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Grade 5

What Math Does a 5th Grader Learn? All 24 Topics, in Order

By Knomi Learning · Updated

The short answer

A 5th grader learns 24 math topics, in 6 units: Place Value and Whole Numbers, Division and Fractions, Decimals, Measurement and Data, Volume and Shapes and Coordinate Plane and Patterns. That is 62 smaller skills in all, taught in the order below, each building on earlier ones.

  • The earlier topics 5th grade leans on most: Adding Fractions (Grade 4), Multi-Digit Multiplication (Grade 4), Factors and Primes (Grade 4), Multi-Digit Division (Grade 4) and Multi-Step Problems (Grade 4).
  • All 62 skills are matched to a Common Core standard.
  • Every one of them has a full lesson on Knomi.

Unit 1: Place Value and Whole Numbers

1

Powers of Ten

The place-value pattern the whole grade runs on: each place is worth ten times the place to its right. The kid multiplies and divides by 10, 100 and 1,000 by shifting digits and writes powers of ten with exponents, which every decimal skill later leans on.

What it covers

  • Place Value and Ten-Times Relationships
  • Multiplying and Dividing by Powers of 10
  • Powers of Ten with Exponents

Builds on

  • Grade 4: Understanding Place Value
  • Grade 4: Reading and Writing Multi-Digit Numbers
  • Grade 4: Comparing and Ordering Whole Numbers
  • Grade 4: Multiplying by 10s, 100s, and 1,000s
  • Grade 4: Dividing Multiples of 10, 100, and 1,000
  • Grade 4: Multiplication Facts to 12 × 12
  • and 1 more
Powers of Ten on the 5th grade map
2

Whole-Number Fluency

Keeps adding and subtracting big numbers sharp and builds the habit of estimating before computing. Grade 5 has no new standard here: it is the safety net under every algorithm in the grade, so a wildly wrong answer starts to feel wrong.

What it covers

  • Adding and Subtracting Large Numbers
  • Rounding to Estimate Answers

Builds on

  • Grade 4: Adding Multi-Digit Numbers
  • Grade 4: Subtracting Multi-Digit Numbers
  • Grade 4: Rounding Whole Numbers
  • Grade 4: Estimating Products
  • Grade 4: Estimating Quotients
Whole-Number Fluency on the 5th grade map
3

Multi-Digit Multiplication

The multiplication algorithm becomes a tool the kid trusts: area models first, then the standard algorithm for 2-digit, 3-digit and bigger factors, with an estimate to catch slips. It is the engine under long division, decimal multiplication and volume.

What it covers

  • Two-Digit Multiplication
  • Multiplying Large Numbers

Builds on

  • Grade 4: Multiplying 2-Digit by 2-Digit Numbers
  • Grade 4: Multiplying 3- and 4-Digit by 1-Digit
  • Grade 3: Distributive Property with Arrays
Multi-Digit Multiplication on the 5th grade map
4

Numerical Expressions

Math grows a grammar: parentheses, brackets and braces decide what happens first, and an expression becomes a way to record a calculation and to compare two without working them out. Grade 6 algebra starts here.

What it covers

  • Expressions and Grouping Symbols
  • Writing and Interpreting Expressions

Builds on

  • Grade 4: Multiplication Facts to 12 × 12
  • Grade 4: Multi-Step Word Problems
  • Grade 4: Times-as-Many Comparisons
  • Grade 3: Two-Step Expressions
  • Grade 3: Missing Factors and Divisors
Numerical Expressions on the 5th grade map
5

Factors and Primes

How whole numbers are built: divisibility tests, factor trees down to primes, and the greatest common factor and least common multiple that make simplifying and common denominators quick. Common Core puts this in Grades 4 and 6; Knomi keeps it here as the fraction toolkit.

