Topics Covered in Maths

Beginners Level: Numbers & Calculations
• Counting to 10. Using number fans and number lines. Conservation of number. One-to-one matching.
• Comparing and ordering 0 - 10. Odd and even numbers. Larger than and smaller than.
• Reading and writing numerals and words to 10.
• Addition and subtraction to 10 using concrete materials and number lines. Counting on and back.
• Number facts to 10. Quick recall of number bonds to 10 using number fans. Understanding difference. Doubles and halves.
• Counting, comparing and ordering 0 – 30. Using number fans and number lines. Conservation of number. Number before, number after.
• Reading and writing numerals and words to 30.
• Counting, comparing and ordering 99. Using number lines and 0 -99 square. Counting in 10s, 2s and 5s.
• Understanding place value (tens and units). Place value cards. Counting money.
• Addition and subtraction to 30. Using place value cards and 100 squares. Missing number sums. Addition of money.
• Review of addition and subtraction facts.

Beginners Level: More Numbers & Calculations
• Counting to 100. Using number lines and number square. Count on and back in 1s and 10s. Using place value cards. Counting money £1, 10p and 1p. Counting in 100s.
• Comparing and ordering 0 to 100. Odd and even numbers to 100. Ordinal numbers and vocabulary.
• Place value (hundreds, tens and units). Identifying the value of a numeral by its place value position.
• Review of number facts to 10. Halving and doubling larger numbers. 0 to 9 addition square. Missing number sums using numbers 1 – 20.
• Addition and subtraction to 100. Using 100 square, number line and place value cards. Commutative law in addition. Difference.
• Simple number sequences. Finding the rule for a sequence.
• Simple fractions. Understanding whole and equal part of whole using one thing and a group of things. One half, one quarter, three quarters. Ordering fractions and mixed numbers to 10.
• Addition and subtraction of numbers to 99 using number lines, number square and place value cards.
• Multiplication (lots of). Using concrete materials and number square. Multiplication using money. Multiplying by 10.
• Division (shared by). Using concrete materials and number square. Division by subtraction. Division using money.
• 2, 5 and 10 times tables. Multiply and divide by 2, 5 and 10.
• Quick methods for mental maths.

Beginners Level: Measures Shape & Space
• Days, weeks, seasons, years. Vocabulary and order and comparative duration.
• The vocabulary of time. (Today, tomorrow, next week, last month, weekend etc.)
• Days, hours, minutes. Analogue time. O’clock, half past and quarter to and quarter past. One hour before, half an hour after. Reading the time on a clock and placing hands correctly on a clock.
• Digital time. Understanding the ‘hours and minutes’ display. Converting between analogue and digital time.
• The vocabulary of length. Comparative length. Accurate measurement (cm). Appropriate units of measurement.
• The vocabulary of weight (mass). Understanding balance. Comparative weight (mass). Weighing using non-standard weights. Weighing accurately using grams. Appropriate units of measurement.
• The vocabulary of capacity. Comparative capacity. Measuring capacity using litres and millilitres. Appropriate units of measurement.
• Two dimensional shape. Corners and sides. Circle, semi-circle, triangle, square, rectangle, pentagon, hexagon, octagon.
• Three dimensional shape. Faces, edges and corners. Pyramid, cube, cuboid, cylinder, cone, sphere. Flat and curved edges and faces.
• Reflective symmetry in simple shapes.
• The vocabulary of position, direction and movement. Right, left, under, through, backwards etc.
• Turns and angles. Creating patterns using reflection and rotation. Quarter and half turns. Right angles.

Beginners Level: Data Handling & Problem Solving
• Using a table to show information. Creating a block graph from the information in a table.
• Using tally charts to collect information. Creating pictograms.
• Reading tables, charts and pictograms and interpreting the information they show. Answering questions using tables, charts and pictograms.
• Solving number and shape and space puzzles using logic.
• Interpreting and solving number problems expressed in words.Understanding the application of computation in real life situations.
• Using money in real life situation. Finding the correct money, working out total cost and giving change.
• Interpreting and solving time and duration problems expressed in words.
• Interpreting and solving measures problems expressed in words.
• Hints and tips for tackling mixed questions presented as a ‘test’.

