CAPS Grade 5 A - camiweb.comcamiweb.com/CAPS/CAPS 2016/CAPS 2016 PDF/CAPS_Grade 5 Englis… ·...
Transcript of CAPS Grade 5 A - camiweb.comcamiweb.com/CAPS/CAPS 2016/CAPS 2016 PDF/CAPS_Grade 5 Englis… ·...
CAMI Education linked to CAPS:
Mathematicsathematicsathematicsathematics: Grade 5: Grade 5: Grade 5: Grade 5
- 1 -
GRADE 5_CAPS CurriculumGRADE 5_CAPS CurriculumGRADE 5_CAPS CurriculumGRADE 5_CAPS Curriculum
Term 1Term 1Term 1Term 1
TOPICSTOPICSTOPICSTOPICS CONCEPTSCONCEPTSCONCEPTSCONCEPTS CAMI KeysCAMI KeysCAMI KeysCAMI Keys
Mental Mental Mental Mental
MathematicsMathematicsMathematicsMathematics
Mental calculations involving:Mental calculations involving:Mental calculations involving:Mental calculations involving:
• Addition and subtraction facts of: � Units
� Multiples of 10
� Multiples of 100
� Multiples of 1 000
• Multiplication of whole numbers to at least 10 × 10
• Multiplication facts of: � Units by multiples of 10
� Units by multiples of 100
� Units by multiples of 1 000
� Units by multiples of 10 000
Number range for counting, ordering, Number range for counting, ordering, Number range for counting, ordering, Number range for counting, ordering,
comparing and representing numbers and comparing and representing numbers and comparing and representing numbers and comparing and representing numbers and
for the place value of digitsfor the place value of digitsfor the place value of digitsfor the place value of digits
• Count backwards and forwards in whole number intervals up to at least
10 000
• Order, compare and represent numbers to at least 4-digit numbers
• Represent odd and even numbers to at least 1 000
• Recognize the place value of digits in whole numbers to at least 4-digit
numbers
• Round off to the nearest 5, 10, 100 and 1 000
Calculation techniquesCalculation techniquesCalculation techniquesCalculation techniques
Use a range of techniques to perform and
3.3.3.103.3.3.103.3.3.103.3.3.10
3.3.4.93.3.4.93.3.4.93.3.4.9
3.3.5.43.3.5.43.3.5.43.3.5.4
3.3.6.43.3.6.43.3.6.43.3.6.4
3.33.33.33.3.5.9.5.9.5.9.5.9
3.3.6.93.3.6.93.3.6.93.3.6.9
1.1.2.71.1.2.71.1.2.71.1.2.7
1.1.2.81.1.2.81.1.2.81.1.2.8
1.7.8.41.7.8.41.7.8.41.7.8.4
1.1.11.1.11.1.11.1.10.30.30.30.3
1.1.6.101.1.6.101.1.6.101.1.6.10
1.1.8.101.1.8.101.1.8.101.1.8.10
1.1.8.51.1.8.51.1.8.51.1.8.5
1.1.8.61.1.8.61.1.8.61.1.8.6
1.1.9.51.1.9.51.1.9.51.1.9.5
1.1.9.91.1.9.91.1.9.91.1.9.9
1.7.9.31.7.9.31.7.9.31.7.9.3
1.7.1.11.7.1.11.7.1.11.7.1.1
1.7.1.51.7.1.51.7.1.51.7.1.5
CAMI Education linked to CAPS:
Mathematicsathematicsathematicsathematics: Grade 5: Grade 5: Grade 5: Grade 5
- 2 -
check written and mental calculations of
whole numbers including:
• Estimation
• Adding and subtracting in columns
• Building up and breaking down numbers
• Using a number line
• Rounding off and compensating
• Doubling and halving
• Using addition and subtraction as inverse operations
• Using multiplication and division as inverse operations
Number range for multiples and factorsNumber range for multiples and factorsNumber range for multiples and factorsNumber range for multiples and factors
• Multiples of 2-digit whole numbers
to at least 100
• Factors of 2-digit whole numbers to
at least 100
Properties of whole numbersProperties of whole numbersProperties of whole numbersProperties of whole numbers
• Recognize and use the commutative, associative and distributive
properties of whole numbers
• 0 in terms of its additive property
• 1 in terms of its multiplicative property
1.7.10.41.7.10.41.7.10.41.7.10.4
1.7.10.81.7.10.81.7.10.81.7.10.8
1.7.3.81.7.3.81.7.3.81.7.3.8 1.7.6.11.7.6.11.7.6.11.7.6.1
1.7.6.21.7.6.21.7.6.21.7.6.2
3.8.8.53.8.8.53.8.8.53.8.8.5
1.8.1.11.8.1.11.8.1.11.8.1.1
1.7.7.11.7.7.11.7.7.11.7.7.1
1.7.7.61.7.7.61.7.7.61.7.7.6
1.11.11.11.1
Whole numbersWhole numbersWhole numbersWhole numbers
Counting,
ordering,
comparing,
representing and place value
of digits
Number range for counting, ordering, Number range for counting, ordering, Number range for counting, ordering, Number range for counting, ordering,
comcomcomcomparing, representing and place value of paring, representing and place value of paring, representing and place value of paring, representing and place value of
digitsdigitsdigitsdigits
• Count forwards and backwards in whole number intervals up to at
least 10 000
• Order, compare and represent numbers to at least 4-digit numbers
• Represent odd and even numbers to at least 1 000
• Recognize the place value of digits in whole numbers to at least 6-digit
1.1.2.71.1.2.71.1.2.71.1.2.7
1.1.2.81.1.2.81.1.2.81.1.2.8
1.7.8.41.7.8.41.7.8.41.7.8.4
1.1.10.31.1.10.31.1.10.31.1.10.3
1.1.6.101.1.6.101.1.6.101.1.6.10
1.1.8.101.1.8.101.1.8.101.1.8.10
1.1.8.51.1.8.51.1.8.51.1.8.5
1.1.8.61.1.8.61.1.8.61.1.8.6
CAMI Education linked to CAPS:
Mathematicsathematicsathematicsathematics: Grade 5: Grade 5: Grade 5: Grade 5
- 3 -
numbers
• Rounding off to the nearest 5, 10, 100 and 1 000
1.1.9.51.1.9.51.1.9.51.1.9.5
1.1.9.91.1.9.91.1.9.91.1.9.9
1.7.9.31.7.9.31.7.9.31.7.9.3
1.7.1.11.7.1.11.7.1.11.7.1.1
1.7.1.51.7.1.51.7.1.51.7.1.5
2.12.12.12.1
Number Number Number Number sentensentensentensentencescescesces
Introduction to
algebraic
expressions
Number sentencesNumber sentencesNumber sentencesNumber sentences
• Write number sentences to describe problem situations
• Solve and complete number sentences by
� Inspection � Trial and improvement
• Check the solution by substitution
3.8.8.13.8.8.13.8.8.13.8.8.1
3.8.8.23.8.8.23.8.8.23.8.8.2
1.11.11.11.1 Whole numbersWhole numbersWhole numbersWhole numbers
Addition and
subtraction
Number range for calculationNumber range for calculationNumber range for calculationNumber range for calculation Addition and subtraction of whole numbers
with at least 5-digit numbers.
