Subject Overview

Content

• Sustainable management of natural resources
• Social Sustainability in Cities, the Role of Citizens, living together in social groups
• Population Dynamics & Migration in High income, middle income, and low-income countries e.g., Germany, China, India, USA, Mali (BW 3.1.1, BW 3.1.1.4)
• Nexus Thinking (e.g., Poverty, Food Security, Global Pandemics/Disease)
• Population Growth – Immigration Challenges (BW 3.1.1, BW 3.1.1.4)
• Peace Treaties – Congress of Vienna and the Treaty of Versailles (BW 3.2.4, BW 3.2.6)
• European Union (BW 3.3.2, BW 3.2.2.2)
• Rights/Protest (e.g., US Civil Rights Movement (early and modern), South African Apartheid, Anti-Apartheid movements (internal, external)) (BW 3.1.2.3)
• Economics, Globalization and Cultures (BW 3.1.1.2)
• Economic agents, their interests and role in the economy: consumers, producers, governments, banks

Skills

Knowledge and Understanding

• Use and interpret a range of discipline-specific terms and symbols.
• Demonstrate substantial knowledge and understanding of content and concepts through descriptions, explanations, and examples.

Investigation

• Develop research questions and justify their relevance.
• Develop action plans and evaluate their use.
• Identify sources.
• Gather and organize relevant information to formulate an argument.
• Collect, record, and verify data.
• Evaluate the process and results of one’s investigation.

Communication

• Create MLA references and citations, use footnotes/endnotes, and construct a bibliography according to recognized conventions.
• Use appropriate forms of writing for different purposes and audiences with appropriate structure.

Critical Thinking

• Consider ideas from multiple perspectives through inquiry; identify the author’s point of view in a passage; recognize unstated assumptions and bias; discuss concepts, issues, models, and theories.
• Evaluate and select information sources and digital tools based on their appropriateness to specific tasks.
• Analyze concepts, issues, models, visual representations, and/or theories.
• Analyze a range of sources/data in terms of origin and purpose, recognizing value and limitations.
• Recognize different perspectives and explain their implications.

Content

Numbers and Number Systems

• Introduction to various forms of numbers
• Basic understanding of number systems

Estimation and Counting

• Estimating groups up to five
• Exploring counting methods and quantities

Measurement

• Introduction to non-standard units of measurement
• Understanding time as a unit of measurement

Mathematical Vocabulary

• Introducing basic terms and language used in mathematics

Data Handling

• Introduction to collecting data
• Understanding and interpreting basic data collections

Geometry

• Identifying basic 2D shapes
• Understanding positional language

Problem Solving

• Introduction to mathematical problem-solving methods and approaches

Skills

Numeracy Skills

• Using number words and numerals to represent quantities in real-life situations
• Counting with and without the aid of physical objects

Comparison

• Recognizing and comparing sets or quantities to determine if they’re equal, more, or less than another set
• Using language terms like “first” and “last” to determine positions

Addition and Subtraction Concepts

• Relating addition to combining objects and subtraction to taking objects away
• Basic understanding of one-to-one correspondence

Geometric Understanding

• Describing and organizing shapes based on their properties

Temporal Skills

• Identifying events using temporal terms
• Sequencing events in order

Data Interpretation

• Collecting and organizing information to derive meaning
• Describing data and understanding basic data representations

Content

Numbers and Number Systems

• Introduction to forms of numbers
• Basic understanding of number systems

Estimation and Counting

• Estimating groups of objects
• Introduction to fractional parts in making a whole

Measurement

• Exploring non-standard units of measurement
• Delving deeper into time as a unit of measurement

Mathematical Vocabulary

• Further enhancing basic terms and language used in mathematics

Data Handling

• Introduction to data collection
• Recognizing and naming basic 2D shapes

Geometry

• Enhancing understanding of positional language

Problem Solving

• Using mathematical approaches to solve basic problems

Skills

Numeracy Skills

• Using number words and numerals to represent real-life quantities
• Estimating objects up to five
• Rote counting up to 20 without objects

