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Skills available for South Africa grade 7 maths curriculum

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7.1 Numbers, Operations and Relationships

7.1.1 Whole numbers
- 7.1.1.a Mental calculations
  - 7.1.1.a.1 Revise the following done in Grade 6:
    - 7.1.1.a.1.1 Multiplication of whole numbers to at least 12 x 12
    - 7.1.1.a.1.2 Multiplication facts for:
      - 7.1.1.a.1.2.a units and tens by multiples of ten
        
        Multiply numbers ending in zeroes (6-B.3)
        
        Multiply numbers ending in zeroes: word problems (6-B.4)
        
        Estimate products (6-B.7)
      - 7.1.1.a.1.2.b units and tens by multiples of 100
        
        Multiply numbers ending in zeroes (6-B.3)
        
        Multiply numbers ending in zeroes: word problems (6-B.4)
        
        Estimate products (6-B.7)
      - 7.1.1.a.1.2.c units and tens by multiples of 1000
        
        Multiply numbers ending in zeroes (6-B.3)
        
        Multiply numbers ending in zeroes: word problems (6-B.4)
        
        Estimate products (6-B.7)
      - 7.1.1.a.1.2.d units and tens by multiples of 10,000
        
        Multiply numbers ending in zeroes (6-B.3)
        
        Multiply numbers ending in zeroes: word problems (6-B.4)
    - 7.1.1.a.1.3 Inverse operation between multiplication and division
      - Multiplicative inverses (7-A.3)
- 7.1.1.b Ordering and comparing whole numbers
  - 7.1.1.b.1 Revise the following done in Grade 6:
    - 7.1.1.b.1.1 order, compare and represent numbers to at least 9-digit numbers
      - Word names for numbers (6-A.2)
    - 7.1.1.b.1.2 recognize and represent prime numbers to at least 100
      - Prime or composite (7-A.1)
    - 7.1.1.b.1.3 round off numbers to the nearest 5, 10, 100 or 1000
- 7.1.1.c Properties of whole numbers
  - 7.1.1.c.1 Revise the following done in Grade 6:
    - 7.1.1.c.1.1 recognize and use the commutative; associative; distributive properties of whole numbers
    - 7.1.1.c.1.2 recognize and use 0 in terms of its additive property (identity element for addition)
      - Properties of addition (6-F.3)
      - Properties of addition and multiplication (7-R.9)
    - 7.1.1.c.1.3 recognize and use 1 in terms of its multiplicative property (identity element for multiplication)
      - Properties of addition and multiplication (7-R.9)
- 7.1.1.d Calculations using whole numbers
  - 7.1.1.d.1 Revise the following done in Grade 6, without use of calculators:
    - 7.1.1.d.1.1 Addition and subtraction of whole numbers to at least 6-digit numbers
      - Add and subtract whole numbers up to millions (6-F.1)
      - Add and subtract whole numbers: word problems (6-F.2)
    - 7.1.1.d.1.2 Multiplication of at least whole 4-digit by 2-digit numbers
    - 7.1.1.d.1.3 Division of at least whole 4-digit by 2-digit numbers
    - 7.1.1.d.1.4 Perform calculations using all four operations on whole numbers, estimating and using calculators where appropriate
- 7.1.1.e Calculation techniques
  - 7.1.1.e.1 Use a range of strategies to perform and check written and mental calculations of whole numbers including:
- 7.1.1.f Multiples and factors
  - 7.1.1.f.1 Revise the following done in Grade 6:
    - 7.1.1.f.1.1 multiples of 2-digit and 3-digit whole numbers
      - Lowest common multiple (7-A.6)
    - 7.1.1.f.1.2 factors of 2-digit and 3-digit whole numbers
    - 7.1.1.f.1.3 prime factors of numbers to at least 100
      - Prime factorisation (6-D.3)
      - Prime factorisation (7-A.2)
  - 7.1.1.f.2 List prime factors of numbers to at least 3-digit whole numbers
    - Prime factorisation (7-A.2)
  - 7.1.1.f.3 Find the LCM and HCF of numbers to at least 3-digit whole numbers, by inspection or factorisation
- 7.1.1.g Solving problems
