## Number and Proportion

## Properties and CalculationsPlace Value and Ordering
Multiply and Divide by 10, 100, 1000
Understand and use place value for decimals, measures and integers of any size (KS3)Stop teaching thousands (Michael Tidd)"This will seem silly at first. Of course we need to teach thousands. But I’m coming to the conclusion that we tackle it in the wrong way in some ways. We expect children to work with increasingly large numbers as they go through primary education, and so once they seem to have grasped hundreds, it seems to make sense to move them onto thousands." Printable place value board and digits (Great Maths Teaching Ideas)Pupils can physically move the digits as they complete multiplication and division problems. Place value interactive (Primary National Strategies)Display on whiteboard for whole-class teaching, or use with small groups/individuals at a computer to support independent work. Conveyor belt interactive (Top Marks)Interactive aimed at primary, but has great visualisation of zeros "falling off" the end of the conveyor belt when not needed any more. Springboard Unit 2 (via LGfL)See pg 8-10 for multiplying and dividing by 10, 100, 1000. Basic practice worksheets (Maths Drills)Standard drill problems with answers. Worksheet collection (greatschools.org)Master the basics (C. Norledge)Standard mixed problems, including extension to simple powers of 10. Workout (StudyMaths)Question generator - good for basic repeated practice. Mini-whiteboards activity (EMaths)Collection of questions for use with mini-whiteboards or hot-seat questioning. Four numbers (C Norledge)Simple starter activity with links to place value (not specifically multiplying and dividing by powers of 10). Always add a zero (C Norledge)Quick task asking pupils to explain why the rule "always add a zero" doesn't work - generates some interesting discussions! Place value video (BBC Skillswise)One-minute video with real-life examples of place value. History of the metric system (C Norledge)Presentation explaining the history of the metric system - leads into the NASA/Lockhead clip mentioned below. The metric system - Eddie Izzard (YouTube)Comedian Eddie Izzard talks about America's attitude to adopting the metric system. NASA - Measuring failure (YouTube)A short clip explaining what happened to the Mars Climate Orbiter, and why it's important to use the same units (metric and Imperial systems). Who Wants to be a Millionaire? (Great Maths Teaching Ideas)PowerPoint version; nice plenary or revision activity. Catchphrase (Laura Rees-Hughes via TES)PowerPoint version; engaging resource. Bingo (Top Marks)Customisable levels of difficulty, pupils choose five numbers from a list of ten. Notes (BBC Skillswise)Explanation of multiplication and division by 10, 100, 1000. Useful to stick into exercise books as a reminder. Standard Form
Interpret and compare numbers in standard form (KS3)Calculate with numbers in standard form (KS4) Worksheet generator (MathsBot)Quick basic generator for converting to and from standard form and four operations with standard form. Includes option to add additional topics for a revision worksheet. CIMT resources (Link)MEP Practice Book with exercises and examples on standard form (pg13 onwards). Worksheet generator from worksheetmath.com**Convert numbers to standard form****Convert standard form to numbers****Mixture of both conversions****Multiply and divide numbers in standard form**
Workouts (StudyMaths)Question generator - good for basic repeated practice. **Converting into standard form****Converting from standard form****Multiplying and dividing in standard form****Adding and subtracting in standard form**
Standard form self-marking exercise (Transum)Question generator with nine levels of difficulty. KESH Maths Takeaway (Link)GCSE practice problems booklet (N.B. 1MA0 specification). Standard form activity (eugenesmith via TES)Quick activity on all types of standard form problems; suitable for revision. Universcale interactive (Nikon)Beautiful interactive presentation exploring the actual size of very large and very small numbers. Real-life standard form conversion (abcdwpresents via TES)26 beautifully presented real-life standard form problems with lots of scope for different classroom activities. Standards Unit N4 (via Craig Barton)Estimating length using standard form - a rich card-sort activity with lots of real-life links. Solar system activity (tj2807 via TES)This GCSE activity gets pupils to use standard form (multiplying, dividing, converting from ordinary numbers) to find the mass and distance from the sun of each of the planets in our solar system. Which is bigger? (C. Norledge)Use the four operations with standard form to work out which of four numbers is larger. Multiplying and dividing standard form loop (Alison Banks via TES)Practice multiplication and division with real-life standard form examples. Ordering and Inequality Notation
Order positive & negative integers, use the number line as a model for ordering of the real numbers (KS3)Use the symbols =, ≠, <, >, ≤, ≥ (KS3) Resources coming soon! Rounding and Estimation
Rounding to Integers and Decimal Places