Comparison and Quantity Judgement

• Recognizing sets or quantities and determining if they’re equal to, more than, or less than another set
• Understanding position with terms like “first” and “last”

Basic Arithmetic Concepts

• Modeling simple joining and separating of whole numbers
• Relating addition to the combination of objects and subtraction to taking objects away

Geometric and Spatial Understanding

• Describing and categorizing shapes based on their properties
• Recognizing events and sequencing them

Data Interpretation

• Collecting and understanding information to grasp the world around
• Organizing and interpreting data collections

Problem-Solving Skills

• Identifying and analyzing problems

Content

Numbers and Number Systems

• Deepening understanding of forms of numbers and number systems
• Enhancing the application of mathematical language

Basic Arithmetic

• Concepts of addition and subtraction with the integration of number lines

Estimation and Evaluation

• Building proficiency in estimating and evaluating sets of objects
• Introducing the concept of fractions

Measurement

• Grasping non-standard units of measurement
• Understanding time as a measure

Patterns and Geometry

• Recognizing and describing patterns
• Identifying and categorizing 2D shapes

Data Interpretation

• Introduction to data handling, sampling techniques, and graphical representations

Spatial Understanding

• Grasping concepts related to space and position

Probability

• Basic understanding of probability and chance events.

Skills

Numeracy Skills

• Identifying and vocalizing numbers from 0 to 30
• Counting objects in a set
• Comparison of quantities using terms like “more,” “less,” “first,” “equals,” etc.

Arithmetic Skills

• Employing ordinal numbers in real scenarios
• Modeling subtraction using objects and writing number sentences
• Solving basic arithmetic problems using number lines

Estimation and Measurement

• Estimating quantities in a set of 20 or less
• Recognizing quantities without counting (subitizing)
• Exploring fractions in daily scenarios
• Comparing objects using comparative terms
• Measuring with non-standard units

Time and Sequence

• Sequencing events and understanding measurement instruments like clocks
• Reading time in both digital and analog formats

Classification and Patterns

• Sorting objects based on attributes
• Recognizing patterns in everyday scenarios

Geometric and Spatial Understanding

• Identifying common 2D shapes
• Using positional language to place and describe objects

Data Interpretation

• Collecting and organizing data
• Using tally marks for data representation

Probability

• Estimating the likelihood of events

Content

Numbers and Number Sense

• Introduction to numbers up to 100
• Basic number lines

Estimation and Counting

• Estimating numbers in a group of 100 or less
• Counting to evaluate the reasonableness of the estimate

Fractions and Parts of a Whole

• Introduction to halves, thirds, and fourths
• Recognizing these fractions in different contexts

Measurement

• Exploring non-standard units of measurement
• Comparing and ordering objects based on length, capacity, and mass

Time and Calendar

• Months of the year, weeks, and days
• Telling time using digital and analogue clocks

Patterns and Functions

• Recognizing, creating, and explaining repeating patterns
• Completing basic number sentences using addition or subtraction

Geometry

• Introduction to 2D and 3D shapes
• Classifying shapes based on properties

Position and Direction

• Understanding positional words (up/down, left/right)
• Basic introduction to directions (North, East, South, West)

Data Handling

• Collecting, organizing, and interpreting data
• Introduction to data display methods (tallies, tables, bar graphs)

Probability

• Understanding chance in daily events
• Predicting outcomes based on simple data

Skills

Numeracy Skills

• Reading, writing, and comparing numbers
• Decomposing numbers
• Estimating and counting objects in groups

Fractional Understanding

• Identifying basic fractions as part of a whole or group using models

Measurement Skills

• Using non-standard units of measurement in real-life scenarios
• Identifying and using standard units of measurement
• Identifying measurement tools

Time Management

• Recognizing the sequence of days, weeks, months, and understanding the calendar
• Telling time to specific intervals (e.g., half and quarter hours)
• Telling time on analog and digital clocks

Pattern Recognition

• Classifying objects based on attributes
• Understanding and creating repeating patterns

