Counting and number names
Students learn to count out loud, point to each object once, and recognize numbers up to 20. Parents may notice their child counting steps, toys, or snacks at home.
What does a student learn in
This is the year numbers start to mean something. Students learn to count past twenty, match numbers to groups of objects, and figure out which group has more. They also start adding and taking away with small numbers, often using fingers or counters. By spring, students can count a pile of up to twenty objects, name basic shapes like circles and squares, and tell you that five and three make eight.
- Counting
- 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 of objects
Students figure out which pile has more, which has fewer, and when two groups are the same. They start to write numbers and use them to describe small sets.
- 3
Adding and taking away
Students put small groups together and take some away, using fingers, blocks, or drawings. They start to see that 5 can be 2 and 3, or 4 and 1.
- 4
Shapes and measuring
Students name circles, squares, triangles, and cubes, and notice these shapes in real objects. They also compare which thing is longer, shorter, or heavier.
- 5
Numbers past ten
Students work with numbers from 11 to 20 and start to see them as a ten plus 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 look at a math problem, figure out what it is asking, and keep trying even when it gets hard.
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Reason Abstractly
Students learn to move between a real problem and the numbers that describe it. They might count five apples, write the number 5, then think about what that number means back in the real world.
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Construct Arguments
Students explain why their math answer makes sense, using objects or drawings as proof. They also listen to a classmate's thinking 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 counting snacks, sorting toys, or figuring out how many are left. Math isn't just a worksheet; it shows up in everyday moments.
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Use Tools Strategically
Students learn to pick the right tool for the job: a ruler to measure, fingers to count, or paper to work out a problem. They think about which tool makes the most sense before they start.
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Attend to Precision
Students choose words carefully when talking about math and check that their numbers and answers make sense. In kindergarten this might mean naming shapes correctly or saying "five blocks" instead of just "some."
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Use Structure
Students notice patterns and shapes in the world around them: that a row of blocks can be counted, that two groups can be compared, or that a design repeats. Recognizing that structure helps students solve new problems with tools they already know.
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Express Regularity
Students notice when the same steps keep giving the same result, like adding zero always leaving a number unchanged. They use that pattern as a shortcut instead of starting over each time.
| Standard | Definition | Code |
|---|---|---|
| Make Sense of Problems | Students look at a math problem, figure out what it is asking, and keep trying even when it gets hard. | IL-MATH.MP.K.1 |
| Reason Abstractly | Students learn to move between a real problem and the numbers that describe it. They might count five apples, write the number 5, then think about what that number means back in the real world. | IL-MATH.MP.K.2 |
| Construct Arguments | Students explain why their math answer makes sense, using objects or drawings as proof. They also listen to a classmate's thinking and say whether they agree or disagree. | IL-MATH.MP.K.3 |
| Model with Mathematics | Students use simple math to make sense of real situations, like counting snacks, sorting toys, or figuring out how many are left. Math isn't just a worksheet; it shows up in everyday moments. | IL-MATH.MP.K.4 |
| Use Tools Strategically | Students learn to pick the right tool for the job: a ruler to measure, fingers to count, or paper to work out a problem. They think about which tool makes the most sense before they start. | IL-MATH.MP.K.5 |
| Attend to Precision | Students choose words carefully when talking about math and check that their numbers and answers make sense. In kindergarten this might mean naming shapes correctly or saying "five blocks" instead of just "some." | IL-MATH.MP.K.6 |
| Use Structure | Students notice patterns and shapes in the world around them: that a row of blocks can be counted, that two groups can be compared, or that a design repeats. Recognizing that structure helps students solve new problems with tools they already know. | IL-MATH.MP.K.7 |
| Express Regularity | Students notice when the same steps keep giving the same result, like adding zero always leaving a number unchanged. They use that pattern as a shortcut instead of starting over each time. | IL-MATH.MP.K.8 |
K-8 Mathematics Content
K-8 Mathematics Content
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Counting and Number
Students count objects, compare groups, and work with numbers up to 20. This is the foundation for everything they'll do with numbers in the years ahead.