Round numbers and measures to an appropriate degree of accuracy, such as a number of decimal places or significant figures (KS3) Teaching Rounding (The Storeroom)A few tips and ideas to get pupils to master basic rounding skills. Standards Unit N3 Rounding Numbers (via Craig Barton)This lesson focuses on rounding to 10, 100 and 1000 but could easily be adapted to decimal places. Codebreaker (MathsPad)Codebreaking worksheet with a mixture of one and two decimal places. Worksheet generator (MathAids)Basic generator allowing selection of tenths, hundredths or thousandths. Mad Maths Minutes (Snappy Maths)Quick basic practice sheets to be done as timed challenge. Worksheets from greatschools.orgSheet one: Rounding decimals to nearest whole.Sheet two: Rounding to nearest tenth.Master the Basics (The Storeroom)Standard questions for basic practice; can be used as a recap starter, main activity or assessment: Rounding numbers interactive (Flash Maths)Flash question generator; great as a starter or revision resource with mini-whiteboards or hot-seat questioning. Starter of the Day (Transum)Quick problems for display on whiteboard. **Rounding distances to the nearest whole****Rounding distances to one decimal places****Rounding distances to two decimal places**
Round the Dice Decimals 1 (Link)Little investigation practising rounding one decimal place to the nearest whole. Requires two dice per pair/group. Question Trade (Teach It Maths)Each pupil has a card with a question on; they pair up, answer each other's question, then trade cards, with the objective of collecting as many answers as possible. This QT focuses on rounding to two decimal places. Rounding to Significant Figures
Round numbers and measures to an appropriate degree of accuracy, such as a number of decimal places or significant figures (KS3)Teaching Rounding (The Storeroom)A few tips and ideas to get pupils to master basic rounding skills. Worksheet generators (MathAids)Basic generator; check out the addition/subtraction and multiplication/division worksheets, which require pupils to calculate with decimals before rounding their answer. Workout (StudyMaths)Question generator - good for basic repeated practice. Round up to five significant figures. Estimation and Approximation
Use approximation through rounding to estimate answers (KS3)Calculate possible resulting errors expressed using inequality notation (KS3) Apply and interpret limits of accuracy when rounding or truncating (KS4) GCSE 9-1 New Content - Error Intervals (Just Maths)From an excellent series of blogs on new GCSE content, this one picks apart the meaning of the objective about limits of accuracy, rounding and truncation. CIMT Y9B Ch14 Estimation and Approximation (Link)Nice consolidation work on rounding to decimal places and significant figures, leading into practice on estimation skills. Also includes an introduction to bounds and error propagation. OCR Topic Check-in (Link)Ten exam-style questions on approximation and estimation. Suggestions for use available from OCR here. Approximation Worksheet (nottcl via TES)Simple worksheet with context-based problems. Rounding and Estimating - Who Dunnit? (JustMaths)Excellent murder mystery; includes some standard form in the last section. Counting Crowds (TwigWorld via YouTube)Estimating the number of people watching Barack Obama's inauguration. Transum:**Hot Estimates**: Estimate the number of chillies in the photograph.-
**Moon Lengths**: Estimate distances on a satellite photograph of the moon. **Big Order**: Requires some real-life estimations before putting numbers in order.**Second Holiday**: Estimation problem using time.**Breathe Easily**: Estimate the number of breaths taken in your lifetime so far.
Lower and Upper Bounds (H)
Apply and interpret limits of accuracy when rounding or truncating, including upper and lower bounds (KS4 Higher only)Resources coming soon! Four Operations
Written Multiplication Methods
Use the four operations, including formal written methods, applied to integers (KS3)Multiplication madness (Part 1 / Part 2 from The Storeroom)My thoughts on the eternal methods debate - grid, lattice or long multiplication? Chinese multiplication (Craig Barton)An argument against Chinese/lattice/Napier's rods. Multiplication methods (Stephen Cavadino)Speed-testing the different methods of multiplication. Moving from a grid to a column method (NCETM)An excellent video using classroom work to show how to structure a move from grid multiplication to the column multiplication algorithm. Written multiplication basics worksheet (C Norledge)Worked examples of four methods for multiplication with questions for pupils to try. Times tables practice (Maths Salamander)Generates times-table questions with options to select particular tables or groups of tables; great for timed practice. Written method worksheets (MathsBlog.co.uk)A huge stack of worksheets with many different levels of problem; targeted at primary curriculum but very useful for work with early secondary as well. Worksheets from greatschools.org**Sheet one**: Multiplying two-digit decimal by integer**Sheet two**: Multiplying three-digit decimal by integer**Sheet three**: Multiplying two digits by two digits**Sheet four**: Multiplying three digits by two digits