Geometric Understanding

• Naming, sorting, and sketching 2D shapes
• Identifying, classifying, and drawing 3D shapes
• Describing locations and movements using positional terms

Data Handling and Interpretation

• Organizing and interpreting data in various formats
• Displaying data using graphs
• Predicting outcomes based on collected data

N1.1.(NPV). Number and Place Value (NPV)

• Count within 100, forwards and backwards, starting with any number
• Reason about the location of numbers to 20 within the linear number system, including comparing using <, >, and =

N1.2.(NF). Number Facts

• Develop fluency in addition and subtraction facts within 10
• Count forwards and backwards in multiples of 2, 5, and 10, up to 10 multiples, beginning with any multiple, and count forwards and backwards through the odd numbers

N1.3.(AS). Addition and Subtraction

• Compose numbers to 10 from 2 parts, and partition numbers to 10 into parts, including recognising odd and even numbers
• Read, write, and interpret equations containing addition (+), subtraction (-), and equals (=) symbols, and relate additive expressions and equations to real-life contexts

N1.6.(G). Geometry

• Recognise common 2D and 3D shapes presented in different orientations, and know that rectangles, triangles, cuboids, and pyramids are not always similar to one another
• Compose 2D and 3D shapes from smaller shapes to match an example, including manipulating shapes to place them in particular orientations

N1.7.(CT). Command Terms

N1.8.(MAP). MAP Testing Relevant Practice

• (n/a)

Content

Number and Arithmetic

• Understanding forms of numbers and number systems
• Mastery of basic arithmetic operations: addition, subtraction, multiplication, and division
• Application of arithmetic in problem-solving and estimation

Advanced Number Concepts

• Dive into fractions, decimals, ratios, and proportions

Measurement and Time

• Grasping concepts of measurement using different units
• Time as a tool of measurement

Algebra and Patterns

• Introduction to basic algebraic concepts
• Recognizing and describing patterns

Geometry

• Exploring the world of shapes and coordinate geometry
• Introduction to symmetry

Data and Probability

• Fundamental skills in data handling
• Basic understanding of statistics, probability, sampling techniques, and graphical representation

Skills

Numeracy Skills

• Mastery of numbers up to 1000: reading, writing, comparing, and ordering
• Advanced understanding of place value
• Subtracting 2-digit numbers using various methods, including regrouping
• Mental arithmetic skills for simple addition and subtraction

Arithmetic Proficiency

• Modeling multiplication as repeated addition with quick recall for certain multiplication tables
• Familiarity with division through sharing and repeated subtractions
• Using models and number lines for arithmetic problem-solving

Measurement and Estimation

• Rounding numbers and analyzing their reasonableness
• Mastery of measurement using standard units
• Telling time accurately using different types of clocks

Geometric Understanding

• Classifying objects by multiple attributes
• Recognizing and sketching 2D shapes and regular polygons
• Identifying points on a grid using ordered pairs
• Grasping properties of reflective symmetry

Data Interpretation

• Gathering data using various methods
• Organizing and interpreting structured data
• Displaying data through various graphical methods

Probability

• Identifying and describing chance events in daily scenarios

N2.1.(NPV). Number and Place Value (NPV)

• Recognize the place value of each digit in two-digit numbers, and compose and decompose two-digit numbers using standard and non-standard partitioning
• Reason about the location of any two-digit number in the linear number system, including identifying the previous and next multiple of 10

N2.2.(NF). Number Facts

• Secure fluency in addition and subtraction facts within 10, through continued practice

N2.3.(AS). Addition and Subtraction

• Add and subtract across 10
• Recognize the subtraction structure of ‘difference’ and answer questions of the form, “How many more…?”
• Add and subtract within 100 by applying related one-digit addition and subtraction facts: add and subtract only ones or only tens to/from a two-digit number
• Add and subtract within 100 by applying related one-digit addition and subtraction facts: add and subtract any two 2-digit numbers

N2.4.(MD). Multiplication and Division

• Recognize repeated addition contexts, representing them with multiplication equations and calculating the product within the 2, 5, and 10 multiplication tables
• Relate grouping problems where the number of groups is unknown to multiplication equations with a missing factor, and to division equations (quotitive division)

N2.5.(F). Fractions

N2.6.(G). Geometry

• Use precise language to describe the properties of 2D and 3D shapes, and compare shapes by reasoning about similarities and differences in properties

N2.8.(MAP) MAP Testing Relevant Practice:

• n/a

Content

Number Concepts

• Deep dive into number forms and understanding of number systems.
• A study of fractions, decimals, ratios, and proportions.