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Operations and Algebraic Thinking
Students learn to add and subtract small numbers to solve simple problems, like figuring out how many apples are left after eating two. This is the first step toward understanding how numbers work together.
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Measurement and Data
Students sort objects into groups and count each group, then show the results in a simple picture graph or chart. They answer basic questions about what the data shows, like which group has more.
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Geometry
Students sort and describe flat shapes like circles and triangles and solid shapes like spheres and cubes. They notice what makes each shape different, such as the number of sides or corners.
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Ratios and Proportional Relationships
Students use simple comparisons, like "twice as many" or "half as much," to solve everyday problems. They figure out how things relate in size or amount before formal fractions begin.
| Standard | Definition | Code |
|---|---|---|
| Counting and Number | Students count objects, compare groups, and work with numbers up to 20. This is the foundation for everything they'll do with numbers in the years ahead. | IL-MATH.K8.K.1 |
| Operations and Algebraic Thinking | Students learn to add and subtract small numbers to solve simple problems, like figuring out how many apples are left after eating two. This is the first step toward understanding how numbers work together. | IL-MATH.K8.K.2 |
| Measurement and Data | Students sort objects into groups and count each group, then show the results in a simple picture graph or chart. They answer basic questions about what the data shows, like which group has more. | IL-MATH.K8.K.3 |
| Geometry | Students sort and describe flat shapes like circles and triangles and solid shapes like spheres and cubes. They notice what makes each shape different, such as the number of sides or corners. | IL-MATH.K8.K.4 |
| Ratios and Proportional Relationships | Students use simple comparisons, like "twice as many" or "half as much," to solve everyday problems. They figure out how things relate in size or amount before formal fractions begin. | IL-MATH.K8.K.5 |
No state assessments at this grade
Students take their next one in Grade 3.
Illinois Assessment of Readiness Mathematics (Grades 3-8)
IAR Mathematics is the spring summative math test for grades 3 through 8, aligned to the Illinois Learning Standards for Mathematics.
- When given:
- spring
- Frequency:
- annual
Common Questions
What math should students know by the end of the year?
By spring, students count objects accurately, recognize and write numbers to 20, and compare small groups to see which has more or fewer. They also add and subtract within 10 using fingers, drawings, or counters, and name basic shapes like circles, squares, and triangles.
How can families help with counting at home?
Count real things during the day. Count steps to the car, grapes on a plate, or socks in the laundry. Ask questions like how many are left after eating two, or which pile has more. Five quick minutes a day builds the habit.
Is it a problem if a student still reverses numbers like 3 or 7?
No. Reversed numbers are normal at this age and usually sort themselves out with practice. Keep a number line or written 0 to 10 nearby so students can check the shape when writing.
How should counting and number sense be sequenced across the year?
Start with counting to 10 and matching one number to one object. Move to comparing groups, then counting to 20, then to 100 by ones and tens. Save adding and subtracting within 10 for the second half of the year, once counting is solid.
Which skills usually need the most reteaching?
Two skills come back again and again: counting one object at a time without skipping or double-counting, and understanding that the last number said tells how many. Build in small-group practice with physical objects all year, not just at the start.
How can families help a student who is stuck on a math problem?
Hand them something to count. Beans, coins, or buttons turn an abstract question into something they can see and move. Ask them to show the problem with the objects before saying an answer.
What does shape and measurement work look like at this age?
Students name flat shapes like circles, squares, triangles, and rectangles, and solid shapes like balls, boxes, and cans. They also compare objects directly, asking which pencil is longer or which cup holds more. Formal rulers and scales come later.
How do teachers know students are ready for first grade math?
Ready students count to 100, write numbers to 20, and add and subtract within 10 without always needing fingers. They can also explain their thinking out loud, even in short sentences, and notice patterns like counting by tens.
Do students need to memorize math facts this year?
Not yet. The goal is understanding what addition and subtraction mean, using objects, fingers, and drawings. Quick recall of sums within 5 is a nice bonus by spring, but pushing flashcards too early can backfire.