Free reference
The 11+ maths syllabus, in teaching order
Every topic an 11+ maths paper can ask for, grouped into 16 areas and numbered 1 to 80 in the order each one should be taught. Use it to work out what to cover next, or to check nothing has been missed. Nothing to sign up for.
16Topic areas
80Lessons in order
463Units
6,773Practice questions
Lesson numbers are the teaching order, not a difficulty rating. A child in Year 6 preparing for an 11+ paper still benefits from checking the early place value topics, because everything after them assumes those are secure.
Place Value and Rounding
6 lessons · 35 units · 516 questions-
1
Lesson 1, Reading Numbers to 100
Place value to 100
- Numbers in words, both directions
- Tens and ones, partitioning a number and saying what each digit is worth
- One more, one less, ten more and ten less, and watching which digit changes
- Comparing and ordering numbers to 100 with the correct symbol
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2
Lesson 2, Reading Numbers to 1,000
Place value to 1,000
- Hundreds, tens and units, building a number from its parts and saying what each digit is worth
- Numbers in words, both directions
- Zero as a placeholder, the difference between 307, 370 and 37
- One, ten and one hundred more and less, including jumps that roll several columns over at once
- Comparing and ordering three-digit numbers, including numbers with different digit counts
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3
Lesson 3, Reading Numbers to 10,000
Place value to 10,000
- Thousands, hundreds, tens and ones, partitioning a number and saying what each digit is worth
- Numbers in words, both directions
- Zero as a placeholder, the difference between 2,006, 2,060 and 2,600
- One, ten, one hundred and one thousand more and less, including jumps that roll several columns over at once
- Comparing and ordering four-digit numbers, including numbers with different digit counts
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4
Lesson 4, Reading Numbers to 1,000,000
Place value to 1,000,000
- The five columns to 100,000, partitioning a five-digit number and saying what each digit is worth
- Reading and writing five-digit numbers, splitting at the comma
- One thousand and ten thousand more and less, including jumps that force an exchange, such as 89,500 to 90,500
- Comparing and ordering numbers to 100,000, including numbers with different digit counts
- The sixth column, reading and writing six-digit numbers all
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5
Lesson 5, Reading Numbers to 1,000,000,000
Place value to 1,000,000,000
- The millions column, the seventh column, and what a digit is worth once a number passes 999,999
- Reading and writing seven-digit numbers, splitting at both commas
- One hundred thousand and one million more and less, including jumps that force an exchange, such as 9,900,000 to 10,000,000
- Comparing and ordering numbers in the millions, including numbers with different digit counts
- Tens and hundreds of millions, reading and writing eight and nine digit numbers
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6
Lesson 6, Rounding Numbers Mastery
Rounding to 10, 100 and 1,000
- Rounding to the nearest 10
- Rounding to the nearest 100
- Rounding to the nearest 1,000
- Rounding to the nearest 10,000
- Rounding to the nearest 100,000
All 6 together: Place Value to a Billion & Rounding Bundle, £23.99. Saves £11.95 against buying them one at a time.