  - 7.1.1.g.1 Solve problems involving whole numbers, including
    - 7.1.1.g.1.1 comparing two or more quantities of the same kind (ratio)
    - 7.1.1.g.1.2 comparing two quantities of different kinds (rate)
      - Unit rates (7-J.5)
    - 7.1.1.g.1.3 sharing in a given ratio where the whole is given
      - Solve proportions (7-J.10)
      - Solve proportions: word problems (7-J.11)
  - 7.1.1.g.2 Solve problems that involve whole numbers, percentages and decimal fractions in financial contexts such as:
    - 7.1.1.g.2.1 profit, loss and discount
    - 7.1.1.g.2.2 budgets
    - 7.1.1.g.2.3 accounts
      - Simple interest (7-M.9)
      - Compound interest (7-M.10)
    - 7.1.1.g.2.4 loans
    - 7.1.1.g.2.5 simple interest
      - Simple interest (7-M.9)
7.1.2 Exponents
- 7.1.2.a Mental calculations
  - 7.1.2.a.1 Determine squares to at least 122 and their square roots
  - 7.1.2.a.2 Determine cubes to at least 63 and cube roots
- 7.1.2.b Comparing and representing numbers in exponential form
  - 7.1.2.b.1 Compare and represent whole numbers in exponential form: ab = a x a x a x... for b number of factors
    - Understanding exponents (7-I.1)
- 7.1.2.c Calculations using numbers in exponential form
  - 7.1.2.c.1 Recognize and use the appropriate laws of operations with numbers involving exponents and square and cube roots
    - Evaluate exponents (7-I.2)
    - Evaluate numerical expressions involving exponents (7-I.6)
  - 7.1.2.c.2 Perform calculations involving all four operations using numbers in exponential form, limited to exponents up to 5, and square and cube roots
    - Evaluate numerical expressions involving exponents (7-I.6)
- 7.1.2.d Solving problems
  - 7.1.2.d.1 Solve problems in contexts involving numbers in exponential form.
    - Compound interest (7-M.10)
7.1.3 Integers
- 7.1.3.a Counting, ordering and comparing integers
  - 7.1.3.a.1 Count forwards and backwards in integers for any interval
    - Integers on number lines (7-B.2)
  - 7.1.3.a.2 Recognize, order and compare integers
    - Understanding integers (7-B.1)
    - Compare and order integers (7-B.5)
- 7.1.3.b Calculations with integers
  - 7.1.3.b.1 Add and subtract with integers
- 7.1.3.c Properties of integers
  - 7.1.3.c.1 Recognise and use commutative and associative properties of addition and multiplication for integers
- 7.1.3.d Solving problems
  - 7.1.3.d.1 Solve problems in contexts involving addition and subtraction with integers
    - Add and subtract integers: word problems (7-C.5)
7.1.4 Common fractions
- 7.1.4.a Ordering, comparing and simplifying fractions
  - 7.1.4.a.1 Revise the following done in Grade 6
    - 7.1.4.a.1.1 compare and order common fractions, including specifically tenths and hundredths
      - Compare and order fractions (7-F.6)
      - Compare fractions: word problems (7-F.7)
  - 7.1.4.a.2 Extend to thousandths
- 7.1.4.b Calculations with fractions
  - 7.1.4.b.1 Revise the following done in Grade 6:
    - 7.1.4.b.1.1 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
    - 7.1.4.b.1.2 finding fractions of whole numbers
      - Multiply fractions and whole numbers (7-G.7)
      - Multiply fractions and whole numbers: word problems (7-G.8)
  - 7.1.4.b.2 Extend addition and subtraction to fractions where one denominator is not a multiple of the other
  - 7.1.4.b.3 Multiplication of common fractions, including mixed numbers, not limited to fractions where one denominator is a multiple of another
- 7.1.4.c Calculation techniques
  - 7.1.4.c.1 Convert mixed numbers to common fractions in order to perform calculations with them
  - 7.1.4.c.2 Use knowledge of multiples and factors to write fractions in the simplest form before or after calculations
  - 7.1.4.c.3 Use knowledge of equivalent fractions to add and subtract common fractions
- 7.1.4.d Solving problems
