
8Grade 8 Standards
Top Mathematicians

Numbers, Operations and Relationships

8.NOR.1.1.1
Mental calculations
• Revise multiplication of whole numbers to at least 12 x 12 

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8.NOR.1.1.2
Ordering and comparing whole numbers
• Revise prime numbers to at least 100 

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8.NOR.1.1.3
Properties of whole numbers
• Revise:
 The commutative; associative; distributive properties of whole numbers
 0 in terms of its additive property (identity element for addition)
 1 in terms of its multiplicative property (identity element for multiplication)
• Recognize the division property of 0, whereby any number divided by 0 is undefined 
8.NOR.1.1.4
Calculations using whole numbers
• Revise calculations using all four operations on whole numbers, estimating and using calculators where appropriate 

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8.NOR.1.1.5
Calculation techniques
• Use a range of techniques to perform and check written and mental calculations of whole numbers including:
 long division
 adding, subtracting and multiplying in columns
 estimation
 rounding off and compensating
 using a calculator 

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8.NOR.1.1.6
Multiples and factors
• Revise:
 Prime factors of numbers to at least 3digit whole numbers
 LCM and HCF of numbers to at least 3digit whole numbers, by inspection or factorisation 
8.NOR.1.1.7
Solving problems
• Solve problems involving whole numbers, including
 comparing two or more quantities of the same kind (ratio)
 comparing two quantities of different kinds (rate)
 sharing in a given ratio where the whole is given
 increasing or decreasing of a number in a given ratio
• Solve problems that involve whole numbers, percentages and decimal fractions in financial contexts such as:
 profit, loss, discount and VAT
 budgets
 accounts
 loans
 simple interest
 hire purchase
 exchange rates 

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8.NOR.1.2.1
Exponents. Mental calculations
• Revise:
 Squares to at least 122 and their square roots
 Cubes to at least 63 and their cube roots 

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8.NOR.1.2.2
Exponents. Comparing and representing numbers in exponential form
• Revise compare and represent whole numbers in exponential form
• Compare and represent integers in exponential form
• Compare and represent numbers in scientific notation, limited to positive exponents 

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8.NOR.1.2.3
Exponents. Calculations using numbers in exponential form
• Establish general laws of exponents, limited to:
 natural number exponents
 a to the m power x an = a to the m power + n
 a to the m power ÷ an = a to the m power – n, if m > n
 (a to the m power)n = a to the m power x n
 (a x t)n = an x tn
 a° = 1
• Recognize and use the appropriate laws of operations using numbers involving exponents and square and cube roots
• Perform calculations involving all four operations with numbers that involve the squares, cubes, square roots and cube roots of integers
• Calculate the squares, cubes, square roots and cube roots of rational numbers 
8.NOR.1.2.4
Exponents. Solving problems
• Solve problems in contexts involving numbers in exponential form 

8.NOR.1.3.1
Counting, ordering and comparing integers
• Revise:
 counting forwards and backwards in integers for any interval
 recognizing, ordering and comparing integers 

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8.NOR.1.3.2
Calculations with integers
• Revise addition and subtraction with integers
• Multiply and divide with integers
• Perform calculations involving all four operations with integers
• Perform calculations involving all four operations with numbers that involve the squares, cubes, square roots and cube roots of integers 

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8.NOR.1.3.3
Properties of integers
• Recognise and use commutative, associative and distributive properties of addition and multiplication for integers
• Recognize and use additive and multiplicative inverses for integers 
8.NOR.1.3.4
Solving problems
• Solve problems in contexts involving multiple operations with integers 
8.NOR.1.4.1
Common fractions. Calculations with fractions
• Revise:
 addition and subtraction of common fractions, including mixed numbers
 finding fractions of whole numbers
 multiplication of common fractions, including mixed numbers
• Divide whole numbers and common fractions by common fractions
• Calculate the squares, cubes, square roots and cube roots of common fractions 

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8.NOR.1.4.2
Common fractions. Calculation techniques
• Revise:
 convert mixed numbers to common fractions in order to perform calculations with them
 use knowledge of multiples and factors to write fractions in the simplest form before or after calculations
 use knowledge of equivalent fractions to add and subtract common fractions
• Use knowledge of reciprocal relationships to divide common fractions 

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8.NOR.1.4.3
Common fractions. Solving problems
• Solve problems in contexts involving common fractions and mixed numbers, including grouping, sharing and finding fractions of whole numbers 
8.NOR.1.4.4
Common fractions. Percentages
• Revise:
 finding percentages of whole numbers
 calculating the percentage of part of a whole
 calculating percentage increase or decrease
• Calculate amounts if given percentage increase or decrease
• Solve problems in contexts involving percentages 

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8.NOR.1.4.5
Common fractions. Equivalent forms
• Revise equivalent forms between:
 common fractions (fractions where one denominator is a multiple of the other)
 common fraction and decimal fraction forms of the same number
 common fraction, decimal fraction and percentage forms of the same number 
8.NOR.1.5.1
Decimal fractions. Ordering and comparing decimal fractions
• Revise:
 ordering, comparing and place value of decimal fractions to at least 3 decimal places
 rounding off decimal fractions to at least 2 decimal place 

