Home / 8th grade

Free Math Games offers 6 top level categories for 8th grade. Taken together, these categories cover the majority of the US math curriculum for 8th grade.

See the list of topics for 8th grade or select a math category from the table below to see the available sub-categories and topics, or go directly to the 8th grade games, lessons and tests.

The CCSS core curriculum for 8th grade covers a range of categories, including:

**Number**

Students work with integers, fractions, decimals, and percentages, deepening their understanding of these number systems. They work with numbers in standard form.**Algebra**

Students further develop their algebraic skills and reasoning abilities. They solve equations and inequalities, and explore sequences and patterns. They explore algebraic concepts such as linear and quadratic functions, graphing and interpreting equations, and algebraic manipulation.**Ratio and proportion**

Students study ratios and proportional relationships, including direct and inverse proportions. They solve problems involving scale factors, rates, and percentages. They also explore the concept of rates of change and their applications in real-world contexts.**Geometry & measures**

Students study properties of 2D and 3D shapes, including angles, lines, and symmetry. They calculate the perimeter, area, and volume of different shapes and solids. They explore trigonometry, including the use of Pythagoras' theorem and basic trigonometric ratios. They also study transformations, such as reflections, translations, rotations, and enlargements.**Probability**

Students explore probability concepts and solve problems involving probability. They learn about independent events, and tree and sample space diagrams.**Statistics**

Students analyze and interpret data using various statistical techniques. They explore concepts of probability and statistical inference, including calculating and interpreting measures of central tendency and dispersion, conducting surveys and experiments, and making predictions based on data.

The 8th grade math curriculum aims to deepen students' mathematical understanding, strengthen their problem-solving skills, and prepare them for more advanced mathematical concepts and topics in subsequent years.

Below is the complete list of topics for 8th grade arranged by category. Click on a topic to view more information.

Number

- Calculate square rootsCalculate the square root or nearest integer to the square root for the given numbers
- Cube rootsIdentify the cube root or nearest integer cube root of each of the given numbers
- Percentage changeCompare two quantities to work out the percentage increase or decrease
- Identify multiples of numbers to 12Identify multiples of numbers up to 12
- LCM using product notationIdentify the lowest common multiple (LCM) of 2 numbers using product notation
- Round decimals to 1 dpRound each of the given decimal values to 1 decimal place (1 dp)
- Round decimals to 2 dpRound each of the given decimal values to 2 decimal places (2 dp)
- Round decimals to 3 dpRound each of the given decimal values to 3 decimal places (3 dp)
- Add mixed fractionsAdd mixed fractions by converting them to improper fractions. Give your answers as improper fractions
- Multiply indicesMultiply indices with the same base by adding powers e.g. 5a³ x 6a² = 30a⁵
- Divide IndicesDivide indices with the same base by subtracting powers e.g. 6b⁵ ÷ 2b² = 3b³
- Find percentages: multiples of 5Find percentages using multiples of 5
- Find percentages: units and decimalsFind percentages using units and decimals
- HCF using product notationIdentify the Highest Common Factor (HCF) using product notation for the given pairs of numbers
- Round numbers to 1 sig figRound large and small numbers to 1 significant figure (1 sig fig / 1 s.f.)
- Round numbers to 2 sig figsRound large and small numbers to 2 significant figures (2 sig figs / 2 s.f.)
- Round numbers to 3 sig figsRound large and small numbers to 3 significant figures (3 sig figs)
- Estimate by rounding to 1 s.f.Use rounding to 1 significant figure (1 sig fig / 1 s.f.) to estimate answers to the given calculations
- Find percentages: simple multiplierFind the quantity using a simple decimal multiplier
- Find percentages: medium multiplierFind the quantity using a medium decimal multiplier
- Find percentages: advanced multiplierFind the quantity using an advanced decimal multiplier
- Subtract fractions: mixedSubtract mixed fractions by subtracting the whole numbers and the fraction parts separately
- Prime factorsIdentify the prime factors of each given number using product notation
- Multiply mixed fractionsMultiply mixed fractions by turning them to improper fractions and multiplying across; answers as improper fractions
- Standard form: largest numberCompare numbers in standard form and identify the largest
- Standard form: smallest numberCompare numbers in standard form and identify the smallest
- Standard form: add and subtractAdd or subtract numbers in standard form
- Standard form: multiply and divideMultiply or divide numbers in standard form
- Divide mixed fractionsDivide mixed fractions by turning them top-heavy then flipping signs and the second fraction; answers as improper fractions

