Home / 7th grade

Free Math Games offers 6 top level categories for 7th grade. Taken together, these categories cover the majority of the US math curriculum for 7th grade.

See the list of topics for 7th grade or select a math category from the table below to see the available sub-categories and topics, or go directly to the 7th grade games, lessons and tests.

The CCSS core curriculum for 7th grade covers a range of categories, including:

**Number**

Students work with integers, fractions, decimals, and percentages, deepening their understanding of these number systems. They develop their understanding of number systems and their operations. They convert between exponents and expanded form.**Algebra**

Students further develop their algebraic skills and reasoning abilities. They simplify and manipulate algebraic expressions, solve equations and inequalities, and apply algebraic techniques to solve problems.**Ratio and proportion**

Students study ratios and proportional relationships, including direct and inverse proportions. They solve problems involving ratios and proportions and learn to interpret and use rates of change in various contexts.**Geometry & measures**

Students study properties of 2D and 3D shapes, including angles, lines, and symmetry. They calculate the perimeter and area of polygons, explore properties of circles, and develop an understanding of volume and surface area of simple 3D shapes.**Probability**

They explore basic probability concepts and solve standard event and non-event problems.**Statistics**

Students analyze and interpret data using various statistical techniques. They calculate and interpret measures of central tendency and dispersion, and they construct and interpret various types of graphs and charts.

The 7th grade maths curriculum focuses on consolidating and extending students' mathematical understanding, while fostering their problem-solving and reasoning skills. It prepares them for more advanced mathematical concepts in subsequent years.

Below is the complete list of topics for 7th grade arranged by category. Click on a topic to view more information.

Number

- 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
- 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 cube numbersIdentify the cube numbers in each group of integers
- 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
- Express quantities as percentagesExpress one quantity as a percentage of another
- 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 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)
- 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 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
- Find percentages: multiples of 5Find percentages using multiples of 5
- 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
- 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 factorsIdentify the prime factors of each given number using product notation
- Decimals: ascending orderChoose the set of decimals, both positive and negative, that are in the correct ascending order
- Fractions: arrange ascendingArrange these sets of fractions in ascending order
- All positive numbers: ascendingChoose the sets of all positive numbers that are in ascending order
- Decimals to fractionsConvert terminating decimals to their equivalent, simplified fraction or improper fraction
- Multiply simple fractionsMultiply pairs of simple fractions and simplify your answers where possible
- Multiply fractions with cancellingMultiply fractions by cross cancelling numbers first
- 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
- Positive numbers: descending orderSelect the set of numbers that are in descending order
- Negative numbers: descending orderSelect the set of negative numbers that are in descending order
- Positive and negative: descendingArrange these lists of positive and negative numbers in descending order
- Divide fractionsDivide fractions by flipping one of the fractions (get the reciprocal of the fraction) and multiplying them
- Expressions: equal or not equalIdentify whether the expressions are equal or not equal

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 positive integer variablesCalculate the value of J by substituting in the given positive integer values for the 2 variables k and m
- Two negative integer variablesCalculate the value of K by substituting in two negative integer variables n and s
- Common termsFactorize out common terms only
- Common number factorsFactorize out common numbers
- 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
- Graphs of form y = c, x = cIdentify the correct equation for graphs with lines parallel to the x-axis or the y-axis
- Linear graphs: value of yFor each equation plotting a linear graph get the value of y given the value of x
- Simplify like & unlike termsSimplify the given expressions by adding and subtracting like and unlike terms
- 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
- Expressions from wordsForm an expression for each of the given scenarios in terms of x and y
- 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
- Divide unlike termsDivide unlike terms with coefficients but no exponents e.g. 4xyz / xz
- Divide unlike terms with exponentsSimplify expressions by dividing unlike terms with coefficients and exponents e.g. 6x⁵y / 3x²
- 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
- 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
- Equations with bracketsFor each equation, expand the bracket and solve for the given variable
- Expand a single bracketUse multiplication to expand a single simple bracket expression e.g. 5(4 + 3x)
- Bracket with x outsideExpand expressions with single brackets that have coefficients of x outside the bracket e.g. 5x(3y - 6x)

Ratio proportion rate

- Convert km to milesUse the approximation 1.6 kilometers ≈ 1 mile to convert distances in kilometers to imperial miles to 1 d.p.
- Convert miles to kilometersUse the approximation 1 mile ≈ 1.6 km to convert imperial miles to metric kilometers (km)
- Convert cm to feetUse the approximation 1 foot ≈ 30 cm to convert lengths in centimeters (cm) to imperial feet 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 inchesUse the approximation 1 inch ≈ 2.5 cm to convert centimeters to imperial inches
- Express as a percentageExpress quantities as percentages by creating a fraction and multiplying 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
- Express quantities as ratiosExpress each of the sets of quantities as a part to part ratio, simplified if possible
- 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
- 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 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
- 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
- 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 compound shapesCalculate the perimeters of the given compound shapes constructed from parallelograms
- 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
- Identify the quadrilateralUse the given properties to identify the quadrilateral
- Lines of symmetry: quadrilateralsHow many lines of symmetry does each of the given shapes have?
- 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
- Identify types of triangleUsing standard conventions identify isosceles, equilateral, right-angle and scalene 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
- 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
- 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
- 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
- Plan view from 3-D shapesIn each instance identify the plan view from the 3-dimensional shape
- Front elevation from 3-D shapeIn each instance identify the front elevation of a given 3-dimensional shape
- Side elevation from 3-D shapeIn each instance identify the side elevation of the given 3-dimensional shape
- Area of trapeziaIn each instance calculate the area of the given trapezium using the formula A = (L1 + L2)/2 x H to 2 d.p.
- 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
- 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
- Calculate the volume of cuboidsUse the standard formula (length x width x height) to calculate the volume of cuboids
- Volume of prismsUse the standard formula (area of cross-section times length) to calculate the volume of prisms 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
- Standard eventsFor each scenario work out the probability of the outcome as a fraction
- Non-eventsWork out the probability of an event NOT occurring expressing each answer as a simplified fraction

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
- Calculate mean: include negative integersCalculate the mean of each set of both positive and negative integers
- Identify the rangeIdentify the range of each set of numbers
- Identify the modeIdentify the mode (most frequent number) for each set of numbers
- Identify the medianIdentify the median (middle value) of each set of numbers
- Identify the outlierIdentify the outlier in each set of numbers
- 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.
- Convert angles to numbersConvert an angle on each pie chart into a number of items or people
- Pie charts: convert numbers to anglesFor each pie chart calculate the angle that represents the given number of items
- Vertical line chart: mean, rangeFind the mean or the range for each of the given vertical line charts

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