Counting and number sense
Students count, read, and write numbers to 120. They build a feel for how numbers grow and start comparing which is bigger or smaller using everyday objects like coins and blocks.
What does a student learn in
This is the year counting turns into real addition and subtraction. Students work with numbers up to 100, learning to add and subtract within 20 and figuring out tens and ones inside a two-digit number. They also start telling time to the half hour and comparing the lengths of everyday objects. By spring, students can solve a small story problem like "I had 8 grapes and ate 3" and explain how they got the answer.
- Addition and subtraction
- Place value
- Word problems
- Telling time
- Measuring length
- 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
Adding and subtracting within 20
Students learn to add and subtract small numbers quickly. They use story problems about toys, snacks, and family to figure out what to add and what to take away.
- 3
Place value to 100
Students see that a number like 47 is made of 4 tens and 7 ones. They add and subtract larger numbers by thinking in groups of ten, the way we count dimes and pennies.
- 4
Measuring and telling time
Students measure things by lining up paper clips or cubes to see how long they are. They also learn to read clocks to the hour and half hour.
- 5
Shapes and equal parts
Students sort and build flat and solid shapes, like squares, triangles, and cubes. They split shapes into halves and quarters, the way a pizza or a sandwich gets cut.
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 read a math problem carefully, figure out what it is asking, and keep trying even when the first attempt does not work.
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Reason Abstractly
Students move back and forth between a real situation and the math that describes it. They can turn a story about apples into an equation, then use the answer to say something true about the apples.
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Construct Arguments
Students explain why their math answer makes sense and listen to how a classmate solved the same problem. They practice saying "I think this because..." and finding where someone's reasoning goes wrong.
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Model with Mathematics
Students use math to figure out real, everyday problems, like counting money at a store or sharing snacks equally. The math they practice in class connects to situations they actually encounter outside school.
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Use Tools Strategically
Students choose the right tool for the math at hand, whether that means reaching for a ruler, counting on fingers, or using a calculator.
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Attend to Precision
Students use the right words, labels, and careful arithmetic when solving and explaining math problems. In first grade, that means saying "more than" instead of "bigger," labeling a count with the right unit, and checking that the numbers in an answer add up correctly.
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Use Structure
Students notice patterns and shapes in numbers and figures, then use what they spot to solve problems. For example, seeing that a ten-frame is always two rows of five helps them count and add faster.
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Express Regularity
Students notice when the same steps keep working the same way, like seeing that adding zero never changes a number. They use that pattern as a shortcut instead of starting from scratch each time.
| Standard | Definition | Code |
|---|---|---|
| Make Sense of Problems | Students read a math problem carefully, figure out what it is asking, and keep trying even when the first attempt does not work. | DC-MATH.MP.1.1 |
| Reason Abstractly | Students move back and forth between a real situation and the math that describes it. They can turn a story about apples into an equation, then use the answer to say something true about the apples. | DC-MATH.MP.1.2 |
| Construct Arguments | Students explain why their math answer makes sense and listen to how a classmate solved the same problem. They practice saying "I think this because..." and finding where someone's reasoning goes wrong. | DC-MATH.MP.1.3 |
| Model with Mathematics | Students use math to figure out real, everyday problems, like counting money at a store or sharing snacks equally. The math they practice in class connects to situations they actually encounter outside school. | DC-MATH.MP.1.4 |
| Use Tools Strategically | Students choose the right tool for the math at hand, whether that means reaching for a ruler, counting on fingers, or using a calculator. | DC-MATH.MP.1.5 |
| Attend to Precision | Students use the right words, labels, and careful arithmetic when solving and explaining math problems. In first grade, that means saying "more than" instead of "bigger," labeling a count with the right unit, and checking that the numbers in an answer add up correctly. | DC-MATH.MP.1.6 |
| Use Structure | Students notice patterns and shapes in numbers and figures, then use what they spot to solve problems. For example, seeing that a ten-frame is always two rows of five helps them count and add faster. | DC-MATH.MP.1.7 |
| Express Regularity | Students notice when the same steps keep working the same way, like seeing that adding zero never changes a number. They use that pattern as a shortcut instead of starting from scratch each time. | DC-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 to recognize simple fractions like one-half by splitting shapes or groups into equal parts.
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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 after some are taken away. They start building the number sense that multiplication and division will rely on later.