Arithmetic Operations

• Advanced arithmetic, encompassing addition and subtraction of both whole and part numbers.
• Mastery of multiplication and division, building upon the foundation set in the previous grades.

Measurement and Estimation

• A thorough understanding of units of measurement.
• Mastery of time, its units, and applications.

Geometrical Concepts

• Studies of shapes and angles.
• Understanding perimeter and area.

Advanced Topics

• Introduction to algebraic concepts.
• Exploring patterns and their relevance in mathematical operations.

Skills

Numeracy Proficiency

• Recognition of ancient number systems from different cultures/periods.
• Ability to read, write, and compare numbers up to 10,000 and beyond.
• Advanced understanding of the place value of 4-digit numbers.
• Enhanced skills in subtracting whole numbers using various methods, including regrouping.

Multiplication and Division

• Deepening understanding of multiplication as repeated addition, arrays, and skip counting.
• Confidence and accuracy when multiplying and dividing numbers.
• Skills to multiply by tens and hundreds and divide 2-digit whole numbers without remainders.

Measurement and Time

• Ability to count, write, and comprehend money amounts in different formats.
• Proficiency in using different measurement units and tools.
• Accurate reading of measurements from various scales.
• Advanced skills in time management and reading different types of clocks.

Estimation and Rounding

• Expertise in estimating quantities, sums, and differences in real-world scenarios.
• Rounding numbers to the nearest tens and hundreds with increasing skill.

Geometrical Understanding

• Explore geometry, identifying different shapes and angles.
• Calculating area and perimeter.

Fractional Understanding

• A deepening understanding of fractions, their interpretations, and applications.
• Identifying equivalent fractions and working with fractions with sums equal to one whole.

Pattern Recognition

• Ability to identify and describe patterns and their underlying rules.

N3.1.(NPV). Number and Place Value (NPV)

• Know that 10 tens are equivalent to 1 hundred, and that 100 is 10 times the size of 10; apply this to identify and work out how many 10s there are in other three-digit multiples of 10.
• Recognise the place value of each digit in three-digit numbers, and compose and decompose three-digit numbers using standard and non-standard partitioning.
• Reason about the location of any three-digit number in the linear number system, including identifying the previous and next multiple of 100 and 10.

N3.2.(NF). Number Facts

• Secure fluency in addition and subtraction facts that bridge 10, through continued practice.
• Recall multiplication facts, and corresponding division facts, in the 10, 5, 2, 4, and 8 multiplication tables, and recognise products in these multiplication tables as multiples of the corresponding number.
• Apply place-value knowledge to known additive and multiplicative number facts (scaling facts by 10).

N3.3.(AS). Addition and Subtraction

• Calculate complements to 100.
• Add and subtract up to three-digit numbers using columnar methods.
• Manipulate the additive relationship:
  • Understand the inverse relationship between addition and subtraction, and how both relate to the part–part–whole structure.
  • Understand and use the commutative property of addition, and understand the related property for subtraction.

N3.4.(MD). Multiplication and Division

• Apply known multiplication and division facts to solve contextual problems with different structures, including quotative and partitive division.

N3.5.(F). Fractions

• Interpret and write proper fractions to represent 1 or several parts of a whole that is divided into equal parts.
• Find unit fractions of quantities using known division facts (multiplication tables fluency).
• Reason about the location of any fraction within 1 in the linear number system.
• Add and subtract fractions with the same denominator, within 1.

N3.6.(G). Geometry

• Recognise right angles as a property of shape or a description of a turn, and identify right angles in 2D shapes presented in different orientations.
• Draw polygons by joining marked points, and identify parallel and perpendicular sides.