The Four Operations and BIDMAS
8 lessons · 54 units · 766 questions-
7
Lesson 7, Mental Addition & Subtraction
Adding and subtracting: mental methods
- Adding and subtracting within 10, and the number bonds every later method is built on
- Adding and subtracting within 20, bridging through ten instead of counting on fingers
- Adding to 100, choosing between adding the tens first and jumping to the next ten
- Subtracting to 100, deciding whether to count back or count up
- Adding to 1000, including near multiples like adding 99 or 199
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8
Lesson 8, Column Addition & Subtraction
Adding and subtracting: written methods
- Setting numbers out in columns, lining up place value and working right to left
- Column addition, carrying a ten into the next column, including a carry of 2 from three numbers
- Column subtraction, exchanging from the column on the left, including exchanging across zeros
- Missing digit puzzles, finding a digit that has been rubbed out of a written calculation
- Missing digits in an addition, using the carry to decide what the hidden digit has to be
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9
Lesson 9, Grid and Column Multiplication
Multiplying
- Grid method with a one digit multiplier, splitting a number into tens and ones
- Grid method with two and three digit numbers, and adding the parts back up
- Column method with a one digit multiplier, carrying into the next column
- Long multiplication, and why the second row starts with a zero
- Three digits by three digits, three rows and two zeros
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10
Lesson 10, Short Division
Dividing
- Remainders, and what the leftover means when a number will not share equally
- Short division on the bus stop, where every digit divides exactly
- Exchanging into the next column, and writing the zeros in the answer instead of skipping them
- Four and five digit numbers, with the remainder at the end
- Two digit divisors by listing the multiples first
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11
Lesson 11, Divisibility & Multiplication Rules
Division rules and multiplication tricks
- Doubling routes
- Multiplying by ten and five
- Multiplying by three and six
- Multiplying by nine and eleven, ten lots first then one lot either way
- Multiplying by seven and twelve
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12
Lesson 12, Squares, Cubes and Roots Mastery
Squares, cubes and roots
- Square numbers, the area of a square with a given side
- Square roots, working back from the area to the side
- Estimating a square root between two whole numbers, then to one decimal place
- Cube numbers, counting one layer then the layers going back
- Cube roots, working back from the volume to the edge
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13
Lesson 13, Order of Operations (BIDMAS) Mastery
BIDMAS
- Which operation happens first, spotting the first step without working the whole calculation out
- Setting it out, rewriting the full calculation one line at a time
- Brackets, including the calculations where putting brackets in changes the answer and the ones where it does not
- Indices and roots
- Hidden brackets, where a fraction line or a root sign groups terms together with no bracket on show
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14
Lesson 14, Inverse Operations & Inserting Brackets Mastery
Inserting brackets and inverse
- Calculation words, what sum, difference, product, quotient, twice, squared and square root each tell you to do
- Words into calculations, turning a written phrase into a calculation with the brackets in the right place
- Working backwards, one and two step function machines, starting at the answer and undoing the last step first
- Longer chains, three steps at once including squares, cubes and roots
- Inserting brackets, putting one pair into a calculation
All 8 together: Four Operations, Powers & BIDMAS Bundle, £29.99. Saves £17.93 against buying them one at a time.
Decimals and Negatives
7 lessons · 43 units · 722 questions-
15
Lesson 15, Comparing and Ordering Decimals Mastery
Place value: decimals
- Numbers between whole numbers, using coins to see what sits between £1 and £2
- Tenths, reading and writing the first decimal place
- Hundredths and thousandths, going further past the decimal point
- Equivalent decimals, why 0.7 and 0.70 are the same value
- Comparing two decimals, lining up place value column by column
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16
Lesson 16, Rounding Decimals to Decimal Places Mastery
Rounding decimals
- Rounding to 1 decimal place, underlining the tenths and reading the single digit to its right
- Rounding to 2 decimal places, and why 8.7337 gives a different answer at every accuracy
- Rounding to 3 decimal places, working with longer numbers like 13.92951
- Trailing zeros and padding, why 1.542 to 4 decimal places has to be written 1.5420
- Rounding that carries, where a 9 goes to 0 and the column on its left goes up
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17
Lesson 17, Significant Figures and Estimation
Significant figures and estimation
- Finding the first significant figure, including numbers that start with zeros
- Rounding to 1 significant figure
- Rounding to 2 and 3 significant figures
- Zeros, the common traps, and working backwards from a rounded number
- Estimating an answer by rounding every number to 1 significant figure
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18
Lesson 18, Multiplying and Dividing by Powers of 10
Multiplying and dividing by powers of 10
- Multiplying whole numbers by 10, 100, 1,000 and 10,000
- Dividing whole numbers, including the answers that cross the decimal point
- Multiplying decimals
- Dividing decimals
- Adjusting a known fact when one number changes, using 12 × 4 = 48 to work out 12 × 400
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19
Lesson 19, Adding and Subtracting Decimals Mastery
Decimals: adding and subtracting
- Adding tenths and hundredths, where a short number like 0.4 has to be written 0.40 before you can add it
- Adding thousandths and ten thousandths, carrying across the point in numbers like 47.352 + 28.6
- Subtracting tenths and hundredths, exchanging from the column to the left
- Subtracting thousandths and ten thousandths, including taking a decimal from a whole number like 5 − 2.35
- Choosing the quickest method, counting up, taking one off both, or setting it out in columns
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20
Lesson 20, Multiplying and Dividing Decimals Mastery
Decimals: multiplying and dividing
- Counting decimal places, by underlining every digit after the point and numbering them
- Multiplying decimals, from 3 × 1.4 up to 3.06 × 0.007
- Dividing by a whole number, including answers smaller than 1 such as 4 ÷ 5 = 0.8
- Dividing by a decimal such as 0.3, 0.04 or 0.012, using equivalent fractions
- Decimals in context, area, missing sides, money, best buy, speed and scale
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21
Lesson 21, Negative Numbers Mastery
Negative numbers
- Numbers below zero, comparing and ordering them, including decimals like −2.5 and −2.05
- Adding and subtracting a positive, where the answer crosses zero, such as 6 − 7 and −5 + 8
- Adding and subtracting a negative, where two signs sit next to each other, such as 5 + −3 and 5 − −3
- Multiplying and dividing, with one rule that covers both, same signs give a positive and different signs give a negative
- Mixed questions and order of operations, including −4² against (−4)² and calculations like −5 + 6 × −2
All 7 together: Decimals, Estimation & Negative Numbers Bundle, £26.99. Saves £14.94 against buying them one at a time.