Calculation techniquesCalculation techniquesCalculation techniquesCalculation techniques
Using a range of techniques to perform and
check written and mental calculations with
whole numbers including:
• Estimation
• Adding and subtracting in columns
• Building up and breaking down numbers
• Using a number line
• Rounding off and compensating
• Doubling and halving
• Using addition and subtraction as inverse operations
• Using multiplication and division as inverse operations
Properties of whole numbersProperties of whole numbersProperties of whole numbersProperties of whole numbers
• Recognize and use the commutative, associative and distributive
properties of whole numbers
1.2.6.81.2.6.81.2.6.81.2.6.8
1.3.7.31.3.7.31.3.7.31.3.7.3
1.3.8.51.3.8.51.3.8.51.3.8.5
1.3.8.61.3.8.61.3.8.61.3.8.6
1.7.10.91.7.10.91.7.10.91.7.10.9
CAMI Education linked to CAPS:
Mathematicsathematicsathematicsathematics: Grade 5: Grade 5: Grade 5: Grade 5
- 4 -
• 0 in terms of its additive property
• 1 in terms of its multiplicative
property
Solving problemsSolving problemsSolving problemsSolving problems
Solve problems involving whole numbers,
including:
• Financial contexts
• Measurement contexts
3.8.4.63.8.4.63.8.4.63.8.4.6
3.8.4.73.8.4.73.8.4.73.8.4.7
2.12.12.12.1
Numeric Numeric Numeric Numeric
patternspatternspatternspatterns
Investigate and extend patternsInvestigate and extend patternsInvestigate and extend patternsInvestigate and extend patterns
• Investigate and extend numeric patterns looking for relationships or
rules of patterns
� Sequences involving a
constant difference or ratio
� Of learner’s own creation
• Describe observed relationships or rules in learner’s own words
Input and output valuesInput and output valuesInput and output valuesInput and output values
Determine input values, output values and
rules for patterns and relationships using
flow diagrams.
Equivalent formsEquivalent formsEquivalent formsEquivalent forms
Determine equivalence of different
descriptions of the same relationship or rule presented
• Verbally
• In a flow diagram
• By a number sentence
4.1.1.64.1.1.64.1.1.64.1.1.6
4.1.4.14.1.4.14.1.4.14.1.4.1
3.2.5.13.2.5.13.2.5.13.2.5.1
3.2.5.23.2.5.23.2.5.23.2.5.2
1111.1.1.1.1
Whole numbersWhole numbersWhole numbersWhole numbers Multiplication
and division
Number range for calculationsNumber range for calculationsNumber range for calculationsNumber range for calculations
• Multiplication of at least whole 3-digit by 2-digit numbers
• Division of at least whole 3-digit by 1-digit numbers
Calculation techniquesCalculation techniquesCalculation techniquesCalculation techniques
• Estimation
1.4.2.41.4.2.41.4.2.41.4.2.4 1.4.2.51.4.2.51.4.2.51.4.2.5
1.4.3.31.4.3.31.4.3.31.4.3.3
1.4.3.41.4.3.41.4.3.41.4.3.4
1.4.4.31.4.4.31.4.4.31.4.4.3
1.4.4.41.4.4.41.4.4.41.4.4.4
CAMI Education linked to CAPS:
Mathematicsathematicsathematicsathematics: Grade 5: Grade 5: Grade 5: Grade 5
- 5 -
• Adding and subtracting in columns
• Building up and breaking down
numbers
• Using a number line
• Rounding off and compensating
• Doubling and halving
• Using addition and subtraction as inverse operations
• Using multiplication and division as inverse operations
Number range for multipNumber range for multipNumber range for multipNumber range for multiples and factorsles and factorsles and factorsles and factors
• Multiples of 2-digit whole numbers to at least 100
• Factors of 2-digit numbers to at least 100
Properties of whole numbersProperties of whole numbersProperties of whole numbersProperties of whole numbers
• Recognize and use the commutative, associative and distributive property
of whole numbers
• 0 in terms of its additive property
• 1 in terms of its multiplicative property
Solving problemsSolving problemsSolving problemsSolving problems
• Solve problems involving whole numbers, including
� Financial contexts
� Measurement contexts
• 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
1.5.3.71.5.3.71.5.3.71.5.3.7
1.5.5.71.5.5.71.5.5.71.5.5.7
1.7.2.21.7.2.21.7.2.21.7.2.2
1.7.2.31.7.2.31.7.2.31.7.2.3
3.8.7.23.8.7.23.8.7.23.8.7.2
4.44.44.44.4
TimeTimeTimeTime
Reading time and time instrumentsReading time and time instrumentsReading time and time instrumentsReading time and time instruments
Read, tell and write time in 12-hour and 24-
3.83.83.83.8.6.6.6.6.6.6.6.6
CAMI Education linked to CAPS:
Mathematicsathematicsathematicsathematics: Grade 5: Grade 5: Grade 5: Grade 5
- 6 -
hour formals on both analogue and digital
instruments in
• Hours
• Minutes
• Seconds Instruments include clocks, watches and
stopwatches.
Reading calendarsReading calendarsReading calendarsReading calendars
Calculations and problem solving related to Calculations and problem solving related to Calculations and problem solving related to Calculations and problem solving related to
time includetime includetime includetime include
Calculation of time intervals where time is
given in
• Seconds and / or minutes
• Minutes and / or hours
• Hours and / or in days
• Days and / or in weeks and / or months
• Months and / or years
• Years and / or decades
History of timeHistory of timeHistory of timeHistory of time
Know how time was measured and
expressed in ancient times.
9.2.1.19.2.1.19.2.1.19.2.1.1
9.2.1.59.2.1.59.2.1.59.2.1.5
9.2.1.69.2.1.69.2.1.69.2.1.6
9.2.1.79.2.1.79.2.1.79.2.1.7
9.2.1.89.2.1.89.2.1.89.2.1.8
9.2.1.99.2.1.99.2.1.99.2.1.9
9.2.4.29.2.4.29.2.4.29.2.4.2
3.8.6.53.8.6.53.8.6.53.8.6.5
9.2.2.39.2.2.39.2.2.39.2.2.3
9.2.2.49.2.2.49.2.2.49.2.2.4
9.2.2.59.2.2.59.2.2.59.2.2.5 9.2.2.69.2.2.69.2.2.69.2.2.6
9.2.2.79.2.2.79.2.2.79.2.2.7
9.2.2.89.2.2.89.2.2.89.2.2.8
9.2.2.99.2.2.99.2.2.99.2.2.9
9.2.3.19.2.3.19.2.3.19.2.3.1
9.2.3.29.2.3.29.2.3.29.2.3.2
9.2.3.39.2.3.39.2.3.39.2.3.3
9.2.3.49.2.3.49.2.3.49.2.3.4 9.2.3.59.2.3.59.2.3.59.2.3.5
5.15.15.15.1 Collecting and Collecting and Collecting and Collecting and
organizing dataorganizing dataorganizing dataorganizing data
• Collect data using tally marks and tables for recording
• Order data from smallest group to largest group
10.1.1.310.1.1.310.1.1.310.1.1.3
5.25.25.25.2 Representing Representing Representing Representing
datadatadatadata
Draw a variety of graphs to display and interpret data including
• Pictographs (many-to-one correspondence)
• Bar graphs
10.1.2.210.1.2.210.1.2.210.1.2.2
10.1.2.310.1.2.310.1.2.310.1.2.3
10.1.2.410.1.2.410.1.2.410.1.2.4
10.1.2.510.1.2.510.1.2.510.1.2.5
5.35.35.35.3 Analyzing, Analyzing, Analyzing, Analyzing,
interpreting and interpreting and interpreting and interpreting and
reporting datareporting datareporting datareporting data
Critically read and interpret data represented in
• Words
• Pictographs
10.1.4.210.1.4.210.1.4.210.1.4.2
10.1.4.110.1.4.110.1.4.110.1.4.1
CAMI Education linked to CAPS:
Mathematicsathematicsathematicsathematics: Grade 5: Grade 5: Grade 5: Grade 5
- 7 -
• Bar graphs
• Pie graphs
Analyze data by answering questions related to
• Data categories
• Data sources and contexts
Summarize data verbally and in short written paragraphs that include:
• Drawing conclusions about the data
• Making predictions based on the
data Examine ungrouped numerical data to
determine the most frequently occurring
score in the data set (mode)
10.3.1.110.3.1.110.3.1.110.3.1.1
3.13.13.13.1
2222----D shapesD shapesD shapesD shapes
Shapes learners need to know and nameShapes learners need to know and nameShapes learners need to know and nameShapes learners need to know and name
• Regular and irregular polygons – triangles, squares, rectangles, other
quadrilaterals, pentagons, hexagons,
heptagons
• Circles
• Similarities and differences between squares and rectangles
Characteristics learners use to distinguish, Characteristics learners use to distinguish, Characteristics learners use to distinguish, Characteristics learners use to distinguish,
describe, sort and compare shapesdescribe, sort and compare shapesdescribe, sort and compare shapesdescribe, sort and compare shapes
• Straight and / curved sides
• Numbers of sides
• Length of sides
• Angles: limited to � Right angles
� Angles smaller than right
angles
� Angles greater than right angles
Further activities to focus learners on Further activities to focus learners on Further activities to focus learners on Further activities to focus learners on
characteristics of shapescharacteristics of shapescharacteristics of shapescharacteristics of shapes
Draw 2-D shapes on grid paper.
