Place value and decimals
Students start the year by extending place value into decimals. They read, write, and compare numbers like 2.45 and 2.405, and they multiply and divide whole numbers by 10, 100, and 1000.
What does a student learn in
This is the year math stretches past whole numbers and into decimals and fractions as full working tools. Students add and subtract fractions with unlike denominators, multiply and divide fractions in real situations, and read decimals out to the thousandths place. They also start writing simple expressions and plotting points on a grid. By spring, students can add 1/2 and 1/3 on paper and explain why 0.7 is bigger than 0.68.
- Fractions
- Decimals
- Multiplying and dividing
- Coordinate grid
- Volume
- Word problems
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
Operations with whole numbers and decimals
Students multiply larger numbers and divide with two-digit divisors. They also add, subtract, multiply, and divide decimals in problems involving money and measurement.
- 3
Fractions as numbers
Students add and subtract fractions with unlike denominators, like 1/3 and 1/4. They also multiply fractions and divide with unit fractions, often using pictures and real situations to make sense of the answers.
- 4
Measurement, data, and volume
Students convert between units like inches and feet or meters and centimeters, and they read line plots with fractional measurements. They also find the volume of boxes by counting unit cubes and using length times width times height.
- 5
Expressions, patterns, and the coordinate plane
Students write and read simple number expressions without solving them, like 3 times (5 plus 2). They plot points on a grid and use pairs of patterns to see how two rules relate.
- 6
Classifying shapes
Students sort two-dimensional shapes by their properties, noticing that a square is also a rectangle and a rhombus. They use these family relationships to explain why a shape belongs in more than one group.
Mastery Learning Standards
The required skills a student should display by the end of Grade 5.
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 situation, turn it into numbers or symbols to solve it, then translate the answer back into what it means in the real world.
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Construct Arguments
Students explain why their math answer is correct and listen critically to classmates' reasoning. They learn to spot flaws in an argument and defend their own thinking with evidence.
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Model with Mathematics
Students use math to make sense of real-world situations, like figuring out the cost of groceries or reading a map. They pick the right tools and numbers, set up a problem, and check whether their answer makes sense.
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Use Tools Strategically
Students choose the right tool for each math problem, whether that means grabbing a calculator, sketching it out on paper, or making a quick estimate in their head.
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Attend to Precision
Students use exact words, labels, and careful calculations when explaining their math work. That means writing the right unit (inches, not just numbers), choosing precise vocabulary, and checking that arithmetic is correct.
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Use Structure
Students notice patterns and hidden structure in numbers, shapes, and equations, then use those patterns as shortcuts to solve problems faster or explain why a method works.
-
Express Regularity
Students notice when the same steps keep showing up in a problem and use that pattern as a shortcut or rule. Instead of starting from scratch each time, they ask why it keeps working.
| 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. | DC-MATH.MP.5.1 |
| Reason Abstractly | Students take a real situation, turn it into numbers or symbols to solve it, then translate the answer back into what it means in the real world. | DC-MATH.MP.5.2 |
| Construct Arguments | Students explain why their math answer is correct and listen critically to classmates' reasoning. They learn to spot flaws in an argument and defend their own thinking with evidence. | DC-MATH.MP.5.3 |
| Model with Mathematics | Students use math to make sense of real-world situations, like figuring out the cost of groceries or reading a map. They pick the right tools and numbers, set up a problem, and check whether their answer makes sense. | DC-MATH.MP.5.4 |
| Use Tools Strategically | Students choose the right tool for each math problem, whether that means grabbing a calculator, sketching it out on paper, or making a quick estimate in their head. | DC-MATH.MP.5.5 |
| Attend to Precision | Students use exact words, labels, and careful calculations when explaining their math work. That means writing the right unit (inches, not just numbers), choosing precise vocabulary, and checking that arithmetic is correct. | DC-MATH.MP.5.6 |
| Use Structure | Students notice patterns and hidden structure in numbers, shapes, and equations, then use those patterns as shortcuts to solve problems faster or explain why a method works. | DC-MATH.MP.5.7 |
| Express Regularity | Students notice when the same steps keep showing up in a problem and use that pattern as a shortcut or rule. Instead of starting from scratch each time, they ask why it keeps working. | DC-MATH.MP.5.8 |
K-8 Mathematics Content
K-8 Mathematics Content
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Counting and Number
Students work with whole numbers, fractions, and basic negative numbers, using what they know about how numbers are built to solve grade-level problems.
