
7Grade 7 Standards
Top Mathematicians

Data Handling

7.DH.1.1
Collect data
• Pose questions relating to social, economic, and environmental issues in own environment
• 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 yes/no type responses
 with multiple choice responses 

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7.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 and distinguishing between ungrouped numerical data by determining:
 mean
 median
 mode
• Identify the largest and smallest scores in a data set and determine the difference between them in order to determine the spread of the data (range) 

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7.DH.2.1
Represent data
• Draw a variety of graphs by hand/technology to display and interpret data (grouped and ungrouped) including:
 bar graphs and double bar graphs
 histograms with given intervals
 pie charts 

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

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7.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 

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7.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) 

7.DH.4.1
Probability
• Perform simple experiments where the possible outcomes are equally likely and:
 list the possible outcomes based on the conditions of the activity
 determine the probability of each possible outcome using the definition of probability 

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7.DH.1.1

Space and Shape (Geometry)

7.G.3.1.1
Classifying 2D shapes
• Describe, sort, name and compare triangles according to their sides and angles, focusing on:
 equilateral triangles
 isosceles triangles
 rightangled triangles
• Describe, sort, name and compare quadrilaterals in terms of:
 length of sides
 parallel and perpendicular sides
 size of angles (rightangles or not)
• Describe and name parts of a circle 

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7.G.3.1.2
Similar and congruent 2D shapes
• Recognize and describe similar and congruent figures by comparing:
 shape
 size 

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7.G.3.1.3
Solving problems
• Solve simple geometric problems involving unknown sides and angles in triangles and quadrilaterals, using known properties. 
7.G.3.2.1
Classifying 3D objects
• Describe, sort and compare polyhedra in terms of:
 shape and number of faces
 number of vertices
 number of edges 

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7.G.3.2.2
Building 3D models
• Revise using nets to create models of geometric solids, including:
 cubes
 prisms 

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7.G.3.3.1
Geometry of straight lines. Define:
• Line segment
• Ray
• Straight line
• Parallel lines
• Perpendicular lines 

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7.G.3.4.1
Transformation Geometry. Transformations
• Recognize, describe and perform translations, reflections and rotations with geometric figures and shapes on squared paper
• Identify and draw lines of symmetry in geometric figures 

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7.G.3.4.2
Transformation Geometry. Enlargements and reductions
• Draw enlargements and reductions of geometric figures on squared paper and compare them in terms of shape and size 

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7.G.3.5.1
Construction of geometric figures. Measuring angles
• Accurately use a protractor to measure and classify angles:
 < 90° (acute angles)
 Rightangles
 > 90° (obtuse angles)
 Straight angles
 > 180° (reflex angles) 
7.G.3.5.2
Construction of geometric figures. Constructions
• Accurately construct geometric figures appropriately using a compass, ruler and protractor, including:
 angles, to one degree of accuracy
 circles
 parallel lines
 perpendicular lines 

7.G.3.1.1

Measurement

7.MT.1.1
Area and perimeter
• Calculate the perimeter of regular and irregular polygons
• Use appropriate formulae to calculate perimeter and area of:
 squares
 rectangles
 triangles 

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7.MT.1.2
Calculations and solving problems
• Solve problems involving perimeter and area of polygons
• Calculate to at least 1 decimal place
• Use and convert between appropriate SI units, including:
 mm² <> cm²
 cm² <> m² 

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

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7.MT.2.2
Calculations and solving problems
• Solve problems involving surface area, volume and capacity
• Use and convert between appropriate SI units, including:
 mm² <> cm²
 cm² <> m²
 mm³ <> cm³
 cm³ <> m³
• Use equivalence between units when solving problems:
 1 cm³ <> 1 ml
 1 m³ <> 1 kl

7.MT.1.1

Numbers, Operations and Relationships

7.NOR.1.1.1
Whole numbers. Mental calculations
• Revise the following done in Grade 6:
 Multiplication of whole numbers to at least 12 x 12
 Multiplication facts for:
 Inverse operation between multiplication and division 
7.NOR.1.1.2
Whole numbers. Ordering and comparing whole numbers
• Revise the following done in Grade 6:
 order, compare and represent numbers to at least 9digit numbers
 recognize and represent prime numbers to at least 100
 round off numbers to the nearest 5, 10, 100 or 1000 
7.NOR.1.1.3
Whole numbers. Properties of whole numbers
• Revise the following done in Grade 6:
 recognize and use the commutative; associative; distributive properties of whole numbers
 recognize and use 0 in terms of its additive property (identity element for addition)
 recognize and use 1 in terms of its multiplicative property (identity element for multiplication) 

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7.NOR.1.1.4
Whole numbers. Calculations using whole numbers
• Revise the following done in Grade 6, without use of calculators:
 Addition and subtraction of whole numbers to at least 6digit numbers
 Multiplication of at least whole 4digit by 2digit numbers
 Division of at least whole 4digit by 2digit numbers
 Perform calculations using all four operations on whole numbers, estimating and using calculators where appropriate 

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7.NOR.1.1.5
Whole numbers. Calculation techniques
• Use a range of strategies 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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7.NOR.1.1.6
Whole numbers. Multiples and factors
• Revise the following done in Grade 6:
 multiples of 2digit and 3digit whole numbers
 factors of 2digit and 3digit whole numbers
 prime factors of numbers to at least 100
• List prime factors of numbers to at least 3digit whole numbers
• Find the LCM and HCF of numbers to at least 3digit whole numbers, by inspection or factorisation 

