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Learning Standards Standards

What does a student learn in ?

This is the year arithmetic stretches into algebra. Students start using letters in place of numbers, so 3 times some unknown becomes 3x, and they solve simple equations to find what x stands for. They also learn to compare amounts using ratios and rates, like miles per hour or the price of one apple. By spring, students can write a short equation for a word problem and solve it.

  • Ratios and rates
  • Variables
  • Solving equations
  • Negative numbers
  • Data and graphs
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

    Ratios and rates

    Students learn to compare amounts using ratios, like 2 cups of flour for every 3 cups of water. They use these to solve everyday problems involving prices, recipes, and speed.

  2. 2

    Fractions and decimals

    Students divide fractions by fractions and get fluent with adding, subtracting, multiplying, and dividing decimals. Expect more problems that mix money, measurement, and long division.

  3. 3

    Negative numbers and the number line

    Students extend the number line to include negatives, working with temperatures below zero, elevations, and account balances. They plot points in all four sections of a coordinate grid.

  4. 4

    Expressions and equations

    Letters start standing in for numbers. Students write and simplify expressions like 3x + 5, solve one-step equations, and use simple inequalities to describe real situations.

  5. 5

    Area, surface area, and volume

    Students find the area of triangles and odd shapes by breaking them into pieces. They also calculate the volume of boxes with fractional sides and the surface area of 3D figures using nets.

  6. 6

    Statistics and data

    Students learn what makes a question a statistical one and summarize data with the mean, median, and range. They read and build dot plots, histograms, and box plots.

Mastery Learning Standards
The required skills a student should display by the end of Grade 6.
Standards for Mathematical Practice

  • Make Sense of Problems

    DC-MATH.MP.6.1

    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.6.2

    Students take a real situation (like splitting a lunch bill) and turn it into numbers and symbols to solve it, then explain what the answer actually means in the original context.

  • Construct Arguments

    DC-MATH.MP.6.3

    Students explain why their math answer is correct, using numbers or examples as proof. They also listen to a classmate's reasoning and point out where it holds up or falls apart.

  • Model with Mathematics

    DC-MATH.MP.6.4

    Students take a real situation (splitting a bill, planning a garden, figuring out a trip) and write an equation or draw a diagram to solve it. Math becomes a tool for problems that exist outside the classroom.

  • Use Tools Strategically

    DC-MATH.MP.6.5

    Students choose the right tool for each math problem, whether that means reaching for a calculator, sketching it out on paper, or making a quick estimate in their head.

  • Attend to Precision

    DC-MATH.MP.6.6

    Students use the right math words, label their answers with the correct units (like inches or dollars), and check that their calculations are exact. Sloppy language or a missing label can make a correct answer look wrong.

  • Use Structure

    DC-MATH.MP.6.7

    Students learn to spot patterns and hidden structure in math problems, like noticing that every even number can be split into two equal groups. Recognizing that structure helps them solve new problems faster without starting from scratch each time.

  • Express Regularity

    DC-MATH.MP.6.8

    When the same steps keep showing up in a problem, students notice the pattern and use it as a shortcut. That habit saves time and builds toward formulas and rules students can apply on their own.

K-8 Mathematics Content

  • Counting and Number

    DC-MATH.K8.6.1

    Sixth graders work with whole numbers, fractions, and negative numbers to solve problems. They use number-system rules to compare, order, and calculate across all three types of numbers.

  • Operations and Algebraic Thinking

    DC-MATH.K8.6.2

    Sixth graders write and solve expressions using addition, subtraction, multiplication, and division. They translate word problems into math notation and work out the answer.

  • Measurement and Data

    DC-MATH.K8.6.3

    Students read and build tables, bar graphs, and dot plots to answer questions about real data. They also find the mean, median, and range to summarize what a set of numbers shows.

  • Geometry

    DC-MATH.K8.6.4

    Students sort, describe, and measure flat and solid shapes, identifying angles, side lengths, area, and volume at a sixth-grade level.

  • Ratios and Proportional Relationships

    DC-MATH.K8.6.5

    Students use ratios to solve everyday problems, like figuring out how far a car travels per gallon or how much of each ingredient goes into a recipe. The math connects two quantities and scales them up or down.

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