  - 7.1.4.d.1 Solve problems in contexts involving common fractions and mixed numbers, including grouping, sharing and finding fractions of whole numbers
- 7.1.4.e Percentages
  - 7.1.4.e.1 Revise the following done in Grade 6:
    - 7.1.4.e.1.1 Finding percentages of whole numbers
      - Percents of numbers and money amounts (7-L.5)
      - Percents of numbers: word problems (7-L.6)
  - 7.1.4.e.2 Calculate the percentage of part of a whole
  - 7.1.4.e.3 Calculate percentage increase or decrease of whole numbers
    - Percent of change (8-J.10)
    - Percent of change: word problems (8-J.11)
  - 7.1.4.e.4 Solve problems in contexts involving percentages
- 7.1.4.f Equivalent forms
  - 7.1.4.f.1 Revise the following done in Grade 6:
    - 7.1.4.f.1.1 recognize and use equivalent forms of common fractions with 1-digit or 2-digit denominators (fractions where one denominator is a multiple of the other)
      - Equivalent fractions (7-F.2)
      - Write fractions in lowest terms (7-F.3)
    - 7.1.4.f.1.2 recognize equivalence between common fraction and decimal fraction forms of the same number
      - Convert between decimals and fractions or mixed numbers (7-H.2)
    - 7.1.4.f.1.3 recognize equivalence between common fraction, decimal fraction and percentage forms of the same number
      - Convert between percents, fractions and decimals (7-L.2)
7.1.5 Decimal fractions
- 7.1.5.a Ordering and comparing decimal fractions
  - 7.1.5.a.1 Revise the following done in Grade 6:
    - 7.1.5.a.1.1 count forwards and backwards in decimal fractions to at least two decimal places
      - Decimal number lines (6-E.9)
      - Decimal number lines (7-D.3)
    - 7.1.5.a.1.2 compare and order decimal fractions to at least two decimal places
    - 7.1.5.a.1.3 place value of digits to at least two decimal places
    - 7.1.5.a.1.4 rounding off decimal fractions to at least 1 decimal place
      - Round decimals (6-E.7)
      - Round decimals (7-D.4)
  - 7.1.5.a.2 Extend all of the above to decimal fractions to at least three decimal places and rounding off to at least 2 decimal places
- 7.1.5.b Calculations with decimal fractions
  - 7.1.5.b.1 Revise the following done in Grade 6:
    - 7.1.5.b.1.1 addition and subtraction of decimal fractions of at least two decimal places
    - 7.1.5.b.1.2 multiplication of decimal fractions by 10 and 100
      - Scientific notation (7-A.8)
  - 7.1.5.b.2 Extend addition and subtraction to decimal fractions of at least three decimal places
  - 7.1.5.b.3 Multiply decimal fractions to include:
    - 7.1.5.b.3.1 decimal fractions to at least 3 decimal places by whole numbers
      - Multiply decimals and whole numbers: word problems (7-E.4)
    - 7.1.5.b.3.2 decimal fractions to at least 2 decimal places by decimal fractions to at least 1 decimal place
      - Multiply decimals (7-E.3)
  - 7.1.5.b.4 Divide decimal fractions to include decimal fractions to at least 3 decimal places by whole numbers
- 7.1.5.c Calculation techniques
  - 7.1.5.c.1 Use knowledge of place value to estimate the number of decimal places in the result before performing calculations
  - 7.1.5.c.2 Use rounding off and a calculator to check results where appropriate
    - Estimate sums, differences and products of decimals (7-E.7)
- 7.1.5.d Solving problems
  - 7.1.5.d.1 Solve problems in context involving decimal fractions
- 7.1.5.e Equivalent forms
  - 7.1.5.e.1 Revise the following done in Grade 6:
    - 7.1.5.e.1.1 recognize equivalence between common fraction and decimal fraction forms of the same number
      - Convert between decimals and fractions or mixed numbers (7-H.2)
    - 7.1.5.e.1.2 recognize equivalence between common fraction, decimal fraction and percentage forms of the same number
      - Convert between percents, fractions and decimals (7-L.2)

