Place value and big numbers
Students read, write, and compare numbers up to a million. They round to the nearest ten, hundred, or thousand and use place value to estimate before they calculate.
What does a student learn in
This is the year math stretches into bigger numbers and fractions start to feel like real amounts. Students work with numbers in the thousands, multiply larger numbers, and divide with remainders. They compare fractions, add fractions with the same bottom number, and start seeing decimals like money. By spring, students can solve a multi-step word problem and explain why a fraction like 3/4 is bigger than 2/3.
- Multi-digit multiplication
- Long division
- Fractions
- Decimals
- Word problems
- Measurement
- Angles and 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
Multiplication and division
Students multiply larger numbers and divide with remainders. They solve word problems with more than one step and check whether the answer makes sense.
- 3
Fractions and equal parts
Students compare fractions, add and subtract fractions with the same bottom number, and start working with decimals like 0.25 and 0.5. They see how a quarter of a pizza relates to a quarter on a number line.
- 4
Shapes, angles, and measurement
Students measure angles, sort shapes by their sides and corners, and convert between units like inches and feet or minutes and hours. They also read graphs and tables to answer real questions.
Mastery Learning Standards
The required skills a student should display by the end of Grade 4.
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's actually asking, and keep trying even when the first approach doesn't work.
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Reason Abstractly
Students take a real problem (like splitting 24 apples into equal groups) and turn it into numbers and symbols to solve it. Then they check that the answer makes sense back in the real situation.
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Construct Arguments
Students explain why their math answer is correct and listen carefully to a classmate's reasoning to decide whether it holds up. They back up their thinking with numbers, drawings, or examples.
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Model with Mathematics
Students use math to figure out real-world problems, like splitting a bill, measuring a room, or planning a schedule. The math connects to something outside the textbook.
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Use Tools Strategically
Students choose the right tool for the job, whether that means grabbing a ruler, reaching for a calculator, or working it out on paper. The point is knowing which tool fits the problem.
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Attend to Precision
Students choose words, labels, and units carefully when solving problems. They check that numbers and measurements make sense before writing a final answer.
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Use Structure
Students learn to spot patterns and hidden structure in math problems, like noticing that multiplying by 4 is just doubling twice. Recognizing that structure helps students solve new problems faster instead of starting from scratch each time.
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Express Regularity
Students notice when the same steps keep showing up in different problems and use that pattern as a shortcut or rule. Instead of starting from scratch each time, they explain why the pattern works.
| Standard | Definition | Code |
|---|---|---|
| Make Sense of Problems | Students read a math problem carefully, figure out what it's actually asking, and keep trying even when the first approach doesn't work. | VT-MATH.MP.4.1 |
| Reason Abstractly | Students take a real problem (like splitting 24 apples into equal groups) and turn it into numbers and symbols to solve it. Then they check that the answer makes sense back in the real situation. | VT-MATH.MP.4.2 |
| Construct Arguments | Students explain why their math answer is correct and listen carefully to a classmate's reasoning to decide whether it holds up. They back up their thinking with numbers, drawings, or examples. | VT-MATH.MP.4.3 |
| Model with Mathematics | Students use math to figure out real-world problems, like splitting a bill, measuring a room, or planning a schedule. The math connects to something outside the textbook. | VT-MATH.MP.4.4 |
| Use Tools Strategically | Students choose the right tool for the job, whether that means grabbing a ruler, reaching for a calculator, or working it out on paper. The point is knowing which tool fits the problem. | VT-MATH.MP.4.5 |
| Attend to Precision | Students choose words, labels, and units carefully when solving problems. They check that numbers and measurements make sense before writing a final answer. | VT-MATH.MP.4.6 |
| Use Structure | Students learn to spot patterns and hidden structure in math problems, like noticing that multiplying by 4 is just doubling twice. Recognizing that structure helps students solve new problems faster instead of starting from scratch each time. | VT-MATH.MP.4.7 |
| Express Regularity | Students notice when the same steps keep showing up in different problems and use that pattern as a shortcut or rule. Instead of starting from scratch each time, they explain why the pattern works. | VT-MATH.MP.4.8 |
K-8 Mathematics Content
K-8 Mathematics Content
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Counting and Number
Grade 4 number work covers whole numbers, fractions, and basic negatives. Students read, compare, and reason about these numbers, building the number sense they need before algebra starts.
