Cambridge HOTmaths CAPS Edition

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Cambridge HOTmaths covers a wealth of Primary and Secondary Mathematics topics

Numbers to 1000 & beyond

• Numbers to 1000
• Ordering numbers
• Numbers beyond 1000
• Splitting & regrouping

Patterns in counting

• Creating number sequences
• Patterns in sequences

Addition & subtraction

• Mental strategies
• Place value strategies
• Using empty number lines
• Written addition
• Written subtraction

Multiplication & division

• Modelling arrays & groups
• Modelling division
• Introducing multiplication strategies
• Building facts

Everyday fractions

• Fractional parts
• Comparing fractions
• Decimals
• Adding & subtracting decimals

Data

• Surveys, tables & tallies
• Column & picture graphs
• Bar graphs

Chance

• Chance language
• Listing outcomes
• Chance experiments

2D shapes & angles

• Symmetrical shapes
• Introducing angles
• 2D shapes
• Introducing quadrilaterals

Length & area

• Measuring length
• Calculating length
• Measuring perimeter
• Comparing areas

Mass & capacity

• Comparing mass
• Measuring mass
• Capacity

Time

• Reading clocks
• Digital clocks
• Measuring duration
• Using a calendar

Money

• Making money
• Money calculations

Location

• Simple maps
• Introducing coordinates

Larger numbers

• Modelling larger numbers
• Ordering larger numbers
• Rounding numbers

Fractions

• Equivalent fractions
• Parts of a group
• Counting with fractions

Decimal fractions & percentages

• Rounding & ordering decimals
• Multiplying & dividing by 10 & 100
• Percentages

Factors & multiples

• Patterns of multiples
• Multiplication facts
• Division facts
• Division with remainders

Calculations

• Applying addition strategies
• Subtraction calculations
• Multiplication by multiples of 10
• Extending multiplication

3D shapes

• Describing shapes
• Prisms & pyramids
• Shapes from nets

2D shapes & position

• Classifying angles
• Features of 2D shapes
• Reflect, translate & rotate
• Compass directions

Understanding whole numbers

• Extending place value
• Comparing whole numbers
• Rounding whole numbers
• Introducing Roman numerals

Addition & subtraction

• Exploring plus & minus
• Addition strategies
• Adding in columns
• Subtraction strategies
• Subtracting in columns

Multiplication & division

• Patterns in multiplication
• Multiplying by 10s, 100s, 1000s
• Multiplication strategies
• Exploring division
• Dividing larger numbers
• Mixed operations
• Primes & composites

Fractions

• Understanding fractions
• Which fractions are the same size?
• Improper fractions & mixed numerals
• Whole numbers & fractions
• Adding & subtracting like fractions

Decimals & percentages

• 10ths, 100ths & 1000ths
• Comparing decimals
• Adding decimals
• Subtracting decimals
• Mult & div decimals by 10, 100, 1000
• Exploring percentages
• Percentages-decimals-fractions

Patterns

• Numbers in designs
• Number patterns
• Mystery number sentences

Angles & 2D shapes

• The language of angles
• Measuring & drawing angles
• Triangles
• Quadrilaterals
• Exploring polygons

3D shapes

• Naming 3D shapes
• Drawing 3D shapes
• Nets
• Different views

Length

• Units of length
• Measuring & recording lengths
• Converting units of length
• Perimeter

Area

• Units of area
• Area of rectangles & squares
• Area of triangles

Volume & capacity

• Measuring volume
• Volume of rectangular prisms
• Measuring capacity
• Linking litres & cubes

Mass

• Units of mass
• Measuring & recording masses
• Converting units of mass

Time

• Calendars & timelines
• Clock times
• Measuring & calculating time
• Timetables

Maps, plans & directions

• Using scale
• Grid coordinates
• Compass directions

Chance

• Describing chance
• What is the chance?
• Chancy tasks

Data

• Average (mean)
• Picture & column graphs
• Reading divided bar graphs
• Introducing sector (pie) graphs
• Line graphs

