Home / 6th grade

Free Math Games offers 6 top level categories for 6th grade. Taken together, these categories cover the majority of the US math curriculum for 6th grade.

See the list of topics for 6th grade or select a math category from the table below to see the available sub-categories and topics, or go directly to the 6th grade games, lessons and tests.

The CCSS core curriculum for 6th grade covers a range of categories, including:

**Number**

Students reinforce their understanding of place value, including whole numbers up to millions, decimals, and negative numbers. They work with operations such as addition, subtraction, multiplication, and division of whole numbers and decimals. Students develop their understanding of fractions, decimals, and percentages. They work on operations with fractions, including simplification and finding equivalent fractions. They convert between fractions, decimals, and percentages and solve problems involving percentages.**Algebra**

Students are introduced to algebraic concepts. They learn about algebraic notation, expressions, and equations. They solve simple linear equations and work with formulas and functions. They explore patterns and relationships and use algebraic methods to solve problems.**Ratio and proportion**

Students explore ratio and proportion, including ratio notation, simplification, and comparison. They solve problems involving direct and indirect proportion and apply proportional reasoning in various contexts.**Geometry & measures**

Students study the properties of geometric shapes, including angles, triangles, quadrilaterals, and circles. They learn about transformations such as reflections, rotations, and translations. They explore properties of 2D and 3D shapes and work with coordinates in the Cartesian plane.**Probability**

Students learn about probability, including theoretical and experimental probability. They calculate probabilities, explore the concept of sample space, and solve problems involving simple and compound events.**Statistics**

Students develop skills in handling data, including data collection, representation, and interpretation. They construct and interpret graphs and charts, calculate measures of central tendency, and understand basic concepts of probability.

In addition to these specific topics, students will also develop their fluency with mathematical concepts and their ability to solve mathematical problems. They will be able to use mathematical reasoning to solve problems in other areas of their lives, such as science, technology, and engineering.

Below is the complete list of topics for 6th grade arranged by category. Click on a topic to view more information.

Number

- Order positive integersSelect the set of positive integers that are in ascending order
- Order negative integersArrange negative integers in ascending order from smallest to largest
- Arrange integers ascendingChoose the set of positive and negative integers that are in correct ascending order
- Identify unit fractionsIdentify the fractions that are unit fractions, or will simplify to unit fractions
- Identify improper fractionsIdentify the fraction or fractions that are improper fractions
- Identify mixed fractionsIdentify the fraction or fractions that are mixed fractions
- Identify equivalent fractionsIdentify the pairs of fractions that are equivalent
- Calculate fractions of amountsCalculate fractions of quantities, e.g. one third of 12 grams, etc.
- Add decimalsAdd decimals by first aligning the decimal points of each number
- Subtract decimalsSubtract decimals by first aligning the decimal points
- Multiply decimalsMultiply decimals by initially removing the decimal point
- Divide decimals by integersDivide decimal numbers by integers
- Divide integers by decimalsDivide integer values by decimal numbers
- Divide decimals by decimalsDivide decimals by decimals
- Identify square numbersIdentify the square numbers in each of the given groups of integers
- Lowest common multiplesIdentify the lowest common multiple (LCM) of 2 numbers
- Round numbers: nearest 10Round each of the given numbers to the nearest 10
- Round numbers: nearest 100Round each given number to the nearest 100
- Round numbers: nearest 1000Round each of the given numbers to the nearest 1000
- Round decimals: nearest integerRound each of the given decimals to the nearest whole number (integer)
- Add fractions: common denominatorAdd fractions with a common denominator
- Add fractions: scale denominatorAdd fractions by scaling up the fraction with the smaller denominator; simplify answers where possible
- Add fractions using LCDAdd fractions by finding the lowest common denominator (LCD); simplify your answers where possible
- Convert exponents to expanded formConvert between base with exponent and expanded form e.g. 3³ <=> 3 x 3 x 3
- Find percentages: multiples of 10Find a percentage using multiples of 10
- Multiply decimals by 10 100 1000Multiply by powers of 10 up to 1000 by moving the digits the correct number of columns to the left
- Divide decimals by 10 100 1000Divide by powers of 10 up to 1000 by moving the digits the correct number of columns to the right
- Identify factorsIdentify the correct set of factors for numbers up to 50
- Highest common factorIdentify the Highest Common Factor (HCF) for the given sets of numbers
- Subtract fractions: common denominatorSubtract fractions which share a common denominator
- Subtract fractions: scale denominatorSubtract fractions by scaling up the fraction with the smaller denominator
- Subtract fractions: LCDSubtract fractions by finding the lowest common denominator (LCD) of the two fractions
- Prime numbersIdentify the prime number or numbers in each of the given lists
- Positive decimalsChoose the set of positive decimals that are in ascending order
- Positive fractions: ascending orderArrange these sets of positive fractions in ascending order
- Decimals to fractionsConvert terminating decimals to their equivalent, simplified fractions
- Fractions to decimalsConvert fractions to their equivalent terminating decimals
- Multiply simple fractionsMultiply pairs of simple fractions and simplify your answers where possible
- Multiply fractions with cancellingMultiply fractions by cross cancelling numbers first
- Fractions of amountsFind fractions of amounts by first dividing by the fraction denominator then multiplying by the numerator
- Percentages to fractionsIdentify the correct, simplified fraction for each of the given percentages
- Percentages to decimalsIdentify the correct decimal for each of the given percentages
- Fractions to percentagesIdentify the correct percentage for each of the given fractions
- Fractions and percentagesCompare by converting both fractions and percentages to decimals; select the larger decimal
- Divide fractionsDivide fractions by flipping one of the fractions (get the reciprocal of the fraction) and multiplying them