Workouts (StudyMaths)Question generator - good for basic repeated practice. Amoeba multiplication game (BBC Skillswise)Based on the grid method for multiplication, with three levels of difficulty. KESH Maths Takeaway (Link / Answers)GCSE practice problems booklet (N.B. 1MA0 specification); covers both multiplication and division of whole numbers. Multiplication video (BBC Skillswise)One-minute video with real-life examples of multiplication. Method in multiplying madness? (NRich)A lovely activity looking at different methods of multiplying whole numbers, including grid, traditional column, Chinese/Gelosia and multiplying with lines. Brilliant for revising multiplication with higher ability, with lots of room for discussion. Long multiplication (NRich)A tricky problem-solving activity, suitable as an extension task for those students who have mastered the traditional long multiplication method. Non-calculator multiplication practice (Don Steward)See the last slide for a great problem-solving puzzle. Max prod (Don Steward)Investigate the largest products that can be made using long multiplication. Short Division
Use the four operations, including formal written methods, applied to integers (KS3)Dare to share fairly interactive (Maths Playground)Excellent interactive for division using 100, 10 and unit blocks. Division by single digit with and without remainder (MathSphere)Sample worksheets on simple short division; aimed at KS2 but applicable for supporting lower KS3 too. Worksheet collection (Maths Drills and Teaching Image)Huge selections of customisable worksheets. Worksheet collection (greatschools.org) - dealing with remaindersSheet one: Two-digit division using fraction remaindersSheet two: Three-digit division using fraction remainders.Sheet three: Dividing three-digit by two-digit with fraction remainders.Master the basics (C. Norledge)Standard questions for basic practice; can be used as a recap starter, main activity or assessment. Workouts (StudyMaths)Question generator - good for basic repeated practice. Starter of the day (Transum)Quick problems for display on whiteboard. **Halve It:**Start with 512 and keep halving. Could be done mentally or with written methods, extends nicely into decimals.**Quickulations**: Quickfire division facts; great with mini-whiteboards.**Digivide**- Arrange the numbers 1-6 to form a correct division statement.
Are you a mathmagician? (Oswego)Pupils answer questions against the clock; use with whole class with mini-whiteboards or as independent work with a computer. Sum sense: Division (Oswego)Drag and drop numbers to make a correct division calculation. Division bingo (BGfL)Interactive division game to practise basic division facts. KESH Maths Takeaway (Link / Answers)GCSE practice problems booklet (N.B. 1MA0 specification); covers both multiplication and division of whole numbers. Don Steward:BBC Skillswise:**Why learn to divide**: One-minute video clip.**Splitting into factors**: Worksheet looking at dividing by splitting the divisor.**Interpreting division problems**: Worksheet with real-life problems and focus on interpreting remainders.
Operations with Negative Numbers
Use the four operations, including formal written methods, applied to negative integers and decimals (KS3)How we teach addition and subtraction of negative numbers (Bruno Reddy)An interesting discussion about teaching strategies for negative numbers. Why is a negative times a negative a positive? (Dr Math)Lots of ideas for explaining to pupils why a negative multiplied by a negative gives a positive result. Numberline ITP (Primary National Strategies)Interactive number line, excellent for supporting all work on addition, subtraction and ordering negative numbers. Negative Numbers (NRich)A look at the history of negative numbers and resistance to them. Interesting reading, and perhaps explains why pupils have difficulty visualising and working with negatives as quantities. BIDMAS Crossnumber puzzle (Teachit Maths)A nice little puzzle combining work on order of operations and negative numbers. Directed number gaps (Don Steward)Fill in the calculations with directed numbers. Basic practice with a difference! Worksheet collection (Maths Drills)Huge selection of customisable worksheets. Basic practice worksheets (Worksheet Math)Excellent worksheet generator with options to select numerical, algebraic or a mixture of problems, and automatic answer generation: Workouts (StudyMaths)Question generator - good for basic repeated practice. Starter of the Day (Transum)Quick problems for display on whiteboard. **Negative Numbers**: Quick negative numbers practice, including use of algebra and substitution.**Negative Vibes**: Activity using negative numbers in the context of temperature.
Negative numbers interactive (Flash Maths)Flash question generator for adding and subtracting directed numbers; great as a starter or revision resource with mini-whiteboards or hot-seat questioning. Connect Three (NRich)Paired game to practise adding and subtracting with negative numbers. Negative numbers boxes game (Labrown20 via TES)I absolutely love this resource - I've got a set laminated in my classroom so pupils can play with whiteboard markers. Adds a nice competitive element to practising adding and subtracting directed numbers. Don Steward:**Combiner les nombres**:**Balloons**: A really challenging balancing problem with positives and negatives.
Negative numbers codebreaker with a twist! (@MathedUp via Twitter)Great activity to practise adding negative numbers - extend as far as needed. BBC Skillswise**Why use negative numbers?**: One-minute video clip.**Reading the weather**: Worksheet ordering and finding the differences between temperatures in the UK.
