Grade 7•Math skills checklist

What should a 7th grader know in math?

The complete grade 7 math skills checklist

Seventh grade deepens algebraic thinking and introduces proportional reasoning. Students master operations with rational numbers and solve multi-step equations. This year builds the critical bridge to high school algebra.

Check your child's level

Ratios & Proportional Relationships

Compute unit rates with fractions

Calculate unit rates involving complex fractions.

Examples: 1/2 mile in 1/4 hour = 2 mph, 3/4 cup per 1/2 serving

Identify proportional relationships

Determine if two quantities are proportional using tables, graphs, and equations.

Examples: y = 3x is proportional, Graph passes through origin with constant slope

Find constant of proportionality

Identify k in y = kx from various representations.

Examples: If y = 4x, then k = 4, Find k from table of values

Solve multi-step ratio problems

Use proportional reasoning for percent increase/decrease and markup/markdown.

Examples: 20% off $50 = $40, Price increased by 15%

The Number System

Add and subtract integers

Fluently add and subtract positive and negative numbers.

Examples: -5 + 8 = 3, 7 - (-3) = 10

Multiply and divide integers

Apply sign rules for multiplication and division.

Examples: -4 × -3 = 12, -15 ÷ 3 = -5

Operations with rational numbers

Add, subtract, multiply, and divide fractions and decimals including negatives.

Examples: -2/3 + 1/4, -0.5 × 1.2

Convert between forms

Convert between fractions, decimals, and percents fluently.

Examples: 3/8 = 0.375 = 37.5%, 0.6 = 3/5

Expressions & Equations

Apply properties to expressions

Simplify expressions using distributive property and combining like terms.

Examples: 3(x + 4) - 2x = x + 12, 5a + 3 - 2a + 7 = 3a + 10

Solve two-step equations

Solve equations of the form px + q = r.

Examples: 2x + 5 = 13 → x = 4, 3x - 7 = 14 → x = 7

Solve two-step inequalities

Solve and graph inequalities; understand when to flip the sign.

Examples: -2x + 5 > 11 → x < -3, 3x - 4 ≤ 8

Write equations from situations

Translate real-world problems into equations and solve.

Examples: Tom has $5 more than twice what Sue has. Together they have $23.

Geometry

Solve problems with scale drawings

Use scale factors to find actual lengths and areas.

Examples: Scale 1 inch = 5 feet; 3 inches on map = 15 feet actual

Draw geometric shapes with conditions

Construct triangles given conditions; determine when triangles are possible.

Examples: Triangle inequality: sum of two sides > third side

Solve angle relationship problems

Use supplementary, complementary, vertical, and adjacent angle relationships.

Examples: Supplementary angles sum to 180°, Vertical angles are equal

Circles & Pi

Understand pi as a ratio

Know that pi (π ≈ 3.14) is the ratio of circumference to diameter for any circle.

Examples: C ÷ d = π for all circles, π ≈ 3.14159...

Find circumference from radius or diameter

Apply C = πd or C = 2πr to calculate distance around a circle.

Examples: r = 5: C = 2π(5) = 10π ≈ 31.4, d = 8: C = 8π ≈ 25.12

Find area of circles

Apply A = πr² to calculate the space inside a circle.

Examples: r = 3: A = π(3)² = 9π ≈ 28.26, d = 10: r = 5, A = 25π

Solve circle word problems

Apply formulas to real-world contexts: fencing, pizza, wheels, gardens.

Examples: Fencing for circular garden uses circumference, Pizza toppings need area

Statistics & Probability

Use random sampling

Understand how random samples represent populations.

Examples: Survey 50 random students to estimate school opinion

Compare two populations

Use measures of center and variability to compare data sets.

Examples: Compare mean and MAD of two groups

Understand probability

Find experimental and theoretical probabilities.

Examples: P(heads) = 1/2, Flip 100 times, expect ~50 heads

Where grade 7 students often struggle

  • Confusing "subtract a negative" with "add a negative" (−(−5) = +5)
  • Forgetting to flip inequality sign when multiplying/dividing by negative
  • Mixing up area (πr²) and circumference (2πr) formulas
  • Not recognizing non-proportional relationships (y = 2x + 1 is NOT proportional)
  • Incorrectly distributing negative signs: −2(x − 3) ≠ −2x − 6
  • Confusing percent OF vs percent change

Signs your child is on track

  • Computes with negative numbers without finger counting or number lines
  • Solves two-step equations and checks answers by substitution
  • Identifies proportional vs non-proportional relationships correctly
  • Fluently converts between fractions, decimals, and percents
  • Sets up equations from word problems independently
  • Uses formulas correctly with units

Coming in grade 8

Mastering these grade 7 skills prepares your child for:

Linear equations and functions
Systems of equations introduction
Transformations and congruence
Pythagorean theorem
Volume of cylinders, cones, and spheres
Bivariate data and scatter plots

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