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

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 a variety of intervals (including 2s, 3s, 5s, 10s, 25s, 50s and 100s) between 0 and at least 10 000.
• Describes and illustrates various ways of counting in different cultures (including local) throughout history.
• Recognises and represents the following numbers in order to describe and compare them:
  • whole numbers to at least 4-digit numbers;
  • common fractions with different denominators including halves, thirds, quarters, fifths, sixths, sevenths and eighths;
  • common fractions in diagrammatic form;
  • decimal fractions of the form 0,5; 1,5 and 2,5 and so on, in the context of measurement;
  • odd and even numbers to at least 1 000;
  • multiples of single-digit numbers to at least 100.

• Recognises the place value of digits in whole numbers to at least 4-digit numbers.
• Recognises and uses equivalent forms of the numbers listed above, including:
  • common fractions with denominators that are multiples of each other;
  • decimal fractions of the form 0,5, 1,5 and 2,5 and so on, in the context of measurement.
• 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, and simple budgets);
  • 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. kg/R).

• Estimates and calculates by selecting and using operations appropriate to solving problems that involve:
  • rounding off to the nearest 10, 100 or 1 000;
  • addition and subtraction of whole numbers with at least 4 digits;
  • addition of common fractions in context;
  • multiplication of at least whole 2-digit by 2-digit numbers;
  • division of at least whole 3-digit by 1-digit numbers;
  • equal sharing with remainders.

• Performs mental calculations involving:
  • addition and subtraction;
  • multiplication of whole numbers to at least 10 x 10.

• Uses a range of techniques to perform written and mental calculations with whole numbers including:
  • building up and breaking down numbers;
  • rounding off and compensating;
  • doubling and halving;
  • using a number-line;
  • using a calculator.

• Uses a range of strategies to check solutions and judges the reasonableness of solutions.
• Recognises, describes and uses:
  • the reciprocal relationship between multiplication and division
    (e.g. if 5 x 3 = 15 then 15 ÷ 3 = 5 and 15 ÷ 5 = 3);
  • the equivalence of division and fractions (e.g. 1 ÷  8 = 1/8);
  • 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.

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

• 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. ÷ 4 = 12).
• Determines, through discussion and comparison, the equivalence of different descriptions of the same relationship or rule presented:
  • verbally;
  • in flow diagrams;
  • by number sentences.

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 the environment including:
  • rectangular prisms, spheres, cylinders, and other objects;
  • prisms and pyramids;
  • circles and rectangles;
  • polygons in terms of the number of sides up to 8-sided figures.

• Describes, sorts and compares two-dimensional shapes and three-dimensional objects from the environment according to geometrical properties including:
  • shapes of faces,
  • number of sides;
  • flat and curved surfaces, straight and curved sides.

• 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 cut-out polygons (supplied);
  • drawing shapes on grid paper.

• Recognises and describes lines of symmetry in two-dimensional shapes, including those in nature and its cultural art forms.
• Makes two-dimensional shapes, three-dimensional objects and patterns from geometric objects and shapes (e.g. tangrams) with a focus on tiling (tessellation) and line symmetry.
• Recognises and describes natural and cultural two-dimensional shapes, three-dimensional objects and patterns in terms of geometric properties.
• Describes changes in the view of an object held in different positions.
• Locates position on a coded (labelled) grid including:
  • maps from given instructions;
  • column and row.

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 calculation and conversion between appropriate time units including seconds, minutes, hours, days, weeks, months and years.
• Uses time-measuring instruments to appropriate levels of precision, including watches and clocks.
• Describes and illustrates ways of measuring and 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).

• Solves problems involving selecting, calculating with and converting between appropriate S.I. units listed above, integrating appropriate contexts for Technology and Natural Sciences.
• 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.

• 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 and tiling) in order to develop an understanding of square units;
  • volume/capacity of three-dimensional objects (by packing or filling them) in order to develop an understanding of cubic units.

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.
• Collects data (alone and/or as a member of a group or team) in the classroom and school environment to answer questions posed by the teacher and the class.
• Organises and records data using tallies and tables.
• Draws a variety of graphs to display and interpret data (ungrouped) including:
  • pictographs with a one-to-one correspondence between data and representation (e.g. one picture = one person);
  • bar graphs.

• Critically reads and interprets data presented in a variety of ways (including own representations and representations in the media - both words and graphs) to draw conclusions and make predictions sensitive to the role of:
  • context (e.g. rural or urban);
  • other human rights issues.

• Compares and classifies events from daily life as:
  • certain that they will happen; or
  • certain that they will not happen; or
  • uncertain.

• Counts the number of possible outcomes for simple trials.