Intermediate Level: Numbers & Calculations
• Counting past 100. Using number lines and number squares. Counting on and back in ones, tens and hundreds.
• Sequences. Finding the rule for sequences for two digit numbers.
• Ordering numbers. Ordinal and cardinal numbers. Smallest to largest and largest to smallest.
• Place value. Understanding the value of a digit according to its position in a number. Using money to introduce decimal notation. Partitioning of numbers into hundreds, tens and units.
• Numbers as words. Words to one thousand.
• Using number facts. Reviewing the addition and subtraction facts using the digits 0 to 9. Understanding the relationship between addition and subtraction.
• Ways to add and subtract to 1000. Using partitioning, looping and hopping along a number line.
• Writing down addition and subtraction.
• Moving to formal written addition and subtraction.
• Times tables. x 2, x 5 and x 10, x 3 and x 4. Understand the relationship between multiplication and division. Commutative law in multiplication. Multiplication and division by 10.
• Fractions. Halves, quarters and tenths. Ordering fractions. Simple equivalence.
• Estimating and rounding. Making simple estimates. Rounding to the nearest ten.
• Using estimating and rounding.

Intermediate Level: More Numbers & Calculations
• Count and order numbers to 1000. Using less than (<) and greater than (>) to order numbers.
• Estimating and rounding. Use rounding to find approximate answers.
• Add and subtract whole tens, hundreds and thousands.
• Multiply and divide using 10. Understand that numbers get ten times larger or smaller.
• Negative numbers. Counting on and back through zero. Ordering numbers including negative numbers.
• Develop mental and written methods to add and subtract numbers to 10 000.
• Use standard written method for addition and subtraction to 100.
• Add and subtract money. Begin to work with decimal notation.
• x 6 and x 9, x 7 and x 8. Explore mental multiplication and division using halving and doubling
• Writing multiplication and division down. The grids method and subtraction or chunking.
• Fractions. Introducing thirds, sixths and eights. Ordering and equivalence.
• Decimals. Understanding tenths and hundredths. Writing decimal numbers as words.
• Estimating and rounding. Use estimation to solve problems

Intermediate Level: Measures Shape & Space
• Estimating time. Choosing appropriate units to measure duration.
• Days of the months. The structure of the year. Understanding leap year.
• Clocks Digital and analogue time. Telling the time in hours and minutes.
• Timetables and calendars. Reading and interpreting a timetable. Reading a calendar.
• Length. Understanding and using millimetre, centimetre and metre.Inch, foot, yard and mile.
• Mass. Understanding and using gram and kilogram. Pounds and ounces.
• Capacity. Understanding and using millilitre and litre. Pints and gallons.
• Accurate measuring. Understanding the importance of measuring accurately and using a ruler.
• Perimeter. Understanding that perimeter is the distance around a shape and measuring accurately.
• Area. Understanding that area is the bounded by the perimeter of a shape and measuring accurately.
• Two dimensional shapes. Rectangles and triangles and the names and properties of special cases.
• Using Carroll diagrams to sort 2D shapes. Quadrilateral, Pentagon, Hexagon and Octagon.
• Circles. The vocabulary of the circle. Radius, diameter, circumference.
• Three dimensional shape. Naming solids. Identifying and sorting solids by their properties. Faces, edges and vertices.
• Nets of simple solids. Building complex shapes form simple solids.
• Symmetry. Finding lines of symmetry. Matching two halves of symmetrical shapes.
• Creating patterns using rotation and reflection.
• Turns and angles. Understanding quarter and half turns. Measuring basic angles using a set square. Measuring angles using degrees.
• Directions. Using compass directions. Position. Simple coordinates.

Intermediate Level: Data Handling & Problem Solving
Tables and bar charts. Creating frequency tables and bar charts.
• Tally charts and pictograms. Collecting data on a tally chart. Making a pictogram. Using symbols to represent data.
• Reading tables. Interpreting pictograms, bar charts and data collection sheets.
• Venn and Carroll diagrams.
• Solving puzzles. Using an understanding of numbers and operations to solve number problems. Using logic. Breaking down a problem into simple steps.
• Word and real life problems involving money, time and measures.
• Tackling tests including QCA questions.