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Measurement and Data
Students read and build simple charts and graphs, then answer questions about what the data shows. They compare amounts, spot the most and least, and draw basic conclusions from the information in front of them.
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Geometry
Students sort and describe flat shapes like squares and triangles alongside solid shapes like cubes and spheres. They notice sides, corners, and faces to explain how shapes are alike or different.
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Ratios and Proportional Relationships
Ratio reasoning shows up in grade 1 as comparing groups, like noticing there are twice as many apples as oranges. Students use that kind of thinking to solve simple real-world problems about quantities and how they relate.
| Standard | Definition | Code |
|---|---|---|
| Counting and Number | Students count, compare, and work with whole numbers up to 120. They start to recognize simple fractions like one-half by splitting shapes or groups into equal parts. | DC-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 after some are taken away. They start building the number sense that multiplication and division will rely on later. | DC-MATH.K8.1.2 |
| Measurement and Data | Students read and build simple charts and graphs, then answer questions about what the data shows. They compare amounts, spot the most and least, and draw basic conclusions from the information in front of them. | DC-MATH.K8.1.3 |
| Geometry | Students sort and describe flat shapes like squares and triangles alongside solid shapes like cubes and spheres. They notice sides, corners, and faces to explain how shapes are alike or different. | DC-MATH.K8.1.4 |
| Ratios and Proportional Relationships | Ratio reasoning shows up in grade 1 as comparing groups, like noticing there are twice as many apples as oranges. Students use that kind of thinking to solve simple real-world problems about quantities and how they relate. | DC-MATH.K8.1.5 |
No state assessments at this grade
Students take their next one in Grade 3.
DC CAPE: Mathematics (Grades 3-8)
DC's spring summative math test for grades 3 through 8, aligned to DC's Common Core-based math standards.
- When given:
- spring
- Frequency:
- annual
MSAA (Multi-State Alternate Assessment)
Alternate assessment for students with the most significant cognitive disabilities, given in grades 3-8 and high school in ELA, math, and science.
- When given:
- spring
- Frequency:
- annual
Common Questions
What math should students know by the end of the year?
Students should count, read, and write numbers to 120, add and subtract within 20, and solve simple word problems. They should also tell time on a clock, compare lengths, and recognize basic shapes. Quick recall of small sums like 4 plus 3 is a good sign of readiness.
How can a parent help with math in 10 minutes at home?
Count coins together, ask how many minutes until dinner, or play a quick card game where students add the two top cards. Real objects like buttons, snacks, or steps up the stairs build number sense faster than worksheets at this age.
What if a student counts on fingers? Is that a problem?
Finger counting is normal and useful in first grade. It helps students see that 7 is 5 and 2 more, which builds toward quick recall later. The goal is faster strategies over time, not banning fingers.
How should addition and subtraction be sequenced across the year?
Start with sums and differences within 10 using counters and number lines, then move to making ten as a strategy, then extend to 20. Word problems should run alongside computation from the start so students learn to pick the operation, not just compute.
Which first grade skills usually need the most reteaching?
Place value with teen numbers trips up many students, since 14 sounds like 40 and looks backward from how it is said. Subtraction across ten and reading a clock to the half hour are the other common sticking points. Plan extra review time for these.
What does a word problem look like at this grade?
Students solve short stories like "There are 8 birds. 3 fly away. How many are left?" They should be able to draw a picture, write a number sentence, and explain the answer in their own words. Expect about one or two steps, not multi-step problems.
Do students need to memorize math facts in first grade?
Quick recall of sums within 10 is the year-end goal, with within-20 facts becoming more automatic by second grade. Short daily practice with flashcards or dice beats long weekly drills. Aim for five focused minutes a day.
How do students show they understand place value?
Students should see 47 as 4 tens and 7 ones, build that number with blocks or bundles of straws, and compare it to other two-digit numbers. Asking "which is bigger, 38 or 83?" and "how do you know?" is a fast check.
How do shapes and measurement fit into the year?
Students name and build shapes like rectangles, triangles, and cubes, and start splitting shapes into halves and quarters. For measurement, they compare lengths directly and use small objects like paperclips as units. These topics work well in shorter units spread across the year.
How can a parent tell if a student is ready for second grade math?
Students should add and subtract small numbers without counting every object, read and write numbers past 100, and tell time to the hour and half hour. If word problems with two numbers feel doable, students are in good shape for the next year.