Counting and adding within twenty
Students count, read, and write numbers up to 120 and start adding and subtracting small numbers. They learn to think of ten as a single unit and use it to make problems easier.
What does a student learn in
This is the year students stop counting one by one and start thinking in tens. Students add and subtract within 20, then work with numbers up to 100 by seeing them as groups of tens and ones. Word problems become a regular part of math, and students explain how they got an answer instead of just saying it. By spring, students can solve a story problem like "I had 8 stickers and got 5 more" and tell you how they figured it out.
- Adding and subtracting
- Place value
- Word problems
- Telling time
- Shapes
- Measurement
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
Strategies for sums and differences
Students move past counting on fingers and start using tricks like making a ten or using doubles. They explain why their answers make sense and check a friend's thinking.
- 3
Place value with tens and ones
Students see that a two-digit number is made of tens and ones, so 47 is four tens and seven ones. They compare numbers and add larger ones using what they know about tens.
- 4
Measuring and telling time
Students line up objects to measure length and read clocks to the hour and half hour. They also sort objects into groups and answer simple questions from a small chart.
- 5
Shapes and equal shares
Students name and build flat and solid shapes and notice what makes a square a square. They split shapes into halves and fourths and see that more pieces means smaller pieces.
Mastery Learning Standards
The required skills a student should display by the end of Grade 1.
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, then keep trying even when the first attempt doesn't work.
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Reason Abstractly
Students take a word problem and turn it into numbers and symbols to solve it, then translate the answer back into plain English to check that it makes sense.
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Construct Arguments
Students explain why their math answer makes sense and listen to how classmates solved the same problem. They practice saying "I think this because..." and finding where another student's thinking went wrong.
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Model with Mathematics
Students use math to make sense of real situations, like figuring out how many apples to buy or splitting snacks evenly. The math they practice in school connects to problems they actually run into outside of it.
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Use Tools Strategically
Students choose the right tool for the problem, whether that means a ruler, a number line, or a pencil and paper. They think before grabbing a tool, not after.
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Attend to Precision
Students choose the right math words and units when they explain their thinking. They check that their numbers and labels (like inches or cents) are correct before they finish.
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Use Structure
Students notice patterns and shapes in numbers and math problems, then use what they see to solve new problems faster. For example, recognizing that adding zero leaves a number unchanged helps them work through similar problems without starting from scratch.
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Express Regularity
Students notice when the same steps keep working the same way, like always adding zero leaves a number unchanged. They use that pattern as a shortcut instead of solving from scratch every time.
| Standard | Definition | Code |
|---|---|---|
| Make Sense of Problems | Students figure out what a math problem is asking before they start solving it, then keep trying even when the first attempt doesn't work. | IL-MATH.MP.1.1 |
| Reason Abstractly | Students take a word problem and turn it into numbers and symbols to solve it, then translate the answer back into plain English to check that it makes sense. | IL-MATH.MP.1.2 |
| Construct Arguments | Students explain why their math answer makes sense and listen to how classmates solved the same problem. They practice saying "I think this because..." and finding where another student's thinking went wrong. | IL-MATH.MP.1.3 |
| Model with Mathematics | Students use math to make sense of real situations, like figuring out how many apples to buy or splitting snacks evenly. The math they practice in school connects to problems they actually run into outside of it. | IL-MATH.MP.1.4 |
| Use Tools Strategically | Students choose the right tool for the problem, whether that means a ruler, a number line, or a pencil and paper. They think before grabbing a tool, not after. | IL-MATH.MP.1.5 |
| Attend to Precision | Students choose the right math words and units when they explain their thinking. They check that their numbers and labels (like inches or cents) are correct before they finish. | IL-MATH.MP.1.6 |
| Use Structure | Students notice patterns and shapes in numbers and math problems, then use what they see to solve new problems faster. For example, recognizing that adding zero leaves a number unchanged helps them work through similar problems without starting from scratch. | IL-MATH.MP.1.7 |
| Express Regularity | Students notice when the same steps keep working the same way, like always adding zero leaves a number unchanged. They use that pattern as a shortcut instead of solving from scratch every time. | IL-MATH.MP.1.8 |
K-8 Mathematics Content
K-8 Mathematics Content
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Counting and Number
Students count, compare, and work with whole numbers up to 120. They start learning about halves and quarters, building a foundation for fractions they'll use in later grades.