7.2 Patterns, Functions and Algebra

7.2.1 Numeric and geometric patterns
- 7.2.1.a Investigate and extend patterns
  - 7.2.1.a.1 Investigate and extend numeric and geometric patterns looking for relationships between numbers, including patterns:
    - 7.2.1.a.1.1 represented in physical or diagram form
      - Find the next shape in a repeating pattern (7-Q.1)
    - 7.2.1.a.1.2 not limited to sequences involving a constant difference or ratio
    - 7.2.1.a.1.3 of learner's own creation
    - 7.2.1.a.1.4 represented in tables
      - Find the constant of proportionality from a table (7-K.1)
      - Complete a table for a two-variable relationship (7-T.4)
  - 7.2.1.a.2 Describe and justify the general rules for observed relationships between numbers in own words
7.2.2 Functions and relationships
- 7.2.2.a Input and output values
  - 7.2.2.a.1 Determine input values, output values or rules for patterns and relationships using:
    - 7.2.2.a.1.1 flow diagrams
    - 7.2.2.a.1.2 tables
    - 7.2.2.a.1.3 formulae
- 7.2.2.b Equivalent forms
  - 7.2.2.b.1 Determine, interpret and justify equivalence of different descriptions of the same relationship or rule presented:
    - 7.2.2.b.1.1 verbally
    - 7.2.2.b.1.2 in flow diagrams
    - 7.2.2.b.1.3 in tables
      - Write a two-variable equation (7-T.5)
    - 7.2.2.b.1.4 by formulae
      - Evaluate variable expressions for number sequences (7-Q.10)
      - Complete a table for a two-variable relationship (7-T.4)
    - 7.2.2.b.1.5 by number sentences
      - Evaluate variable expressions for number sequences (7-Q.10)
      - Complete a table for a two-variable relationship (7-T.4)
7.2.3 Algebraic expressions
- 7.2.3.a Algebraic language
  - 7.2.3.a.1 Recognize and interpret rules or relationships represented in symbolic form
  - 7.2.3.a.2 Identify variables and constants in given formulae and/or equations
    - Identify terms and coefficients (6-T.6)
    - Identify independent and dependent variables (7-T.2)
7.2.4 Algebraic equations
- 7.2.4.a Number sentences
  - 7.2.4.a.1 Write number sentences to describe problem situations
  - 7.2.4.a.2 Analyse and interpret number sentences that describe a given situation
  - 7.2.4.a.3 Solve and complete number sentences by:
    - 7.2.4.a.3.1 inspection
    - 7.2.4.a.3.2 trial and improvement
  - 7.2.4.a.4 Determine the numerical value of an expression by substitution.
  - 7.2.4.a.5 Identify variables and constants in given formulae or equations
    - Identify terms and coefficients (6-T.6)
7.2.5 Graphs
- 7.2.5.a Interpreting graphs
  - 7.2.5.a.1 Analyse and interpret global graphs of problem situations, with special focus on the following trends and features:
    - 7.2.5.a.1.1 linear or non-linear
      - Identify linear and nonlinear functions (8-Z.1)
    - 7.2.5.a.1.2 constant, increasing or decreasing
      - Find the constant of proportionality from a graph (7-K.4)
      - Write a two-variable equation (7-T.5)
- 7.2.5.b Drawing graphs
  - 7.2.5.b.1 Draw global graphs from given descriptions of a problem situation, identifying features listed above
    - Identify the graph of an equation (7-T.6)
    - Graph a two-variable equation (7-T.7)