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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 the pieces of a problem fit together.
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Measurement and Data
Students read and build tables and graphs, then answer real questions from the data, like which category was biggest or how totals compare.
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Geometry
Students sort and describe flat shapes (like squares and triangles) and solid shapes (like cubes and cones), measuring angles and sides to explain what makes each shape what it is.
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Ratios and Proportional Relationships
Students use ratio reasoning to solve practical problems, like figuring out how many supplies are needed for a class or how far a car travels in a given time. This is an introduction to comparing quantities that builds through middle school.
| Standard | Definition | Code |
|---|---|---|
| Counting and Number | Grade 4 number work covers whole numbers, fractions, and basic negatives. Students read, compare, and reason about these numbers, building the number sense they need before algebra starts. | VT-MATH.K8.4.1 |
| Operations and Algebraic Thinking | Students practice adding, subtracting, multiplying, and dividing to solve word problems and write number sentences that show how the pieces of a problem fit together. | VT-MATH.K8.4.2 |
| Measurement and Data | Students read and build tables and graphs, then answer real questions from the data, like which category was biggest or how totals compare. | VT-MATH.K8.4.3 |
| Geometry | Students sort and describe flat shapes (like squares and triangles) and solid shapes (like cubes and cones), measuring angles and sides to explain what makes each shape what it is. | VT-MATH.K8.4.4 |
| Ratios and Proportional Relationships | Students use ratio reasoning to solve practical problems, like figuring out how many supplies are needed for a class or how far a car travels in a given time. This is an introduction to comparing quantities that builds through middle school. | VT-MATH.K8.4.5 |
Assessments
The state tests students at this grade and subject take.
VTCAP: Mathematics (Grades 3-9)
Vermont's spring summative math test for grades 3 through 9, aligned to Vermont's Common Core-based math standards.
- When given:
- spring
- Frequency:
- annual
NAEP (National Assessment of Educational Progress)
Federally administered sample-based assessment in reading, mathematics, science, and writing. NAEP results inform state-by-state comparisons rather than individual student or school accountability.
- When given:
- biennial in winter
- Frequency:
- every two years
Common Questions
What math will students learn this year?
Students work with larger whole numbers into the thousands, learn long multiplication and division, and start working with fractions in a serious way. They also measure with rulers and clocks, read graphs, and sort shapes by their angles and sides.
How can I help with math at home in just a few minutes?
Cook together and double a recipe, split a pizza into equal parts, or count change at the store. Asking how students figured something out matters more than getting a quick right answer.
Why is so much time spent on fractions this year?
Fractions are the bridge to almost everything in middle school math, including decimals, percents, and ratios. Students need to see that one half and two fourths are the same amount, and to add and compare fractions with the same bottom number.
What should students know by the end of the year to be ready for next grade?
Students should multiply and divide multi-digit numbers, add and subtract fractions with the same denominator, and solve word problems with more than one step. They should also measure accurately and read a basic graph.
How should multiplication and division be sequenced across the year?
Build fact fluency early, then move into area models and partial products before the standard algorithm. Division usually needs the most time, so plan to revisit it in short bursts after the first unit rather than treating it as one and done.
My child still counts on fingers. Is that a problem?
By this grade, fact recall should be fairly quick. Practice a few facts a night with flashcards or a short game, and focus on the ones that trip students up most often. Fingers are a fallback, not the goal.
Which topics tend to need the most reteaching?
Fraction equivalence, multi-digit division, and word problems with extra information usually need a second pass. Build in review weeks after winter and spring break so these come back into rotation before the year ends.
How much should students explain their thinking, not just get the answer?
Explaining thinking is now a core part of the work. Students should be able to say why a strategy works and spot a mistake in someone else's reasoning, in writing or out loud. A correct answer with no explanation is only half the task.