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Operations and Algebraic Thinking
Students use addition, subtraction, multiplication, and division to solve word problems and write expressions that show how they got there.
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Measurement and Data
Students read and build tables, graphs, and simple data summaries to answer real questions about the world. The focus is on making sense of what the numbers say, not just plotting them.
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Geometry
Students sort and measure flat shapes like squares and triangles, and solid shapes like cubes and cylinders. They use what they know about angles, sides, and faces to group shapes and explain how they are alike or different.
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Ratios and Proportional Relationships
Students use ratio reasoning to solve problems where two quantities are compared or scaled, like figuring out how many cups of flour to use when doubling a recipe or splitting items into equal groups.
| Standard | Definition | Code |
|---|---|---|
| Counting and Number | Students work with whole numbers, fractions, and basic negative numbers, using what they know about how numbers are built to solve grade-level problems. | DC-MATH.K8.5.1 |
| Operations and Algebraic Thinking | Students use addition, subtraction, multiplication, and division to solve word problems and write expressions that show how they got there. | DC-MATH.K8.5.2 |
| Measurement and Data | Students read and build tables, graphs, and simple data summaries to answer real questions about the world. The focus is on making sense of what the numbers say, not just plotting them. | DC-MATH.K8.5.3 |
| Geometry | Students sort and measure flat shapes like squares and triangles, and solid shapes like cubes and cylinders. They use what they know about angles, sides, and faces to group shapes and explain how they are alike or different. | DC-MATH.K8.5.4 |
| Ratios and Proportional Relationships | Students use ratio reasoning to solve problems where two quantities are compared or scaled, like figuring out how many cups of flour to use when doubling a recipe or splitting items into equal groups. | DC-MATH.K8.5.5 |
Assessments
The state tests students at this grade and subject take.
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 this year?
Students should add, subtract, multiply, and divide with whole numbers and decimals, work with fractions including adding and subtracting ones with different bottom numbers, and understand place value through the thousandths. They should also graph points, find the volume of a box, and solve multi-step word problems.
How can families help with math at home in just a few minutes a day?
Cook together and double or halve a recipe to practice fractions. While shopping, ask how much three items cost or what the change should be. Measuring a room, splitting a pizza, or reading a sports stat all count as real math practice.
My child says they are bad at fractions. What helps?
Start with food and rulers, not worksheets. Cut a sandwich into fourths, then into eighths, and talk about which pieces are bigger and why. Once fractions feel like real pieces of real things, adding and subtracting them on paper gets much easier.
How should the year be sequenced?
A common path is place value and decimal operations first, then multiplication and division with larger numbers, then fraction operations, then measurement and volume, and finally the coordinate plane and shape classification. Fraction work usually needs the most time, so protect it.
Which skills usually need the most reteaching?
Adding and subtracting fractions with different bottom numbers, dividing whole numbers by unit fractions, and multiplying decimals tend to slip. Place value misconceptions also resurface when students start moving the decimal point. Build in short spiral review on these every few weeks.
What does mastery look like by spring?
Students can solve a multi-step word problem, choose the right operation, estimate to check if the answer is reasonable, and explain their reasoning out loud. They can also work fluently with decimals to the hundredths and add or subtract fractions with unlike bottom numbers.
Does my child still need to practice multiplication facts?
Yes. Quick recall of basic facts up to 12 by 12 makes everything else this year faster, including long division, fractions, and decimal work. Five minutes of flashcards or a fact game a few times a week is enough.
How do I know students are ready for next year?
They should handle fraction and decimal operations without freezing, solve a word problem with two or three steps, and explain why an answer makes sense. If they can tackle an unfamiliar problem and try something reasonable, they are ready for ratios and pre-algebra work.