What should a Grade 5 student know in math?
Fraction arithmetic in full, decimals to the thousandths, volume, the coordinate plane, and numerical expressions.
Grade 5 math practice — adaptive, verified, parent-run
6,221 verified practice questions across 63 Common Core concepts for Grade 5
What should a Grade 5 student know?
Fifth grade finishes elementary arithmetic. Your child adds, subtracts, multiplies, and divides fractions, and works with decimals to the thousandths. Middle-school algebra stands directly on this fluency.
New ideas: volume as a measurable property, plotting points on the coordinate plane, and writing and interpreting numerical expressions. A strong fifth grader walks into ratios and negative numbers ready.
The curriculum map
Every Common Core concept we cover for Grade 5
Geometry
- Classify 2D figures in a hierarchy
- Classify two-dimensional figures in a hierarchy based on properties
- Graph points in the first quadrant to represent problems
- Interpret coordinate values in context
- Locate points using ordered pairs on a coordinate plane
- Understand coordinate axes and the origin
- Understand that subcategory attributes apply to all members
Measurement and Data
- Apply volume formulas V = lwh and V = Bh
- Convert among standard measurement units within a system
- Count unit cubes to measure volume
- Find volume by packing and verify with multiplication
- Find volume of composite figures by adding volumes
- Make a line plot with fractional measurements (grade 5)
- Make line plots with fractions and solve problems
- Measure volume by counting unit cubes
- Relate volume to multiplication and addition
- Solve fraction operation problems using line plot data
- Understand concepts of volume measurement
- Understand unit cube and cubic units
- Use measurement conversions in multi-step problems
Number and Operations — Fractions
- Add and subtract fractions with unlike denominators
- Add and subtract mixed numbers with unlike denominators
- Add fractions with unlike denominators
- Compare product size to factor size without computing
- Create a story context for fraction multiplication
- Divide a unit fraction by a whole number
- Divide unit fractions and whole numbers
- Estimate fraction sums and differences and assess reasonableness
- Explain effect of multiplying by fractions greater or less than 1
- Find area of rectangle with fractional side lengths
- Interpret a fraction a/b as a divided by b
- Interpret multiplication as scaling
- Multiply a fraction or whole number by a fraction
- Solve real-world problems with fraction multiplication
- Solve word problems with division leading to fraction answers
- Solve word problems with fraction addition and subtraction (unlike denominators)
- Solve word problems with fraction and mixed number multiplication
- Solve word problems with unit fraction division
- Subtract fractions with unlike denominators
Number and Operations in Base Ten
- Add and subtract decimals to hundredths
- Compare decimals to thousandths
- Divide decimals to hundredths
- Divide with 2-digit divisors
- Explain patterns when multiplying or dividing by powers of 10
- Fluently multiply multi-digit whole numbers using standard algorithm
- Illustrate and explain division with 2-digit divisors
- Multiply decimals to hundredths
- Perform operations with decimals to hundredths
- Read and write decimals to thousandths
- Read, write, and compare decimals to thousandths
- Round decimals to any place using place value
- Understand 10× and 1/10 place value relationships
- Understand the place value system to thousandths
- Use whole-number exponents to denote powers of 10
Operations and Algebraic Thinking
- Analyze patterns and relationships with coordinate graphing
- Evaluate expressions with grouping symbols
- Evaluate expressions with parentheses, brackets, and braces
- Form and graph ordered pairs from two patterns
- Generate two numerical patterns using given rules
- Identify relationships between corresponding terms in two patterns
- Interpret numerical expressions without evaluating
- Write and interpret numerical expressions
- Write expressions that record calculations
Diagnosis, not just marking
Where Grade 5 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 5 math — questions parents ask
How much math practice does a Grade 5 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 5 session to that budget and to your child's pace — a quick day never becomes a marathon.
How does Algo School help with Grade 5 math at home?
Algo School generates short daily sessions from 6,221 verified Grade 5 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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