7.3 Space and Shape (Geometry)

7.3.1 Geometry of 2D shapes
- 7.3.1.a Classifying 2D shapes
  - 7.3.1.a.1 Describe, sort, name and compare triangles according to their sides and angles, focusing on:
    - 7.3.1.a.1.1 equilateral triangles
      - Classify triangles (7-U.4)
    - 7.3.1.a.1.2 isosceles triangles
      - Classify triangles (7-U.4)
    - 7.3.1.a.1.3 right-angled triangles
      - Classify triangles (7-U.4)
  - 7.3.1.a.2 Describe, sort, name and compare quadrilaterals in terms of:
    - 7.3.1.a.2.1 length of sides
      - Classify quadrilaterals (7-U.6)
    - 7.3.1.a.2.2 parallel and perpendicular sides
      - Classify quadrilaterals (7-U.6)
    - 7.3.1.a.2.3 size of angles (right-angles or not)
      - Classify quadrilaterals (7-U.6)
  - 7.3.1.a.3 Describe and name parts of a circle
    - Parts of a circle (6-W.11)
- 7.3.1.b Similar and congruent 2D shapes
  - 7.3.1.b.1 Recognize and describe similar and congruent figures by comparing:
    - 7.3.1.b.1.1 shape
      - Similar and congruent figures (7-V.12)
    - 7.3.1.b.1.2 size
      - Similar and congruent figures (7-V.12)
- 7.3.1.c Solving problems
  - 7.3.1.c.1 Solve simple geometric problems involving unknown sides and angles in triangles and quadrilaterals, using known properties.
7.3.2 Geometry of 3D objects
- 7.3.2.a Classifying 3D objects
  - 7.3.2.a.1 Describe, sort and compare polyhedra in terms of:
    - 7.3.2.a.1.1 shape and number of faces
    - 7.3.2.a.1.2 number of vertices
      - Identify polyhedra (6-Y.1)
      - Which figure is being described? (6-Y.2)
    - 7.3.2.a.1.3 number of edges
      - Identify polyhedra (6-Y.1)
      - Which figure is being described? (6-Y.2)
- 7.3.2.b Building 3D models
  - 7.3.2.b.1 Revise using nets to create models of geometric solids, including:
    - 7.3.2.b.1.1 cubes
      - Nets of three-dimensional figures (7-X.2)
    - 7.3.2.b.1.2 prisms
      - Nets of three-dimensional figures (7-X.2)
7.3.3 Geometry of straight lines
- 7.3.3.a Define:
  - 7.3.3.a.1 Line segment
    - Lines, line segments and rays (7-U.10)
  - 7.3.3.a.2 Ray
    - Lines, line segments and rays (7-U.10)
  - 7.3.3.a.3 Straight line
    - Lines, line segments and rays (7-U.10)
  - 7.3.3.a.4 Parallel lines
    - Parallel, perpendicular and intersecting lines (7-U.11)
  - 7.3.3.a.5 Perpendicular lines
    - Parallel, perpendicular and intersecting lines (7-U.11)
7.3.4 Transformation Geometry
- 7.3.4.a Transformations
  - 7.3.4.a.1 Recognize, describe and perform translations, reflections and rotations with geometric figures and shapes on squared paper
  - 7.3.4.a.2 Identify and draw lines of symmetry in geometric figures
    - Symmetry (7-V.1)
- 7.3.4.b Enlargements and reductions
  - 7.3.4.b.1 Draw enlargements and reductions of geometric figures on squared paper and compare them in terms of shape and size
7.3.5 Construction of geometric figures
- 7.3.5.a Measuring angles
  - 7.3.5.a.1 Accurately use a protractor to measure and classify angles:
    - 7.3.5.a.1.1 < 90° (acute angles)
      - Name, measure and classify angles (7-U.2)
    - 7.3.5.a.1.2 Right-angles
      - Name, measure and classify angles (7-U.2)
    - 7.3.5.a.1.3 > 90° (obtuse angles)
      - Name, measure and classify angles (7-U.2)
    - 7.3.5.a.1.4 Straight angles
      - Name, measure and classify angles (7-U.2)
    - 7.3.5.a.1.5 > 180° (reflex angles)
- 7.3.5.b Constructions
  - 7.3.5.b.1 Accurately construct geometric figures appropriately using a compass, ruler and protractor, including:
    - 7.3.5.b.1.1 angles, to one degree of accuracy
      - Construct a congruent angle (7-W.3)
    - 7.3.5.b.1.2 circles
    - 7.3.5.b.1.3 parallel lines
      - Construct parallel lines (7-W.5)
    - 7.3.5.b.1.4 perpendicular lines
      - Construct a perpendicular line (7-W.4)