What it covers

  • Divisibility Rules
  • Primes and Prime Factorization
  • Common Factors and Multiples

Builds on

  • Grade 4: Factor Pairs and Multiples
  • Grade 4: Prime and Composite Numbers
  • Grade 4: Simplifying Fractions
  • Grade 3: Even and Odd Numbers
Factors and Primes on the 5th grade map

Unit 2: Division and Fractions

6

Fraction Foundations

Fractions become numbers: 3/4 is 3 divided by 4, equivalent fractions name the same amount, and a common denominator makes the pieces the same size. All Grade 5 fraction work, and long division's remainders, lean on these three ideas.

What it covers

  • Fractions as Division
  • Equivalent Fractions and Simplest Form
  • Common Denominators

Builds on

  • Grade 4: Mixed Numbers and Improper Fractions
  • Grade 4: Understanding Remainders
  • Grade 4: Making Equivalent Fractions
  • Grade 4: Simplifying Fractions
  • Grade 4: Fraction Models and Number Lines
  • Grade 4: Factor Pairs and Multiples
  • and 3 more
Fraction Foundations on the 5th grade map
7

Long Division

Long division finished: one-digit divisors to fluency, two-digit divisors with trial quotients, four-digit dividends, remainders written as fractions when the story wants it, and multi-step problems that use the whole toolkit.

What it covers

  • Division with One-Digit Divisors
  • Division with Two-Digit Divisors
  • Long Division with Larger Dividends
  • Multi-Step Word Problems

Builds on

  • Grade 4: Dividing 3- and 4-Digit by 1-Digit
  • Grade 4: Interpreting Remainders in Word Problems
  • Grade 4: Multi-Step Word Problems
Long Division on the 5th grade map
8

Adding Fractions

Unlike denominators at last: rewrite with a common denominator, then add and subtract fractions and mixed numbers, regrouping wholes when needed, and use benchmarks to catch answers like 1/2 + 2/5 = 3/7.

What it covers

  • Unlike Denominators
  • Adding and Subtracting Mixed Numbers
  • Fraction Word Problems

Builds on

  • Grade 4: Like Denominators
  • Grade 4: Mixed Numbers and Improper Fractions
  • Grade 4: Adding and Subtracting Mixed Numbers
  • Grade 4: Fraction Word Problems
  • Grade 4: Multi-Step Word Problems
Adding Fractions on the 5th grade map
9

Multiplying Fractions

Why half of a third is a sixth: a fraction of a whole number, a fraction of a fraction, area with fractional sides, and predicting whether multiplying will stretch or shrink, before mixed numbers and real problems.

What it covers

  • Multiplying Fractions by Whole Numbers
  • Multiplying Fractions by Fractions
  • Area with Fractional Side Lengths
  • Multiplication as Scaling
  • Multiplying Mixed Numbers
  • Fraction Multiplication Word Problems

Builds on

  • Grade 4: Multiplying Fractions by Whole Numbers
  • Grade 4: Mixed Numbers and Improper Fractions
  • Grade 4: Fraction Models and Number Lines
  • Grade 4: Perimeter and Area of Rectangles
  • Grade 4: Times-as-Many Comparisons
  • Grade 4: Multiplying Mixed Numbers
  • and 4 more
Multiplying Fractions on the 5th grade map
10

Dividing Fractions

How many thirds fit in 2? Division with unit fractions in both directions, tied back to multiplication so every answer can be checked, then stories where the hard part is choosing which division it is.

What it covers

  • Relating Division to Multiplication
  • Dividing Unit Fractions by Whole Numbers
  • Dividing Whole Numbers by Unit Fractions
  • Fraction Division Word Problems

Builds on

  • Grade 3: Relating Multiplication and Division
  • Grade 3: Division as Sharing and Grouping
  • Grade 3: Unit Fractions
  • Grade 3: Placing Fractions on the Number Line
  • Grade 3: Whole Numbers as Fractions
Dividing Fractions on the 5th grade map

Unit 3: Decimals

11

Understanding Decimals

Place value keeps going past the decimal point: tenths, hundredths, thousandths, each a tenth of the place before. The kid reads, compares and orders decimals and slides them along powers of ten. 0.4 beats 0.39 even though 39 beats 4.