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Operations and Algebraic Thinking
Students add and subtract to solve simple word problems, like figuring out how many apples are left or how many are needed altogether. They start building the thinking patterns that make multiplication and division make sense later.
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Measurement and Data
Students read simple charts and graphs to answer questions about real information, like how many students picked each favorite color. They also organize data into tables to spot patterns and compare amounts.
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Geometry
Students sort and describe flat shapes (like squares and circles) and solid shapes (like cubes and cones), and start measuring their sides and angles. The focus is on noticing what makes each shape different from the others.
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Ratios and Proportional Relationships
Students use ratio reasoning to solve everyday math problems at the first-grade level, such as comparing groups of objects or figuring out how many of one thing go with another.
| Standard | Definition | Code |
|---|---|---|
| Counting and Number | Students count, compare, and work with whole numbers up to 120. They start learning about halves and quarters, building a foundation for fractions they'll use in later grades. | IL-MATH.K8.1.1 |
| Operations and Algebraic Thinking | Students add and subtract to solve simple word problems, like figuring out how many apples are left or how many are needed altogether. They start building the thinking patterns that make multiplication and division make sense later. | IL-MATH.K8.1.2 |
| Measurement and Data | Students read simple charts and graphs to answer questions about real information, like how many students picked each favorite color. They also organize data into tables to spot patterns and compare amounts. | IL-MATH.K8.1.3 |
| Geometry | Students sort and describe flat shapes (like squares and circles) and solid shapes (like cubes and cones), and start measuring their sides and angles. The focus is on noticing what makes each shape different from the others. | IL-MATH.K8.1.4 |
| Ratios and Proportional Relationships | Students use ratio reasoning to solve everyday math problems at the first-grade level, such as comparing groups of objects or figuring out how many of one thing go with another. | IL-MATH.K8.1.5 |
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?
Students should add and subtract within 20, count to 120, and read and write numbers in that range. They should also tell time to the hour and half hour, compare lengths, and sort shapes by their parts like sides and corners.
How can I help with math at home in just a few minutes a day?
Count things together while cooking or driving, like steps to the door or forks on the table. Ask quick story problems such as, there are 8 grapes and 3 more, how many now? Five minutes a day of counting and small story problems goes a long way.
My child counts on fingers. Is that a problem?
No. Finger counting is a normal step and helps students see how numbers come apart and back together. Over time, encourage breaking numbers into friendlier parts, like 8 plus 5 becomes 8 plus 2 plus 3.
What does mastery of addition and subtraction look like at this level?
Students should add and subtract within 20 with reasonable speed and accuracy, using strategies like making ten or counting on. Sums and differences within 10 should be close to automatic by spring.
How should I sequence the year?
Most teachers start with addition and subtraction within 10, then build place value to 100 in the middle of the year. Save measurement, time, and shapes for shorter units that can sit between the bigger number work.
Which skills usually need the most reteaching?
Subtraction within 20 and word problems with an unknown in different positions are the common sticking points. Plan extra time for problems like, 5 plus what equals 13, and for two-digit numbers where students confuse the tens and ones.
What should reading and writing numbers look like at home?
Students should read and write numbers up to 120 and understand that a number like 34 means 3 tens and 4 ones. Practice with coins, page numbers, and house numbers on a walk gives plenty of real examples.
How do I know students are ready for next year?
By spring, students should solve word problems within 20, count and write to 120, tell time to the half hour, and recognize basic shapes by their sides and corners. Quick fact recall within 10 and steady work with two-digit numbers are the strongest signals.