Angles Angles Angles Angles limited to
• Right angles
8.1.1.48.1.1.48.1.1.48.1.1.4
8.1.1.58.1.1.58.1.1.58.1.1.5
CAMI Education linked to CAPS:
Mathematicsathematicsathematicsathematics: Grade 5: Grade 5: Grade 5: Grade 5
- 8 -
• Angles smaller than right angles
• Angles greater than right angles
4.34.34.34.3
Capacity/Capacity/Capacity/Capacity/ VolumeVolumeVolumeVolume
Practical measuring of 3Practical measuring of 3Practical measuring of 3Practical measuring of 3----D objects byD objects byD objects byD objects by
• Estimating
• Measuring
• Recording
• Comparing and ordering
Measuring instrumentsMeasuring instrumentsMeasuring instrumentsMeasuring instruments
Measuring spoons, measuring cups,
measuring jugs
UnitsUnitsUnitsUnits
Milliliter (ml), litre (l)
Calculations and problemCalculations and problemCalculations and problemCalculations and problem----solving related to solving related to solving related to solving related to
capacity / volume includecapacity / volume includecapacity / volume includecapacity / volume include
• Solving problems in contexts using capacity / volume
• Converting between litres and milliliters limited to examples with
whole numbers and fractions
9.1.3.49.1.3.49.1.3.49.1.3.4 9.5.1.49.5.1.49.5.1.49.5.1.4
3.8.6.33.8.6.33.8.6.33.8.6.3
Term 2Term 2Term 2Term 2
Mental Mental Mental Mental
MathematicsMathematicsMathematicsMathematics
See Term 1See Term 1See Term 1See Term 1
1.11.11.11.1 Whole numbersWhole numbersWhole numbersWhole numbers
Counting,
ordering,
comparing,
representing
and place value
of digits
Number range for counting, ordering, Number range for counting, ordering, Number range for counting, ordering, Number range for counting, ordering, comparing, representing and place value of comparing, representing and place value of comparing, representing and place value of comparing, representing and place value of
digitsdigitsdigitsdigits
• Count forwards and backwards in whole number intervals up to at
least 10 000
• Order, compare and represent numbers to at least 6-digit numbers
• Represent odd and even numbers to at least 1 000
• Recognize the place value of digits in whole numbers to at least 6-digit
numbers
1.1.2.71.1.2.71.1.2.71.1.2.7
1.1.2.81.1.2.81.1.2.81.1.2.8
1.7.8.41.7.8.41.7.8.41.7.8.4
1.1.10.31.1.10.31.1.10.31.1.10.3 1.1.6.101.1.6.101.1.6.101.1.6.10
1.1.8.101.1.8.101.1.8.101.1.8.10
1.1.8.51.1.8.51.1.8.51.1.8.5
1.1.8.61.1.8.61.1.8.61.1.8.6
1.1.9.51.1.9.51.1.9.51.1.9.5
CAMI Education linked to CAPS:
Mathematicsathematicsathematicsathematics: Grade 5: Grade 5: Grade 5: Grade 5
- 9 -
• Rounding off to the nearest 5, 10, 100 and 1 000
1.1.9.91.1.9.91.1.9.91.1.9.9
1.7.9.31.7.9.31.7.9.31.7.9.3
1.7.1.11.7.1.11.7.1.11.7.1.1
1.7.1.51.7.1.51.7.1.51.7.1.5
1.11.11.11.1
Whole numbersWhole numbersWhole numbersWhole numbers
Addition and subtraction
Number range for calculationNumber range for calculationNumber range for calculationNumber range for calculation
Addition and subtraction of whole numbers
with at least 5-digit numbers.
Calculation techniquesCalculation techniquesCalculation techniquesCalculation techniques
Using a range of techniques to perform and
check written and mental calculations with
whole numbers including:
• Estimation
• Adding and subtracting in columns
• Building up and breaking down numbers
• Using a number line
• Rounding off and compensating
• Doubling and halving
• Using addition and subtraction as
inverse operations
• Using multiplication and division as
inverse operations
Properties of whole numbersProperties of whole numbersProperties of whole numbersProperties of whole numbers
• Recognize and use the commutative, associative and distributive
properties of whole numbers
• 0 in terms of its additive property
• 1 in terms of its multiplicative property
Solving problemsSolving problemsSolving problemsSolving problems
Solve problems involving whole numbers,
including:
• Financial contexts
• Measurement contexts
1.2.6.81.2.6.81.2.6.81.2.6.8
1.31.31.31.3.7.3.7.3.7.3.7.3 1.3.8.51.3.8.51.3.8.51.3.8.5
1.3.8.61.3.8.61.3.8.61.3.8.6
3.8.4.63.8.4.63.8.4.63.8.4.6
3.8.4.73.8.4.73.8.4.73.8.4.7
CAMI Education linked to CAPS:
Mathematicsathematicsathematicsathematics: Grade 5: Grade 5: Grade 5: Grade 5
- 10 -
1.21.21.21.2
Common Common Common Common
fractionsfractionsfractionsfractions
Concepts,Concepts,Concepts,Concepts, skills and number range skills and number range skills and number range skills and number range
• Describing and ordering fractions
• Count forwards and backwards in fractions
• Compare and order common fractions to at least twelfths
Calculations with fractionsCalculations with fractionsCalculations with fractionsCalculations with fractions
• Addition of common fractions with the same denominator
• Recognize, describe and use the equivalence of division and fractions
Solving problemsSolving problemsSolving problemsSolving problems
Solve problems in contexts involving
common fractions, including grouping and
sharing.
Equivalents formsEquivalents formsEquivalents formsEquivalents forms
Recognize and use equivalent forms of
common fractions with denominators which
are multiples of each other.