Algebra

- Term-to-termFor each arithmetic or geometric sequence, find the next term
- Position to termFind the value of term n for the given linear sequences
- Two negative integer variablesCalculate the value of K by substituting in two negative integer variables n and s
- Fraction valuesCalculate by substituting in 2 fraction variables s and t
- Positive integers: 3 variablesCalculate the value of J by substituting in positive integer values for the 3 variables k, m and n
- Negative integers: 3 variablesCalculate S by substituting in negative integer values for the 3 variables p, q and r
- Common termsFactorize out common terms only
- Common number factorsFactorize out common numbers
- Both terms and numbersFactorize out both terms and numbers in each of the given expressions
- Basic linear formulasUse algebraic methods to make the specified variable the subject of each of the linear formulae
- Form expression: perimeter of squaresForm an expression for the perimeter of each of the given squares in terms of x
- Form expression: perimeter of rectanglesForm an expression for the perimeter of each of the given rectangles in terms of x and y
- Form expression: perimeter of trianglesForm an expression for the perimeter of each of the given triangles in terms of x
- Express the area of squaresExpress the area of each of the given squares in terms of x
- Express the area of rectanglesExpress the area of each of the given rectangles in terms of x
- Calculate gradients of linear graphsFor each linear graph or pair of points on a line, find the gradient of the line
- y = mx + c - gradient, y-interceptFor each equation of form y = mx + c identify the gradient or the y-intercept of the line
- Parallel linesInterpret equations of form (or reducible to) y = mx + c to identify which would produce parallel lines
- Add unit fractions of like termsAdd unit fraction amounts of like terms e.g. 1/5x + 1/2x
- Subtract fractions of like termsSubtract fractional amounts of like terms e.g. ¾x - ½x
- Form expression: angles in triangleForm simplified expressions for the sum of the interior angles of each triangle in terms of x
- Find the nth term valueGiven an nth term rule, find the value of the specified term in the sequence
- Sequence from nth term ruleIdentify the sequence that follows the given linear nth term expression
- nth term rule from sequenceChoose the correct nth term expression for each of the linear sequences
- Quadratic equation: value of yFor each quadratic equation, given a value for x, calculate a value for y
- Expressions from wordsForm an expression for each of the given scenarios in terms of x and y
- Identify graphsIdentify the correct equation for each of the given graphs
- Multiply like termsSimplify expressions by multiplying like terms with exponents e.g. 2y² x 2y²
- Multiply like & unlike termsSimplify expressions by multiplying like & unlike terms with exponents and / or coefficients e.g. b x 3c² x b² x d
- Terms on both sidesUse algebraic methods to rearrange and solve for x, terms on both sides, no fractions
- Terms on one side, fractionsUse algebraic methods to rearrange and solve for x, terms on one side, with fractions
- Terms on both sides, fractionsUse algebraic methods to rearrange and solve for x, terms on both sides, with fractions
- Expand two binomialsIn each instance use FOIL or a similar technique to expand the double brackets e.g. (x + 3)² = x² + 6X + 9

