Counting and place value to 1000
Students learn to read, write, and count numbers up to 1000. They start to see that a 3 in the hundreds spot means something different than a 3 in the ones spot.
What does a student learn in
This is the year math grows past counting into thinking in groups of tens and hundreds. Students add and subtract within 100 quickly, then stretch those moves out to 1,000 using mental math and paper. They start measuring with rulers in inches and centimeters, reading clocks, and counting coins and bills. By spring, students can solve a word problem like "I had 47 pennies and got 28 more," show the work, and explain the answer.
- Place value
- Addition and subtraction
- Word problems
- Measurement
- Telling time
- Money
- Basic shapes
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
Addition and subtraction within 100
Students add and subtract two-digit numbers quickly and accurately. Expect them to start solving these in their head and to explain the steps they used.
- 3
Word problems and money
Students tackle short word problems and start working with coins and dollar bills. They figure out how much things cost and how much change is left.
- 4
Measurement, time, and graphs
Students measure objects with rulers in inches and centimeters and tell time to the nearest five minutes. They also read simple bar graphs and picture graphs.
- 5
Shapes and equal parts
Students name and draw shapes by their sides and corners and split shapes into equal halves, thirds, and fourths. This is the early groundwork for fractions next year.
Mastery Learning Standards
The required skills a student should display by the end of Grade 2.
Standards for Mathematical Practice
Standards for Mathematical Practice
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Make Sense of Problems
Students read a math problem, figure out what it's asking, and keep trying even when the answer isn't obvious. They check their work and ask whether the answer makes sense.
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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 what it means in real life. Math and meaning go together.
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Construct Arguments
Students explain why their math answer makes sense, using numbers or shapes as proof. They also listen to a classmate's reasoning and say whether they agree or disagree, and why.
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Model with Mathematics
Students use math to make sense of real situations: drawing a picture to split a bill, writing a number sentence to figure out how many chairs fit in a room, or sketching a graph to track something they notice.
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Use Tools Strategically
Students choose the right tool for the math in front of them: a ruler to measure, a number line to count up, scratch paper to work it out. Picking the right tool is part of solving the problem.
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Attend to Precision
Students choose exact words, labels, and units when they explain their math thinking. They check that numbers in a problem, like a measurement or a count, match what the question is actually asking.
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Use Structure
Students notice patterns and rules in math, like how columns on a hundreds chart count by tens or how shapes fit together. They use those patterns as shortcuts to solve new problems faster.
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Express Regularity
Students notice when a math procedure keeps working the same way and start to use that pattern as a shortcut. For example, they might realize that adding zero never changes a number, without having to work it out every time.
| Standard | Definition | Code |
|---|---|---|
| Make Sense of Problems | Students read a math problem, figure out what it's asking, and keep trying even when the answer isn't obvious. They check their work and ask whether the answer makes sense. | IL-MATH.MP.2.1 |
| Reason Abstractly | Students take a word problem and turn it into numbers and symbols to solve it, then translate the answer back into what it means in real life. Math and meaning go together. | IL-MATH.MP.2.2 |
| Construct Arguments | Students explain why their math answer makes sense, using numbers or shapes as proof. They also listen to a classmate's reasoning and say whether they agree or disagree, and why. | IL-MATH.MP.2.3 |
| Model with Mathematics | Students use math to make sense of real situations: drawing a picture to split a bill, writing a number sentence to figure out how many chairs fit in a room, or sketching a graph to track something they notice. | IL-MATH.MP.2.4 |
| Use Tools Strategically | Students choose the right tool for the math in front of them: a ruler to measure, a number line to count up, scratch paper to work it out. Picking the right tool is part of solving the problem. | IL-MATH.MP.2.5 |
| Attend to Precision | Students choose exact words, labels, and units when they explain their math thinking. They check that numbers in a problem, like a measurement or a count, match what the question is actually asking. | IL-MATH.MP.2.6 |
| Use Structure | Students notice patterns and rules in math, like how columns on a hundreds chart count by tens or how shapes fit together. They use those patterns as shortcuts to solve new problems faster. | IL-MATH.MP.2.7 |
| Express Regularity | Students notice when a math procedure keeps working the same way and start to use that pattern as a shortcut. For example, they might realize that adding zero never changes a number, without having to work it out every time. | IL-MATH.MP.2.8 |
K-8 Mathematics Content
K-8 Mathematics Content
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Counting and Number
Students count, compare, and work with whole numbers and simple fractions. This is the foundation for everything from reading a number line to splitting a shape into equal parts.
