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Learning Standards Standards

What does a student learn in ?

This is the year math stops being about whole numbers and starts being about lines, slopes, and the relationships between them. Students work with negative exponents, square roots, and very large or very small numbers written in scientific notation. They learn to graph straight lines, solve equations with a variable on both sides, and figure out where two lines cross. By spring, students can look at a real-world situation, write an equation for it, and graph the line that matches.

  • Linear equations
  • Slope and graphs
  • Exponents
  • Scientific notation
  • Square roots
  • Systems of equations
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

    Rational and irrational numbers

    Students learn that some numbers, like the square root of 2 or pi, cannot be written as simple fractions. They place these numbers on a number line and compare their sizes.

  2. 2

    Exponents and scientific notation

    Students work with very large and very small numbers using powers of ten. They write distances in space or sizes of cells in a shorter form and do basic math with them.

  3. 3

    Linear equations and slope

    Students solve equations with a variable on both sides and study lines on a graph. They learn what slope means as a steady rate of change, like miles per hour or dollars per week.

  4. 4

    Systems of equations

    Students solve two equations at once to answer questions with two unknowns, like figuring out the price of a sandwich and a drink when given two combo totals.

  5. 5

    Functions and real-world relationships

    Students study how one quantity depends on another, like how far a car goes based on time. They read these relationships from tables, graphs, and short rules.

  6. 6

    Geometry and the Pythagorean theorem

    Students use the Pythagorean theorem to find missing side lengths of right triangles and distances on a map. They also work with transformations, angles, and the volume of cones, cylinders, and spheres.

Mastery Learning Standards
The required skills a student should display by the end of Grade 8.
Standards for Mathematical Practice

  • Make Sense of Problems

    DC-MATH.MP.8.1

    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.8.2

    Students take a real problem, strip it down to numbers and symbols to solve it, then translate the answer back into what it actually means in context.

  • Construct Arguments

    DC-MATH.MP.8.3

    Students back up their math answers with reasons, then listen to classmates' thinking and explain where they agree or disagree.

  • Model with Mathematics

    DC-MATH.MP.8.4

    Students take a real-world situation, like splitting a bill or figuring out how long a trip takes, and write an equation or draw a diagram to make sense of it.

  • Use Tools Strategically

    DC-MATH.MP.8.5

    Students choose the right tool for the job, whether that means grabbing a calculator, sketching by hand, or making a quick estimate. The goal is knowing when each approach helps and when it gets in the way.

  • Attend to Precision

    DC-MATH.MP.8.6

    Students use the right math words and label answers with the correct units, like inches or dollars. They check their calculations carefully so small errors don't lead to wrong answers.

  • Use Structure

    DC-MATH.MP.8.7

    Students learn to spot patterns and hidden structure in math problems, like noticing that a shape or equation follows a rule they already know. That shortcut helps them solve new problems faster.

  • Express Regularity

    DC-MATH.MP.8.8

    When a calculation keeps working the same way, students notice the pattern and write a rule for it instead of repeating the same steps every time.

K-8 Mathematics Content

  • Counting and Number

    DC-MATH.K8.8.1

    Grade 8 students work with whole numbers, fractions, and negative numbers to solve problems. They use what they know about how numbers relate to each other, including place value and rational number rules, to reason through math at this level.

  • Operations and Algebraic Thinking

    DC-MATH.K8.8.2

    Students use addition, subtraction, multiplication, and division to write expressions and solve problems. At this grade, that work involves variables, exponents, and equations with multiple steps.

  • Measurement and Data

    DC-MATH.K8.8.3

    Students read and build tables, graphs, and basic statistical summaries to make sense of real data. They use those tools to spot patterns and draw conclusions.

  • Geometry

    DC-MATH.K8.8.4

    Students describe, sort, and measure flat and solid shapes, finding angles, side lengths, area, and volume to solve problems.

  • Ratios and Proportional Relationships

    DC-MATH.K8.8.5

    Students use ratios and proportions to solve everyday problems, like figuring out unit prices, scaling a recipe, or comparing speeds. The math connects numbers to real situations they'll actually encounter.

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
National Monitoring

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
Official source
Common Questions
  • What math will students work on this year?

    Students move past arithmetic into early algebra. They solve equations with a variable on both sides, graph lines and find slope, work with square roots and exponents, and start to think about functions as rules that turn one number into another. Geometry includes angles, triangles, and the Pythagorean theorem.

  • How can a parent help with homework without remembering all the math?

    Ask students to explain what the problem is asking before they pick up a pencil. Then ask what they tried and where they got stuck. Most of the work happens when students put the steps into their own words, even if a parent has not seen this math in years.

  • What should students be able to do by the end of the year?

    Solve a linear equation and check the answer, graph a line from an equation, find the slope between two points, and use the Pythagorean theorem to find a missing side. Students should also read a scatter plot and describe the pattern in plain words.

  • How should the year be sequenced?

    Most teachers start with exponents and roots, move into linear equations, then connect equations to graphs and slope. Functions come next, then geometry with the Pythagorean theorem and transformations, and bivariate data at the end. The early algebra work pays off in every later unit.

  • Which topics usually need the most reteaching?

    Slope as a rate of change, solving equations with variables on both sides, and the difference between a function and a non-function. Many students can compute slope but cannot explain what it means in a story problem, so build in time for that.

  • What can practice at home look like in ten minutes?

    Pick a real number from a receipt, a bill, or a sports stat and ask what it means per item, per minute, or per game. That kind of rate question is the heart of slope. Quick mental math with negative numbers and fractions also helps, since both show up constantly.

  • How do teachers know students are ready for high school math?

    Students should be able to set up an equation from a word problem, solve it, and explain whether the answer makes sense. They should also be comfortable with negative numbers, fractions, and graphs without a calculator doing the thinking for them.

  • What if a student is still shaky on fractions and negative numbers?

    Fold quick review into the new work instead of stopping to reteach a whole unit. When solving an equation lands on a fraction or a negative answer, slow down and talk through that step. Students catch up faster when the review is tied to a problem they actually care about solving.