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 12 x 12. 



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 Order, compare and represent numbers to at least 9digit numbers 



2.2. Represent prime numbers to at least 100 



2.3. Recognizing the place value of digits in whole numbers to at least 9digit numbers. 



2.4. Round off to the nearest 5, 10, 100, 1 000, 100 000 and 1 000 000 


3. Number range for calculations: 



3.1. Addition and subtraction of whole numbers of at least 6 digits 



3.2. Multiplication of at least whole 4digit by 3digit numbers 



3.3. Division of at least whole 4digit by 3digit numbers 



3.4. Multiple operations on whole numbers with or without brackets 


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. estimation4.1.2. adding, subtracting and multiplying in columns
4.1.3. long division
4.1.4. building up and breaking down numbers
4.1.5. rounding off and compensating
4.1.6 using addition and subtraction as inverse operations
4.1.7. using multiplication and division as inverse operations
4.1.8. using a calculator 


5. Number range for multiples and factors 



5.1. Multiples of 2digit and 3digit numbers 



5.2. Factors of 2digit and 3digit whole numbers 



5.3. Prime factors of 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 and decimal fractions, including :Financial contextsMeasurement 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. Compare and order common fractions, including tenths and hundredths 


2. Calculations with fractions: 



2.1.1. Addition and subtraction of common fractions in which one denominator is a multiple of another 



2.1.2. Addition and subtraction of mixed numbers 



2.1.3. Fractions of whole numbers 


3. Solving problems 



3.1. Solve problems in contexts involving common fractions, including grouping and sharing 


4. Percentages 



4.1. Find percentages of whole numbers 


5. Equivalent forms 



5.1. Recognize and use equivalent forms of common fractions with 1digit or 2digit denominators (fractions in which one denominator is a multiple of another) 



5.2. Recognize equivalence between common fraction and decimal fraction forms of the same number 



5.3. Recognize equivalence between common fraction, decimal fraction and percentage forms of the same number. 

DECIMAL FRACTIONS



1. Recognizing, ordering and place value of decimal fractions 



1.1. Count forwards and backwards in decimal fractions to at least two decimal places 



1.2. Compare and order decimal fractions to at least two decimal places 



1.3. Place value of digits to at least two decimal places 


2. Calculations with decimal fractions 



1.2. Addition and subtraction of decimal fractions with at least two decimal places 



2.2. Multiply decimal fractions by 10 and 100 


3. Solving problems 



1.1. Solve problems in context involving decimal fractions 


4. Equivalent forms 



4.1. Recognize equivalence between common fraction and decimal fractions forms of the same number 



4.2. Recognize equivalence between common fraction, decimal fraction and percentage forms of the same number. 

PATTERNS, FUNCTIONS AND ALGEBRA


NUMERIC PATTERNS



1. Investigate and extend patterns 



1.1. Investigate and extent numeric patterns looking for relationships of rules of patterns1.1.1. sequences not limited to a constant difference or ratio1.1.2. of learner’s own creation
1.1.3. represented in tables 



1.2. Describe the general rules for the observes relationships 


2. Input and output values 



2.1. Determine input values, output values and rules for the patterns and relationships using



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
 Represented in tables




1.2. Describe the general rules for the observes relationships 


2. Input and output values 



2.1. Determine input values, output values and rules for the patterns and relationships using



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


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 2D SHAPES



1. Range of shapes 



1.1. Recognize visualize and name 2D shapes in the environment and geometric settings, focusing on
 Regular and irregular polygons – triangles, squares, rectangles, parallelograms, other quadrilaterals, pentagons, hexagons, heptagons, octagons
 Circles
 Similarities and differences between rectangles and parallelograms



2. Characteristics of shapes 



2.1. Describe, sort and compare 2D shapes in terms of
 Number of sides
 Lengths of sides
 Sizes of angles
 Acute
 Right
 Obtuse
 Straight
 Reflex
 Revolution



3. Further activities 



3.1. Draw 2D shapes on grid paper 



3.2. Draw circles, patterns in circles and patterns with circles using a pair of compasses 


4. Angles 



4.1. Recognize and name the following angles in 2D shapes:
 Acute
 Right
 Obtuse
 Straight
 Reflex
 Revolution


PROPERTIES OF 3D OBJECTS



1. Range of objects 



1.1. Recognize, visualize and name 3D objects in the environment and geometric settings, focusing on
 Rectangular prisms
 Cubs
 Tetrahedrons
 Pyramids
 Similarities and differences between tetrahedrons and other pyramids