Number systems

• Base 10 & other bases
• Exploring Roman numerals
• Negative numbers

Extending the operations

• Multiplying by two digits
• Dealing with remainders
• Order of operations

Further fractions

• Comparing fractions
• Add & subtract related fractions
• Fractions of a group
• Multiples of fractions

Further decimals & percentages

• Multiplying decimals
• Dividing decimals
• Calculating with percentages

Using symbols for numbers

• Writing rules
• Rules to patterns
• Unknown numbers

Circles, symmetry & resizing

• Circles
• Symmetry
• Enlarging & reducing

Using measurement

• Comparing perimeter & area
• Surface area
• Calculations using mass

Whole numbers

• Egyptian & Mayan numerals
• Roman & Greek numerals
• Index notation
• Place value & bases
• Rounding & estimating
• Adding whole numbers
• Subtracting whole numbers
• Multiplying whole numbers
• Dividing whole numbers
• Long division methods
• Order of operations & indices

Exploring numbers

• Number patterns
• Factors & multiples
• Highest common factor (HCF)
• Lowest common multiple (LCM)
• Divisibility tests
• Prime & composite numbers
• Factor trees
• HCF & LCM for large numbers
• Square roots
• Cube roots

Fractions

• What is a fraction?
• Improper versus mixed
• Equivalent fractions
• Comparing & ordering fractions
• This as a fraction of that
• Adding & subtracting fractions
• Adding & subtracting mixed numerals
• Multiplying fractions
• Multiplying mixed numerals
• Dividing by simple fractions
• Divisions involving fractions
• From a fraction to the whole

Decimals

• What is the point?
• Changing decimals to fractions
• Changing fractions to decimals
• Ordering decimals
• Adding & subtracting decimals
• Multiplying & squaring decimals
• Strategies for decimal divisions
• Rounding decimals
• Introducing recurring decimals
• Money

Percentages

• Percentages as fractions
• Writing fractions as percentages
• Linking percentages & decimals
• Fractions/decimals/percentages

Applying percentages

• Percentage of a quantity
• One amount as a percentage of another
• Percentage increase & decrease
• Profit & loss
• Finding the whole amount

Integers

• What are directed numbers?
• Adding & subtracting positive integers
• Two signs together
• Multiplying integers
• Dividing integers
• Mixing the operations

Ratios & rates

• What is a ratio?
• Using ratios
• Scales expressed as ratios
• Introducing rates

Introducing algebra

• What is algebra?
• Algebra pictures
• Words into algebra
• Substitution
• Picture patterns & pronumerals
• Number patterns & pronumerals
• Patterns on the number grid
• Adding & subtracting terms
• Multiplying & dividing terms
• Equivalent expressions

Manipulating algebra

• Linking algebra & number rules
• Removing grouping symbols
• Introducing factorising
• Algebraic fractions
• Formulas in spreadsheets

Equations & inequalities

• Working backwards
• Keeping the balance
• Guess, check & improve
• A formal approach
• Equations to solve problems
• Equations & formulas
• Introducing inequalities

The number plane

• The first quadrant
• All four quadrants
• Graphs from equations
• Equations from lines
• Comparing lines & equations
• Intersecting lines

Time

• Units of time
• Time calculations
• Time zones

Length, perimeter & area

• Length
• Perimeter problems
• Formula for area of a rectangle
• Formula for area of a triangle
• Areas of parallelograms
• Converting area units & estimating

Volume & surface area

• Volume, capacity & prisms
• Volume of any prism
• Surface area of prisms

Pythagoras' theorem

• What is Pythagoras' theorem?
• Length of the hypotenuse
• Length of any side
• Pythagoras, perimeter & area

Circles & cylinders

• Pi & the circumference
• Area of a circle
• Volume of a cylinder

Transformation & symmetry

• Translation
• Reflection & symmetry
• Rotation & symmetry

Angles

• Points, lines & angles
• Some angle relationships
• Angles in parallel lines

Plane shapes & triangles

• Plane shapes
• Classifying triangles
• Angle sum of a triangle
• Exterior angles of triangles