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Operations and Algebraic Thinking
Students practice adding, subtracting, multiplying, and dividing to solve word problems and write number sentences that show how they got their answer.
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Measurement and Data
Students read and build simple charts and graphs to answer questions about data. They figure out what the numbers mean and explain what the information shows.
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Geometry
Students sort flat shapes (like squares and triangles) and solid shapes (like cubes and cones) by their sides, corners, and faces. They also measure and describe what makes each shape different from the others.
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Ratios and Proportional Relationships
Students use ratios to solve everyday problems, like figuring out how many apples are needed if one bag holds four and you need three bags. They see how two quantities relate and use that relationship to find a missing number.
| Standard | Definition | Code |
|---|---|---|
| Counting and Number | Students count, compare, and work with whole numbers and simple fractions. This is the foundation for everything from reading a number line to splitting a shape into equal parts. | IL-MATH.K8.2.1 |
| Operations and Algebraic Thinking | Students practice adding, subtracting, multiplying, and dividing to solve word problems and write number sentences that show how they got their answer. | IL-MATH.K8.2.2 |
| Measurement and Data | Students read and build simple charts and graphs to answer questions about data. They figure out what the numbers mean and explain what the information shows. | IL-MATH.K8.2.3 |
| Geometry | Students sort flat shapes (like squares and triangles) and solid shapes (like cubes and cones) by their sides, corners, and faces. They also measure and describe what makes each shape different from the others. | IL-MATH.K8.2.4 |
| Ratios and Proportional Relationships | Students use ratios to solve everyday problems, like figuring out how many apples are needed if one bag holds four and you need three bags. They see how two quantities relate and use that relationship to find a missing number. | IL-MATH.K8.2.5 |
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 100 quickly, count and group up to 1,000, tell time on a clock, measure with a ruler, and work with coins and dollar bills. They should also solve word problems with one or two steps and recognize basic shapes.
How can families help with math at home in 10 minutes a day?
Cooking, shopping, and games are the best practice. Count change at the store, time how long chores take, double a recipe, or play a quick card game where the higher number wins. Short and regular beats long and rare.
My child counts on fingers. Should I worry?
Not yet. Finger counting is normal at this age and helps build number sense. Over the year, practice quick facts like pairs that make 10 and doubles, which slowly replaces finger counting with memory.
How should addition and subtraction be sequenced across the year?
Start with facts within 20 and strategies like making 10 and using doubles. Move to two-digit problems with place value blocks, then mental strategies, and finish with regrouping on paper. Word problems should run alongside the whole year, not wait until the end.
What skills usually need the most reteaching?
Regrouping in subtraction, telling time to five minutes, and counting mixed coins are the common sticking points. Place value beyond 100 also slips when students rely on rote counting instead of grouping by tens and hundreds.
How can families help with word problems?
Read the problem out loud together and ask what is happening before doing any math. Acting it out with toys or drawing a quick picture helps more than rushing to an answer. It is fine to talk through it even if the answer comes slowly.
How much should students memorize math facts?
By the end of the year, students should know addition and subtraction facts within 20 from memory. Daily five-minute practice with flashcards, dice, or quick oral quizzes works well. Speed comes after understanding, not before.
How do I know students are ready for next year?
They can add and subtract two-digit numbers with regrouping, explain their thinking, measure with a ruler in inches or centimeters, tell time to five minutes, and solve two-step word problems. Confidence with place value into the hundreds is the clearest signal.