What it covers

  • Decimal Place Value to Thousandths
  • Comparing and Ordering Decimals
  • Decimals and Powers of Ten

Builds on

  • Grade 4: Decimal Notation for Hundredths
  • Grade 4: Tenths and Hundredths as Fractions
  • Grade 4: Comparing and Ordering Decimals
  • Grade 3: Numbers on the Number Line
Understanding Decimals on the 5th grade map
12

Adding Decimals

Round decimals to any place to predict answers, then add and subtract decimals by lining up place values, with the estimate standing guard against misplaced digits.

What it covers

  • Rounding Decimals
  • Adding and Subtracting Decimals

Builds on

  • Grade 4: Rounding Whole Numbers
  • Grade 4: Adding and Subtracting Decimals
  • Grade 4: Subtracting Multi-Digit Numbers
Adding Decimals on the 5th grade map
13

Decimals and Percents

Three names for one amount: 3/4, 0.75 and 75%. The kid converts between fractions and decimals and meets the percent sign as hundredths in disguise; percents are Grade 6 in Common Core, but kids this age meet them everywhere.

What it covers

  • Fractions as Decimals
  • Percents as Hundredths

Builds on

  • Grade 4: Decimals and Fractions on Number Lines
  • Grade 4: Tenths and Hundredths as Fractions
  • Grade 4: Multiplying Fractions by Whole Numbers
Decimals and Percents on the 5th grade map
14

Multiplying Decimals

Where the whole-number algorithm meets fraction thinking: multiply decimals by whole numbers and by each other, placing the decimal point by reasoning about size, never by a rule taken on faith.

What it covers

  • Multiplying Decimals by Whole Numbers
  • Multiplying Decimals by Decimals

Builds on

  • Grade 4: Multiplying Fractions by Whole Numbers
Multiplying Decimals on the 5th grade map
15

Dividing Decimals

The end of the place-value chain: divide decimals by whole numbers, keep dividing past a remainder to get a decimal quotient, and divide by a decimal by asking how many tenths fit or by scaling both numbers.

What it covers

  • Dividing Decimals by Whole Numbers
  • Dividing by Decimals
Dividing Decimals on the 5th grade map

Unit 4: Measurement and Data

16

Unit Conversions

Turn a measurement into another unit of the same system: time's base 60, metric's powers of ten, customary's irregular factors. One idea runs under all three: a bigger unit means a smaller number.

What it covers

  • Converting Units of Time
  • Converting Metric Units
  • Converting Customary Units

Builds on

  • Grade 4: Time and Elapsed Time
  • Grade 4: Relative Sizes of Units
  • Grade 4: Converting Metric Units
  • Grade 4: Converting Customary Units
  • Grade 3: Elapsed Time
Unit Conversions on the 5th grade map
17

Data and Averages

Real data two ways: line plots of measurements in halves, fourths and eighths, where fraction arithmetic answers the questions, and the mean, a total shared out evenly. The mean is Grade 6 in Common Core; the other curricula teach it by this age.

What it covers

  • Line Plots with Fractional Data
  • Averages

Builds on

  • Grade 4: Line Plots with Fractions
  • Grade 4: Making Equivalent Fractions
  • Grade 4: Adding Multi-Digit Numbers
Data and Averages on the 5th grade map
18

Money and Measurement

The grade's real-world capstone: prices and change, unit costs, and measurements in mixed units. The work is deciding which operation the story needs, converting along the way, and letting an estimate keep the answer honest.

What it covers

  • Decimal and Money Word Problems
  • Multi-Step Measurement Word Problems

Builds on

  • Grade 4: Measurement Word Problems
Money and Measurement on the 5th grade map

Unit 5: Volume and Shapes

19

Volume

A new measurement: how much space a solid takes up. The kid packs boxes with unit cubes, counts them in layers, and finds the V = l × w × h and V = B × h formulas hiding in the layers.