Factors, Multiples and Primes
3 lessons · 13 units · 234 questions-
22
Lesson 22, Factors and Multiples Mastery
Factors, multiples and factorising skills
- Recognising multiples, and building times tables nobody learns, 13, 17, 18, 19 and beyond
- Divisibility tests for 2, 3, 4, 5, 6, 9 and 10, and combining them for bigger numbers
- Finding every factor of a number using factor pairs, and knowing when to stop
- Finding two numbers with a given product and sum
- The same skill with negative pairs
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23
Lesson 23, HCF and LCM Mastery
HCF and LCM, including worded problems
- Finding the highest common factor by listing the factors of each number and ringing what they share
- Finding the lowest common multiple by counting up from the bigger number until the smaller one catches it
- Choosing between them, splitting something into equal groups needs the HCF, two things repeating until they line up needs the LCM
- Working backwards, finding a missing number from a given HCF or LCM
- Leftover questions, the smallest number that leaves 1 over when shared into two different group sizes
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24
Lesson 24, Primes and Prime Factorisation Mastery
Prime numbers and prime factors
- What makes a number prime, exactly two different factors, and why 1 does not count
- Finding the primes with a sieve, then testing a bigger number like 91 that looks prime and is not
- Factor trees, splitting a number all
- Index form, writing 360 as 2³ × 3² × 5
- HCF and LCM from prime factors, using a Venn diagram to sort the shared primes from the rest
All 3 together: Factors, Multiples & Primes Bundle, £11.99. Saves £5.98 against buying them one at a time.
Fractions
5 lessons · 24 units · 390 questions-
25
Lesson 25, Intro to Fractions
Introduction to fractions
- Writing fractions from equal parts, shaded and unshaded
- Equivalent fractions
- Simplifying fractions
- Converting mixed numbers to improper fractions
- Converting improper fractions to mixed numbers
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26
Lesson 26, Adding and Subtracting Fractions Mastery
Adding and subtracting fractions
- 4 units, in order, Same Denominator, Choosing the Right Denominator, Different Denominator, and Mixed & Improper Fractions
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27
Lesson 27, Multiplying and Dividing Fractions Mastery
Multiplying and dividing fractions
- Adding and subtracting fractions with the same denominator
- Choosing the right common denominator
- Adding and subtracting with different denominators
- Mixed numbers and improper fractions
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28
Lesson 28, Fractions of Amounts Mastery
Fractions of amounts, increase and decrease
- Unit fractions of an amount
- Non-unit fractions of an amount, and comparing fractions of two different amounts
- Increasing and decreasing an amount by a fraction
- Finding the fraction of a change
- Successive fractions, where one fraction is applied, then a second fraction is applied to what's left
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29
Lesson 29, Reverse Fractions Mastery
Reverse fractions
- Finding the whole from a unit fraction
- Finding the whole from a non-unit fraction
- Reversing a fraction increase or decrease
- Reverse fraction questions with decimal answers
- Multi-step reverse fraction word problems
All 5 together: Fractions Mastery Bundle, £19.99. Saves £9.96 against buying them one at a time.
