7th grade math

Program of study for 7th grade

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.

• Identify improper fractions
  
  Identify the fraction or fractions that are improper fractions
• Identify mixed fractions
  
  Identify the fraction or fractions that are mixed fractions
• Identify equivalent fractions
  
  Identify the pairs of fractions that are equivalent
• Add decimals
  
  Add decimals by first aligning the decimal points of each number
• Subtract decimals
  
  Subtract decimals by first aligning the decimal points
• Multiply decimals
  
  Multiply decimals by initially removing the decimal point
• Divide decimals by integers
  
  Divide decimal numbers by integers
• Divide integers by decimals
  
  Divide integer values by decimal numbers
• Divide decimals by decimals
  
  Divide decimals by decimals
• Identify cube numbers
  
  Identify the cube numbers in each group of integers
• 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
• Express quantities as percentages
  
  Express one quantity as a percentage of another
• 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 numbers: nearest 100
  
  Round each given number to the nearest 100
• Round numbers: nearest 1000
  
  Round each of the given numbers to the nearest 1000
• Round decimals: nearest integer
  
  Round each of the given decimals to the nearest whole number (integer)
• 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 fractions: common denominator
  
  Add fractions with a common denominator
• Add fractions: scale denominator
  
  Add fractions by scaling up the fraction with the smaller denominator; simplify answers where possible
• Add fractions using LCD
  
  Add fractions by finding the lowest common denominator (LCD); simplify your answers where possible
• Convert exponents to expanded form
  
  Convert between base with exponent and expanded form e.g. 3³ <=> 3 x 3 x 3
• Find percentages: multiples of 10
  
  Find a percentage using multiples of 10
• Find percentages: multiples of 5
  
  Find percentages using multiples of 5
• 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
• Subtract fractions: common denominator
  
  Subtract fractions which share a common denominator
• Subtract fractions: scale denominator
  
  Subtract fractions by scaling up the fraction with the smaller denominator
• Subtract fractions: LCD
  
  Subtract fractions by finding the lowest common denominator (LCD) of the two fractions
• Prime factors
  
  Identify the prime factors of each given number using product notation
• Decimals: ascending order
  
  Choose the set of decimals, both positive and negative, that are in the correct ascending order
• Fractions: arrange ascending
  
  Arrange these sets of fractions in ascending order
• All positive numbers: ascending
  
  Choose the sets of all positive numbers that are in ascending order
• Decimals to fractions
  
  Convert terminating decimals to their equivalent, simplified fraction or improper fraction
• Multiply simple fractions
  
  Multiply pairs of simple fractions and simplify your answers where possible
• Multiply fractions with cancelling
  
  Multiply fractions by cross cancelling numbers first
• Percentages to fractions
  
  Identify the correct, simplified fraction for each of the given percentages
• Percentages to decimals
  
  Identify the correct decimal for each of the given percentages
• Fractions to percentages
  
  Identify the correct percentage for each of the given fractions
• Fractions and percentages
  
  Compare by converting both fractions and percentages to decimals; select the larger decimal
• Positive numbers: descending order
  
  Select the set of numbers that are in descending order
• Negative numbers: descending order
  
  Select the set of negative numbers that are in descending order
• Positive and negative: descending
  
  Arrange these lists of positive and negative numbers in descending order
• Divide fractions
  
  Divide fractions by flipping one of the fractions (get the reciprocal of the fraction) and multiplying them
• Expressions: equal or not equal
  
  Identify whether the expressions are equal or not equal

• 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 positive integer variables
  
  Calculate the value of J by substituting in the given positive integer values for the 2 variables k and m
• Two negative integer variables
  
  Calculate the value of K by substituting in two negative integer variables n and s
• Common terms
  
  Factorize out common terms only
• Common number factors
  
  Factorize out common numbers
• 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
• Graphs of form y = c, x = c
  
  Identify the correct equation for graphs with lines parallel to the x-axis or the y-axis
• Linear graphs: value of y
  
  For each equation plotting a linear graph get the value of y given the value of x
• Simplify like & unlike terms
  
  Simplify the given expressions by adding and subtracting like and unlike terms
• 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
• Expressions from words
  
  Form an expression for each of the given scenarios in terms of x and y
• 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
• Divide unlike terms
  
  Divide unlike terms with coefficients but no exponents e.g. 4xyz / xz
• Divide unlike terms with exponents
  
  Simplify expressions by dividing unlike terms with coefficients and exponents e.g. 6x⁵y / 3x²
• Terms on one side, one-step equations
  
  In each instance use simple algebraic methods to solve for the given variable in these one-step equations
• Terms on one side, two-step equations
  
  For each two-step equation use algebraic methods to solve for the given variable
• 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
• Equations with brackets
  
  For each equation, expand the bracket and solve for the given variable
• Expand a single bracket
  
  Use multiplication to expand a single simple bracket expression e.g. 5(4 + 3x)
• Bracket with x outside
  
  Expand expressions with single brackets that have coefficients of x outside the bracket e.g. 5x(3y - 6x)

• 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 miles to kilometers
  
  Use the approximation 1 mile ≈ 1.6 km to convert imperial miles to metric kilometers (km)
• 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 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 inches
  
  Use the approximation 1 inch ≈ 2.5 cm to convert centimeters to imperial inches
• Express as a percentage
  
  Express quantities as percentages by creating a fraction and multiplying 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
• Express quantities as ratios
  
  Express each of the sets of quantities as a part to part ratio, simplified if possible
• 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
• Ratio in its simplest form
  
  Use division to express each ratio in its simplest form
• Equivalent ratios
  
  Identify 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 milliliters
  
  Convert volumes given in liters (L) into milliliters (ml) by multiplying by 1000
• Convert liters to cm³
  
  Convert liters (L) to cubic centimeters (cm³) by multiplying by 1000
• 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
• Share a quantity into parts
  
  Add up the parts and divide the quantity by the total number of parts to get the different shares

• Count edges of 3D shapes
  
  Work out the total number of edges for each of the given solids
• Count vertices of 3D shapes
  
  Work out the total number of vertices for each of the given solids
• Count faces of 3D shapes
  
  Work out the total number of faces for each of the given solids
• Perimeter of compound shapes
  
  Calculate the perimeters of the given compound shapes constructed from parallelograms
• 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
• Identify the quadrilateral
  
  Use the given properties to identify the quadrilateral
• Lines of symmetry: quadrilaterals
  
  How many lines of symmetry does each of the given shapes have?
• 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
• Identify types of triangle
  
  Using standard conventions identify isosceles, equilateral, right-angle and scalene 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
• 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
• Angles on a straight line
  
  Use the angles on a straight line rule to find the missing angles
• Angles around a point
  
  Use the angles around a point rule to find the missing angles
• Angles in a triangle
  
  Use the fact that angles within a triangle sum to 180° to find the missing angles
• 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
• Plan view from 3-D shapes
  
  In each instance identify the plan view from the 3-dimensional shape
• Front elevation from 3-D shape
  
  In each instance identify the front elevation of a given 3-dimensional shape
• Side elevation from 3-D shape
  
  In each instance identify the side elevation of the given 3-dimensional shape
• Area of trapezia
  
  In 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 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
• 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
• Calculate the volume of cuboids
  
  Use the standard formula (length x width x height) to calculate the volume of cuboids
• Volume of prisms
  
  Use the standard formula (area of cross-section times length) to calculate the volume of prisms 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
• Standard events
  
  For each scenario work out the probability of the outcome as a fraction
• Non-events
  
  Work out the probability of an event NOT occurring expressing each answer as a simplified fraction

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