Algebra

- Next termFor each given arithmetic sequence, find the next term
- Find the ruleFor each arithmetic or geometric sequence find the rule to extend the sequence
- Find term from ruleFind the specified term given the first term and the rule
- Two positive integer variablesCalculate the value of J by substituting in the given positive integer values for the 2 variables k and m
- Coordinates of a pointIn each instance identify the correct coordinates for the point on the graph
- Plotting coordinatesTake the plotted points and the additional point coordinates to identify the polygon that is formed
- Perimeter: squaresForm an expression for the perimeter of each of the given squares in terms of x
- Perimeter: rectanglesForm an expression for the perimeter of each of the rectangles in terms of x and y
- Add like termsSimplify expressions by adding algebraic like terms such as a + a or b² + 3b² or 5c³ + 3c³
- Subtract like termsSimplify expressions by subtracting quantities of like terms such as 5x - 3x or 13x² - 5x²
- Add and subtract like termsSimplify expressions by adding and subtracting like terms such as 5x - 3x + 6x
- Add & subtract unlike termsSimplify expressions by adding and subtracting unlike terms e.g. a + a - b or 2x - 3y + 5x
- Identify like & unlike termsDecide whether each expression consists of like terms or unlike terms
- Count terms in expressionsCount the number of terms in each of the given expressions
- Interpret algebraic notationFor each expression, convert between algebraic notation and expanded form e.g. 3c = c + c + c
- Match expressions to descriptionsMatch simple algebraic expressions to the correct word description of the expression
- Multiply like termsSimplify expressions by multiplying like terms with no exponents to give answers raised to a power
- Multiply unlike termsSimplify expressions by multiplying quantities of unlike terms with no exponents e.g. 2b x 3c
- Terms on one side, one-step equationsIn each instance use simple algebraic methods to solve for the given variable in these one-step equations
- Terms on one side, two-step equationsFor each two-step equation use algebraic methods to solve for the given variable