Ratio
3 lessons · 19 units · 286 questions-
30
Lesson 30, Introduction to Ratio
Introduction to ratio and equivalent ratios
- Writing ratios from diagrams, counting each group and writing the parts in the right order
- Writing ratios from written information
- Fractions and ratios
- Simplifying ratios by dividing every part by the same number
- Ratios with different units
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31
Lesson 31, Recipes, Scaling and Best Buys
Recipes and best buys
- Scaling with a whole number multiplier
- The unitary method, going through one person when nothing divides cleanly
- The common factor method, stepping down to a shared number then back up
- The common multiple method, stepping up to a shared number then back down
- Full multi-ingredient recipes, where your child picks the method
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32
Lesson 32, Sharing and Ratio Problems
Sharing and ratio problems
- Sharing a quantity in a 2-part ratio
- Sharing in a 3-part ratio, including questions that ask only for the largest or the smallest share
- Difference problems, where the question gives the gap instead of the total
- Forming ratios from context, including "three times as many" wording, fractions and remainders
- Multi-step and changing ratios, where amounts are added, removed or spent after the sharing is done
All 3 together: Ratio & Proportion Mastery Bundle, £11.99. Saves £5.98 against buying them one at a time.
Percentages
3 lessons · 15 units · 262 questions-
33
Lesson 33, Percentages of Amounts Mastery
Percentages of amounts
- The facts to know by heart, 50% is a half, 25% is a quarter, 10% is a tenth and 1% is a hundredth
- Repeating a tenth to reach 20%, 30%, 40% and up to 90%
- Half a tenth and small steps of 1%
- Splitting any percentage into tens and ones
- Taking a small piece off the whole
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34
Lesson 34, Percentage Increase, Decrease and Change Mastery
Percentage increase, decrease and change
- Increasing an amount by a percentage, both by adding the change on and by finding the new percentage in one step
- Decreasing an amount, including sale wording like 20% off, and choosing whichever route is fewer steps
- Writing one amount as a percentage of another, including when the units differ
- Multi-step problems, successive changes, best buys, and taking a percentage of what is left
- Percentage change, comparing the change with the original amount and never with the new one
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35
Lesson 35, Reverse Percentages Mastery
Reverse percentages
- Round percentages that divide neatly into 100
- Percentages above 100%
- Non-round percentages, where finding 1% first is the only reliable route
- Increases and decreases, finding the amount before the change happened
- Successive changes, two percentage changes one after the other
All 3 together: Percentages Bundle, £11.99. Saves £5.98 against buying them one at a time.
Fractions, Decimals and Percentages
2 lessons · 10 units · 180 questions-
36
Lesson 36, Fractions, Decimals & Percentages Mastery
Fractions, decimals and percentages 1
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37
Lesson 37, Fractions, Decimals & Percentages Mastery
Fractions, decimals and percentages 2
All 2 together: Fractions, Decimals & Percentages Mastery, £7.99.