2. Characteristics of objects 



2.1. Describe, sort and compare 3D objects in terms of
 Number and shape of faces
 Number of vertices
 Number of edges



3. Further activities 



3.1. Make 3D models using:
 Drinking straws, toothpicks etc
 Nets


SYMETRY



1. Symmetry 



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

TRANSFORMATIONS



1. Enlarge and reductions 



1.1. Draw enlargement and reductions of 2D shapes to compare size and shape of



2. Describe patterns 



1.1. Refer to lines, 2D shapes, 3D objects, lines of symmetry, rotations, reflections and translations when describing patterns
 In nature
 From modern everyday life
 From our cultural heritage


VIEWING OF OBJECTS



1. Position and views 



1.1. Links the position of viewer to views of:
 Single everyday objects or collections of objects
 Single or composite geometric objects


POSITION AND MOVEMENT



1. Location and directions 



1.1. Locate position of objects, drawings or symbols on a grid with alphanumeric grid references 



1.2. Locate positions of objects on a map by using alphanumeric grid references 



1.3. Give directions to move between positions or places on a map 

MEASUREMENT


LENGTH



1. Practical measuring of 2D shapes and 3D 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 problemsolving 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 should include common fraction and decimal fractions to 2 decimal places 

MASS



1. Practical measuring of 3D objects by 



1.1. Estimating 



1.2. Measuring 



1.3. Recording 



1.4. Comparing and ordering 


2. Measuring instruments: 



2.1. bathroom scales (analogue and digital), kitchen scales, (analogue and digital) and balances 


3. Units 



3.1. grams (g) and kilograms (kg) 


4. Calculations and problemsolving involving mass include: 



4.1. problems in contexts involving mass 



4.2. converting between grams and kilograms 



4.3. conversions should include fraction and decimal forms (to 2 decimal places) 

CAPACITY / VOLUME



1. Practical measuring of 3D objects by 



1.1. estimating 



1.2. measuring 



1.3. recording 



1.4. comparing and ordering 


2. Measuring instruments 



2.1. measuring jugs 


3. Units 



3.1. millilitres (ml) litres (ℓ) and kilolitres (kl) 


4. Calculations and problem solving involving capacity/volume include: 



4.1. problems in contexts involving capacity/volume 



4.2. converting between kilolitres, litres and millilitresConversions should include fraction and decimal forms (to 2 decimal places) 

TIME



1. Reading time and time instruments 



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




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. Reading time zone maps and calculating time differences based on time zones 



3.3. Calculation of time intervals where time is given in
 Seconds andor minutes
 Minutes and/or hours
 Hours and/or days
 Days, weeks and/or months
 Years and/or decades
 Centuries, decades and/or years



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 (analogue and digital) 


3. Units 



3.1. degrees Celsius 



4. Calculations in problemsolving 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. Continue to find areas of regular and irregular shapes by counting squares on grids 



2.2. Develop rules for calculating the areas of squares and rectangles 


3. Measurement of volume 



3.1. Continue to find volume/capacity of objects by packing or filing them 



3.2. Develop an understanding of why the volume of rectangular prisms is given by length multiplied by width multiplied by height. 



3.3. Investigate relationship between perimeter and area of rectangles and squares 



3.4. Investigate relationship between surface area and volume of rectangular prisms 

HISTORY OF MEASUREMENT



1. Know some ways in which people measured and recorded measurement in the past 

DATA HANDLING


COLLECTING AND ORGANISING DATA



1. Collect data 



1.1. using tally marks and tables for recording 



1.2. using simple questionnaires (yes/no type response) 


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 (manytoone correspondence) 



1.2. bar graphs and double bar graphs 

INTERPRETING DATA



1. Interpreting data 



1.1. Critically read and interpret data represented in:1.1.1. Words1.1.2. Pictographs
1.1.3. Bar graphs
1.1.4. Double bar graphs
1.1.5. Pie charts 


2. Analysing data 



2.1. Analyse data by answering questions related to:2.1.1. data categories, including data intervals2.1.2. data sources and contexts
2.1.3. central tendencies – (mode and median) 


3. Reporting data 



3.1. Summarise data verbally and in short written paragraphs that includes3.1.1. drawing conclusions about the data3.1.2. making predictions based on the data 


4. Ungrouped data 



4.1. Examine ungrouped numerical data to determine4.1.1. the most frequently occurring score in the data set (mode)4.1.2. the middlemost score in the data set (median) 

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 50 trials. 
