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

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 whole number intervals and fractions.
• Describes and illustrates various ways of writing numbers 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 6-digit numbers;
  • common fractions to at least twelfths;
  • decimal fractions of the form 0,5, 1,5 and 2,5 and so on, in the context of measurement;
  • 0 in terms of additive inverses;
  • 1 in terms of multiplicative inverses;
  • multiples of single-digit numbers to at least 100;
  • factors of at least any 2-digit whole number.

• Recognises the place value of digits in whole numbers to at least 6-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, profit and loss, 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 (e.g. learners/teacher).

• 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 with at least 5 digits;
  • addition and subtraction of common fractions with the same denominator and whole numbers with common fractions (mixed numbers);
  • multiplication of at least whole 3-digit by 2-digit numbers;
  • division of at least whole 3-digit by 2-digit numbers;
  • finding fractions of whole numbers which result in whole numbers;
  • equivalent fractions.

• 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:
  • adding and subtracting in columns;
  • building up and breaking down numbers;
  • rounding off and compensating;
  • doubling and halving;
  • using a calculator.

• Uses a range of strategies to check solutions and judge 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 natural and cultural forms and geometric settings including those previously dealt with and focusing on:
  • similarities and differences between cubes and rectangular prisms;
  • similarities and differences between squares and rectangles.

• Describes, sorts and compares two-dimensional shapes and three-dimensional objects from the environment and from drawings or pictures according to properties including:
  • number and/or shape of faces;
  • number and/or length of 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 models of geometric objects using polygons they have cut out;
  • cutting open models or geometric objects (e.g. boxes) to trace their nets;
  • drawing shapes on grid paper.

• Recognises, describes and performs rotations (turns), reflections (flips) and translations (slides) using geometric figures and solids.
• Makes two-dimensional shapes, three-dimensional objects and patterns from geometric shapes and describes these in terms of:
  • tessellations;
  • line and rotational symmetry;
  • movement including rotations, reflections and translations.

• Recognises and describes natural and cultural two-dimensional shapes, three-dimensional objects and patterns in terms of geometric properties.
• Describes and sketches views of a simple three-dimensional object in different positions.
• Locates position on a coded (labelled) grid including maps and traces a path between positions following verbal and written instructions.

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 decades, centuries and millennia.
• Uses time-measuring instruments to appropriate levels of precision including watches and stopwatches.
• 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 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;
  • thermometers to measure temperature.

• 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 objects (by packing or filling them) in order to develop an understanding of cubic units.

• Recognises and describes right angles in two-dimensional shapes, three-dimensional objects and the environment.

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.
• Makes and uses simple data collection sheets that involve counting objects in order to collect data (alone and/or as a member of a group or team) to answer questions posed by the teacher and the class.
• Organises and records data using tallies and tables.
• Examines ungrouped numerical data to determine the most frequently occurring score (mode) of the data set in order to describe central tendencies.
• Draws a variety of graphs to display and interpret data (ungrouped) including:
  • pictographs with a many-one correspondence and appropriate keys (e.g. one picture = ten persons);
  • bar graphs.

• Critically reads and interprets data presented in a variety of ways (including own representations, 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);
  • categories within the data (e.g. gender and race);
  • other human rights issues.

• Compares, classifies and orders events from daily life on a scale from ‘certain that they will happen’ to ‘certain that they will not happen’.
• 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.