Algebra and Sequences
10 lessons · 60 units · 850 questions-
38
Lesson 38, Writing Algebraic Expressions Mastery
Introduction to algebra and basic expressions
- Writing addition and subtraction expressions from words
- Writing multiplication and division expressions from words, including a number divided by a letter
- Explaining what a given expression means, working backwards from the algebra to the words
- Turning one-step worded scenarios into expressions
- Building multi-step expressions with a bar model that always stays in simplest form
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39
Lesson 39, Collecting Like Terms Mastery
Collecting terms
- Like and unlike terms, spotting the difference and why the variable and power both have to match
- Parts of an expression, coefficients, variables, powers, signs, terms and constants explained through live examples
- Collecting basic like terms, including negative terms
- Mixing letters and constants in the same expression
- Collecting terms with powers
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40
Lesson 40, Function Machines Mastery
Function machines
- Forward machines, apply a rule to a number to find the output
- Backward machines, undo a rule using inverse operations to find the input
- Building expressions from a one-step machine
- Building expressions from a two-step and three-step machine
- Algebra machines with one step
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41
Lesson 41, Multiplying and Dividing Terms Mastery
Multiplying and dividing terms
- Multiplying numbers and letters
- Multiplying powers of the same base
- Multiplying terms with coefficients and powers
- Dividing simple terms
- Dividing powers of the same base
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42
Lesson 42, One-Step Equations Mastery
Solving one-step equations
- Solving one-step equations by addition and subtraction
- Solving one-step equations by multiplication
- Solving one-step equations by division
- Writing non-whole-number answers as a simplified fraction or a decimal
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43
Lesson 43, Solving Multi-Step Equations Mastery
Solving two-step equations
- Describing what a two-step expression does to a variable
- Solving 2-step equations
- Solving 3-step equations, including brackets and fractions
- Solving equations with the letter on both sides
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44
Lesson 44, Substitution Mastery
Substitution
- One-step substitution, swapping a letter for its number in a simple expression
- Squaring and order of operations
- Two-step expressions, where two operations have to happen in the right order
- Three- and four-step expressions, building up to longer multi-operation expressions
- Substituting into expressions with more than one variable
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45
Lesson 45, Forming and Solving Equations Mastery
Forming and solving equations
- Creating expressions from words
- Forming and solving equations from number puzzles
- Shape and angle equations, perimeters, triangles, quadrilaterals, angles on a line and around a point
- Age problems
- Trickier multi-step word problems
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46
Lesson 46, Solving Simultaneous Equations by Elimination
Simultaneous equations
- Adding and subtracting two equations to eliminate a variable
- Scaling an equation
- Spotting elimination in real-world scenarios, working out which quantity cancels between two orders or two groups
- The strategy choice, deciding whether to add or subtract before touching the numbers
- Solving full pairs of equations by elimination
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47
Lesson 47, Sequences Mastery
Sequences
- Finding the next term
- Finding missing terms
- Geometric sequences
- The nth term rule (simple)
- The nth term rule with an adjustment
All 10 together: Algebra Mastery Bundle, £35.99. Saves £23.91 against buying them one at a time.
Angles and Symmetry
5 lessons · 31 units · 242 questions-
48
Lesson 48, Angles Mastery
Angles: identifying 90, 180 and 360 degrees
- Identifying angle types, acute, obtuse, right, straight, and reflex
- Measuring angles accurately with a protractor
- Working with reflex angles, angles greater than 180°
- Finding missing angles on a line, at a point, and using angle facts
- Forming and solving equations from angle facts
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49
Lesson 49, Identifying Shapes Mastery
Identifying 2D and 3D shapes
- 2D shapes and polygons, naming shapes from a triangle up to a decagon
- Triangles, classifying equilateral, isosceles and scalene by their sides and angles
- Parallel lines, spotting which lines point the same way and never meet
- Quadrilaterals, telling squares, rectangles, rhombuses, kites and trapeziums apart by their properties
- Parts of a circle, naming the radius, diameter and circumference on sight
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50
Lesson 50, Angles in a Triangle Mastery
Angles in triangles
- Angle sum in a triangle, explored hands-on before any rule is given
- Missing angles in scalene and right-angled triangles
- Isosceles triangles, finding the top angle or both base angles
- Angles on a line and around a point
- Exterior angles, including straight-line and reflex-angle problems
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51
Lesson 51, Angles in Polygons Mastery
Angles in quadrilaterals and polygons
- Angles in quadrilaterals
- Finding the total interior angles of any polygon
- Finding one interior angle of a regular polygon
- Two-step missing angle problems, including concave and irregular shapes
- Compound polygons meeting at a junction
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52
Lesson 52, Symmetry Mastery
Line and rotational symmetry
- Lines of symmetry in shapes and letters
- Reflecting shapes and pictures across a mirror line
- Order of rotational symmetry
- Reflecting coordinates and shapes on a grid, including lines like x = 3 and y = -2
- Six hands-on Explore tools your child can play with freely, including building a symmetric picture on a grid, spotting the deliberate mistake in a reflection, rotating 12 shapes and letters to find their order of symmetry, and reflecting points and shapes on a coordinate grid
All 5 together: Angles & Symmetry Mastery Bundle, £19.99. Saves £9.96 against buying them one at a time.