Number Line Foldable (via Resourceaholic)Print a foldable number line to stick in the back of exercise books, so pupils can refer to it as they need it. Math Vegas (HannahJoy21 via TES)Whole-class competition (played in teams) - a brilliant way to finish off a topic on negative numbers. Integer Song 2 (arithmecode via YouTube)Silly song about good guys and bad guys; not recommended for first teaching or understanding, but great for emergency work with Year 11. Order of Operations and Inverse Operations
Use conventional notation for the priority of operations, including brackets, powers, roots & reciprocalsRecognise and use relationships between operations including inverse operations (KS3) Standards N5: Understanding the laws of arithmetic (via Craig Barton)Excellent card sort linking order of operations and shape representations; great for laying the groundwork for similar work using algebra. BODMAS Cities (Andy Lutwyche via TES)Codebreaking activity with names of five international cities; more interesting than straight practice problems with a good mix of power and bracket calculations as well. Addition, multiplication and division (greatschools.org)Simple worksheet useful for introducing inverse operations. Master the Basics (The Storeroom)Standard questions for basic practice; can be used as a recap starter, main activity or assessment. Maths Target (Flash Maths)Countdown-type starter activity - pupils use four numbers to reach a target. Order of operations workout (StudyMaths)Question generator - good for basic repeated practice. KESH Maths Takeaway (Link)GCSE practice problems booklet (N.B. 1MA0 specification) Sixes (The Storeroom)Use four sixes and any mathematical operations to make the numbers from 1 to 10. Transum (Starter of the Day)**Missing Operations**- Pupils fill in the missing operations in some BIDMAS problems with large numbers.**Clock Equate**- A decent little starter for practising simple operations with scope to extend further.
Broken Calculator Flash application (Suffolk Maths)Pupils work out how to input calculations into a broken calculator using BIDMAS. The file is a direct download and can be run without Internet connection. Make 100 (NRich)Use operation signs in between the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 to make an answer of 100. Pupils could try and find more than one solution. There's a poster version available which may be useful to display on an interactive board. Bonfire Night BIDMAS (The Storeroom)Use the digits in the date 5/11/1605 and mathematical operations to make as many integers from 0 to 40 as possible. This works nicely as a whole-class activity. Order of operations Tarsia (Craig Barton via TES)Standard Tarsia puzzle with a nice mixture of BIDMAS problems. BIDMAS Murder Mystery (CPerkins92 via TES)Murder mystery using Britain's Got Talent judges as suspects; great for a summary or bit of revision. Factors, Multiples and Primes
Factors, Multiples and Primes
Use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors and common multiples (KS3)Primitives (Ptolemy)A beautiful visualisation of factors; although more focused towards prime factor decomposition, it may be appropriate to show this to students or ask them to draw similar factor diagrams. Sieve of Erastothenes gif (Wikimedia Commons)Useful if you don't have time to complete a Sieve with pupils.Finding factors (Super Teacher Worksheets)Decent basic worksheet for finding factors. Worksheet generators (WorksheetMath)Basic practice sheets for factors, multiples, primes, common factors and common multiples. Worksheet collection (greatschools.org)**Sheet one**: Straightforward problems finding factors of numbers.**Sheet two**: Factors of numbers from 1 to 30.**Sheet three**: Factors of numbers from 31 to 65.**Sheet four**: Factors of numbers from 66 to 100.**Sheet five**: Multiples of 2, 5 and 10.**Sheet six**: Multiples of 3 and 4.**Sheet seven**: Multiples of 6, 7 and 8.**Sheet eight**: Multiples of numbers from 6 to 12.**Sheet nine**: Finding the greatest common factor.
Factors and multiples - Master the Basics (C Norledge)Mixed practice with simple factor and multiple problems. Find the common factors - Multiple choice starter (C Norledge)Can be done with mini-whiteboard or ABCD cards; pupils pick the common factor(s) of given numbers. Workouts (StudyMaths)Question generator - good for basic repeated practice. Factors starter (Ben Cooper via TES)Quick multiple-choice activity for use as starter/plenary, good with mini-whiteboards. Factor frenzy (Teach It Maths)Compete to fill a grid with factors; play in small groups. Requires dice. Gozinto (Craig Barton)Dice game working with multiples; a lovely way to fill a few minutes. Requires counters and dice. Factors and multiples game (NRich)Paired game, great activity for consolidation of factors and multiples. Premade instructions and game boards are available from Access Maths. Factor pairs revision game (matematiko via TES)A fantastically rich revision activity based on factors, but including a lot of other areas of mathematics. Brilliant for a general revision lesson. Divisible by 8 (The Storeroom)Look for patterns in multiples of 8. Starter of the Day (Transum)**Abundant Buses**: Nice activity looking at a topic that's not technically on the National Curriculum, but offers a great bit of practice on finding factors.**Hotel Digital**: Finding multiples of 7 in context, linking to finding lowest common multiple.
Find the factors (Link)More puzzles than you will ever need, but these are superb little starters for getting pupils to practise finding factors or times table knowledge. Don Steward**Product Puzzles**: Fill factors in a four-by-four grid to equal the products outside.**Factorgrams**: Pupils draw arrows to show "is a factor". Lovely for drawing out the distinction between factors and multiples.**Cancelling Down**: Cancel fractions with large denominators using knowledge of factors and multiples.