2.1.3.12.1.3.12.1.3.12.1.3.1
2.1.3.22.1.3.22.1.3.22.1.3.2
2.1.4.32.1.4.32.1.4.32.1.4.3
2.1.4.52.1.4.52.1.4.52.1.4.5
2.1.4.62.1.4.62.1.4.62.1.4.6
2.1.5.22.1.5.22.1.5.22.1.5.2 2.1.5.52.1.5.52.1.5.52.1.5.5
2.2.1.12.2.1.12.2.1.12.2.1.1
2.2.1.22.2.1.22.2.1.22.2.1.2
2.2.1.32.2.1.32.2.1.32.2.1.3
2.2.2.32.2.2.32.2.2.32.2.2.3
2.2.3.12.2.3.12.2.3.12.2.3.1
2.2.3.22.2.3.22.2.3.22.2.3.2
2.2.3.32.2.3.32.2.3.32.2.3.3 2.2.5.72.2.5.72.2.5.72.2.5.7
3.4.5.23.4.5.23.4.5.23.4.5.2
3.4.5.33.4.5.33.4.5.33.4.5.3
3.4.5.43.4.5.43.4.5.43.4.5.4
3.4.5.53.4.5.53.4.5.53.4.5.5
3.4.5.63.4.5.63.4.5.63.4.5.6
3.4.5.73.4.5.73.4.5.73.4.5.7
3.4.5.83.4.5.83.4.5.83.4.5.8 3.4.6.23.4.6.23.4.6.23.4.6.2
3.4.6.33.4.6.33.4.6.33.4.6.3
3.4.6.43.4.6.43.4.6.43.4.6.4
3.8.5.23.8.5.23.8.5.23.8.5.2
4.14.14.14.1
LengthLengthLengthLength
Practical measuring of 2Practical measuring of 2Practical measuring of 2Practical measuring of 2----D shapes and 3D shapes and 3D shapes and 3D shapes and 3----D D D D
objects by:objects by:objects by:objects by:
• Estimating
• Measuring
• Recording
• Comparing and ordering
Measuring instrumentsMeasuring instrumentsMeasuring instrumentsMeasuring instruments
Rulers, meter sticks, tape measures, trundle
wheels
UnitsUnitsUnitsUnits
Millimetres (mm), centimeters (cm), metres (m), kilometers (km)
9.1.1.29.1.1.29.1.1.29.1.1.2
9.1.2.19.1.2.19.1.2.19.1.2.1
9.1.2.39.1.2.39.1.2.39.1.2.3
CAMI Education linked to CAPS:
Mathematicsathematicsathematicsathematics: Grade 5: Grade 5: Grade 5: Grade 5
- 11 -
Calculations and prCalculations and prCalculations and prCalculations and problemoblemoblemoblem----solving related to solving related to solving related to solving related to
lengthlengthlengthlength
Solve problems in context related to length.
Conversations include converting between any of the following units:
mm , cm , m , km
Conversions limited to whole numbers and
fractions.
3.8.6.13.8.6.13.8.6.13.8.6.1
1.11.11.11.1
Whole numbersWhole numbersWhole numbersWhole numbers
Multiplication
Number range forNumber range forNumber range forNumber range for calculations calculations calculations calculations
Multiplication of at least whole 3-digit by 2-
digit numbers
Calculation techniquesCalculation techniquesCalculation techniquesCalculation techniques
Using a range of techniques to perform and
check written and metal calculations of
whole numbers including:
• Estimation
• Building up and breaking down numbers
• Using a number line
• Rounding off and compensating
• Doubling and halving
Number range for multiples and factorsNumber range for multiples and factorsNumber range for multiples and factorsNumber range for multiples and factors
• Multiples of 2-digit whole numbers to at least 100
• Factors of 2-digit numbers to at least 100
Properties of whole numbersProperties of whole numbersProperties of whole numbersProperties of whole numbers
• Recognize and use the commutative, associative and distributive property
of whole numbers
• 0 in terms of its additive property
• 1 in terms of its multiplicative property
1.4.2.41.4.2.41.4.2.41.4.2.4
1.4.2.51.4.2.51.4.2.51.4.2.5 1.4.3.31.4.3.31.4.3.31.4.3.3
1.4.3.41.4.3.41.4.3.41.4.3.4
1.4.4.31.4.4.31.4.4.31.4.4.3
1.4.4.41.4.4.41.4.4.41.4.4.4
1.4.6.61.4.6.61.4.6.61.4.6.6
1.4.6.71.4.6.71.4.6.71.4.6.7
CAMI Education linked to CAPS:
Mathematicsathematicsathematicsathematics: Grade 5: Grade 5: Grade 5: Grade 5
- 12 -
Solving problemsSolving problemsSolving problemsSolving problems
• Solve problems involving whole numbers, including
� Financial contexts
� Measurement contexts
• Solve problems involving whole numbers, including
� Comparing two or more
quantities of the same kind (ratio)
3.8.7.23.8.7.23.8.7.23.8.7.2
3.23.23.23.2 Properties of 3Properties of 3Properties of 3Properties of 3----
D objectsD objectsD objectsD objects
Objects learners need to know and name:
• Rectangular prisms and other prisms
• Cubes
• Cylinders
• Cones
• Pyramids
• Similarities and differences between
• Cubes and rectangular prisms
Characteristics learners use to distinguish,
describe, sort and compare shapes
• Shape of faces
• Number of faces
• Flat and curved surfaces
• Further activities to focus learners on characteristics of objects
• Make 3-D models using cut-out polygons
• Cutting open boxes to trace and describe their nets
8.1.2.38.1.2.38.1.2.38.1.2.3
Class activityClass activityClass activityClass activity
2.22.22.22.2
Geometric Geometric Geometric Geometric
patternspatternspatternspatterns
Investigate and extend patternsInvestigate and extend patternsInvestigate and extend patternsInvestigate and extend patterns
• Investigate and extend geometric patterns looking for relationships or
rules of patterns
� Represented in physical or
diagram form
� Sequences involving a
4444.1.1.7.1.1.7.1.1.7.1.1.7
CAMI Education linked to CAPS:
Mathematicsathematicsathematicsathematics: Grade 5: Grade 5: Grade 5: Grade 5
- 13 -
constant difference
� Of learner’s own creation
• Describe observed relationships or rules in learner’s own words
Input and output valuesInput and output valuesInput and output valuesInput and output values
Determine input values, output values and
rules for the patterns and relationships using
flow diagrams.
Equivalent formsEquivalent formsEquivalent formsEquivalent forms
Determine equivalence of different
descriptions of the same relationship or rule
presented
• Verbally
• In a flow diagram
• By a number sentence
3.2.6.23.2.6.23.2.6.23.2.6.2
3.33.33.33.3
SymmetrySymmetrySymmetrySymmetry
Recognize, draw and describe lines of Recognize, draw and describe lines of Recognize, draw and describe lines of Recognize, draw and describe lines of
symmetry in 2symmetry in 2symmetry in 2symmetry in 2----D shapesD shapesD shapesD shapes
8.10.1.48.10.1.48.10.1.48.10.1.4
8.10.1.58.10.1.58.10.1.58.10.1.5
1.11.11.11.1
WhWhWhWhole numbersole numbersole numbersole numbers
Division
Number range for calculationsNumber range for calculationsNumber range for calculationsNumber range for calculations
Division of at least whole 3-digit by 2-digit
numbers
Calculation techniquesCalculation techniquesCalculation techniquesCalculation techniques Use a range of techniques to perform and
check written and mental calculations with
whole numbers including:
• Estimation
• Building up and breaking down numbers
• Using multiplications and division as inverse operations
Number range for counting, ordering and Number range for counting, ordering and Number range for counting, ordering and Number range for counting, ordering and
representing, and place value of digitsrepresenting, and place value of digitsrepresenting, and place value of digitsrepresenting, and place value of digits
• Recognize the place value of digits in whole numbers to at least 6-digit
numbers
• Round off to the nearest 10, 100 and
1.5.1.71.5.1.71.5.1.71.5.1.7
1.5.1.101.5.1.101.5.1.101.5.1.10
1.5.5.11.5.5.11.5.5.11.5.5.1
1.5.5.21.5.5.21.5.5.21.5.5.2 1.5.5.31.5.5.31.5.5.31.5.5.3
1.5.5.41.5.5.41.5.5.41.5.5.4
1.5.5.51.5.5.51.5.5.51.5.5.5
1.5.5.61.5.5.61.5.5.61.5.5.6
1.5.7.11.5.7.11.5.7.11.5.7.1
1.5.7.21.5.7.21.5.7.21.5.7.2
1.5.7.31.5.7.31.5.7.31.5.7.3 1.5.8.11.5.8.11.5.8.11.5.8.1
3.5.5.33.5.5.33.5.5.33.5.5.3
3.8.2.63.8.2.63.8.2.63.8.2.6
3.1.4.33.1.4.33.1.4.33.1.4.3
