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ANNUAL NATIONAL ASSESSMENT

MATHS GRADE 5

ADDITIONAL EXERCISES

 

The following list of “Curriculum Assessment Standards”mirrors the National Curriculum (CAPS) requirements.

National Curriculum (CAPS) demand that education for a learner should be addressed according to specific requirements. To evaluate any learning material (textbooks or workbooks) you should be aware of the progressive, per term, prerequisites as per the Educational Department Teacher Guidelines.

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NUMBERS, OPERATIONS AND RELATIONSHIPS

WHOLE NUMBERS

1. Mental calculations involving:
1.1. Addition and subtraction of:

  • Units
  • Multiples of 10
  • Multiples of 100
  • Multiples of 1 000
1.2. Multiplication of whole numbers to at least 10 x 10
1.3. Multiplication facts of:

  • Units and tens by multiples of 10
  • Units and tens by multiples of 100
  • Units and tens by multiples of 1 000
  • Units and tens by multiples of 10 000

 

2. Number range for counting, ordering, comparing, representing and place value of digits:
2.1. Count forwards and backwards in whole number intervals up to at least 10 000
2.2. Order, compare and represent numbers to at least 6-digit numbers
2.3. Represent odd and even numbers to at least 1 000
2.4. Recognizing the place value of digits in whole numbers to at least 6-digit numbers
2.5. Round off to the nearest 5, 10, 100 and 1 000
3. Number range for calculations:
3.1. Addition and subtraction of whole numbers of at least 5 digits
3.2. Multiplication of at least whole 3-digit by 2-digit numbers
3.3. Division of at least whole 3-digit by 2-digit numbers
4. Calculation techniques
4.1. Using a range of techniques to perform and check written and mental calculations of whole numbers including:

4.1.1 estimation

4.1.2 adding, subtracting in columns

4.1.3 building up and breaking down numbers

4.1.4 using a number line

4.1.5 rounding off and compensating

4.1.6 doubling and halving

4.1.7 using addition and subtraction as inverse operations

4.1.8 using multiplication and division as inverse operations

5. Number range for multiples and factors
5.1. Multiples of 2-digits whole numbers to at least 100
5.2. Factors of 2-digit whole numbers to at least 100
6. Properties of whole numbers
6.1. Recognize and use the commutative, associative, distributive properties of whole numbers
6.2. 0 in terms of its additive property
6.3. 1 in terms of its multiplicative property
7. Solving problems
7.1. Solve problems involving whole numbers including :

  • Financial contexts
  • Measurement contexts
7.2. Solve problems involving whole numbers, including:

  • Comparing two or more quantities of the same kind (ratio)
  • Comparing two quantities of different kinds (rate)
  • Grouping and equal sharing with remainders

Common Fractions

1. Describing and ordering fractions:
1.1. Count forwards and backwards in fractions
1.2. Compare and order common fractions to at least twelfths.
2. Calculations with fractions:
2.1. Addition and subtraction of common fractions with the same denominators.
2.2. Addition and subtraction of mixed numbers
2.3. Fractions of whole numbers which result in whole numbers
2.4. Recognize, describe and use the equivalence of division and fractions.
3. Solving problems
3.1. Solve problems in contexts involving common fractions, including grouping and sharing
4. Equivalent forms
4.1. Recognize and use equivalent forms of common fractions (fractions in which one denominator is a multiple of another)

PATTERNS, FUNCTIONS AND ALGEBRA

NUMERIC PATTERNS

1. Investigate and extend patterns
1.1. Investigate and extent numeric patterns looking for relationships of rules of patterns

  • sequences not limited to a constant difference or ratio
  • of learner’s own creation
  • represented in tables

 

1.2. Describe observed relationships or rules in learner’s own words
2. Input and output values
2.1. Determine input values, output values and rules for the patterns and relationships using

  • Flow diagrams
  • Tables
3. Equivalent forms
3.1. Determine equivalence of different descriptions of the same relationship or rule presented