Exploring quadrilaterals

• Angle sum of a quadrilateral
• Exploring trapeziums & kites
• Exploring parallelograms & rectangles
• Exploring rhombuses & squares

Congruent & similar shapes

• Congruent shapes
• Which shapes are similar?
• Scale factors for similar figures

Constructions in geometry

• Bisecting angles & intervals
• Constructing lines & angles

3D shapes

• Faces, edges & vertices
• Classifying solids
• 3D drawings & projections

Chance

• The language of chance
• Listing possible outcomes
• Theoretical probability

Sets

• Introducing sets
• Comparing sets
• Using Venn diagrams

Representing data

• Using sector graphs
• Creating divided bar graphs
• Scatter diagrams
• Line, conversion & step graphs
• Travel graphs
• Frequency tables
• Histograms & polygons
• Grouping data
• Dot plots
• Stem-and-leaf plots
• Graphs & spreadsheets

Analysing data

• Exploring the mean
• The mode, the median & range
• Analysing dot plots
• Analysing stem-and-leaf plots
• Analysing tables

Number notations

• Significant figures & rounding
• Scientific notation
• Exploring recurring decimals
• Converting rates

Earning money

• Wages & salaries
• Extra earnings
• Part-time work
• Tax & other deductions
• Budgeting

Buying, borrowing, investing

• Best buys, discounts, sales tax
• Buying on credit
• Simple interest
• Compound interest
• Compound interest formula
• Depreciation
• Loans

Indices

• Multiplying & dividing terms
• Powers upon powers
• Negative indices & reciprocals
• Fractional indices & roots

Algebraic expressions

• Adding & subtracting fractions
• Multiplying & dividing fractions
• Expanding & simplifying
• Factorising
• Extending algebraic fractions
• Using algebra

Linear equations & inequalities

• Solving linear equations
• Equations with brackets
• Equations with fractions
• Problems & formulas
• Inequalities
• Extending inequalities

Simultaneous equations

• Graphs, tables or guess & check
• Using the substitution method
• Using the elimination method
• Solving problems simultaneously

Surds

• Reals, rationals & surds
• Operations with surds
• Rewriting surds
• Binomial surds

Quadratic expressions

• Expanding binomial products
• Factorising monic quadratics
• Factorising non-monic quadratics
• Special products & factors
• Other factorisations
• Simplifying using factors

Quadratic equations

• How many solutions?
• Solving using factors
• Completing the square
• The quadratic formula
• Simultaneous quadratics

Number plane: Calculations

• Midpoint
• Distance using graphs
• Gradient using graphs
• Distance formula
• Gradient formula

Number plane: Straight lines

• Slopes & intercepts
• Tables to graph lines
• Reading the equation
• Gradient-intercept graphs
• Determining the equation

Number plane: Curves

• Plotting curves
• Parabolas
• Hyperbolas

Perimeter & area

• Perimeters & arcs
• Area of a kite & a rhombus
• Area of a trapezium
• Areas of parts of circles

Volume

• Volumes of prisms & cylinders
• Volumes of pyramids
• Volumes of cones
• Volumes of spheres

Surface area

• Surface areas of prisms
• Surface areas of cylinders
• Surface areas of pyramids
• Surface areas of cones & spheres

Trigonometry: Introduction

• Naming the sides
• The tangent ratio
• Using the tangent ratio
• The sine & cosine ratios
• Side lengths using any ratio
• Calculating angles
• Applying trigonometry

Trigonometry: Minutes & bearings

• Splitting the degree
• Sides & angles
• What are bearings?
• Using bearings

Trig beyond right triangles

• The unit circle
• Related ratios
• Trig relationships
• Area using trig
• Sine rule
• Cosine rule

Reasoning in geometry

• Angles in polygons
• Tests for congruent triangles
• Writing reasons
• Similar triangles

Probability

• Relative frequency
• Using relative frequency
• Calculating probability

Data collection

• Cumulative frequency
• Cumulative frequency histograms
• Grouping data

Data analysis

• Centres for grouped data
• Box-and-whisker plots
• Standard deviation & distribution

Bivariate data

• Distance/time graphs
• Other line graphs
• Graphs with curves