Number-type cards (Churchill Maths)Problem-solving activity, great for practising factors, multiples, primes and other number properties. Prison investigation (Suffolk Maths)Worksheet-based version of the prison investigation, reinforcing idea that square numbers have an odd number of factors. Factors and multiples puzzle (NRich)Use logic and reasoning to arrange statements and numbers. Requires a board and cards per pair. Divisibility testing (The Storeroom)Extend work on factors and multiples by looking at divisibility tests for 2, 5, 10, 100, 3 and 9. Counting cogs (NRich)Working with factors, multiples and common factors to solve problems involving meshing cogs. Could be a good way in to exploring common factors. Drag and drop Venn diagrams (Flash Maths)Question generator using factors, multiples, primes, squares, cubes etc. Factors, multiples and primes interactive (MathsPad)A selection of interactive whiteboard activities, including a Venn diagram puzzle, a grid puzzle and some work on prime numbers. Prime match (Edutopia)Card sort activity using primes, composites, factors and multiples. Product of Primes, HCF and LCM
Use the concepts and vocabulary of highest common factor, lowest common multiple and prime factorisation, including using product notation and the unique factorisation property (KS3)Factor Trees (Don Steward)Some great worksheets/templates for introducing factor trees for finding product of prime factors. Tricks and Tips: HCF and LCM (Jo Morgan)Six different methods for finding HCF and LCM with discussion of which to teach pupils. Worksheet generators (WorksheetMath)Basic practice sheets: **Prime factorisation****HCF from prime factorisation****LCM from prime factorisation****HCF and LCM from prime factorisation**
HCF and LCM Star Matching (Teach It Maths)Pupils match triangles around a pentagon and hexagon to create a star using HCF and LCM; a different twist on basic skills practise. HCF/LCM Bingo (Stephen Peacock via TES)Bingo activity with prepared cards. Number of Factors (Median)A really interesting way to visualise and explore factors and prime factorisation including squares and cubes. Interactive Factor Tree (Math Playground)Nice little flash app for demonstrating use of factor trees to find the product of prime factors. Powers and Roots
Square and Cube Numbers
Use integer powers and associated real roots: square, cube and higher (KS3)Square numbers? (Crewton Ramone's House of Math)Excellent lesson idea using manipulatives to discover squares. Video demonstrations (via YouTube)**Square numbers demo:**Using linking cubes to explore how square numbers get their name.**Cube numbers demo**: Using linking cubes to explore how cube numbers get their name.
Basic practice (Maths Worksheets 4 Kids)Large selection including squaring fractions, decimals and negatives. Square Numbers (Worksheet Fun)A really nice template for recording square numbers - could be printed on A5 and stuck into books. Workouts (StudyMaths)Question generator - good for basic repeated practice: Spooky Sequences (Oswego)Find the missing square number in the sequence - a quick game for use on interactive board or independent practice. Transum (Starter of the Day)**Square thinkers**: Find two square numbers which sum to give a third. Could also be useful as an introduction to Pythagoras Theorem.**Square pairs**: Arrange the numbers 1 - 15 so that adjacent sums are square numbers.**Square and even**: Magic square puzzle.**Pears make squares**: Problem-solving using the sums of square numbers.
Consecutive Squares (Transum)Look for patterns in the difference of squares of two consecutive numbers. If applicable, pupils could prove their result using algebra. Cycling Squares (Magical Maths)Arrange a set of numbers so that each adjoining pair makes a square number. Video-based with solution. Premier League of Square Numbers (3-11 Maths)Allocate seats at a football stadium in square groups. NRich:**One Wasn't Square**: Problem involving squares and sums of squares. Could be modeled using pupils as described in the activity.**Picturing Square Numbers**: Linking sums of consecutive odd numbers to square numbers.**Two Primes Make One Square**: Can you make square numbers by adding two prime numbers together? Does it always work?
Don Steward:**Making Squares**: A great problem to really stretch pupils.
SMILE Maths (via STEM centre)Collection of resources including some great stuff on square numbers. Integer Indices
Use integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5 (KS3)Calculate with integer indices (KS4) Index Notation (CIMT)Useful exercises for practising use of index notation for positive integer bases. Integer Indices Codebreaker (The Storeroom)Short puzzle activity to practise using simple laws of indices for integer bases. Master the Basics (The Storeroom)Standard questions for basic practice; can be used as a recap starter, main activity or assessment. Indices Four-in-a-Row (Teach It Maths)Paper version of four-in-a-row matching game; pupils pair up correct expressions containing indices. Sum of Consecutive Cubes (The Storeroom)Compare the sum of consecutive numbers to the sum of consecutive cubes. Can you find a generalisation? Consecutive Power Sums (The Storeroom)Look for patterns in consecutive powers written as sums. Don Steward**Find the Power:**Some really challenging power questions.**Tree**: Nice problem involving visualisation of powers, might also be a good link into exponential growth.**Powers of 11**: Exploring interesting patterns in powers of 11.**Sierpinski Triangles**: A good opportunity to explore the links between powers and these fractal patterns.