What it covers

  • Volume with Unit Cubes
  • Volume of Rectangular Prisms

Builds on

  • Grade 4: Solid Shapes and Nets
  • Grade 4: Perimeter and Area of Rectangles
  • Grade 4: Multiplying 2-Digit by 1-Digit Numbers
  • Grade 3: Understanding Area
  • Grade 3: Area of Rectangles by Multiplying
  • Grade 3: Multiplication with Arrays
  • and 1 more
Volume on the 5th grade map
20

Volume Problem Solving

Volume put to work: cut L-shaped solids into boxes and add the pieces, then solve how-much-fits problems, including working backward to a missing edge.

What it covers

  • Volume of Composite Figures
  • Volume Word Problems

Builds on

  • Grade 4: Area and Perimeter Problem Solving
  • Grade 4: Multi-Step Word Problems
  • Grade 3: Area of Composite Figures
  • Grade 3: Missing Side Lengths from Area
Volume Problem Solving on the 5th grade map
21

Angles and Triangles

Shapes by their properties, not their looks. The kid polishes the Grade 4 vocabulary of lines and angles, then classifies triangles by sides and by angles at once: one triangle can wear two labels.

What it covers

  • Points, Lines, and Angles
  • Classifying Triangles

Builds on

  • Grade 4: Points, Lines, Rays, and Segments
  • Grade 4: Parallel and Perpendicular Lines
  • Grade 4: Angle Types and Angles in Circles
  • Grade 4: Measuring and Drawing Angles
  • Grade 4: Classifying Triangles
Angles and Triangles on the 5th grade map
22

Quadrilaterals

The quadrilateral family tree: a square really is a rectangle and a rhombus, and in Knomi a parallelogram is a trapezoid too. Reasoning with the hierarchy is early deductive logic dressed as shape sorting.

What it covers

  • Classifying Quadrilaterals
  • Shape Hierarchies

Builds on

  • Grade 4: Classifying Quadrilaterals
  • Grade 3: Classifying Quadrilaterals
  • Grade 3: Attributes of 2-D Shapes
Quadrilaterals on the 5th grade map

Unit 6: Coordinate Plane and Patterns

23

Coordinate Plane

Two number lines meet and every point gets an address. The kid plots and reads first-quadrant points until (x, y) is automatic, then uses coordinates for maps and real data; swapping x and y is the slip to watch for.

What it covers

  • Coordinate Plane Basics
  • Coordinate Plane Word Problems

Builds on

  • Grade 4: Parallel and Perpendicular Lines
  • Grade 4: Line Graphs and Choosing a Display
  • Grade 4: Perimeter and Area of Rectangles
  • Grade 3: Numbers on the Number Line
  • Grade 3: Placing Fractions on the Number Line
  • Grade 3: Pattern Rules and Input/Output Tables
Coordinate Plane on the 5th grade map
24

Patterns and Graphs

Two number rules run side by side, the relationship between them shows, and the pairs, graphed, line up as points: the grade's quiet preview of functions.

What it covers

  • Generating and Comparing Number Patterns
  • Graphing Number Patterns

Builds on

  • Grade 4: Number and Shape Patterns
  • Grade 4: Input/Output Tables and Rules
Patterns and Graphs on the 5th grade map

Questions parents ask

How many math topics are in 5th grade?

On Knomi's map, 5th grade math has 24 topics in 6 units, made of 62 smaller skills.

What should a student know before starting 5th grade math?

The earlier topics 5th grade leans on most are Adding Fractions (Grade 4), Multi-Digit Multiplication (Grade 4), Factors and Primes (Grade 4), Multi-Digit Division (Grade 4) and Multi-Step Problems (Grade 4). A student who is quick and sure with those is ready. Each topic below lists exactly what it builds on.

Is this 5th grade math list aligned to Common Core?

Common Core is the spine. All 62 skills carry a Common Core reference, and the order follows the usual US course.

Does Knomi teach 5th grade math?

Every one of them has a full lesson on Knomi. The 5th grade map is open to anyone, with no account needed to look around.

See 5th grade math as a map.

Every topic above, with lines to what it needs first. Open it and look around, no account needed.

Open the Grade 5 map

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