CAMI Education linked to CAPS:
Mathematicsathematicsathematicsathematics: Grade 5: Grade 5: Grade 5: Grade 5
- 14 -
1 000
Number range for multiples and factorsNumber range for multiples and factorsNumber range for multiples and factorsNumber range for multiples and factors
• Multiples of 2-digit numbers to at least 100
• Factors of 2-digit whole numbers to at least 100
Multiplication factsMultiplication factsMultiplication factsMultiplication facts
• Units by multiples of 10
• Units by multiples of 100
PropertiesPropertiesPropertiesProperties of whole numbers of whole numbers of whole numbers of whole numbers
• Recognize and use the commutative, associative and distributive properties
of whole numbers
• 1 in terms of its multiplicative property
Solving problemsSolving problemsSolving problemsSolving problems
Solve problems in contexts involving whole
numbers, including financial contexts
SolvSolvSolvSolve problems involving whole numbers, e problems involving whole numbers, e problems involving whole numbers, e problems involving whole numbers,
including:including:including:including:
• Comparing two or more quantities of the same unit (ratio)
• Comparing two quantities of different kinds (rate)
• Grouping and equal sharing with remainders
3.8.7.23.8.7.23.8.7.23.8.7.2
Term 3Term 3Term 3Term 3
Mental Mental Mental Mental
MathematicsMathematicsMathematicsMathematics
Same as Term 1Same as Term 1Same as Term 1Same as Term 1
1.21.21.21.2
Common Common Common Common fractfractfractfractionsionsionsions
Concepts, skills and number rangeConcepts, skills and number rangeConcepts, skills and number rangeConcepts, skills and number range
• Count forwards and backwards in fractions
• Compare and order common fractions to at least twelfths
2.1.3.12.1.3.12.1.3.12.1.3.1
2.1.3.22.1.3.22.1.3.22.1.3.2 2.1.4.32.1.4.32.1.4.32.1.4.3
2.1.4.52.1.4.52.1.4.52.1.4.5
2.1.4.62.1.4.62.1.4.62.1.4.6
2.1.5.22.1.5.22.1.5.22.1.5.2
CAMI Education linked to CAPS:
Mathematicsathematicsathematicsathematics: Grade 5: Grade 5: Grade 5: Grade 5
- 15 -
Calculations with fractionsCalculations with fractionsCalculations with fractionsCalculations with fractions
• Addition of common fractions with the same denominator
• Addition and subtraction of mixed numbers
• Fractions of whole numbers which result in whole numbers
• Recognize, describe and use the equivalence of division and fractions
Solving problemsSolving problemsSolving problemsSolving problems
Solve problems in contexts involving
common fractions, including grouping and
sharing.
Equivalents forEquivalents forEquivalents forEquivalents formsmsmsms
Recognize and use equivalent forms of
common fractions with denominators which
are multiples of each other
2.1.5.52.1.5.52.1.5.52.1.5.5
2.2.1.12.2.1.12.2.1.12.2.1.1
2.2.1.22.2.1.22.2.1.22.2.1.2
2.2.1.32.2.1.32.2.1.32.2.1.3
2.2.1.42.2.1.42.2.1.42.2.1.4
2.2.2.32.2.2.32.2.2.32.2.2.3
2.2.3.12.2.3.12.2.3.12.2.3.1 2.2.3.32.2.3.32.2.3.32.2.3.3
2.2.5.72.2.5.72.2.5.72.2.5.7
3.4.5.23.4.5.23.4.5.23.4.5.2
3.4.5.33.4.5.33.4.5.33.4.5.3
3.4.5.43.4.5.43.4.5.43.4.5.4
3.4.5.53.4.5.53.4.5.53.4.5.5
3.4.5.63.4.5.63.4.5.63.4.5.6
3.4.5.83.4.5.83.4.5.83.4.5.8 3.4.6.23.4.6.23.4.6.23.4.6.2
3.4.6.33.4.6.33.4.6.33.4.6.3
3.4.6.43.4.6.43.4.6.43.4.6.4
2.2.3.22.2.3.22.2.3.22.2.3.2
4.24.24.24.2
MassMassMassMass
Practical measuring of 3Practical measuring of 3Practical measuring of 3Practical measuring of 3----D objects by D objects by D objects by D objects by
Estimating, measuring, recording,
comparing and ordering
Measuring instrumentsMeasuring instrumentsMeasuring instrumentsMeasuring instruments
Bathroom scales, kitchen scales and balances
UnitsUnitsUnitsUnits
Grams (g) and kilograms (kg)
Calculations aCalculations aCalculations aCalculations and problemnd problemnd problemnd problem----solving related to solving related to solving related to solving related to
mass includemass includemass includemass include Solve problems in contexts related to mass
Converting between grams and kilograms
limited to examples with whole numbers
and fractions.
9.1.2.29.1.2.29.1.2.29.1.2.2
9.1.2.39.1.2.39.1.2.39.1.2.3
3.8.6.23.8.6.23.8.6.23.8.6.2
1.11.11.11.1
Whole numbersWhole numbersWhole numbersWhole numbers
Counting,
Number range for counting, ordering, Number range for counting, ordering, Number range for counting, ordering, Number range for counting, ordering,
comparing, representing and place value of comparing, representing and place value of comparing, representing and place value of comparing, representing and place value of
digidigidigidigitstststs
CAMI Education linked to CAPS:
Mathematicsathematicsathematicsathematics: Grade 5: Grade 5: Grade 5: Grade 5
- 16 -
ordering,
comparing,
representing
and place value
of digits
• Count forwards and backwards in whole number intervals up to at
least 10 000
• Order, compare and represent numbers to at least 6-digit numbers
• Represent odd and even numbers to at least 1 000
• Recognize the place value of digits in whole numbers to at least 6-digit
numbers
• Rounding off to the nearest 5, 10, 100 and 1 000
1.1.2.71.1.2.71.1.2.71.1.2.7
1.1.2.81.1.2.81.1.2.81.1.2.8
1.7.8.41.7.8.41.7.8.41.7.8.4
1.1.10.31.1.10.31.1.10.31.1.10.3
1.1.6.101.1.6.101.1.6.101.1.6.10 1.1.8.101.1.8.101.1.8.101.1.8.10
1.1.8.51.1.8.51.1.8.51.1.8.5
1.1.8.61.1.8.61.1.8.61.1.8.6
1.1.9.51.1.9.51.1.9.51.1.9.5
1.1.9.91.1.9.91.1.9.91.1.9.9
1.7.9.31.7.9.31.7.9.31.7.9.3
1.7.1.11.7.1.11.7.1.11.7.1.1 1.7.1.51.7.1.51.7.1.51.7.1.5
1.11.11.11.1 Whole numbersWhole numbersWhole numbersWhole numbers
Addition and
subtraction
Number range for cNumber range for cNumber range for cNumber range for calculationalculationalculationalculation Addition and subtraction of whole numbers
with at least 5-digit numbers.
Calculation techniquesCalculation techniquesCalculation techniquesCalculation techniques
Using a range of techniques to perform and
check written and mental calculations with
whole numbers including:
• Estimation
• Adding and subtracting in columns
• Building up and breaking down numbers
• Using a number line
• Rounding off and compensating
• Doubling and halving
• Using addition and subtraction as inverse operations
• Using multiplication and division as inverse operations
Properties of whole numbersProperties of whole numbersProperties of whole numbersProperties of whole numbers
• Recognize and use the commutative, associative and distributive
properties of whole numbers
1.2.6.81.2.6.81.2.6.81.2.6.8
1.3.7.31.3.7.31.3.7.31.3.7.3
1.3.8.51.3.8.51.3.8.51.3.8.5
1.3.8.61.3.8.61.3.8.61.3.8.6
CAMI Education linked to CAPS:
Mathematicsathematicsathematicsathematics: Grade 5: Grade 5: Grade 5: Grade 5
- 17 -
• 0 in terms of its additive property
• 1 in terms of its multiplicative
property
Solving problemsSolving problemsSolving problemsSolving problems
Solve problems involving whole numbers,
including:
• Financial contexts
• Measurement contexts
3.8.4.63.8.4.63.8.4.63.8.4.6
3.8.4.73.8.4.73.8.4.73.8.4.7
3.53.53.53.5
Viewing objectsViewing objectsViewing objectsViewing objects
Position and viewsPosition and viewsPosition and viewsPosition and views
Link the position of viewer to views of
single everyday objects, collections of
everyday objects or scenes from everyday
life.