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8.NOR.1.5.2
Decimal fractions. Calculations with decimal fractions
• Revise:
 addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places
 division of decimal fractions by whole numbers
• Extend multiplication to 'multiplication by decimal fractions' not limited to one decimal place
• Extend division to 'division of decimal fractions by decimal fractions'
• Calculate the squares, cubes, square roots and cube roots of decimal fractions 

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8.NOR.1.5.3
Decimal fractions. Calculation techniques
• Use knowledge of place value to estimate the number of decimal places in the result before performing calculations
• Use rounding off and a calculator to check results where appropriate 
8.NOR.1.5.4
Decimal fractions. Solving problems
• Solve problems in context involving decimal fractions 

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8.NOR.1.5.5
Decimal fractions. Equivalent forms
• Revise equivalent forms between:
 common fraction and decimal fraction forms of the same number
 common fraction, decimal fraction and percentage forms of the same number

8.NOR.1.1.1

Space and Shape (Geometry)

8.G.3.1.1
Classifying 2D shapes
• Identify and write clear definitions of triangles in terms of their sides and angles, distinguishing between:
 equilateral triangles
 isosceles triangles
 rightangled triangles
• Identify and write clear definitions of quadrilaterals in terms of their sides and angles, distinguishing between:
 parallelogram
 rectangle
 square
 rhombus
 trapezium
 kite 

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8.G.3.1.2
Similar and congruent 2D shapes
• Identify and describe the properties of congruent shapes
• Identify and describe the properties of similar shapes 
8.G.3.1.3
Solving problems
• Solve geometric problems involving unknown sides and angles in triangles and quadrilaterals, using known properties and definitions. 
8.G.3.2.1
Classifying 3D objects
• Describe, name and compare the 5 Platonic solids in terms of the shape and number of faces, the number of vertices and the number of edges 
8.G.3.2.2
Building 3D models
• Revise using nets to create models of geometric solids, including:
 cubes
 prisms
 pyramids 

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8.G.3.3.1
Geometry of straight lines. Angle relationships
• Recognize and describe pairs of angles formed by:
 perpendicular lines
 intersecting lines
 parallel lines cut by a transversal 
8.G.3.3.2
Geometry of straight lines. Solving problems
• Solve geometric problems using the relationships between pairs of angles described above 
8.G.3.4.1
Transformations
• Recognize, describe and perform transformations with points on a coordinate plane, focusing on:
 reflecting a point in the Xaxis or Yaxis
 translating a point within and across quadrants
• Recognize, describe and perform transformations with triangles on a coordinate plane, focusing on the coordinates of the vertices when:
 reflecting a triangle in the Xaxis or Yaxis
 translating a triangle within and across quadrants
 rotating a triangle around the origin 

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8.G.3.4.2
Enlargements and reductions
• Use proportion to describe the effect of enlargement or reduction on area and perimeter of geometric figures 
8.G.3.5.1
Constructions
• Accurately construct geometric figures appropriately using a compass, ruler and protractor, including:
 bisecting lines and angles
 perpendicular lines at a given point or from a given point
 triangles
 quadrilaterals
• Construct angles of 30°, 45°, 60° and their multiples without using a protractor 
8.G.3.5.2
Investigating properties of geometric figures
• By construction, investigate the angles in a triangle, focusing on:
 the sum of the interior angles of triangles
 the size of angles in an equilateral triangle
 the sides and base angles of an isosceles triangle
• By construction, investigate sides and angles in quadrilaterals, focusing on:
 the sum of the interior angles of quadrilaterals
 the sides and opposite angles of parallelograms 

8.G.3.1.1

Measurement

8.MT.1.1
Area and perimeter
• Use appropriate formulae to calculate perimeter and area of:
 squares
 rectangles
 triangles
 circles
• Calculate the areas of polygons, to at least 2 decimal places, by decomposing them into rectangles and/or triangles
• Use and describe the relationship between the radius, diameter and circumference of a circle in calculations
• Use and describe the relationship between the radius and area of a circle in calculations 

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8.MT.1.2
Calculations and solving problems
• Solve problems, with or without a calculator, involving perimeter and area of polygons and circles
• Calculate to at least 2 decimal places
• Use and describe the meaning of the irrational number Pi (π) in calculations involving circles
• Use and convert between appropriate SI units, including: mm² <> cm² <> m² <> km² 

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8.MT.2.1
Surface area and volume
• Use appropriate formulae to calculate the surface area, volume and capacity of:
 cubes
 rectangular prisms
 triangular prisms
• Describe the interrelationship between surface area and volume of the objects mentioned above 

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8.MT.2.2
Calculations and solving problems
• Solve problems, with or without a calculator, involving surface area, volume and capacity
• Use and convert between appropriate SI units, including:
 mm² <> cm² <> m² <> km²
 mm³ <> cm³ <> m³
 ml (cm³) <> l <> kl 