  • Verbally
  • In a flow diagram
  • In a table
  • By a number sentence

GEOMETRIC PATTERNS

1. Investigate and extend patterns
1.1. Investigate and extend geometric patterns looking for relationships or rules of patterns

  • Represented in physical or diagram form
  • Sequences not limited to a constant difference or ratio
  • Of learner’s own creation
1.2. Describe observed relationships or rules in learner’s own words
2. Input and output values
2.1. Determine input values, output values and rules for the patterns and relationships using flow diagrams
3. Equivalent forms
3.1. Determine equivalence of different descriptions of the same relationship or rule presented

  • Verbally
  • In a flow diagram
  • By a number sentence

NUMBER SENTENCES

1. Number sentences
1.1. Write number sentences to describe problem situations
1.2. Solve and complete number sentences by

  • Inspection
  • Trial and improvement
1.3. Check solution by substitution

SPACE AND SHAPE (GEOMETRY)

PROPERTIES OF 2-D SHAPES

1. Range of shapes
1.2. Recognize visualize and name 2-D shapes in the environment and geometric settings, focusing on

  • Regular and irregular polygons – triangles, squares, rectangles, other quadrilaterals, pentagons, hexagons, heptagons
  • Circles
  • Similarities and differences between squares and rectangles
2.Characteristics of shapes
2.1. Describe, sort and compare 2-D shapes in terms of

  • Straight and curved sides
  • Number of sides
  • Lengths of sides
  • Angles in shapes, limited to
    • Right angles
    • Angles smaller than right angles
    • Angles greater than right angles
3. Further activities
3.1. Draw 2-D shapes on grid paper
4. Angles
4.1. Recognize and describe angles in 2-D shapes:

  • Right angles
  • Angles smaller than right angle
  • Angles greater than right angles

PROPERTIES OF 3-D OBJECTS

1. Range of objects
1.1. Recognize, visualize and name 3-D objects in the environment and geometric settings, focusing on

  • Rectangular prisms and other prisms
  • Cubes
  • Cylinders
  • Cones
  • Pyramids
  • Similarities and differences between cubes and rectangular prisms
2. Characteristics of objects
2.1. Describe, sort and compare 3-D objects in terms of

  • Shape of faces
  • Number of faces
  • Flat and curved surfaces
3. Further activities
3.1. Make 3-D models using cut out polygons
3.2 Cut open boxes to trace and describe their nets

SYMETRY

1. Symmetry
1.1. Recognize, draw and describe line(s) of symmetry in 2‑D shapes

USE TRANSFORMATIONS TO MAKE COMPOSITE SHAPES

1. Make composite 2-D shapes including shapes with line symmetry by tracing and moving a 2-D shape in one or more of the following ways:

  • By rotation
  • By translation
  • By reflection
2. Use transformations to make tessellations
2.1. Make tessellated patterns including some patterns with line symmetry by tracing and moving 2-D shapes in one or more of the following ways

  • By rotation
  • By translation
  • By reflection
3. Describe patterns
3.1. Refer to lines, 2-D shapes, 3-D objects, lines of symmetry, rotations, reflections and translations when describing patterns

  • In nature
  • From modern everyday life
  • From our culture heritage

VIEWING OF OBJECTS

1. Position and views
1.1. Links the position of viewer to views of:
1.1.1. Single everyday objects
1.1.2. Collections of everyday objects or everyday scenes

POSITION AND MOVEMENT

1. Location and directions
1.1. Locate position of objects, drawings or symbols on a grid with alpha-numeric grid references
1.2. Locate positions of objects on a map by using alpha-numeric grid references
1.3. Follows directions to trace a path between positions on a map