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7.NOR.1.1.7
Whole numbers. 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
• Solve problems that involve whole numbers, percentages and decimal fractions in financial contexts such as:
 profit, loss and discount
 budgets
 accounts
 loans
 simple interest 

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7.NOR.1.2.1
Exponents. Mental calculations
• Determine squares to at least 122 and their square roots
• Determine cubes to at least 63 and cube roots 

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7.NOR.1.2.2
Exponents. Comparing and representing numbers in exponential form
• Compare and represent whole numbers in exponential form: ab = a x a x a x... for b number of factors 

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7.NOR.1.2.3
Exponents. Calculations using numbers in exponential form
• Recognize and use the appropriate laws of operations with numbers involving exponents and square and cube roots
• Perform calculations involving all four operations using numbers in exponential form, limited to exponents up to 5, and square and cube roots 

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7.NOR.1.2.4
Exponents. Solving problems
• Solve problems in contexts involving numbers in exponential form. 

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7.NOR.1.3.1
Integers. Counting, ordering and comparing integers
• Count forwards and backwards in integers for any interval
• Recognize, order and compare integers 

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7.NOR.1.3.2
Integers. Calculations with integers
• Add and subtract with integers 
7.NOR.1.3.3
Integers. Properties of integers
• Recognise and use commutative and associative properties of addition and multiplication for integers 

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7.NOR.1.3.4
Integers. Solving problems
• Solve problems in contexts involving addition and subtraction with integers 
7.NOR.1.4.1
Common fractions. Ordering, comparing and simplifying fractions
• Revise the following done in Grade 6
 compare and order common fractions, including specifically tenths and hundredths
• Extend to thousandths 

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7.NOR.1.4.2
Common fractions. Calculations with fractions
• Revise the following done in Grade 6:
 addition and subtraction of common fractions, including mixed numbers, limited to fractions with the same denominator or where one denominator is a multiple of another
 finding fractions of whole numbers
• Extend addition and subtraction to fractions where one denominator is not a multiple of the other
• Multiplication of common fractions, including mixed numbers, not limited to fractions where one denominator is a multiple of another 

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7.NOR.1.4.3
Common fractions. Calculation techniques
• 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 

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7.NOR.1.4.4
Common fractions. Solving problems
• Solve problems in contexts involving common fractions and mixed numbers, including grouping, sharing and finding fractions of whole numbers 

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7.NOR.1.4.5
Common fractions. Percentages
• Revise the following done in Grade 6:
 Finding percentages of whole numbers
• Calculate the percentage of part of a whole
• Calculate percentage increase or decrease of whole numbers
• Solve problems in contexts involving percentages 

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7.NOR.1.4.6
Common fractions. Equivalent forms
• Revise the following done in Grade 6:
 recognize and use equivalent forms of common fractions with 1digit or 2digit denominators (fractions where one denominator is a multiple of the other)
 recognize equivalence between common fraction and decimal fraction forms of the same number
 recognize equivalence between common fraction, decimal fraction and percentage forms of the same number 
7.NOR.1.5.1
Decimal fractions. Ordering and comparing decimal fractions
• Revise the following done in Grade 6:
 count forwards and backwards in decimal fractions to at least two decimal places
 compare and order decimal fractions to at least two decimal places
 place value of digits to at least two decimal places
 rounding off decimal fractions to at least 1 decimal place
• Extend all of the above to decimal fractions to at least three decimal places and rounding off to at least 2 decimal places 

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7.NOR.1.5.2
Decimal fractions. Calculations with decimal fractions
• Revise the following done in Grade 6:
 addition and subtraction of decimal fractions of at least two decimal places
 multiplication of decimal fractions by 10 and 100
• Extend addition and subtraction to decimal fractions of at least three decimal places
• Multiply decimal fractions to include:
 decimal fractions to at least 3 decimal places by whole numbers
 decimal fractions to at least 2 decimal places by decimal fractions to at least 1 decimal place
• Divide decimal fractions to include decimal fractions to at least 3 decimal places by whole numbers 

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7.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 
7.NOR.1.5.4
Decimal fractions. Solving problems
• Solve problems in context involving decimal fractions 

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7.NOR.1.5.5
Decimal fractions. Equivalent forms
• Revise the following done in Grade 6:
 recognize equivalence between common fraction and decimal fraction forms of the same number
 recognize equivalence between common fraction, decimal fraction and percentage forms of the same number

7.NOR.1.1.1

Patterns, Functions and Algebra

7.PFA.2.1.2
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
• Describe and justify the general rules for observed relationships between numbers in own words 

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7.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 

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7.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 number sentences 

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7.PFA.2.3.1
Algebraic expressions. Algebraic language
• Recognize and interpret rules or relationships represented in symbolic form
• Identify variables and constants in given formulae and/or equations 
7.PFA.2.4.1
Algebraic equations. Number sentences
• Write number sentences to describe problem situations
• Analyse and interpret number sentences that describe a given situation
• Solve and complete number sentences by:
 inspection
 trial and improvement
• Determine the numerical value of an expression by substitution.
• Identify variables and constants in given formulae or equations 

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7.PFA.2.5.1
Graphs. Interpreting graphs
• Analyse and interpret global graphs of problem situations, with special focus on the following trends and features:
 linear or nonlinear
 constant, increasing or decreasing 

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7.PFA.2.5.2
Graphs. Drawing graphs
• Draw global graphs from given descriptions of a problem situation, identifying features listed above 

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7.PFA.2.1.2