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

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 decimals.
• Describes and illustrates written number systems different to own.
• Recognises and represents the following numbers in order to describe and compare them:
  • whole numbers to at least 9-digit numbers;
  • decimal fractions to at lease two decimal places;
  • common fractions including specifically tenths, hundreds and percentages;
  • 0 in terms of additive property;
  • 1 in terms of its multiplicative property;
  • multiples and factors of at least any 2-digit and 3-digit whole number;
  • prime numbers to at least 100.

• Recognises the place value of digits in:
  • whole numbers to at least 9-digit numbers;
  • decimal fractions to at least 2 decimal places.

• Recognises and uses equivalent forms of the numbers listed above, including:
  • common fractions with 1-digit or 2-digit denominators;
  • decimal fractions to at least 2 decimal places;
  • 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 buying and selling, profit and loss, simple budgets, reading and interpreting accounts, and discount);
  • measurements in Natural Sciences and Technology contexts.

• Solves problems that involve:
  • comparing two or more quantities of the same kind (ratio);
  • comparing two quantities of different kinds (rate, e.g. wages/day)

• Estimates and calculates by selecting and using operations appropriate to solving problems that involve:
  • rounding off to the nearest 5, 10, 100 or 1 000;
  • addition and subtraction of whole numbers;
  • addition and subtraction of common fractions with denominators which are multiples of each other and whole numbers with common fractions (mixed numbers);
  • multiplication of at least whole 4-digit by 3-digit numbers;
  • division of at least whole 4-digit by 3-digit numbers;
  • finding fractions of whole numbers;
  • equivalent fractions;
  • addition and subtraction of positive decimals with at least 2 decimal places;
  • finding percentages of whole numbers;
  • multiple operations on whole numbers with or without brackets.

• Performs mental calculations involving:
  • addition and subtraction;
  • multiplication of whole numbers to at least 12 x 12.

• Uses a range of techniques to perform written and mental calculations with whole numbers including:
  • adding, subtracting and multiplying in columns;
  • long division;
  • building up and breaking down numbers;
  • rounding off and compensating;
  • using a calculator.

• Uses a range of strategies to check solutions and judge the reasonableness of solutions.
• Recognises, describes and uses:
  • divisibility rules for 2, 5, 10, 100 and 1 000;
  • the commutative, associative and distributive properties with whole numbers (the expectation is that learners should be able to use the properties and not necessarily know the names).

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 observed relationships or rules in own words.
• Determines output values for given input values, or input values for given output values, using:
  • verbal descriptions;
  • flow diagrams;
  • tables.

• Writes number sentences to describe a problem situation, including problems within contexts that may be used to build awareness of human rights, social, economic, cultural and environmental issues.
• Solves or completes number sentences by inspection or by trial-and-improvement, checking the solutions by substitution (e.g. 2 x– 8 = 0).
• Determines, through discussion and comparison, the equivalence of different descriptions of the same relationship or rule presented:
  • verbally;
  • in flow diagrams;
  • by number sentences;
  • in tables.

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 two-dimensional shapes and three-dimensional objects in natural and cultural forms and geometric settings including those previously dealt with and focusing on:
  • similarities and differences between tetrahedrons and other pyramids;
  • similarities and differences between rectangles and parallelograms.

• Describes and classifies two-dimensional shapes and three-dimensional objects in terms of properties including:
  • faces, vertices and edges;
  • length of sides;
  • angle size of corners.

• Investigates and compares (alone and/or as a member of a group or team) two-dimensional shapes and three-dimensional objects studied in this grade according to properties listed above by:
  • making three-dimensional models using:
    • drinking straws to make a skeleton,
    • nets provided by the teacher;

  • drawing shapes on grid paper;
  • using a pair of compasses to draw circles, patterns in circles, and patterns with circles.

• Uses the vocabulary and properties of rotations, reflections and translations to describe the relationships between distinct two-dimensional shapes and three-dimensional objects within patterns (including transformations and symmetry).
• Draws enlargements and reductions of two-dimensional shapes (at least quadrilaterals and triangles) using grid paper to compare their size and shape.
• Recognises and describes natural and cultural two-dimensional shapes, three-dimensional objects and patterns in terms of geometric properties.
• Draws and interprets sketches of simple three-dimensional objects from different positions (perspectives).
• Locates positions on a coded grid, describes how to move between positions on the grid, and recognises maps as grids.

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:

• Reads, tells and writes analogue, digital and 24-hour time to at least the nearest minute and second.
• Solves problems involving calculations and conversion between appropriate time units including time zones and differences.
• Describes and illustrates ways of representing time in different cultures throughout history.
• Estimates, measures, records, compares and orders two-dimensional shapes and three-dimensional objects using S.I. units with appropriate precision for:
  • mass using grams (g) and kilograms (kg);
  • capacity using millilitres (ml) and litres (l);
  • length using millimetres (mm), centimetres (cm), metres (m) and kilometres (km);
  • temperature using degree Celsius scale.

• Solves problems involving selecting, calculating with and converting between appropriate S.I units listed above, integrating with appropriate Technology and Natural Sciences contexts.
• Uses appropriate measuring instruments (with understanding of their limitations) to appropriate levels of precision including:
  • bathroom scales, kitchen scales and balances to measure mass;
  • measuring jugs to measure capacity;
  • rulers, metre sticks, tape measures and trundle wheels to measure length;
  • thermometers to measure temperature.

• Describes and illustrates ways of measuring in different cultures throughout history, including informal measuring systems.
• Investigates and approximates (alone and/or as a member of a group or team):
  • perimeter using rulers or measuring tapes;
  • area of polygons (using square grids) in order to develop rules for calculating the area of squares and rectangles;
  • volume/capacity of objects (by packing or filling them) in order to develop rules for calculating volume of rectangular prisms.

• Investigates relationships between the perimeter and area of rectangles and squares.
• Investigates relationships between surface area, volume and the dimensions of rectangular prisms.
• Recognises and describes angles in two-dimensional shapes, three-dimensional objects and the environment in terms of:
  • right angles;
  • angles smaller than right angles;
  • angles greater than right angles.

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 simple questions about own school and family environment, and identifies appropriate data sources in order to address human rights, social, political, cultural, environmental and economic issues in that environment.
• Uses simple data collection sheets (requiring tallies) and simple 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 posed by the teacher, class and self.
• Distinguishes between samples and populations.
• Organises and records data using tallies and tables.
• Examines ungrouped numerical data to determine the most frequently occurring score (mode) and the midpoint (median) of the data set in order to describe central tendencies.
• Draws a variety of graphs by hand/technology to display and interpret data (grouped and ungrouped) including:
  • pictographs with a many-one correspondence and appropriate keys;
  • bar graphs and double bar graphs.

• Critically reads and interprets data presented in a variety of ways (including own representations, representations in the media - words, graphs, pie graphs) 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);
  • other human rights issues.

• Predicts the likelihood of events in daily life based on observation, and places them on a scale from ‘impossible’ to ‘certain’.
• Lists possible outcomes for simple experiments (including tossing a coin, rolling a die, and spinning a spinner).
• Counts the frequency of actual outcomes for a series of trials.