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8.MT.3.1
Develop and use the Theorem of Pythagoras
• Investigate the relationship between the lengths of the sides of a rightangled triangle to develop the Theorem of Pythagoras
• Determine whether a triangle is a rightangled triangle or not if the length of the three sides of the triangle are known
• Use the Theorem of Pythagoras to calculate a missing length in a rightangled triangle, leaving irrational answers in surd form 

8.MT.1.1

Patterns, Functions and Algebra

8.PFA.2.1.1
Numeric and geometric patterns. Investigate and extend patterns
• Investigate and extend numeric and geometric patterns looking for relationships between numbers, including patterns:
 represented in physical or diagram form
 not limited to sequences involving a constant difference or ratio
 of learner's own creation
 represented in tables
 represented algebraically
• Describe and justify the general rules for observed relationships between numbers in own words or in algebraic language 

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8.PFA.2.2.1
Functions and relationships. Input and output values
• Determine input values, output values or rules for patterns and relationships using:
 flow diagrams
 tables
 formulae
 equations 

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8.PFA.2.2.2
Functions and relationships. Equivalent forms
• Determine, interpret and justify equivalence of different descriptions of the same relationship or rule presented:
 verbally
 in flow diagrams
 in tables
 by formulae
 by equations 

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8.PFA.2.3.1
Algebraic language
• Revise the following done in Grade 7:
 recognize and interpret rules or relationships represented in symbolic form
 identify variables and constants in given formulae and/or equations
• Recognize and identify conventions for writing algebraic expressions
• Identify and classify like and unlike terms in algebraic expressions
• Recognize and identify coefficients and exponents in algebraic expressions 

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8.PFA.2.3.2
Expand and simplify algebraic expressions
• Use commutative, associative and distributive laws for rational numbers and laws of exponents to:
 add and subtract like terms in algebraic expressions
 multiply integers and monomials by:
 divide the following by integers or monomials:
 simplify algebraic expressions involving the above operations
• Determine the squares, cubes, square roots and cube roots of single algebraic terms or like algebraic terms
• Determine the numerical value of algebraic expressions by substitution 

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8.PFA.2.4.1
Equations
• Revise the following done in Grade 7:
 set up equations to describe problem situations
 analyse and interpret equations that describe a given situation
 solve equations by inspection
 determine the numerical value of an expression by substitution.
 identify variables and constants in given formulae or equations
• Use substitution in equations to generate tables of ordered pairs
• Extend solving equations to include:
 using additive and multiplicative inverses
 using laws of exponents 

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8.PFA.2.5.1
Interpreting graphs
• Revise the following done in Grade 7:
 analyse and interpret global graphs of problem situations, with a special focus on the following trends and features:
• Extend the focus on features of graphs to include:
 maximum or minimum
 discrete or continuous 
8.PFA.2.5.2
Drawing graphs
• Draw global graphs from given descriptions of a problem situation, identifying features listed above
• Use tables or ordered pairs to plot points and draw graphs on the Cartesian plane 

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8.PFA.2.1.1

Data Handling

8.DH.1.1
Collect data
• Pose questions relating to social, economic, and environmental issues
• Select appropriate sources for the collection of data (including peers, family, newspapers, books, magazines)
• Distinguish between samples and populations, and suggest appropriate samples for investigation
• Design and use simple questionnaires to answer questions with multiple choice responses 

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8.DH.1.2
Organize and summarize data
• Organize (including grouping where appropriate) and record data using
 tally marks
 tables
 stemandleaf displays
• Group data into intervals
• Summarize data using measures of central tendency, including:
 mean
 median
 mode
• Summarize data using measures of dispersion, including:
 range
 extremes 

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8.DH.2.1
Represent data
• Draw a variety of graphs by hand/technology to display and interpret data including:
 bar graphs and double bar graphs
 histograms with given and own intervals
 pie charts
 brokenline graphs 

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8.DH.3.1
Interpret data
• Critically read and interpret data represented in:
 words
 bar graphs
 double bar graphs
 pie charts
 histograms
 brokenline graphs 

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8.DH.3.2
Analyse data
• Critically analyse data by answering questions related to:
 data categories, including data intervals
 data sources and contexts
 central tendencies (mean, mode, median)
 scales used on graphs
 samples and populations
 dispersion of data
 error and bias in the data 

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8.DH.3.3
Report data
• Summarize data in short paragraphs that include
 drawing conclusions about the data
 making predictions based on the data
 identifying sources of error and bias in the data
 choosing appropriate summary statistics for the data (mean, median, mode, range)
 the role of extremes in the data 

8.DH.4.1
Probability
• Consider a simple situation (with equally likely outcomes) that can be described using probability and:
 list all the possible outcomes
 determine the probability of each possible outcome using the definition of probability
 predict with reasons the relative frequency of the possible outcomes for a series of trials based on probability
 compare relative frequency with probability and explains possible differences 

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8.DH.1.1