• Place value. Reading, writing and understanding numbers up to a million.
• Ordering whole numbers. Using <, >, = and = to order numbers and money.
• Estimating whole numbers. Rounding numbers to find approximate answers.
• Negative numbers. Using < and > to order negative numbers. Simple sequences including negative numbers.
• Equivalent fractions. Understanding and finding equivalent fractions.
• Mixed and improper fractions. Changing from mixed number to improper fraction and back.
• Ordering and using fractions. Finding a fraction of a number, length, weight or amount of money.
• Understanding decimals. Converting from fractions to decimal fractions.
• Ordering and rounding decimal fractions. Using a number line to order by tenth or hundredth. Rounding decimal fractions to the nearest whole number.
• Calculators. How to use a calculator. Basic functions and spotting mistakes!
• Percentages. Understanding the relationship between fractions, decimals and percentages.
• ‘for every’ questions. Introducing ratio.
• Written and mental methods for addition and subtraction.
• Multiplication using the grids method, short multiplication and introducing long multiplication.
• Division using chunking and introducing short division.
• Checking answers. Using estimation and an understanding of the effect of operations to check your answers.

Advanced level: More Numbers & Calculations
• Place value. Understanding the effect of multiplying and dividing by 10 and 100.
• Ordering decimals. Understanding the function of the decimal point. Using
• Rounding to the nearest thousand, hundred, ten, whole number or tenth.
• Estimation. Understanding that estimation gives an approximate answer.
• Negative numbers. Adding and subtracting negative numbers. Simple problems using negative numbers.
• Patterns. Triangular numbers. Diagrammatic representations of number patterns. Squares and primes. Finding the prime numbers to 100.
• Multiplication facts. Knowing and using addition, subtraction and multiplication facts. The rules for odd and even numbers.
• Divisibility. Factors and multiples. Tests for divisibility.
• Equivalent fractions. Numerator and denominator. Simplifying fractions. Manipulating fractions. Changing fractions into decimal fractions.
• Ratio and proportion. Understanding the difference between ratio and proportion.
• Fractions and percentages. Understanding the relationship between fraction, decimals and percentages
• Addition and subtraction. Mental and written including decimal calculations.
• Multiplication and division. Mental and written including decimal calculations.
• Using a calculator.

Advanced level: Shape Space & Measures
• 24 hour time. Converting from 12 to 24 hour time. Moving through midnight.
• Using timetables. Reading and understanding timetables. Finding duration.
• World time, date lines and summer time. Understanding the principle of world time and using time difference. Understand the effect of summer or daylight saving time.
• Working with length, weight and capacity, imperial and metric.
• Mass and weight. Understanding the difference.
• Perimeter and area. Calculating perimeter and area of shapes given the length of their sides. Finding the area of a right angle triangle using half base times height.
• The properties of two dimensional shapes. Understanding irregular 2D shapes.
• Direction and position. Coordinates in four quadrants. Perpendicular, parallel, diagonal and intersecting lines.
• Turns and angles. The angles on a straight line add to 180°. The angles in a triangle add to 180°. Equilateral, isosceles and scalene triangles. Rotation through the origin.
• Measuring and drawing angles accurately. Acute, obtuse and reflex angles.
• Reflection in one and two mirror lines introducing translation.
• Three dimensional shapes, cubes and nets of solids.

Advanced level: Data Handling & Problem Solving
• Probability. Understanding certainly, very likely, unlikely and impossible.
• Using a tally chart and frequency table.
• Displaying data on bar charts, pie charts line charts and graphs.
• Interpreting data from a bar chart, pie chart, line0 chart or graph. Finding the mean, median, mode and range of displayed data.
• Using knowledge of operations and logic to solve puzzles. Strategies for tackling number and shape and space problems.
• Word and real life problems involving money, time and measures.Strategies for tackling word and real life problems.
• Tackling tests including QCA questions.

Expert Level: Numbers & Calculations
• Place value. Reading, writing and understanding numbers up to a million with five decimal places.
• Multiplying and dividing by 10, 100 and 1000.
• Powers (indices). Basic calculations using numbers with powers. Understanding negative powers.
• Very large and very small numbers. Writing numbers in standard form.
• Addition and subtraction including numbers in standard form.
• The Standard Written Method for multiplication and division including numbers in standard form.
• Using < and > to compare decimals very large and very small numbers including numbers in standard form.
• Prime numbers, multiples and factors and divisibility.
• Squares and cubes. Square roots and cube roots.
• Manipulating fractions. Adding and subtracting fractions including mixed numbers.
• Ratio and proportion. Finding ratio in its simplest form. Problems relating to ratio and proportion.
• Working with fractions, decimals and percentages.
• Mental strategies.