3.3.3.3.1111
Properties of 2Properties of 2Properties of 2Properties of 2----D shapesD shapesD shapesD shapes
Shapes learners need to know and nameShapes learners need to know and nameShapes learners need to know and nameShapes learners need to know and name
• Regular and irregular polygons – triangles, squares, rectangles, other
quadrilaterals, pentagons, hexagons, heptagons
• Circles
• Similarities and differences between
squares and rectangles
CharCharCharCharacteristics learners use to distinguish, acteristics learners use to distinguish, acteristics learners use to distinguish, acteristics learners use to distinguish,
describe, sort and compare shapesdescribe, sort and compare shapesdescribe, sort and compare shapesdescribe, sort and compare shapes
• Straight and / curved sides
• Numbers of sides
• Length of sides
• Angles: limited to � Right angles
� Angles smaller than right
angles
� Angles greater than right
angles
Further activities toFurther activities toFurther activities toFurther activities to focus learners on focus learners on focus learners on focus learners on
characteristics of shapescharacteristics of shapescharacteristics of shapescharacteristics of shapes
Draw 2-D shapes on grid paper. Angles Angles Angles Angles limited to
• Right angles
8.1.1.48.1.1.48.1.1.48.1.1.4
8.1.1.58.1.1.58.1.1.58.1.1.5
CAMI Education linked to CAPS:
Mathematicsathematicsathematicsathematics: Grade 5: Grade 5: Grade 5: Grade 5
- 18 -
• Angles smaller than right angles
• Angles greater than right angles
3.43.43.43.4 TransformationsTransformationsTransformationsTransformations
Use transformations to create composite Use transformations to create composite Use transformations to create composite Use transformations to create composite shapesshapesshapesshapes
Create composite 2-D shapes including
shapes with line symmetry by tracing and
moving a 2-D shape by
• Rotation
• Translation
• Reflection
Use transformations to create tesseUse transformations to create tesseUse transformations to create tesseUse transformations to create tessellationsllationsllationsllations
Make tessellated patterns including some
patterns with line symmetry by tracing and
moving 2-D shapes by
• Rotation
• Translation
• Reflection
Describe patternsDescribe patternsDescribe patternsDescribe patterns
Refer to lines, 2-D shapes, 3-D objects and /
or lines of symmetry and / or rotations and / or reflections and / or translations when
describing patterns
Class activityClass activityClass activityClass activity
4.54.54.54.5
TemperatureTemperatureTemperatureTemperature
Practical measuring of temperature byPractical measuring of temperature byPractical measuring of temperature byPractical measuring of temperature by
Estimating, measuring, recording,
comparing and ordering
Measuring instrumentsMeasuring instrumentsMeasuring instrumentsMeasuring instruments
Thermometers
UnitsUnitsUnitsUnits
Degrees Celsius (°C)
Calculations and problemCalculations and problemCalculations and problemCalculations and problem----solving related to solving related to solving related to solving related to
temperaturetemperaturetemperaturetemperature
Solve problems in contexts involving
temperature.
9.1.49.1.49.1.49.1.4
3.8.6.53.8.6.53.8.6.53.8.6.5
CAMI Education linked to CAPS:
Mathematicsathematicsathematicsathematics: Grade 5: Grade 5: Grade 5: Grade 5
- 19 -
Calculate temperature differences limited to
positive whole numbers.
5.15.15.15.1
Collecting and Collecting and Collecting and Collecting and
organizing dataorganizing dataorganizing dataorganizing data
• Collect data using tally marks and tables for recording
• Order data from smallest group to largest group
10.1.1.310.1.1.310.1.1.310.1.1.3
5.25.25.25.2
Representing Representing Representing Representing
datadatadatadata
Draw a varDraw a varDraw a varDraw a variety of graphs to display and iety of graphs to display and iety of graphs to display and iety of graphs to display and
interpret data including:interpret data including:interpret data including:interpret data including:
• Pictographs with a many-to-one representation
• Bar graphs
10.1.2.210.1.2.210.1.2.210.1.2.2
10.1.2.310.1.2.310.1.2.310.1.2.3
10101010.1.2.5.1.2.5.1.2.5.1.2.5
5.35.35.35.3
Analyzing, Analyzing, Analyzing, Analyzing,
interpreting and interpreting and interpreting and interpreting and reporting datareporting datareporting datareporting data
Critically read and interpret data Critically read and interpret data Critically read and interpret data Critically read and interpret data
represented in represented in represented in represented in
• Words
• Pictographs
• Bar graphs
• Pie graphs
Analyze data by answering questions Analyze data by answering questions Analyze data by answering questions Analyze data by answering questions
related to:related to:related to:related to:
• Data categories
• Data sources and contexts
Summarize data Summarize data Summarize data Summarize data verbally and in short verbally and in short verbally and in short verbally and in short
written paragraphs that include:written paragraphs that include:written paragraphs that include:written paragraphs that include:
• Drawing conclusions about the data
• Making predictions based on the data
10.1.4.210.1.4.210.1.4.210.1.4.2 10.1.4.110.1.4.110.1.4.110.1.4.1
10.3.1.110.3.1.110.3.1.110.3.1.1
2.12.12.12.1
Numeric Numeric Numeric Numeric patternspatternspatternspatterns
Investigate and extend patternsInvestigate and extend patternsInvestigate and extend patternsInvestigate and extend patterns
• Investigate and extend numeric patterns looking for relationships or
rules of patterns � Sequences involving a
constant difference or ratio
4.1.1.64.1.1.64.1.1.64.1.1.6 4.1.4.14.1.4.14.1.4.14.1.4.1
CAMI Education linked to CAPS:
Mathematicsathematicsathematicsathematics: Grade 5: Grade 5: Grade 5: Grade 5
- 20 -
� Of learner’s own creation
• Describe observed relationships or rules in learner’s own words
Input and output valuesInput and output valuesInput and output valuesInput and output values
Determine input values, output values and
rules for patterns and relationships using
flow diagrams.
Equivalent formsEquivalent formsEquivalent formsEquivalent forms
Determine equivalence of different
descriptions of the same relationship or rule
presented
• Verbally
• In a flow diagram
• By a number sentences
3.2.5.13.2.5.13.2.5.13.2.5.1 3.2.5.23.2.5.23.2.5.23.2.5.2
1.11.11.11.1
Whole numbersWhole numbersWhole numbersWhole numbers
Multiplication
Number range for calculationsNumber range for calculationsNumber range for calculationsNumber range for calculations
Multiplication of at least whole 3-digit by 1-
digit numbers
Calculation techniquesCalculation techniquesCalculation techniquesCalculation techniques
Use a range of techniques to perform and check written and mental calculations of
whole numbers including
• Estimation
• Building up and breaking down numbers
Number range for counting, ordering, Number range for counting, ordering, Number range for counting, ordering, Number range for counting, ordering,
representing and place value of digitsrepresenting and place value of digitsrepresenting and place value of digitsrepresenting and place value of digits
• Recognize the place value of digits in whole numbers to at least 6-digit
numbers
• Round off to the nearest 10, 100 or 1000
Number range for multiples and factorsNumber range for multiples and factorsNumber range for multiples and factorsNumber range for multiples and factors
• Multiples of 2-digit numbers to at least 100
1.4.2.41.4.2.41.4.2.41.4.2.4
1.4.2.51.4.2.51.4.2.51.4.2.5
1.4.3.31.4.3.31.4.3.31.4.3.3
1.4.3.41.4.3.41.4.3.41.4.3.4
1.4.4.31.4.4.31.4.4.31.4.4.3 1.4.4.41.4.4.41.4.4.41.4.4.4
1.4.6.61.4.6.61.4.6.61.4.6.6
1.4.6.71.4.6.71.4.6.71.4.6.7
3.8.3.53.8.3.53.8.3.53.8.3.5
CAMI Education linked to CAPS:
Mathematicsathematicsathematicsathematics: Grade 5: Grade 5: Grade 5: Grade 5
- 21 -
• Factors of 2-digit whole numbers to at least 100
Multiplication facts forMultiplication facts forMultiplication facts forMultiplication facts for
• Units by multiples of 10
• Units by multiples of 100
Properties of whole numbersProperties of whole numbersProperties of whole numbersProperties of whole numbers
• Recognize and use the commutative, associative and distributive properties
with whole numbers
• 1 in terms of its multiplicative property
Solving problemsSolving problemsSolving problemsSolving problems
Solve problems in contexts involving whole
numbers, including financial contexts.
