Grade 6•Math skills checklist

What should a 6th grader know in math?

The complete grade 6 math skills checklist

Sixth grade bridges arithmetic and algebra. Students master ratios, extend the number line to negatives, and begin working with variables. Gaps here create major struggles in algebra.

Check your child's level

Ratios & Proportional Relationships

Understand ratio concepts

Use ratio language to describe relationships between quantities.

Examples: 3:2 ratio of boys to girls, For every 2 cups flour, use 1 cup sugar

Find unit rates

Calculate and use unit rates to solve problems.

Examples: $15 for 3 pounds = $5 per pound, 120 miles in 2 hours = 60 mph

Use ratio reasoning

Solve problems using tables, tape diagrams, and double number lines.

Examples: If 3 apples cost $6, how much do 5 apples cost?

Understand percentages

Find percent of a number and solve percent problems.

Examples: 25% of 80 = 20, What percent of 50 is 15?
Common misconception

The Number System

Divide fractions by fractions

Fluently divide fractions using the "invert and multiply" method.

Examples: 2/3 ÷ 1/4 = 8/3, 1/2 ÷ 3/4 = 2/3

Compute with multi-digit decimals

Add, subtract, multiply, and divide decimals fluently.

Examples: 12.5 × 3.4, 45.6 ÷ 0.8

Understand negative numbers

Locate, compare, and order positive and negative numbers.

Examples: -5 < -2, |-7| = 7

Plot points in all four quadrants

Use signed numbers as coordinates on the coordinate plane.

Examples: Plot (-3, 4), Identify quadrant for (2, -5)

Expressions & Equations

Write and evaluate expressions

Translate word problems into algebraic expressions with variables.

Examples: 5 more than x → x + 5, Twice a number decreased by 3 → 2n - 3

Apply properties of operations

Use distributive, commutative, and associative properties.

Examples: 3(x + 4) = 3x + 12, 2 + 5 + 8 = 2 + 8 + 5

Solve one-step equations

Solve equations of the form x + p = q and px = q.

Examples: x + 5 = 12 → x = 7, 3x = 15 → x = 5
Common misconception

Write and solve inequalities

Represent constraints with inequalities and graph solutions.

Examples: x > 5, n ≤ 10

Statistics & Geometry

Understand statistical variability

Recognize that data has variability and can be described by center and spread.

Examples: Mean, median, mode, Range, interquartile range

Find area of polygons

Calculate area of triangles, quadrilaterals, and composite shapes.

Examples: Triangle area = 1/2 × base × height

Find volume of rectangular prisms

Apply V = lwh with fractional edge lengths.

Examples: Volume of 2.5 × 3 × 4 = 30 cubic units

Find surface area

Calculate total area of all faces using nets or formulas.

Examples: SA of box 3×4×5 = 2(12+15+20) = 94, SA of cube = 6s²

Where grade 6 students often struggle

  • Confusing ratios with fractions (a ratio of 3:5 is not the same as 3/5)
  • Thinking negative × negative = negative
  • Seeing the equals sign as "the answer goes here" instead of balance
  • Inverting BOTH fractions when dividing (only invert the divisor)
  • Converting percents incorrectly (25% ≠ 25, it equals 0.25)
  • Not checking if equation solutions actually work

Signs your child is on track

  • Can set up ratio tables and find missing values
  • Comfortable with negative numbers on a number line
  • Writes equations from word problems (not just solves given equations)
  • Explains the meaning of variables, not just computes with them
  • Can estimate percent calculations mentally (25% is about 1/4)
  • Self-corrects by substituting answers back into equations

Coming in grade 7

Mastering these grade 6 skills prepares your child for:

Proportional relationships and constant of proportionality
Operations with negative numbers
Two-step equations and inequalities
Scale drawings and geometric constructions
Probability concepts
Circumference and area of circles

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