Powers Tarsia Puzzle (fionajones88 via TES)Straightforward puzzle practising simple integer powers. Indices Dominoes (Teach It Maths)Simple applications of multiplication, division and power of a power laws. Working with Roots
Distinguish between exact representations of roots and their decimal approximations (KS3)Calculate with roots (KS4) Coming soon! Surds and Roots (H)
Estimate powers and roots of any given positive numberCalculate exactly with surds Simplify surd expressions involving squares and rationalise denominators (KS4 Higher only) Basic Practice Worksheets (Worksheet Math)Excellent comprehensive selection of worksheet generators, including all forms of surd simplifications, bracket expansion and three difficulty levels for rationalising the denominator. Quick picks: **Simplifying surds****Adding and subtracting surds****Multiplying and dividing surds****Multiply two brackets****Mixed rationalising the denominator**
Workouts (StudyMaths)Question generator - good for basic repeated practice. KESH Maths Takeaway (Link / Answers)GCSE practice problems booklet (N.B. 1MA0 specification) Fractional Indices (H)
Calculate with fractional indices (KS4 Higher only)Mental Powers Codebreaker (Teach It Maths)Plenty of practice on all types of indices questions, including brackets, negative and fractional indices - great for a bit of revision. Fractional Indices (Virtual Textbook via National Stem Centre)Interactive Excel spreadsheet with lots of problems and examples on fractional indices; use as examples or as quick problems for pupils to answer. Fractional and negative indices workout (Study Maths)Question generator - good for basic repeated practice. Negative and fractional indices bingo game (Clea Rogers via TES)Challenging bingo game to practice negative and fractional indices. KESH Maths Takeaway (Link)GCSE practice problems booklet (N.B. 1MA0 specification) Standards Unit N12: Using indices (via Craig Barton)Excellent card match activity using negative and fractional indices, both with numbers and algebraic expressions. Fractional Indices Dominoes (Craig Barton via TES)A challenging dominoes/Tarsia activity with plenty of tricky negative and fractional indices; also appropriate for A Level. Indices package (Susan Wall via National Stem Centre) A selection of great activities aimed at Post-16 but relevant for Higher GCSE. ## Fractions, Decimals and PercentagesFraction Calculations
Equivalent Fractions and Simplifying Fractions
Recognise and show, using diagrams, families of common equivalent fractionsUse factors and multiples to recognise equivalent fractions and simplify where appropriate (KS2) BLOG Which is Bigger? (The Storeroom)Introducing fractions by discussing how to compare two fractions in great depth. Triplets (Math Playground)Group pairs of equivalent fractions and a representative diagram. Equivalent Fraction Builder (Illuminations)Use diagrams to build families of equivalent fractions. Worksheet generator (MathAids)Basic generator options to pick denominators to make problems easier or more challenging. Catchphrase Equivalent Fractions (Numberloving)Pupils come up with equivalent fractions to those shown to reveal the picture. Equivalent Fractions Frenzy (Math Warehouse)Quick game for revision or use on board with whole class. Finding equivalent fractions (Maths4Life package via Excellence Gateway)Lesson plan for exploring equivalent fractions in the context of money amounts. What fraction am I? (via Craig Barton)Pupils find equivalent fractions using clues - "I am equivalent to ½ . The sum of my numerator and denominator is 15." Eduplace have a worksheet with a similar set of puzzles.Fraction Machine (TES IBoard)Interactive resource requiring pupils to find the missing denominator of an equivalent fraction. Equivalent Fraction Weights Interactive (Teacher Led)An excellent visual representation of equivalent fraction comparisons using weights to show which is larger. Fraction Wall (Visnos)Excellent interactive fraction wall; can be customised to include any fraction. Equivalent Fractions Tarsia (Thomas Pitts via TES)Standard Tarsia puzzle. Equivalent Fractions Snap (Craig Barton via TES)Quick snap game using equivalent fractions. Improper Fractions and Mixed Numbers