Solve problems involving whole numbers,
including
• Comparing two or more quantities of the same kind (ratio)
• Comparing two quantities of different kinds (rate)
3.8.7.23.8.7.23.8.7.23.8.7.2
Term 4Term 4Term 4Term 4
Mental Mental Mental Mental
mathematicsmathematicsmathematicsmathematics
Same as Term 1Same as Term 1Same as Term 1Same as Term 1
1.11.11.11.1
Whole numbersWhole numbersWhole numbersWhole numbers
Counting,
ordering, comparing,
representing
and place value
of digits
Number range for counting, ordering, Number range for counting, ordering, Number range for counting, ordering, Number range for counting, ordering,
comparing, representing and place value of comparing, representing and place value of comparing, representing and place value of comparing, representing and place value of
digitsdigitsdigitsdigits
• Count forwards and backwards in whole number intervals up to at
least 10 000
• Order, compare and represent
numbers to at least 6-digit numbers
• Represent odd and even numbers to
at least 1 000
• Recognize the place value of digits
in whole numbers to at least 6-digit
1.1.2.71.1.2.71.1.2.71.1.2.7 1.1.2.81.1.2.81.1.2.81.1.2.8
1.7.8.41.7.8.41.7.8.41.7.8.4
1.1.10.31.1.10.31.1.10.31.1.10.3
1.1.6.101.1.6.101.1.6.101.1.6.10
1.1.8.101.1.8.101.1.8.101.1.8.10
1.1.8.51.1.8.51.1.8.51.1.8.5
CAMI Education linked to CAPS:
Mathematicsathematicsathematicsathematics: Grade 5: Grade 5: Grade 5: Grade 5
- 22 -
numbers
• Rounding off to the nearest 5, 10, 100 and 1 000
1.1.8.61.1.8.61.1.8.61.1.8.6
1.1.9.51.1.9.51.1.9.51.1.9.5
1.1.9.91.1.9.91.1.9.91.1.9.9
1.1.3.91.1.3.91.1.3.91.1.3.9
1.7.1.11.7.1.11.7.1.11.7.1.1
1.7.1.51.7.1.51.7.1.51.7.1.5
1.11.11.11.1 Whole numbersWhole numbersWhole numbersWhole numbers
Addition and
subtraction
Number range for calculationsNumber range for calculationsNumber range for calculationsNumber range for calculations Addition and subtraction of whole numbers
of at least 5 digits.
Calculation techniquesCalculation techniquesCalculation techniquesCalculation techniques
Using a range of techniques to perform and
check written and mental calculations with
whole numbers including:
• Estimation
• Building up and breaking down numbers
• Rounding off and compensating
• Doubling and halving
• Using a number line
• Using addition and subtraction as inverse operations
Number range foNumber range foNumber range foNumber range for multiples and factorsr multiples and factorsr multiples and factorsr multiples and factors
Multiples of 2-digit numbers to at least 100
Properties of whole numbersProperties of whole numbersProperties of whole numbersProperties of whole numbers
Recognize and use the commutative and
associative properties with whole numbers.
Solving problemsSolving problemsSolving problemsSolving problems
Solve problems in contexts involving whole
numbers, including financial contexts.
1.2.6.81.2.6.81.2.6.81.2.6.8
1.3.7.31.3.7.31.3.7.31.3.7.3
1.3.8.51.3.8.51.3.8.51.3.8.5
1.3.8.61.3.8.61.3.8.61.3.8.6
3.23.23.23.2 Properties of Properties of Properties of Properties of
3333----D objectsD objectsD objectsD objects
ObjectObjectObjectObjects learners need to know and name:s learners need to know and name:s learners need to know and name:s learners need to know and name:
• Rectangular prisms and other prisms
• Cubes
• Cylinders
• Cones
8.1.8.1.8.1.8.1.2.32.32.32.3
CAMI Education linked to CAPS:
Mathematicsathematicsathematicsathematics: Grade 5: Grade 5: Grade 5: Grade 5
- 23 -
• Pyramids
• Similarities and differences between
cubes and rectangular prisms
Characteristics learners use to distinguish, Characteristics learners use to distinguish, Characteristics learners use to distinguish, Characteristics learners use to distinguish,
describe, sort and compare shapesdescribe, sort and compare shapesdescribe, sort and compare shapesdescribe, sort and compare shapes
• Shape of faces
• Numbers of faces
• Flat and curved surfaces
Further activities to focus learners on Further activities to focus learners on Further activities to focus learners on Further activities to focus learners on
characteristics of objectscharacteristics of objectscharacteristics of objectscharacteristics of objects
• Create 3-D models using cut-out polygons
• Cutting open boxes to trace and describe their nets
1.21.21.21.2
Common Common Common Common
fractionsfractionsfractionsfractions
Describing and ordering fractionsDescribing and ordering fractionsDescribing and ordering fractionsDescribing and ordering fractions
• Count forwards and backwards in fractions
• Compare and order common fractions to at least twelfths
Calculations with fractionsCalculations with fractionsCalculations with fractionsCalculations with fractions
• Addition of common fractions with the same denominator
• Addition and subtraction of mixed numbers
• Fractions of whole numbers which result in whole numbers
• Recognize, describe and use the equivalence of division and fractions
Solving problemsSolving problemsSolving problemsSolving problems Solve problems in contexts involving
common fractions, including grouping and
sharing.
Equivalents formsEquivalents formsEquivalents formsEquivalents forms
Recognize and use equivalent forms of
common fractions with denominators which
2.1.3.12.1.3.12.1.3.12.1.3.1
2.1.3.22.1.3.22.1.3.22.1.3.2
2.1.4.32.1.4.32.1.4.32.1.4.3
2.1.4.52.1.4.52.1.4.52.1.4.5
2.1.4.62.1.4.62.1.4.62.1.4.6 2.1.5.22.1.5.22.1.5.22.1.5.2
2.1.5.52.1.5.52.1.5.52.1.5.5
2.2.2.2.2.2.2.2.1.11.11.11.1
2.2.1.22.2.1.22.2.1.22.2.1.2
2.2.1.32.2.1.32.2.1.32.2.1.3
2.2.1.42.2.1.42.2.1.42.2.1.4
2.2.2.32.2.2.32.2.2.32.2.2.3
2.2.3.32.2.3.32.2.3.32.2.3.3 2.2.3.12.2.3.12.2.3.12.2.3.1
2.2.5.72.2.5.72.2.5.72.2.5.7
3.4.5.23.4.5.23.4.5.23.4.5.2
3.4.5.33.4.5.33.4.5.33.4.5.3
3.4.5.43.4.5.43.4.5.43.4.5.4
3.4.5.53.4.5.53.4.5.53.4.5.5
3.4.5.63.4.5.63.4.5.63.4.5.6
3.4.5.73.4.5.73.4.5.73.4.5.7 3.4.5.83.4.5.83.4.5.83.4.5.8
3.4.6.23.4.6.23.4.6.23.4.6.2
3.4.3.4.3.4.3.4.6.36.36.36.3
CAMI Education linked to CAPS:
Mathematicsathematicsathematicsathematics: Grade 5: Grade 5: Grade 5: Grade 5
- 24 -
are multiples of each other.
