 10, compare two groups to see which has more, and name basic shapes like circles, squares, and triangles.
How can families practice counting at home?
Count real things together: stairs, crackers, socks in the laundry. Ask questions like how many are left after eating two, or which pile has more. Five minutes a day builds the number sense students use all year.
What if a student still mixes up numbers like 6 and 9 or 12 and 21?
This is common and usually fades with practice. Write numbers together on paper, point to numbers on a clock or microwave, and say them out loud. Tracing numbers in the air or in sand helps the shapes stick.
How should counting and number work be sequenced across the year?
Start with counting to 10 with objects, then build to 20 with one-to-one matching before pushing to 100 by rote. Save written numerals until students can count the quantity reliably. Addition and subtraction within 10 fit best after students can compare groups.
Which skills usually need the most reteaching?
Counting past the teens trips up many students, especially 13, 14, and 15. One-to-one correspondence with groups larger than 10 also needs repeated practice. Plan short daily warm-ups for both rather than one long unit.
Do students need to memorize addition facts this year?
Memorizing is not the goal yet. Students should be able to figure out sums and differences within 10 using fingers, counters, or drawings. Speed comes later once the meaning of adding and taking away is solid.
How can families help with shapes and measurement?
Point out shapes on signs, boxes, and food. Compare two objects and ask which is longer, heavier, or holds more. Sorting laundry or silverware also counts as real math practice.
How do teachers know students are ready for first grade math?
Ready students can count a group of 20 objects accurately, write numbers to 20, and solve simple add and take-away stories within 10 using objects or drawings. They can also name common shapes and tell which group has more or fewer.