7.4 Measurement

7.4.1 Area and perimeter of 2D shapes
- 7.4.1.a Area and perimeter
  - 7.4.1.a.1 Calculate the perimeter of regular and irregular polygons
    - Perimeter (7-Y.1)
  - 7.4.1.a.2 Use appropriate formulae to calculate perimeter and area of:
    - 7.4.1.a.2.1 squares
    - 7.4.1.a.2.2 rectangles
    - 7.4.1.a.2.3 triangles
- 7.4.1.b Calculations and solving problems
  - 7.4.1.b.1 Solve problems involving perimeter and area of polygons
    - Area and perimeter: word problems (7-Y.6)
  - 7.4.1.b.2 Calculate to at least 1 decimal place
    - Area and perimeter: word problems (7-Y.6)
  - 7.4.1.b.3 Use and convert between appropriate SI units, including:
    - 7.4.1.b.3.1 mm² <-> cm²
      - Convert square and cubic units of length (8-L.3)
    - 7.4.1.b.3.2 cm² <-> m²
      - Convert square and cubic units of length (8-L.3)
7.4.2 Surface area and volume of 3D objects
- 7.4.2.a Surface area and volume
  - 7.4.2.a.1 Use appropriate formulae to calculate the surface area, volume and capacity of:
    - 7.4.2.a.1.1 cubes
      - Volume (7-Y.7)
      - Surface area (7-Y.8)
    - 7.4.2.a.1.2 rectangular prisms
      - Volume (7-Y.7)
      - Surface area (7-Y.8)
  - 7.4.2.a.2 Describe the interrelationship between surface area and volume of the objects mentioned above
    - Perimeter, area and volume: changes in scale (7-Y.9)
- 7.4.2.b Calculations and solving problems
  - 7.4.2.b.1 Solve problems involving surface area, volume and capacity
    - Perimeter, area and volume: changes in scale (7-Y.9)
  - 7.4.2.b.2 Use and convert between appropriate SI units, including:
    - 7.4.2.b.2.1 mm² <-> cm²
      - Convert square and cubic units of length (8-L.3)
    - 7.4.2.b.2.2 cm² <-> m²
      - Convert square and cubic units of length (8-L.3)
    - 7.4.2.b.2.3 mm³ <-> cm³
      - Convert square and cubic units of length (8-L.3)
    - 7.4.2.b.2.4 cm³ <-> m³
      - Convert square and cubic units of length (8-L.3)
  - 7.4.2.b.3 Use equivalence between units when solving problems:
    - 7.4.2.b.3.1 1 cm³ <-> 1 ml
      - Compare and convert metric units (7-O.2)
      - Convert between cubic metres and litres (8-L.4)
    - 7.4.2.b.3.2 1 m³ <-> 1 kl
      - Convert between cubic metres and litres (8-L.4)
7.4.3 The Theorem of Pythagoras

