What should a Grade 6 student know in math?
Ratios and rates, dividing fractions, negative numbers, expressions and first equations, and statistical thinking.
Grade 6 math practice — adaptive, verified, parent-run
9,200 verified practice questions across 86 Common Core concepts for Grade 6
What should a Grade 6 student know?
Sixth grade opens middle school. Ratios and unit rates reframe multiplication, fraction division clicks into place, and the number line grows negative numbers. This is where math starts feeling abstract — on purpose.
Your child writes and evaluates expressions with variables, solves one-step equations, and meets statistics as a way to describe variability. Parents often see the first real wobble here; catching it per-concept matters.
The curriculum map
Every Common Core concept we cover for Grade 6
Expressions and Equations
- Analyze relationships between dependent and independent variables
- Analyze variable relationships using graphs and tables
- Apply properties to generate equivalent expressions
- Determine when two expressions are equivalent
- Evaluate expressions at specific variable values
- Generate equivalent expressions
- Identify equivalent expressions
- Identify parts of expressions using mathematical terms
- Represent inequality solutions on number lines
- Solve equations of the form px = q
- Solve equations of the form x + p = q
- Solve one-step equations with nonnegative rationals
- Understand solving as finding values that make statements true
- Understand solving equations and inequalities
- Use substitution to verify solutions
- Use variables to represent numbers in problems
- Use variables to represent unknowns in expressions
- Write algebraic expressions from verbal descriptions
- Write and evaluate expressions with exponents
- Write and evaluate numerical expressions with exponents
- Write and represent inequalities
- Write equations relating dependent and independent variables
- Write inequalities to represent constraints
- Write, read, and evaluate expressions with variables
Geometry
- Apply volume formulas with fractional edge lengths
- Draw polygons on coordinate plane and find side lengths
- Draw polygons on the coordinate plane from vertex coordinates
- Find area of special quadrilaterals and polygons
- Find area of triangles by composing or decomposing
- Find area of triangles, quadrilaterals, and polygons
- Find side lengths of coordinate polygons
- Find surface area using nets
- Find volume of prism with fractional edges by packing
- Find volume of rectangular prisms with fractional edges
- Represent 3D figures using nets
- Represent 3D figures with nets and find surface area
Ratios and Proportional Relationships
- Find a percent of a quantity and solve percent problems
- Make tables of equivalent ratios and find missing values
- Solve unit rate problems
- Understand ratio concepts
- Understand unit rate as a/b for ratio a:b
- Understand unit rates
- Use rate language in ratio contexts
- Use ratio and rate reasoning to solve problems
- Use ratio language to describe relationships
- Use ratio reasoning to convert measurement units
Statistics and Probability
- Calculate measures of center (mean and median)
- Calculate measures of variability (IQR and MAD)
- Describe a distribution by center, spread, and shape
- Display data in plots
- Display data on dot plots, histograms, and box plots
- Distinguish statistical from non-statistical questions
- Recognize statistical questions
- Relate choice of measures to distribution shape and context
- Report observations and describe the measured attribute
- Summarize numerical data sets
- Understand data distributions
- Understand measure of center vs measure of variation
- Understand measures of center and variation
The Number System
- Create a story context for fraction division
- Distinguish absolute value comparisons from ordering
- Divide fractions by fractions
- Find distances between points using coordinates and absolute value
- Find GCF and LCM and use distributive property
- Find the greatest common factor of two numbers
- Find the least common multiple of two numbers
- Fluently add and subtract multi-digit decimals
- Fluently divide multi-digit numbers
- Fluently divide multi-digit numbers using standard algorithm
- Fluently multiply and divide multi-digit decimals
- Fluently operate with multi-digit decimals
- Graph points in all four quadrants
- Interpret and compute quotients of fractions
- Interpret inequalities as positions on number line
- Plot rational numbers on number line and coordinate plane
- Rational numbers on number line and coordinate plane
- Recognize opposites on the number line
- Represent quantities with positive and negative numbers in context
- Solve word problems with fraction division
- Understand absolute value as distance from zero
- Understand ordering and absolute value of rational numbers
- Understand positive and negative as opposite directions
- Understand positive and negative numbers
- Understand signs of coordinates indicate quadrants
- Use distributive property to factor sums with common factors
- Write and interpret ordering statements in real-world contexts
Diagnosis, not just marking
Where Grade 6 students actually go wrong
For these concepts we've written up the specific mistaken rules children apply — what each one sounds like at the kitchen table, and why it feels right to them. Free to read, no account needed.
Grade 6 math — questions parents ask
How much math practice does a Grade 6 student need each day?
Short and daily beats long and rare. Most families set a 10–30 minute time budget; Algo School sizes each Grade 6 session to that budget and to your child's pace — a quick day never becomes a marathon.
How does Algo School help with Grade 6 math at home?
Algo School generates short daily sessions from 9,200 verified Grade 6 questions, checks every answer, and adapts the next session to what your child actually mastered. When they're stuck, an answer-guarded AI tutor coaches with questions and hints — and you get an email brief after every tutoring session. Homeschool families use the per-concept mastery record as their assessment evidence.
Math practice for every band — home and homeschool, Grade 1 through Algebra 2.
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