Ratio proportion rate

- Convert mm into cmConvert lengths given in millimeters (mm) to centimeters (cm) by dividing the value by 10
- Convert cm to mConvert lengths given in centimeters (cm) into meters (m) by dividing the value by 100
- Convert m to kmConvert distances given in meters (m) into kilometers (km) by dividing the value by 1000
- Convert km to mConvert distances given in kilometers (km) into meters (m) by multiplying by 1000
- Convert m to cmConvert lengths given in meters (m) into centimeters (cm) by multiplying by 100
- Convert cm to mmConvert lengths given in centimeters (cm) into millimeters (mm) by multiplying by 10
- Express quantities as ratiosExpress each of the sets of quantities as a part to part ratio, simplified if possible
- Ratio in its simplest formUse division to express each ratio in its simplest form
- Equivalent ratiosIdentify the ratios that are equivalent e.g. 1:2 and 3:6
- Convert grams to milligramsConvert masses given in grams (g) to milligrams (mg) by multiplying the value by 1000
- Convert kilograms to gramsConvert masses given in kilograms (kg) to grams (g) by multiplying the value by 1000
- Convert tonnes to kilogramsConvert masses given in tonnes (t) into kilograms (kg) by multiplying by 1000
- Convert cm³ or ml to liters (L)Convert volumes given in cubic centimeters (cm³) or milliliters (ml) to liters (L) by multiplying by 1000
- Convert liters to millilitersConvert volumes given in liters (L) into milliliters (ml) by multiplying by 1000
- Convert liters to cm³Convert liters (L) to cubic centimeters (cm³) by multiplying by 1000
- Share a quantity into partsAdd up the parts and divide the quantity by the total number of parts to get the different shares

Geometry & measures

- Count edges of 3D shapesWork out the total number of edges for each of the given solids
- Count vertices of 3D shapesWork out the total number of vertices for each of the given solids
- Count faces of 3D shapesWork out the total number of faces for each of the given solids
- Perimeter of rectanglesUse the formula P=2(L+W) to calculate the perimeters of the given rectangles
- Perimeter of trianglesUse the formula P = 3L to calculate the perimeters of each of the equilateral triangles
- Perimeter of parallelogramsUse the formula Perimeter = 2(Base + Side) to calculate the perimeters of the given parallelograms
- Perimeter of trapezoidsCalculate the perimeters of the given trapezoids by adding the lengths of all its sides
- Perimeter of compound shapesCalculate the perimeters of the given compound shapes constructed from parallelograms
- Identify the quadrilateralUse the given properties to identify the quadrilateral
- Parts of the circle 1Identify the following parts of a circle: radius, diameter, circumference; calculate radius and diameter
- Lines of symmetry: quadrilateralsHow many lines of symmetry does each of the given shapes have?
- Identify types of triangleUsing standard conventions identify isosceles, equilateral, right-angle and scalene triangles
- Angles on a straight lineUse the angles on a straight line rule to find the missing angles
- Angles around a pointUse the angles around a point rule to find the missing angles
- Angles in a triangleUse the fact that angles within a triangle sum to 180° to find the missing angles
- Area of rectanglesCalculate the areas of the given rectangles using the formula area = length x height, A = L x W
- Area of trianglesUse the formula area = ½ x base x height to calculate the areas of the given equilateral triangles
- Area of parallelogramsCalculate the areas of the given parallelograms
- Area of compound shapesCalculate the areas of the given compound shapes constructed from parallelograms to 2 d.p.
- Calculate the volume of cuboidsUse the standard formula (length x width x height) to calculate the volume of cuboids

Probability

- How likely is the event?Decide whether each of the given events is likely, unlikely, certain or impossible
- Standard eventsFor each scenario work out the probability of the outcome as a fraction

Statistics

- Calculate the meanCalculate the mean for each set of positive integers
- Calculate mean: include negative integersCalculate the mean of each set of both positive and negative integers
- Match bar charts to dataSelect the data that is correctly represented in each of the bar charts
- Read bar chart valuesRead off correct values from each bar chart
- Match data to frequency tableIn each instance decide whether the frequency table correctly matches the given raw data
- Match vertical line chart to dataIn each instance decide whether the given vertical line chart matches the frequency table data
- Pictograms: interpret dataFor each of the given pictograms identify the number of people who like different fruit

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