MEASUREMENT

LENGTH

1. Practical measuring of 2-D shapes and 3-D objects by
1.1. estimating
1.2. measuring
1.3. recording
1.4. comparing and ordering
2. Measuring instruments
2.1. rulers, metric sticks, tape measures, trundle wheels
3. Units
3.1. millimetres (mm), centimetres (cm), metres (m), kilometres (km)
4. Calculations and problem-solving involving length
4.1. Solve problems in contexts involving length
4.2. Conversions include converting between any of the following units:

  • Millimetres (mm)
  • Centimetres (cm)
  • Metres (m)
  • Kilometres (km)
4.3. Conversions limited to whole numbers and common fractions

MASS

1. Practical measuring of 3-D objects by
1.1. Estimating
1.2. Measuring
1.3. Recording
1.4. Comparing and ordering
2. Measuring instruments:
2.1. bathroom scales, kitchen scales and balances

3. Units

3.1. grams (g) and kilograms (kg)
4. Calculations and problem-solving involving mass include:

4.1. problems in contexts involving mass

4.2. converting between grams and kilograms limited to examples with whole numbers and fractions

CAPACITY / VOLUME

1. Practical measuring of 3-D objects by
1.1. estimating
1.2. measuring
1.3. recording
1.4. comparing and ordering
2. Measuring instruments
2.1. measuring spoons, measuring cups, measuring jugs
3. Units
3.1. millilitres (ml) litres (ℓ)
4. Calculations and problem solving involving capacity/volume include:
4.1. problems in contexts involving capacity/volume
4.2. converting between litres and millilitres limited to examples with whole numbers and fractions

TIME

1. Reading time and time instruments
1.1. Read, tell and write time in 12-hour and 24-hour formats on both analogue and digital instruments in

  • Hours
  • Minutes
  • Seconds
1.2. Instruments include clocks, watches and stopwatches
2. Reading calendars
3. Calculators and problem solving time include
3.1. Problem in contexts involving time
3.2. Calculation of time intervals where time is given in

  • Seconds and/or minutes
  • Minutes and/or hours
  • Hours and/or days
  • Days, weeks and/or months
  • Years and/or decades
4. History of time
4.1. Know some ways in which time was measured and represented in the past

TEMPERATURE

1. Practical measuring of temperature by
1.1. estimating
1.2. measuring
1.3. recording
1.4. comparing and ordering
2. Measuring instruments
2.1. thermometers
3. Units
3.1. degrees Celsius
4. Calculations and problem-solving related to temperature include:
4.1. problems in contexts related to temperatures
4.2. calculating temperature differences limited to positive whole numbers

PERIMETER, SURFACE AREA AND VOLUME

1. Perimeter
1.1. Measure perimeter using rulers or measuring tapes
2. Measurement of area
2.1. Find areas of regular and irregular shapes by counting squares on grids in order to develop and understanding of square units.
3. Measurement of volume
3.1. Find volume/capacity of objects by packing or filing them in order to develop an understanding of cubic units

DATA HANDLING

COLLECTING AND ORGANISING DATA

1. Collect data using tally marks and tables for recording
2. Order data from smallest group to largest group

REPRESENTING DATA

1. Draw a variety of graphs to display and interpret data including:
1.1. pictographs (many-to-one correspondence)
1.2. bar graphs

INTERPRETING DATA

1. Interpreting data
1.1. Critically read and interpret data represented in:

  • Words
  • Pictographs
  • Bar graphs
  • Pie charts
2. Analysing data
2.1. Analyse data by answering questions related to:

  • data categories
  • data sources and contexts
3. Reporting data
3.1. Summarise data verbally and in short written paragraphs that include

3.1.1. drawing conclusions about the data

3.1.2. making predictions based on the data

4. Ungrouped data
4.1. Examine ungrouped numerical data to determine the most frequently occurring score in the data set (mode)

PROBABILITY

1. Probability experiments
1.1. Perform simple repeated events and list possible outcomes for experiments such as:

  • Tossing a coin
  • Rolling a dice
  • Spinning a spinner
1.2. Count and compare the frequency of actual outcomes for a series of trials up to 20 trials.

 

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