N3.4.(MD). Multiplication and Division

• Apply known multiplication and division facts to solve contextual problems with different structures, including quotative and partitive division.

N3.5.(F). Fractions

• Interpret and write proper fractions to represent 1 or several parts of a whole that is divided into equal parts.
• Find unit fractions of quantities using known division facts (multiplication tables fluency).
• Reason about the location of any fraction within 1 in the linear number system.
• Add and subtract fractions with the same denominator, within 1.

N3.6.(G). Geometry

• Recognise right angles as a property of shape or a description of a turn, and identify right angles in 2D shapes presented in different orientations.
• Draw polygons by joining marked points, and identify parallel and perpendicular sides.

Content

Numerical Foundations

• Deep dive into various forms of number and number systems, including understanding Roman numerals.
• Advanced place value explorations with emphasis on understanding 5-digit numbers.

Basic Operations

• Advanced techniques in addition and subtraction, especially involving decimals.
• Mastery in multiplication and division, reinforcing and extending the range of calculations.

Fractional and Decimal Understanding

• Dive deeper into fractions and decimals with emphasis on real-life applications and comparisons.
• Introduction to factors and multiples, leading to recognition of prime and composite numbers.

Advanced Numerical Concepts

• Estimation techniques for real-life situations.
• Introductory lessons on ratio and proportion.
• Introduction to exponents and their applications.

Measurement

• Advanced lessons in measurement and understanding different units of measurement.
• Explorations into capacity, volume, and mass, including conversions.
• Mastery of time, involving calculations and understanding durations.

Algebraic Foundations

• Introductory algebra concepts.
• Recognition and creation of patterns using various representations.

Geometrical Concepts

• Introduction to geometry fundamentals and basic trigonometry.
• Advanced studies on shapes, angles, perimeter, and area.
• Mastery in metric conversion for various units of measurement.

Coordinate Geometry and Transformations

• Introduction to the coordinate plane and basic operations.

Data Management and Probability

• Lessons on graphing, data handling, sampling techniques, and graphical representation.
• Introductory lessons on probability, leading to understanding chances and predictions.

Skills

N4.8.(MAP) MAP Testing Relevant Practice:
n/a

Content

Numerical Foundations

• Comprehensive study of number forms and the evolution of number systems.
• Advanced studies in addition and subtraction with emphasis on diverse place values.
• Mastery in understanding the place value system, especially in decimals.

Factors, Multiples, and Estimation

• A deeper dive into factors and multiples, emphasizing the understanding of HCF and LCM.
• Mastery in estimation techniques, focusing on real-world applications.

Fractional & Decimal Understanding

• Advanced studies in fractions, ratio, and proportion.
• Dive deeper into decimal studies, understanding tenths, hundredths, and thousandths.

Advanced Numerical Concepts

• Extended lessons on exponents and roots.
• Exploration of patterns through pattern and function.

Measurement and Conversions

• Advanced concepts in measurement using standard units.
• Emphasis on understanding and applying metric conversions in real-world situations.
• Mastery of time concepts, ensuring full understanding of 12 and 24-hour clocks.

Geometry and Space

• Explorations into geometrical elements, including shapes, angles, and triangle properties.
• Introductory trigonometry.
• Advanced studies in perimeter, area, and volume.

Coordinate Geometry and Transformations

• Further studies on the coordinate plane and locating positions.
• Understanding geometric transformations, such as translations, reflections, rotations, and enlargements.

Statistics, Data, and Probability

• Lessons on statistics, data handling, graphing, and data sampling techniques.
• Introduction to graphical representation with emphasis on various graph forms.
• Mastery of probability concepts, focusing on predictions, experiments, and interpretations.