Ratio proportion rate

- Convert miles to kilometersUse the approximation 1 mile ≈ 1.6 km to convert imperial miles to metric kilometers (km)
- Convert km to milesUse the approximation 1.6 kilometers ≈ 1 mile to convert distances in kilometers to imperial miles to 1 d.p.
- Convert inches to cmUse the approximation 1 inch ≈ 2.54 cm to convert imperial inches to metric centimeters to 2 d.p.
- Convert cm to feetUse the approximation 1 foot ≈ 30 cm to convert lengths in centimeters (cm) to imperial feet to 1 d.p.
- Convert cm to inchesUse the approximation 1 inch ≈ 2.5 cm to convert centimeters to imperial inches
- Increase by a percentageDerive the actual increase from the percentage increase and add it to the original quantity or amount
- Decrease by a percentageDerive the actual decrease from the percentage decrease and subtract it from the original quantity
- Express as a percentageExpress quantities as percentages by creating a fraction and multiplying by 100
- Calculate percentage increaseGet the percentage increase by expressing the increase as a fraction of the original and multiplying by 100
- Calculate percentage decreaseGet the percentage decrease by expressing the decrease as a fraction of the original and multiplying that amount by 100
- Calculate speedUse the speed formula speed s = distance d / time t to calculate speeds to 1 d.p.
- Calculate distance, timeRe-arrange the speed formula to calculate distance or time to 1 d.p.
- Speed from a graphUsing speed time graphs find the speed at the given time
- Fastest speed, slowest speedUsing speed time graphs identify the highest speed or the lowest speed attained
- Calculate densityIn each instance calculate the density using the density formula d = mass / volume to 1 d.p.
- Unit price: best valueIdentify the better value for money option by doing unit price calculations
- Directly or inversely proportionalIdentify which of the graphs and equations are directly proportional, inversely proportional or neither
- Direct proportion problemsSolve problems involving direct proportion where two quantities increase at the same rate
- Inverse proportion problemsSolve problems involving inverse proportion where one quantity increases as the other decreases (to 2 d.p.)
- Actual distanceWork out the real distance between two points represented on maps and scale diagrams (to 2 d.p.)
- Distance on a map or diagramUse a scale and an actual distance to work out the distance between 2 points on a map or scale diagram to 2 d.p.
- Express fractions as ratiosExpress each of the given fractions as a part to whole ratio
- Express percentages as ratiosExpress each of the given percentages as a part to whole ratio
- Express decimals as ratiosExpress each of the given decimals as a part to whole ratio
- Equivalent ratiosIdentify the ratios that are equivalent e.g. 1:2 and 3:6
- Express ratios as fractionsExpress part to part ratios as fraction proportions of the whole
- Express ratios as percentagesExpress each part to whole ratio as a part to whole percentage
- Express quantities as % with calculatorExpress quantities of wholes as percentages by converting to a fraction and multiplying by 100 to (1 d.p.)
- Increase by % with calculatorDerive the actual increase from the percentage increase and add it to the original quantity or amount (to 1 d.p.)
- Decrease by % with calculatorCalculate the new quantity or amount by using a decimal multiplier; answers to 2 d.p.
- Convert cm³ to mm³Convert cubic centimeters (cm³) to cubic millimeters (mm³) by multiplying by 1000
- Convert m³ to cm³Convert cubic meters (m³) to cubic centimeters (cm³) by multiplying by 1,000,000
- Specific parts and quantityPair up specific quantities with specific parts