7.5 Data Handling

7.5.1 Collect, organize and summarize data
- 7.5.1.a Collect data
  - 7.5.1.a.1 Pose questions relating to social, economic, and environmental issues in own environment
  - 7.5.1.a.2 Select appropriate sources for the collection of data (including peers, family, newspapers, books, magazines)
  - 7.5.1.a.3 Distinguish between samples and populations and suggest appropriate samples for investigation
    - Identify representative, random and biased samples (7-AA.5)
  - 7.5.1.a.4 Design and use simple questionnaires to answer questions:
    - 7.5.1.a.4.1 with yes/no type responses
    - 7.5.1.a.4.2 with multiple choice responses
- 7.5.1.b Organize and summarize data
  - 7.5.1.b.1 Organize (including grouping where appropriate) and record data using
    - 7.5.1.b.1.1 tally marks
    - 7.5.1.b.1.2 tables
      - Create frequency charts (7-Z.10)
    - 7.5.1.b.1.3 stem-and-leaf displays
      - Interpret stem-and-leaf plots (7-Z.4)
  - 7.5.1.b.2 Group data into intervals
  - 7.5.1.b.3 Summarize and distinguishing between ungrouped numerical data by determining:
  - 7.5.1.b.4 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)
7.5.2 Represent data
- 7.5.2.a Represent data
  - 7.5.2.a.1 Draw a variety of graphs by hand/technology to display and interpret data (grouped and ungrouped) including:
    - 7.5.2.a.1.1 bar graphs and double bar graphs
      - Create bar graphs (7-Z.7)
    - 7.5.2.a.1.2 histograms with given intervals
      - Create histograms (7-Z.9)
    - 7.5.2.a.1.3 pie charts
      - Pie charts and central angles (7-Z.12)
7.5.3 Interpret, analyse, and report data
- 7.5.3.a Interpret data
  - 7.5.3.a.1 Critically read and interpret data represented in:
    - 7.5.3.a.1.1 words
    - 7.5.3.a.1.2 bar graphs
      - Interpret bar graphs (7-Z.6)
    - 7.5.3.a.1.3 double bar graphs
      - Interpret bar graphs (7-Z.6)
    - 7.5.3.a.1.4 pie charts
      - Interpret pie charts (7-Z.11)
      - Pie charts and central angles (7-Z.12)
    - 7.5.3.a.1.5 histograms
      - Interpret histograms (7-Z.8)
- 7.5.3.b Analyse data
  - 7.5.3.b.1 Critically analyse data by answering questions related to:
    - 7.5.3.b.1.1 data categories, including data intervals
    - 7.5.3.b.1.2 data sources and contexts
      - Identify representative, random and biased samples (7-AA.5)
    - 7.5.3.b.1.3 central tendencies (mean, mode, median)
    - 7.5.3.b.1.4 scales used on graphs
      - Interpret histograms (7-Z.8)
      - Interpret line graphs (7-Z.13)
- 7.5.3.c Report data
  - 7.5.3.c.1 Summarize data in short paragraphs that include
    - 7.5.3.c.1.1 drawing conclusions about the data
    - 7.5.3.c.1.2 making predictions based on the data
    - 7.5.3.c.1.3 identifying sources of error and bias in the data
    - 7.5.3.c.1.4 choosing appropriate summary statistics for the data (mean, median, mode)
7.5.4 Probability
- 7.5.4.a Probability
  - 7.5.4.a.1 Perform simple experiments where the possible outcomes are equally likely and:
    - 7.5.4.a.1.1 list the possible outcomes based on the conditions of the activity
      - Compound events: find the number of outcomes (7-BB.5)
      - Counting principle (7-BB.6)
    - 7.5.4.a.1.2 determine the probability of each possible outcome using the definition of probability
      - Probability of simple events (7-BB.1)
      - Probability of opposite, mutually exclusive and overlapping events (7-BB.2)

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7.1 Numbers, Operations and Relationships

7.1.1 Whole numbers

7.1.1.a Mental calculations

7.1.1.a.1 Revise the following done in Grade 6:

7.1.1.a.1.1 Multiplication of whole numbers to at least 12 x 12

7.1.1.a.1.2 Multiplication facts for:

7.1.1.a.1.2.a units and tens by multiples of ten

7.1.1.a.1.2.b units and tens by multiples of 100

7.1.1.a.1.2.c units and tens by multiples of 1000

7.1.1.a.1.2.d units and tens by multiples of 10,000

7.1.1.a.1.3 Inverse operation between multiplication and division

7.1.1.b Ordering and comparing whole numbers

7.1.1.b.1 Revise the following done in Grade 6:

7.1.1.b.1.1 order, compare and represent numbers to at least 9-digit numbers

7.1.1.b.1.2 recognize and represent prime numbers to at least 100

7.1.1.b.1.3 round off numbers to the nearest 5, 10, 100 or 1000

7.1.1.c Properties of whole numbers

7.1.1.c.1 Revise the following done in Grade 6:

7.1.1.c.1.1 recognize and use the commutative; associative; distributive properties of whole numbers

7.1.1.c.1.2 recognize and use 0 in terms of its additive property (identity element for addition)

7.1.1.c.1.3 recognize and use 1 in terms of its multiplicative property (identity element for multiplication)

7.1.1.d Calculations using whole numbers

7.1.1.d.1 Revise the following done in Grade 6, without use of calculators:

7.1.1.d.1.1 Addition and subtraction of whole numbers to at least 6-digit numbers

7.1.1.d.1.2 Multiplication of at least whole 4-digit by 2-digit numbers

7.1.1.d.1.3 Division of at least whole 4-digit by 2-digit numbers

7.1.1.d.1.4 Perform calculations using all four operations on whole numbers, estimating and using calculators where appropriate

7.1.1.e Calculation techniques

7.1.1.e.1 Use a range of strategies to perform and check written and mental calculations of whole numbers including:

7.1.1.e.1.1 long division

7.1.1.e.1.2 adding, subtracting and multiplying in columns

7.1.1.e.1.3 estimation

7.1.1.e.1.4 rounding off and compensating

7.1.1.e.1.5 using a calculator

7.1.1.f Multiples and factors

7.1.1.f.1 Revise the following done in Grade 6:

7.1.1.f.1.1 multiples of 2-digit and 3-digit whole numbers

7.1.1.f.1.2 factors of 2-digit and 3-digit whole numbers

7.1.1.f.1.3 prime factors of numbers to at least 100

7.1.1.f.2 List prime factors of numbers to at least 3-digit whole numbers

7.1.1.f.3 Find the LCM and HCF of numbers to at least 3-digit whole numbers, by inspection or factorisation

7.1.1.g Solving problems

7.1.1.g.1 Solve problems involving whole numbers, including

7.1.1.g.1.1 comparing two or more quantities of the same kind (ratio)

7.1.1.g.1.2 comparing two quantities of different kinds (rate)

7.1.1.g.1.3 sharing in a given ratio where the whole is given

7.1.1.g.2 Solve problems that involve whole numbers, percentages and decimal fractions in financial contexts such as:

7.1.1.g.2.1 profit, loss and discount

7.1.1.g.2.2 budgets

7.1.1.g.2.3 accounts

7.1.1.g.2.4 loans

7.1.1.g.2.5 simple interest

7.1.2 Exponents

7.1.2.a Mental calculations

7.1.2.a.1 Determine squares to at least 122 and their square roots

7.1.2.a.2 Determine cubes to at least 63 and cube roots

7.1.2.b Comparing and representing numbers in exponential form

7.1.2.b.1 Compare and represent whole numbers in exponential form: ab = a x a x a x... for b number of factors

7.1.2.c Calculations using numbers in exponential form

7.1.2.c.1 Recognize and use the appropriate laws of operations with numbers involving exponents and square and cube roots

7.1.2.c.2 Perform calculations involving all four operations using numbers in exponential form, limited to exponents up to 5, and square and cube roots

7.1.2.d Solving problems

7.1.2.d.1 Solve problems in contexts involving numbers in exponential form.

7.1.3 Integers

7.1.3.a Counting, ordering and comparing integers

7.1.3.a.1 Count forwards and backwards in integers for any interval

7.1.3.a.2 Recognize, order and compare integers

7.1.3.b Calculations with integers

7.1.3.b.1 Add and subtract with integers

7.1.3.c Properties of integers

7.1.3.c.1 Recognise and use commutative and associative properties of addition and multiplication for integers

7.1.3.d Solving problems

7.1.3.d.1 Solve problems in contexts involving addition and subtraction with integers

7.1.4 Common fractions

7.1.4.a Ordering, comparing and simplifying fractions

7.1.4.a.1 Revise the following done in Grade 6

7.1.4.a.1.1 compare and order common fractions, including specifically tenths and hundredths