Skills

In Grade-5 Mathematics, Students Will:

• Be adept in comparing and operating on whole numbers, fractions, and decimals.
• Master addition and subtraction techniques, especially with diverse place values.
• Recall multiplication and division facts efficiently.
• Understand and identify factors and multiples, especially HCF and LCM.
• Develop proficiency in estimation using fractions, decimals, and percentages.
• Convert between fractions, decimals, and percentages.
• Understand the relationship between exponents and roots.
• Analyze, describe, and classify various shapes using appropriate geometric vocabulary.
• Master measurements, especially in real-world contexts, and understand the precision and accuracy of tools.
• Convert units of measurement and understand their applications.
• Analyze patterns, functions, and represent rules through various means.
• Apply geometric knowledge in calculating perimeters, areas, and volumes.
• Work with coordinate geometry to solve positional problems.
• Understand and apply transformations to geometric figures.
• Collect, organize, interpret, and conclude data through various graphical representations.
• Understand statistical measures such as mean, median, mode, and range.
• Master the concept of probability and differentiate between predictions and experiment results.

N5.1.(NPV). Number and Place Value (NPV)

• Know that 10 tenths are equivalent to 1 one, and that 1 is 10 times the size of 0.1. Know that 100 hundredths are equivalent to 1 one, and that 1 is 100 times the size of 0.01. Know that 10 hundredths are equivalent to 1 tenth, and that 0.1 is 10 times the size of 0.01.
• Recognise the place value of each digit in numbers with up to 2 decimal places, and compose and decompose numbers with up to 2 decimal places using standard and non-standard partitioning.
• Reason about the location of any number with up to 2 decimal places in the linear number system, including identifying the previous and next multiple of 1 and 0.1 and rounding to the nearest of each.
• Divide 1 into 2, 4, 5, and 10 equal parts, and read scales/number lines marked in units of 1 with 2, 4, 5, and 10 equal parts.
• Convert between units of measure, including using common decimals and fractions.

N5.2.(NF). Number Facts

• Secure fluency in multiplication table facts, and corresponding division facts, through continued practice.
• Apply place-value knowledge to known additive and multiplicative number facts (scaling facts by 1 tenth or 1 hundredth).

N5.3.(AS). Addition and Subtraction

• Solve problems involving ratio relationships.

N5.4.(MD). Multiplication and Division

• Multiply and divide numbers by 10 and 100; understand this as equivalent to making a number 10 or 100 times the size, or 1 tenth or 1 hundredth times the size.
• Find factors and multiples of positive whole numbers, including common factors and common multiples, and express a given number as a product of 2 or 3 factors.
• Multiply any whole number with up to 4 digits by any one-digit number using a formal written method.
• Divide a number with up to 4 digits by a one-digit number using a formal written method, and interpret remainders appropriately for the context.

N5.5.(F). Fractions

• Find non-unit fractions of quantities.
• Find equivalent fractions and understand that they have the same value and the same position in the linear number system.
• Recall decimal fraction equivalents for 1/2, 1/4, 1/5, and 1/10, and for multiples of these proper fractions.

N5.6.(G). Geometry

• Compare angles, estimate and measure angles in degrees (°), and draw angles of a given size.
• Compare areas and calculate the area of rectangles (including squares) using standard units.

N5.7.(CT) Command Terms I:

N5.7.(CT) Command Terms II:

N4.8.(MAP) MAP Testing Relevant Practice:
n/a

Grade 5 Extended

Content

Numbers and Number Systems

• Representing quantities in different forms
• Exponents and roots
• Classifying numbers (factors and multiples)

Fractions

• Representing fractions in different forms
• Simplifying fractions
• Using number operations (subtraction, multiplication, division, and addition)
• Using mathematical strategies to solve real-life problems involving fractions

Fractions as Percentages

• Representing percentages in different forms (decimals, fractions, ratio)
• Converting between equivalent forms of numbers (fractions, decimals, percentages)

Algebraic Expressions and Equations

• Using correct terminology
• Representing patterns in different forms (diagrams, sequences, tables, words)

Geometric Constructions

• Perimeter, area, and volume

Data Management

Integers

Skills

• Problem Solving
• Analytical/critical thinking
• Interpretation and representation of data
• Mathematical reasoning (pattern recognition and generalisation)
• Communication of mathematical concepts
• Application of mathematical strategies to real-life situations