Geometry & measures

- Identify similar shapesIdentify the pairs of shapes which are similar
- Describe the bearingIn each instance identify if the type of bearing is acute, obtuse or reflex
- Estimate the bearingChoose the most appropriate three figure bearing from the given options
- Identify polygons from propertiesUse the given properties to identify the polygon
- Lines of symmetry: polygonsIdentify the number of lines of symmetry possessed by each of the given polygons
- Rotational symmetry: quadrilateralsIdentify the order of rotational symmetry for each of the given quadrilaterals
- Rotational symmetry: polygonsIdentify the order of rotational symmetry for each of the given polygons
- Parts of the circle 2Identify parts of the circle: arc, chord, sector, segment and tangent
- Calculate the hypotenuseUse Pythagoras' theorem to calculate the hypotenuse for these right-angle triangles to 2 decimal places
- Find the missing lengthUse Pythagoras' theorem to calculate the length of a side that is not the hypotenuse to 2 decimal places
- Identify congruent, similar trianglesIdentify triangles which are congruent, similar or neither
- Labels for sides, anglesIdentify the standard conventions for labeling the angles and sides of different types of triangles
- Column vectorsIdentify the correct shape on the graph for the given column vector
- Describe translationsIn each instance identify the correct column vector for the given translation
- Angles around parallel linesUse parallel line rules to find alternate, corresponding and allied angles
- Parallel lines and shapesUse parallel line rules to find the missing angle in each of the given shapes
- Triangles: scale factorsIn each instance find the scale factor between the two similar triangles
- Triangles: length from scale factorsUse scale factor ratios to work out lengths on the smaller or larger of the given triangles
- Other shapes: length from scale factorFind and use the scale factor to work out lengths on similar shapes that are not triangles
- Identify names of sidesIdentify whether the marked sides of right angle triangles are the hypotenuse, adjacent or opposite
- Circumference of circlesUsing the formula C = 2πr calculate the circumference of circles to 2 decimal places
- Circumference of semicirclesUse C = πr + 2r to calculate the circumference of the given semicircles to 2 decimal places
- Identify reflectionsIdentify the correct shape for the described reflection
- Describe reflectionsIdentify the line of symmetry (also called the mirror line) for each of the reflections
- Vertically opposite anglesIn each instance use vertically opposite angles to find the missing angle
- Exterior angles of regular polygonsUse the number of sides to calculate the exterior angles for each of the given regular polygons
- Number of sides from exterior angleUse the exterior angle to calculate the number of sides for each of the given regular polygons
- Interior angle from exterior angleUse the exterior angle for each regular polygon to calculate the interior angle
- Sum of interior anglesCalculate the sum of the interior angles for each of the given polygons
- Area of compound shapesCalculate the areas of the given compound shapes constructed from parallelograms to 2 d.p.
- Area of circlesUsing the formula A = πr² calculate the area of the given circles to 2 decimal places
- RotationIdentify the correct shape on the grid for the described rotation
- Describe rotationIn each instance identify the correct description for the given rotation
- Positive integer scale factorsIdentify the correct shape on the graph for the given positive integer scale factor enlargement
- Negative scale factorsIdentify the correct shape on the graph for the given negative scale factor enlargement
- Calculate surface area of cubesUse multiplication or the formula SA = 6H² to calculate the surface area of cubes
- Calculate surface area of cuboidsUse pairs of sides to calculate the total surface area of cuboids using the formula SA =2(LW+LH+HW)
- Surface area of triangular prismsUsing a net or otherwise calculate the total surface area of triangular prisms to 2 d.p.
- Calculate volume of cubesUse the standard formula L³ (length cubed) to calculate the volume of cubes
- Volume of prismsUse the standard formula (area of cross-section times length) to calculate the volume of prisms to 2 d.p.
- Calculate the volume of cylindersUse the standard formula (area of cross-section times length) to calculate the volume of cylinders to 2 d.p.

Probability

- Venn diagrams: 2 categoriesFind the missing value for each of the given Venn diagrams
- Venn diagrams: 3 categoriesFind the missing value for each of the given 3 category Venn diagrams
- Independent eventsFind the probability of different outcomes using the AND & OR rules
- Sample space diagramsAnswer probability questions based on the given sample space diagrams
- Tree diagrams: replacementFind the probabilities using tree diagrams with both replacement and no replacement of items

Statistics

- Grouped frequency tablesIn each instance decide whether the grouped frequency table matches the raw data
- Grouped frequency table: midpointIdentify the correct midpoint for the specified range in each grouped frequency table
- Grouped frequency table: modal group, rangeIdentify the modal group or largest range for each grouped frequency table
- Identify the medianIdentify the median (middle value) of each set of numbers
- Identify the outlierIdentify the outlier in each set of numbers
- Construct scatter graphsIdentify the correct steps for constructing a scatter graph from the options offered
- Polarity, strength of correlationIdentify the polarity and strength of any linear correlation for each of the given scatter graphs
- Line of best fitIdentify which of the lines is closest to being a line of best fit for the data
- Using lines of best fitIn each instance use the given line of best fit to predict approximate values
- Mean mode median rangeCalculate the mean, mode, median or range for the given frequency tables to 2 d.p.
- Vertical line chart: mean, rangeFind the mean or the range for each of the given vertical line charts
- Match data to diagramIn each instance select the correct data for the given stem and leaf diagram
- Stem & leaf: mode median rangeFind the mode, median and range for each of these stem and leaf diagrams
- Primary vs secondary dataIn each instance identify whether the data described is primary or secondary

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