Area, Perimeter and Volume
5 lessons · 31 units · 392 questions-
53
Lesson 53, Perimeter of Shapes Mastery
Perimeter and compound shapes
- Counting squares on a grid to find a perimeter
- Adding every side when all the lengths are given
- Finding a missing side when the perimeter is known
- Writing and solving a perimeter in algebra
- Working out unlabelled sides on a compound shape
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54
Lesson 54, Area of Squares, Rectangles and Triangles
Area of squares, rectangles and triangles
- Counting area on grids, including shapes that are not full rectangles
- Area of squares and rectangles, including mixed units such as 1.5m by 60cm
- Finding a missing side length from the area, including square numbers and two-digit division
- Area of triangles, including right-angled and obtuse triangles
- Finding a missing base or height when the area is given
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55
Lesson 55, Area of Trapezia and Compound Shapes
Area of trapezia and compound shapes
- Area of a trapezium, using the formula (a + b) ÷ 2 × h
- Finding a missing side when the area is already given
- Area of compound shapes built from rectangles, triangles and trapezia joined together
- Finding area by taking away a shape
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56
Lesson 56, Volume of 3D Shapes Mastery
Volume of 3D shapes
- What volume actually means, counting unit cubes to build the idea before any formula
- Volume of a prism, cross-section area × depth, including cubes and cuboids
- Working backwards from a given volume to find a missing length
- Volume of triangular and trapezoidal prisms, spotting which lengths are actually needed
- Volume of a cylinder, using a given circular area
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57
Lesson 57, Surface Area Mastery
Surface area
- Area revision, rectangles, triangles and compound shapes
- Counting the squares on each face of a solid cuboid
- Reading the surface area off a net
- Surface area of a cuboid using the three pairs of faces
- Surface area of a cube
All 5 together: Area, Perimeter & Volume Mastery Bundle, £19.99. Saves £9.96 against buying them one at a time.
Averages and Range
4 lessons · 22 units · 369 questions-
58
Lesson 58, Mode, Median & Range Mastery
Mode, median and range
- Finding the mode from a bar chart, a tally chart, a list of words and a list of numbers
- Lists with two modes, and lists with no mode at all
- Finding the range, including negative temperatures and one decimal place values
- Finding the median from an odd number of values, by crossing off from both ends
- Finding the median from an even number of values, by adding the two middle numbers and dividing by 2
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59
Lesson 59, Mean and Reverse Mean Mastery
Mean and reverse mean
- Finding the mean of a set of numbers, including sets with negative values
- Finding the total when the mean and the number of values are given
- Reverse mean, working backwards from a given mean to a missing value
- Range, mode and median alongside the mean
- What happens to the mean when a value is added, removed or changed
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60
Lesson 60, Averages & Range from Tables Mastery
Averages and range from tables
- Reading a frequency table, including what a row really stands for
- The mode, the value with the highest frequency
- The range, largest value take away smallest value, and why the frequency column has nothing to do with it
- The median, using (n + 1) ÷ 2 to find the position, then counting down a running total
- The mean, building the value × frequency column, totalling it, then dividing by the total frequency
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61
Lesson 61, Averages Problem Solving Mastery
Problems with averages
- Changing the list, working out what happens to the mean when a value is added, removed or replaced
- Hitting a target mean
- Missing numbers from clues, finding a whole set of numbers from its mean, median, mode and range
- What changes and what does not, adding the same amount to every value or multiplying every value
- Two groups working backwards, finding one group's mean or size from the combined mean
All 4 together: Averages & Range Bundle, £15.99. Saves £7.97 against buying them one at a time.