Recognise mixed numbers and improper fractions and convert from one form to the other (KS2)BLOG: Teaching improper fractions and mixed numbers (The Storeroom)Blog post about teaching improper and mixed conversions using link cubes and bar modelling. There's Nothing Improper About Them (UEN)Full lesson on improper fractions and mixed numbers using shape manipulatives. Sharing Cakes (via NCETM)Pupils match up words, diagrams and division calculations to explore sharing amounts of cakes between numbers of people. Great for exploring all sorts of themes on fractions, but particularly relevant to mixed and improper. I would now probably adapt this activity in the light of bar modelling to use rectangular objects, such as chocolate bars. Improper fractions codebreaker (Teach It Maths)Brilliant codebreaker requiring pupils to work both ways with mixed and improper conversions. Worksheet generator (MathAids)Basic generator with options to choose denominators to differentiate problems. Fractions puzzles (via Ms Diaz's Class)Some lovely fractions riddles to solve; see pg 14 and 15 for improper fraction and mixed number conversions. Converting between mixed and improper (BBC Skillswise)Quick matching worksheet; students match mixed, improper and the intermediate calculation. Fraction format maze (Worksheet Works)Maze requiring pupils to identify either improper fractions or mixed numbers to find a path from one side to the other. Pupils can then convert their path to the alternative form for a bit of standard practice. Worksheets from greatschools.orgSheet one: Converting improper fractions to mixed numbers.Sheet two: Conversions both ways.Find the Mistake (Ben Cooper via TES)PowerPoint with 10 incorrect questions on improper and mixed conversions; students need to identify the mistake that has been made in each case. This could make a good plenary or quick consolidation/reminder activity. PacMan Improper and Mixed (Sheppard Software)In this PacMan game, the ghosts have improper fractions written on them. The player has to eat the fractions in order according to the mixed number shown on the bottom. Could be nice for a bit of computer room work or independent practice. Improper to Mixed Fraction Tool (TES IBoard)Quick interactive on converting improper fractions to mixed numbers by extracting one unit (whole) at a time. Fractions ITP (Primary National Strategies)A really useful interactive resource for all work on fractions. Improper and Mixed Matching Cards (JamesCMartin via TES)Simple set of improper fractions and mixed numbers matching cards for a quick card sort activity. Improper and Mixed Tarsia (chuckieirish via TES)A couple of Tarsia puzzles practising improper and mixed conversion. WARNING: One of the answers is wrong and will need changing using the Tarsia software before printing the puzzle (see comments on TES). Fractions of Amounts
Recognise, find and write fractions of a discrete set of objects (KS2)Interpret fractions as operators (KS3)13 ways of looking at a half (PBS Kids)Interactive/game investigation which offers a nice route into looking at fractions of amounts. Swite (via TES) has some excellent supporting resources to turn this into a whole-class activity.Thinking blocks - Fractions (Math Playground)Interactive context-based problems using bar modelling to find fractions of amounts. Find a fraction of a quantity - Prezi (P. Mattock)Full lesson with some great worked examples and problems using bar modelling. Fractions of amounts using a bar diagram YouTube tutorial (C. Norledge)Video tutorial with examples, Arithmetic: Fractions (CIMT)See Section 10.1 for shading fractions and Section 10.3 for fractions of amounts. Fractions of amounts maze (clangercrazy via TES)Fractions of amounts problems differentiated three ways; students solve problems to find a path through the maze. Basic practice worksheet (Worksheet Math)Excellent worksheet generator with options to select unit numerator or any numerator. Fractions of amounts worksheet bundle (duncant01 via TES)Good collection of fraction of amounts problems, including worded/context-based questions. Worksheet collection (greatschools.org)**Sheet one:**Simple fractions of amounts with unit denominators.**Sheet two**: Mixed fractions of amounts problems.**Sheet three**: Fractions of amounts with decimals.
Fractions Spider (Flash Maths)Infinite generating starter to practise finding fractions of amounts. Fractions dartboard (Topmarks)This interactive generates more problems than you'll ever need on fractions of amounts, and could be done in books, verbally or on mini-whiteboards. The site also has a bingo-based game which could be used in a similar way.KESH Maths Takeaway (Link)GCSE practice problems booklet (N.B. 1MAo specification) BBC Skillswise:**Changing Recipes**: Problems involving converting/adapting recipes using fraction calculations.**Fractions of time**: Looking at halves, quarters and three-quarters in the context of time.**Why use fractions?:**Short video with real-life examples of fraction use.**Fractions of something**: Visualising fraction models using pizza, chocolate, water jug and population.
Fractangle (Transum)Complicated-looking problems with a quick, easy solution. Don Steward:**Fractions 'of'**: Linking fractions of amounts with multiplication.**Fraction that is a triangle**: Working with triangles inside a rectangle; nice links to area.
NRich**Chocolate:**A great problem to explore by actually using tables/chocolate bars and encouraging pupils to draw their responses.**Peaches today, peaches tomorrow**: Low-entry problem with plenty of scope for deep extension.
