Revised National Curriculum Statement Grades R-9 (Schools) - Grade Seven

Learning Area: Mathematics

Learning Outcome 1:  Numbers, Operations and Relationships

The learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems.

Assessment standards

We know this when the learner:

• Counts forwards and backwards in the following ways:
  • in decimal intervals;
  • in integers for any intervals.

• Describes and illustrates the historical and cultural development of numbers (e.g. integers, common fractions).
• Recognises, classifies and represents the following numbers in order to describe and compare them:
  • integers;
  • decimals (to at least three decimal places), fractions and percentages;
  • factors including prime factors of 3-digit whole numbers;
  • numbers in exponential form including squares of natural numbers to at least 12 ², cubes of natural numbers to at least 5 ³, and their square and cube roots.

• Recognises and uses equivalent forms of the rational numbers listed above, including:
  • common fractions;
  • decimals;
  • percentages.

• Solves problems in context including contexts that may be used to build awareness of other Learning Areas, as well as human rights, social, economic and environmental issues such as:
  • financial (including profit and loss, budgets, accounts, loans, simple interest, hire purchase, exchange rates);
  • measurements in Natural Sciences and Technology contexts.
• Solves problems that involve ratio and rate.
• Estimates and calculates by selecting and using operations appropriate to solving problems that involve:
  • rounding off numbers to at lease one decimal place;
  • multiple operations with integers;
  • addition, subtraction and multiplication of common fractions;
  • addition, subtraction and multiplication of positive decimals to at least 2 decimal places;
  • division of positive decimals with at least 3 decimal places by whole numbers;
  • finding percentages;
  • exponents.

• Performs mental calculations involving squares of natural numbers to at least 10 ² and cubes of natural numbers to at least 5 ³.
• Uses a range of techniques to perform calculations including:
  • using the commutative, associative and distributive properties with positive rational numbers and zero;
  • using a calculator.

• Uses a range of strategies to check solutions and judges the reasonableness of solutions.
• Recognises, describes and uses:
  • algorithms for finding equivalent fractions;
  • the commutative, associative and distributive properties with positive rational numbers and zero (the expectation is that learners should be able to use these properties and not necessarily to know the names of the properties).

Learning Outcome 2:  Patterns, Functions and Algebra

The learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills.

Assessment standards

We know this when the learner:

• Investigates and extends numeric and geometric patterns looking for a relationship or rules, including patterns:
  • represented in physical or diagrammatic form;
  • not limited to sequences involving constant difference or ratio;
  • found in natural and cultural contexts;
  • of the learner’s own creation;
  • represented in tables.

• Describes, explains and justifies observed relationships or rules in own words.
• Represents and uses relationships between variables in order to determine input and/or output values in a variety of ways using:
  • verbal descriptions;
  • flow diagrams;
  • tables.

• Constructs mathematical models that represent, describe and provide solutions to problem situations, showing responsibility toward the environment and the health of others (including problems within human rights, social, economic, cultural and environmental contexts).
• Solves or completes number sentences by inspection or by trial-and-improvement, checking the solutions by substitution (e.g. 2 x- 8 = 4).
• Describes a situation by interpreting a graph of the situation, or draws a graph from a description of a situation (e.g. height of a roller-coaster car over time; the speed of a racing car going around a track).
• Determines, analyses and interprets the equivalence of different descriptions of the same relationship or rule presented:
  • verbally;
  • in flow diagrams;
  • in tables;
  • by equations or expressions;

• in order to select the most useful representation for a given situation.

Learning Outcome 3:  Space and Shape (Geometry)

The learner will be able to describe and represent characteristics and relationships between two-dimensional shapes and three-dimensional objects in a variety of orientations and positions.

Assessment standards

We know this when the learner:

• Recognises, visualises and names geometric figures and solids in natural and cultural forms and geometric settings, including those previously dealt with as well as focusing on:
  • similarities and differences between different polyhedra;
  • similarities and differences between all quadrilaterals including kites and trapeziums.

• In contexts that include those that may be used to build awareness of social, cultural and environmental issues, describes and classifies geometric figures and solids in terms of properties, including:
  • faces, vertices and edges;
  • sides and angles of polygons (with focus on, but not limited to, triangles and quadrilaterals);
  • parallel and perpendicular sides.

• Uses a pair of compasses, ruler and protractor to accurately construct geometric figures for investigation of own property and design of nets.
• Designs and uses nets to make models of geometric solids studied up to and including this grade.
• Uses transformations (rotations, reflections and translations) and symmetry to investigate (alone and/or as a member of a group or team) properties of geometric figures.
• Recognises and describes the properties of similar and congruent figures and the difference between them.
• Draws and interprets sketches of solids from different perspectives.
• Locates positions on co-ordinate systems (ordered grids) and maps using:
  • horizontal and vertical change;
  • compass directions.

Learning Outcome 4:  Measurement

The learner will be able to use appropriate measuring units, instruments and formulae in a variety of contexts.

Assessment standards

We know this when the learner:

• Solves problems involving time, including relating time, distance and speed.
• Solves problems involving:
  • length;
  • perimeter and area of polygons;
  • volume and surface area of rectangular prisms.

• Solves problems using a range of strategies including:
  • estimating;
  • calculating to at least 2 decimal places;
  • using and converting between appropriate S.I. units.

• Describes and illustrates ways of measuring in different cultures throughout history, including metric and other formal measuring systems.
• Calculates, by selecting and using appropriate formulae:
  • perimeter of polygons;
  • area of triangles, rectangles and squares;
  • volume of triangular and rectangular based prisms.

• Describes interrelationships between perimeter and area of geometric figures.
• Describes interrelationships between surface area and volume of geometric solids.
• Classifies angles into acute, right, obtuse, straight, reflex or revolution.
• Estimates, compares, measures and draws angles accurate to one degree using protractors

Learning Outcome 5:  Data Handling

The learner will be able to collect, summarise, display and critically analyse data in order to draw conclusions and make predictions, and to interpret and determine chance variation.

Assessment standards

We know this when the learner:

• Poses questions relating to human rights, social, economic, environmental and political issues in own environment.
• Selects appropriate sources for the collection of data (including peers, family, newspapers, books, magazines).
• Uses simple questionnaires (with a variety of possible responses) and designs and uses questionnaires (with yes/no type responses) in order to collect data (alone and/or as a member of a group or team) to answer questions.
• Distinguishes between samples and populations, and suggests appropriate samples for investigation (including random samples).
• Organises (including grouping where appropriate) and records data using tallies, tables and stem-and-leaf displays.
• Summarises ungrouped numerical data by determining mean, median and mode as measures of central tendency and distinguishes between them.
• Identifies the largest and smallest scores in a data set and determines the difference between them in order to determine the spread of the data (range).
• Draws 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;
  • line and broken-line graphs.

• Critically reads and interprets data presented in a variety of ways to draw conclusions and make predictions sensitive to the role of:
  • context (e.g. rural or urban, national or provincial);
  • categories within the data (e.g. age, gender, race);
  • scales used in graphs as a source of error and bias;
  • choice of summary statistics (mean, median or mode);
  • any other human rights and inclusivity issues.

• Performs simple experiments where the possible outcomes are equally likely and:
  • lists the possible outcomes based on the conditions of the activity;
  • determines the frequency of actual outcomes for a series of trials;
  • determines the relative frequency using the definition of relative frequency (see Mathematics Learning Area Glossary).