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Learning Standards Standards

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
Source: District of Columbia DC Academic Content Standards
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. 1

    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.

  2. 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. 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. 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. 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. 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

  • Make Sense of Problems

    DC-MATH.MP.5.1

    Students read a math problem carefully, figure out what it's actually asking, and keep trying even when the first approach doesn't work.

  • Reason Abstractly

    DC-MATH.MP.5.2

    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.

  • Construct Arguments

    DC-MATH.MP.5.3

    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.

  • Model with Mathematics

    DC-MATH.MP.5.4

    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.

  • Use Tools Strategically

    DC-MATH.MP.5.5

    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.

  • Attend to Precision

    DC-MATH.MP.5.6

    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.

  • Use Structure

    DC-MATH.MP.5.7

    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

    DC-MATH.MP.5.8

    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.

K-8 Mathematics Content

  • Counting and Number

    DC-MATH.K8.5.1

    Students work with whole numbers, fractions, and basic negative numbers, using what they know about how numbers are built to solve grade-level problems.

  • Operations and Algebraic Thinking

    DC-MATH.K8.5.2

    Students use addition, subtraction, multiplication, and division to solve word problems and write expressions that show how they got there.

  • Measurement and Data

    DC-MATH.K8.5.3

    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.

  • Geometry

    DC-MATH.K8.5.4

    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.

  • Ratios and Proportional Relationships

    DC-MATH.K8.5.5

    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.

Assessments
The state tests students at this grade and subject take.
State Summative

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
Official source
Alternate assessment

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
Official source