3.4.6.43.4.6.43.4.6.43.4.6.4
1.11.11.11.1
Whole numbersWhole numbersWhole numbersWhole numbers
Division
Number range for calculationsNumber range for calculationsNumber range for calculationsNumber range for calculations
Division of at least whole 3-digit by 2-digit
numbers
Calculation techniquesCalculation techniquesCalculation techniquesCalculation techniques
Use a range of techniques to perform and
check written and mental calculations with whole numbers including:
• Estimation
• Building up and breaking down numbers
Number range for counting, ordering and Number range for counting, ordering and Number range for counting, ordering and Number range for counting, ordering and
representing, and place value of digitsrepresenting, and place value of digitsrepresenting, and place value of digitsrepresenting, and place value of digits
• Recognize the place value of digits in whole numbers to at least 6-digit
numbers
• Round off to the nearest 10, 100 and 1 000
Number range for multiples and factorsNumber range for multiples and factorsNumber range for multiples and factorsNumber range for multiples and factors
• Multiples of 2-digit numbers to at
least 100
• Factors of 2-digit whole numbers to
at least 100
Multiplication factsMultiplication factsMultiplication factsMultiplication facts
• Units by multiples of 10
• Units by multiples of 100
PropPropPropProperties of whole numberserties of whole numberserties of whole numberserties of whole numbers
• Recognize and use the commutative, associative and distributive properties
of whole numbers
• 1 in terms of its multiplicative property
Solving problemsSolving problemsSolving problemsSolving problems
1.5.1.71.5.1.71.5.1.71.5.1.7
1.5.1.101.5.1.101.5.1.101.5.1.10
1.5.5.11.5.5.11.5.5.11.5.5.1
1.5.5.21.5.5.21.5.5.21.5.5.2
1.5.5.31.5.5.31.5.5.31.5.5.3
1.5.5.41.5.5.41.5.5.41.5.5.4 1.5.5.51.5.5.51.5.5.51.5.5.5
1.5.5.61.5.5.61.5.5.61.5.5.6
1.5.7.11.5.7.11.5.7.11.5.7.1
1.5.7.21.5.7.21.5.7.21.5.7.2
1.5.7.31.5.7.31.5.7.31.5.7.3
1.5.8.11.5.8.11.5.8.11.5.8.1
3.5.5.33.5.5.33.5.5.33.5.5.3 3.8.2.63.8.2.63.8.2.63.8.2.6
3.1.4.33.1.4.33.1.4.33.1.4.3
CAMI Education linked to CAPS:
Mathematicsathematicsathematicsathematics: Grade 5: Grade 5: Grade 5: Grade 5
- 25 -
Solve problems in contexts involving whole
numbers, including financial contexts
Solve problems involving whole numbers, Solve problems involving whole numbers, Solve problems involving whole numbers, Solve problems involving whole numbers,
including:including:including:including:
• Comparing two or more quantities of the same unit (ratio)
• Comparing two quantities of different kinds (rate)
• Grouping and equal sharing with remainders
3.8.7.23.8.7.23.8.7.23.8.7.2
4.64.64.64.6
Perimeter, area Perimeter, area Perimeter, area Perimeter, area and volumeand volumeand volumeand volume
PerimeterPerimeterPerimeterPerimeter
Measure perimeter using rules or measuring tapes.
Measurement of areaMeasurement of areaMeasurement of areaMeasurement of area
Find areas of regular and irregular shapes by
counting squares on grids in order to
develop an understanding of square units.
Measurement of volumeMeasurement of volumeMeasurement of volumeMeasurement of volume Find volume / capacity of objects by
packing or filling them in order to develop
an understanding of cubic units.
9.3.1.39.3.1.39.3.1.39.3.1.3
9.3.1.59.3.1.59.3.1.59.3.1.5
9.3.2.19.3.2.19.3.2.19.3.2.1
9.3.2.39.3.2.39.3.2.39.3.2.3
9.3.2.49.3.2.49.3.2.49.3.2.4
9.5.1.39.5.1.39.5.1.39.5.1.3
3.63.63.63.6
Position and Position and Position and Position and
movementmovementmovementmovement
Location and directionLocation and directionLocation and directionLocation and direction
Locate position of objects / drawings/
symbols on a grid using alpha-numeric grid
references.
Locate positions of objects on a map using
alpha-numeric grid references.
Follow directions to trace a path between
positions on a map.
9.6.1.19.6.1.19.6.1.19.6.1.1
9.6.1.29.6.1.29.6.1.29.6.1.2
9.6.1.39.6.1.39.6.1.39.6.1.3
3.43.43.43.4
TransformationsTransformationsTransformationsTransformations
Use transformations to create composite Use transformations to create composite Use transformations to create composite Use transformations to create composite
shapesshapesshapesshapes
Make composite 2-D shapes including
shapes with line symmetry by tracing and
Class activityClass activityClass activityClass activity
CAMI Education linked to CAPS:
Mathematicsathematicsathematicsathematics: Grade 5: Grade 5: Grade 5: Grade 5
- 26 -
moving a 2-D shape in one or more of the
following ways:
• By rotation
• By translation
• By reflection
Use transformations to make tessellationsUse transformations to make tessellationsUse transformations to make tessellationsUse transformations to make tessellations
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
Describe patternsDescribe patternsDescribe patternsDescribe patterns
Refer to lines, 2-D shapes, 3-D objects and /
or lines of symmetry and / or rotations and
/ or reflections and / or translations when describing patterns
2.22.22.22.2
Geometric Geometric Geometric Geometric
patternspatternspatternspatterns
Investigate and extend patternsInvestigate and extend patternsInvestigate and extend patternsInvestigate and extend patterns
• Investigate and extend geometric patterns looking for relationships or
rules of patterns:
� Represented in physical or
diagram form
� Sequences involving a
constant difference or ratio
� Of learner’s own words
Input and output valuesInput and output valuesInput and output valuesInput and output values
Determine input values, output values and
rules for the patterns and relationships using
flow diagrams.
Equivalent formsEquivalent formsEquivalent formsEquivalent forms
Determine equivalence of different descriptions of the same relationship or rule
presented
• Verbally
CAMI Education linked to CAPS:
Mathematicsathematicsathematicsathematics: Grade 5: Grade 5: Grade 5: Grade 5
- 27 -
• In a flow diagram
• By a number sentence
4.1.1.74.1.1.74.1.1.74.1.1.7
3.2.6.23.2.6.23.2.6.23.2.6.2
2.32.32.32.3
Number Number Number Number sentencessentencessentencessentences
(Introduction to
algebraic
expressions)
Number sentencesNumber sentencesNumber sentencesNumber sentences
• Write number sentences to describe problem situations
• Solve and complete number sentences by:
� Inspection
� Trial and improvement
• Check solution by substitution
3.5.6.23.5.6.23.5.6.23.5.6.2 3.5.6.33.5.6.33.5.6.33.5.6.3
5.25.25.25.2
ProbabilityProbabilityProbabilityProbability
Perform simple repeated events and list
possible outcomes for events such as
• Tossing a coin
• Rolling a die
• Spinning a spinner
Count and compare the frequency of actual
outcomes for a series of trials up to 20
trials.
10.2.1.310.2.1.310.2.1.310.2.1.3
10.2.1.410.2.1.410.2.1.410.2.1.4