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 6digit 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 6digit 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 3digit by 2digit numbers 



3.3. Division of at least whole 3digit by 2digit 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 2digits whole numbers to at least 100 



5.2. Factors of 2digit 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



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 2D SHAPES




1. Range of shapes 



1.2. Recognize visualize and name 2D 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 2D 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 2D shapes on grid paper 


4. Angles 



4.1. Recognize and describe angles in 2D shapes:
 Right angles
 Angles smaller than right angle
 Angles greater than right angles


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 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 3D objects in terms of
 Shape of faces
 Number of faces
 Flat and curved surfaces



3. Further activities 



3.1. Make 3D 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 2D shapes including shapes with line symmetry by tracing and moving a 2D 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 2D shapes in one or more of the following ways
 By rotation
 By translation
 By reflection



3. Describe patterns 



3.1. 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 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 alphanumeric grid references 



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



1.3. Follows directions to trace a path between positions 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 limited to whole numbers and common fractions 

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, kitchen scales 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 limited to examples with whole numbers and fractions


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 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 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. 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 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. 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 (manytoone 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. 