Expert Level: More Numbers & Calculations
• Powers of ten. The vocabulary of very large and very small numbers.
• Rounding. To the nearest ten thousand, thousand, hundred, ten or whole number. To 1, 2 or 3 decimal places. Using a calculator to find the decimal equivalent of a fraction.
• Negative numbers. Addition, subtraction, multiplication and division including negative numbers.
• Prime numbers. Factors, prime factors and lowest common multiple. Highest common factor.
• Power laws. Multiplying and dividing powers. Finding square and cube roots of powers.
• Adding and subtracting fractions. Using lowest common multiple to add and subtract complex fractions. Problems involving fractions.
• Multiplying and dividing fractions. Simplifying by cancelling.
• Ratio and proportion. Working with volume and surface area. Problems involving ratio and proportion.
• Percentages. Understanding percentage increase and percentage decrease.
• Order of operations. BODMAS
• Using a basic calculator using the memory function and introducing the advanced scientific calculator.

Expert Level: Algebra
• Letters for numbers. Expression, equations and formulas.
• Simplifying. Expanding brackets, taking out common factors and collecting like terms.
• Rules of algebra. Addition, subtraction multiplication and division.
• Solving equations. The balance method, the inverse method and trial and improvement.
• Graphs. Straight line graphs. Finding the intercept and the slope. Recognising y = mx + c.
• Drawing line graphs.
• Simultaneous equations. Solving simultaneous equations by eliminating a variable or substitution.
• Finding a graphical solution to a pair of simultaneous equations.
• Finding equations in word problems.
• Applications of algebra. Famous formulas. Fahrenheit to Centigrade and Euler.
• Inequalities. Solving linear inequalities. Showing solutions on a number line. Graphs to show the solution set for simultaneous inequalities.
• Non-liner inequalities. Solving non-linear equations.
• Sequences. Describing a sequence using term-to-term and position methods. Finding the nth term.
• Staircase diagrams. Understanding limiting values.
• Functions. Using a function machine. Testing formulas. Inverse functions
• Graphs of functions.

Expert Level: Shape Space & Measures
• Measures. The vocabulary of measurement. Converting between measures. Problems involving measures. Approximate equivalents. Time, distance and speed. Average speed.
• Lines, angles and bearings. Measuring angles. Using a protractor to construct angles. Acute, obtuse and reflex angles. Internal and external angles. Supplementary and complementary angles. Drawing and calculating bearings. Perpendicular and parallel lines. Vertically opposite angles. Corresponding and alternate angles. The sum of internal angles
• Polygons and Pythagoras. Angles in polygons. Using Pythagoras.
• Congruence and similarity. The rules for congruency.
• Reflection, rotation, translation and enlargement. Lines and planes of symmetry. Rotation about a point. Object and image. Describing translations. Scale factor.
• Coordinates. Understanding and using coordinates for reflection, rotation, translation.
• Recognising and describing transformations.
• Nets of solids. Plan and elevation. Construction of perpendiculars, bisectors, angles and polygons using ruler and compasses.
• Perimeter and area, volume and surface area. Formula to find area, volume and surface area. Finding the surface area and volume of complex solids.
• Circles and cylinders. The vocabulary of the circle. Introducing p. 2pr, pr² and pr²h. Calculating circumference and surface area. Calculating the area of a sector of a circle.
• Trigonometrical ratios. Sine, cosine and tangent. Calculating angles and the length of sides.
• Word and real life problems using measures.

Expert Level: Data Handling
• Surveys. Discrete and indiscrete data. Collecting data. Tally charts, surveys and questionnaires.
• Class intervals. Choosing suitable class intervals.
• Understanding and finding the mean, mode and median of a set of data.The mid point of each class interval. Modal and median class.
• Statistics ranges. Calculating the range of a set of statistical data. Quartiles. Stem and leaf diagrams.
• Using statistics to solve word problems.
• Charts and diagrams. Frequency graphs, bar charts, compound bar charts. Frequency polygons.
• Line and scatter graphs. The line of best fit.
• Interpreting data. Reading information from all kinds of charts and diagrams.
• Measuring, calculating and using probability. Drawing a probability line. Sample space and possible outcomes. Percentage chance. Combined probabilities. Probabilities with and without replacement. Practical probability experiments. Comparing experimental and theoretical probabilities.