8th grade math

Program of study for 8th grade

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.

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

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

• Convert miles to kilometers
  
  Use the approximation 1 mile ≈ 1.6 km to convert imperial miles to metric kilometers (km)
• Convert km to miles
  
  Use the approximation 1.6 kilometers ≈ 1 mile to convert distances in kilometers to imperial miles to 1 d.p.
• Convert inches to cm
  
  Use the approximation 1 inch ≈ 2.54 cm to convert imperial inches to metric centimeters to 2 d.p.
• Convert cm to feet
  
  Use the approximation 1 foot ≈ 30 cm to convert lengths in centimeters (cm) to imperial feet to 1 d.p.
• Convert cm to inches
  
  Use the approximation 1 inch ≈ 2.5 cm to convert centimeters to imperial inches
• Increase by a percentage
  
  Derive the actual increase from the percentage increase and add it to the original quantity or amount
• Decrease by a percentage
  
  Derive the actual decrease from the percentage decrease and subtract it from the original quantity
• Express as a percentage
  
  Express quantities as percentages by creating a fraction and multiplying by 100
• Calculate percentage increase
  
  Get the percentage increase by expressing the increase as a fraction of the original and multiplying by 100
• Calculate percentage decrease
  
  Get the percentage decrease by expressing the decrease as a fraction of the original and multiplying that amount by 100
• Calculate speed
  
  Use the speed formula speed s = distance d / time t to calculate speeds to 1 d.p.
• Calculate distance, time
  
  Re-arrange the speed formula to calculate distance or time to 1 d.p.
• Speed from a graph
  
  Using speed time graphs find the speed at the given time
• Fastest speed, slowest speed
  
  Using speed time graphs identify the highest speed or the lowest speed attained
• Calculate density
  
  In each instance calculate the density using the density formula d = mass / volume to 1 d.p.
• Unit price: best value
  
  Identify the better value for money option by doing unit price calculations
• Directly or inversely proportional
  
  Identify which of the graphs and equations are directly proportional, inversely proportional or neither
• Direct proportion problems
  
  Solve problems involving direct proportion where two quantities increase at the same rate
• Inverse proportion problems
  
  Solve problems involving inverse proportion where one quantity increases as the other decreases (to 2 d.p.)
• Actual distance
  
  Work out the real distance between two points represented on maps and scale diagrams (to 2 d.p.)
• Distance on a map or diagram
  
  Use 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 ratios
  
  Express each of the given fractions as a part to whole ratio
• Express percentages as ratios
  
  Express each of the given percentages as a part to whole ratio
• Express decimals as ratios
  
  Express each of the given decimals as a part to whole ratio
• Equivalent ratios
  
  Identify the ratios that are equivalent e.g. 1:2 and 3:6
• Express ratios as fractions
  
  Express part to part ratios as fraction proportions of the whole
• Express ratios as percentages
  
  Express each part to whole ratio as a part to whole percentage
• Express quantities as % with calculator
  
  Express quantities of wholes as percentages by converting to a fraction and multiplying by 100 to (1 d.p.)
• Increase by % with calculator
  
  Derive the actual increase from the percentage increase and add it to the original quantity or amount (to 1 d.p.)
• Decrease by % with calculator
  
  Calculate the new quantity or amount by using a decimal multiplier; answers to 2 d.p.
• Convert cm³ to mm³
  
  Convert cubic centimeters (cm³) to cubic millimeters (mm³) by multiplying by 1000
• Convert m³ to cm³
  
  Convert cubic meters (m³) to cubic centimeters (cm³) by multiplying by 1,000,000
• Specific parts and quantity
  
  Pair up specific quantities with specific parts

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

• Venn diagrams: 2 categories
  
  Find the missing value for each of the given Venn diagrams
• Venn diagrams: 3 categories
  
  Find the missing value for each of the given 3 category Venn diagrams
• Independent events
  
  Find the probability of different outcomes using the AND & OR rules
• Sample space diagrams
  
  Answer probability questions based on the given sample space diagrams
• Tree diagrams: replacement
  
  Find the probabilities using tree diagrams with both replacement and no replacement of items

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