Data, Charts and Graphs
5 lessons · 29 units · 408 questions-
62
Lesson 62, Data Tables, Tally Charts & Frequency Tables Mastery
Data tables, tally charts and frequency tables
- Tally charts, recording one response at a time and counting in gates of five
- Frequency tables, reading a single row, totalling the column and comparing two categories
- Reading data tables, including tables where each row carries two measures
- Completing tables, finding a missing frequency from the total, and spotting when the total on its own is not enough
- Grouped frequency tables, sorting a list of raw values into groups that do not overlap
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63
Lesson 63, Two-Way Tables Mastery
Two-way tables
- Reading a two-way table, what one cell means and how its row heading and column heading together name it
- Totals and missing numbers, finding the line that has only one gap left, filling it, then checking both routes to the grand total agree
- Building a table from a description, drawing the grid and the headings first, then placing one fact at a time
- Probability from a two-way table, including given that questions where the denominator is a row or column total rather than the whole table
- A final 12-question mixed review pulling from all 4 units, with its two reference tables printed above the questions
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64
Lesson 64, Venn Diagrams and Carroll Diagrams Mastery
Venn diagrams and Carroll diagrams
- Sorting into a Carroll diagram, testing each card against both labels
- Reading a Carroll diagram, finding a missing box from the totals and checking the grand total agrees along the rows and down the columns
- Reading a two circle Venn diagram, the four regions and why the middle is counted once in the grand total but sits inside both circle totals
- Completing a Venn diagram from a written description, placing the middle first and working outwards
- Three circle Venn diagrams, the centre, the three overlaps and the three single regions, filled one fact at a time
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65
Lesson 65, Bar Charts, Line Graphs & Pictograms Mastery
Bar charts, line graphs and pictograms
- Pictograms, reading the key first and working out what half a symbol or a quarter of a symbol is worth
- Reading bar charts, following the top of a bar across to the scale, including values that read off at a small line between two labelled numbers
- Completing and drawing bar charts, finding a value on the scale, drawing the bar up to it, and choosing the scale that makes the data fit
- Comparative bar charts, using the key to read two groups above the same label and find the difference between them
- Grouped bar charts, reading a bar that counts everything between two numbers, and what that kind of chart can never tell you
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66
Lesson 66, Pie Charts Mastery
Pie charts
- Reading a pie chart as a fraction, counting the equal parts, naming the share and simplifying it
- Using a stated total, finding how many the sector is worth by taking that fraction of the total
- Percentage labels, reading them off, adding them to check the chart makes 100 and finding the one that has been rubbed out
- Angles, sharing 360° between the whole set
- Drawing a pie chart from a frequency table, working out every angle, marking each spoke and checking the last sector closes the circle at 360°
All 5 together: Tables, Charts & Diagrams Bundle, £19.99. Saves £9.96 against buying them one at a time.
Coordinates, Units and Time
5 lessons · 30 units · 440 questions-
67
Lesson 67, Coordinates Mastery
Coordinates
- Reading and plotting coordinates, x before y every time, including points that sit on an axis
- All four quadrants, including negative values and what a matching x or y value tells you
- Shapes and missing vertices
- Midpoints of a line, and working backwards from a midpoint to find the missing end point
- Lines and patterns
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68
Lesson 68, Transformations Mastery
Reflections, enlargements and translations
- Translations on squared paper, counting the squares across and up from one corner and moving every other corner the same way
- Translations with coordinates
- Reflections in a drawn mirror line, matching each corner to its own gap on the other side
- Reflections in the axes and in a named line such as x = 3, where counting equal gaps is the only method that works
- Enlargements by 2, 3 and 4 and by a half or a third, including what happens to the perimeter
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69
Lesson 69, Converting Units Mastery
Converting units: distance, liquid and weight
- Length one step at a time, mm to cm, cm to m and m to km, taught one step per slide
- Length in multi step jumps, mm to m and cm to km, chaining two steps into a single factor
- Mass, grams and kilograms
- Capacity, millilitres and litres
- Miles, kilometres and imperial units, worked out on an equivalent ratio table and always stated as about, because the conversion is not exact
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70
Lesson 70, Time, Timetables and Calendars Mastery
Time problems, timetables and calendars
- Reading analogue clocks, and converting between 12-hour and 24-hour time, including the midday and midnight cases most children get wrong
- Units of time, seconds, minutes, hours, days and weeks, and why the base is 60 rather than 10
- Durations, counting on a number line to find how long something lasted, and working backwards from an end time
- Timetables, reading a cell, timing a journey, and choosing the latest service that still arrives in time
- Calendars, days in each month, weekday jumps in sevens, and the leap year rule including why 1900 was not one
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71
Lesson 71, Speed, Distance and Time Mastery
Speed, distance and time
- Finding the speed, dividing a journey down until the table says what happens in one hour
- Finding the distance, scaling the one hour row up, including half hours, quarter hours and 90 minute journeys
- Finding the time, whole hours, half hours, minutes only trips such as 6 miles at 24 mph, and arrival times from a start time
- Average speed for a whole journey, there and back trips, and the difference between the moving average and the overall average that includes a stop
- Reading distance-time graphs, distance from home at a given time, the length of a rest, the furthest point, and total distance travelled
All 5 together: Coordinates, Measures & Time Bundle, £19.99. Saves £9.96 against buying them one at a time.
Probability
3 lessons · 17 units · 260 questions-
72
Lesson 72, Combinations Mastery
Combinations
- Listing every combination once, using an ordered grid
- The multiplying shortcut
- Three or more groups of choices multiplied together
- Making two-digit and three-digit numbers from digit cards, with and without repeats
- Combinations with a restriction, and counting pairs such as handshakes
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73
Lesson 73, Introduction to Probability Mastery
Probability: single events and totals of 1
- Writing a probability as a fraction, successful outcomes over total outcomes
- The 0 to 1 likelihood scale, matching a chance to impossible, unlikely, even chance, likely or certain
- Comparing two chances by writing both over the same denominator
- Probabilities that add to 1, and finding the chance of an event not happening
- Expected outcomes
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74
Lesson 74, Probability with Multiple Events Mastery
Probability: independent and dependent events
- Sample spaces for two events, listing every outcome in a grid before counting
- The AND rule, multiplying the chances of two independent events
- Tree diagrams for two independent events, multiplying along a route and adding separate routes
- Two picks without replacement, where the second fraction changes because a counter has gone
- Deciding whether two events are independent or dependent, and saying why
All 3 together: Probability Bundle, £11.99. Saves £5.98 against buying them one at a time.
Puzzles and Problem Solving
6 lessons · 30 units · 456 questions-
75
Lesson 75, Sudoku Logic Mastery
Sudoku
- The three rules, one of each number in every row, every column and every box
- Only One Place, finding the square that has just one number left
- Letting a box decide, when a number has only one home left inside it
- Maybe marks, writing down every number a square could still be
- Not marks, crossing off what a square cannot be until one number survives
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76
Lesson 76, Roman Numerals Mastery
Roman numerals
- The seven symbols and what each one is worth, from I to M
- Building numbers by adding
- The six subtractive pairs, IV, IX, XL, XC, CD and CM
- Numbers to 1,000 and reading years
- Puzzles and problems, including calculations written in numerals and Roman clock faces
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77
Lesson 77, Number Bases & Binary Mastery
Different bases and binary
- Bases all around us, why we count in tens and where base 60 and dozens still turn up today
- Reading binary, working out that 1101 is worth 13
- Writing binary, turning 25 into 11001 one column at a time
- Base detective, reading and writing numbers in base 3, base 4 and base 5
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78
Lesson 78, Anagrams & Codes Mastery
Anagrams and codes
- Word scramblers, using the clue first and the letters second
- Anagrams hidden inside a sentence, where the sentence is the clue
- Letter codes, finding the jump from the word to its code
- Tougher codes, where every letter moves by a different amount and the alphabet loops round
- Letter series and analogies, the two letter lines that appear on every paper
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79
Lesson 79, Magic Squares & Number Pyramids Mastery
Magic squares and number pyramids
- Number pyramids, adding upwards and working backwards by subtracting, with negatives and decimals from the start
- Magic squares, finding the magic total, using the centre as a shortcut, and spotting the square that is not magic
- Product and factor squares, where every row, column and diagonal multiplies to the same number instead of adding
- Algebra puzzles, with n and 2n sitting in the grid or on the bricks
- Exam challenge, arranging four numbers to hit a target top brick and squares built from nine numbers in a row
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80
In the bundle
Mixed problem solving
All 6 together: Reasoning & Problem Solving Bundle, £23.99. Saves £5.96 against buying them one at a time.
Want all 80 in one go?
The Complete 11+ Maths Course is every lesson on this page on a single page, numbered 1 to 80 so you always know what to do next. £200 against £479.20 bought one lesson at a time, and new lessons are added free.
Prefer to start smaller? Pick the block your child needs from the list above, or work through the free practice questions first to find out where the gaps are.