Fractions, fractions, fractions (Solve my Maths) Large collection of fraction activities, most differentiated three ways. Adding and Subtracting Fractions
Use the four operations, including formal written methods, applied to proper and improper fractions and mixed numbers, all both positive and negative (KS3)Teaching adding and subtracting fractions (Part 1 / Part 2 from The Storeroom)My approach to adding and subtracting fractions using bar modelling. Adding and subtracting with bar models - worth sticking with (Peter Mattock)Peter's experiences using bar modelling to add and subtract fractions - this one's definitely worth a read! Adding fractions inquiry (via Inquiry Maths)Using number lines and unit fractions to explore fraction addition. Examples - Adding fractions using a bar (C. Norledge)Examples for display/discussion on whiteboard. Adding and subtracting fractions bar (Active Maths)A lovely little interactive to assist with bar modelling of fractions. Requires small subscription. Don Steward:**Common dechocolateater**:**Same name**:**Fraction Pattern Add One / Two / Three**: Standard problems with a pattern.**Four digits, two fractions**: Arrange the digits 2, 3, 4 and 5 to make the smallest and largest possible fraction additions.**Seven 20ths**: Find solutions to fraction subtraction problem with answer 7/20.**Fraction triangles****: Nice puzzles for addition and subtraction - these work well as a simple extension activity.****Someone**: Interesting problem linking fraction addition patterns and perfect numbers.
NRich**Keep it simple**: Exploring Egyptian (unit) fractions; a nice activity linking work on fractions and factors.**Egyptian Fractions**: Article from NRich with background and history on Egyptian (unit) fractions with links to suggested activities. Surrey University also have a**very extensive page on Egyptian fractions**, with many problems that could be adapted for the classroom.
BLOG: Maths Puzzles Galore (The Storeroom)Links to a few lovely activities - these can be more interesting and motivating than a standard worksheet. Adding fractions starter activity (Eugene Smith via TES)A superb puzzle to practice adding fractions - gets a good response every time I use it. Magic squares with fractions (TeachIt Maths)Magic square activities to practice adding and subtracting fractions and mixed numbers. Worksheet collection (Maths Drills):**Adding fractions with easy common denominators****Subtracting fractions with easy common denominators****Adding and subtracting proper and improper fractions****Adding and subtracting mixed numbers**
Worksheet generators (Worksheet Math)Basic practice sheets with options to choose difficulty level of denominators: Worksheet collection (greatschools.org)**Sheet one**: Adding with common denominators and simplifying.**Sheet two**: Adding with common denominators then simplifying including mixed numbers.**Sheet three**: Adding with different denominators and converting to mixed numbers.**Sheet four**: Adding mixed numbers with common denominators.**Sheet five**: Adding mixed numbers with different denominators.**Sheet six**: Subtracting with common denominators and simplifying.**Sheet seven**: Subtracting with different denominators.**Sheet eight**: Subtracting mixed numbers.
Master the Basics (C. Norledge)Sets of basic questions optimised for whiteboard display; quick alternative to textbooks. Find the mistakes (C. Norledge)Get pupils to identify and correct mistakes in a fraction addition problem. Works well as a plenary-type activity or short assessment. Workouts (StudyMaths)Question generator - good for basic repeated practice. Fraction Pattern Add One / Two / Three (Don Steward)Standard problems with a pattern. Closest to 1 (C. Norledge)Use a combination of fraction additions to make a calculation as close to 1 as possible. Has scope for further extension. Why not add tops and bottoms (Craig Barton via TES)Problem and demo reinforcing the idea that you don't just add the tops and bottoms of fractions. Adding fractions interactive (Math Playground)Self-checking programme which generates questions on adding fractions. Spreadsheet generator (dwatson802 via TES)Infinite self-checking question generator in the form of an Excel spreadsheet. Fractions jigsaw (NRich)Nice little jigsaw puzzle in a similar vein to Tarsia; uses simple denominators so good for pupils who are just beginning to add and subtract fractions. Adding and subtracting fractions Tarsia (Craig Barton via TES)Comprehensive Tarsia puzzle for addition and subtraction of fractions; includes a mixture of like denominators, unlike denominators and some mixed number answers. Adding fractions mystery (C. Norledge)This is based on an adding fractions mystery from Numberloving - I had to change the numbers as the original was too challenging for my class.Multiplying and Dividing Fractions
Use the four operations, including formal written methods, applied to proper and improper fractions and mixed numbers, all both positive and negative (KS3)Fractions ITP (Primary National Strategy)Excellent for all fractions work to support use of bar modelling; particularly good for creating visual models for division. Fraction Multiplication Excel Interactive (NRich)Bar model interactive for multiplying two proper fractions. BLOG: Maths puzzles galore (The Storeroom)Links to a few lovely activities - these can be more interesting and motivating than a standard worksheet. Fractions maze (danwalker via TES)Brilliant maze activity with all four operations using fractions, including mixed numbers. The PowerPoint also includes some wrong answer problems for pupils to correct, and a blank template so pupils can construct their own mazes. Worksheet generators (Worksheet Math)Basic practice sheets with options to choose difficulty level of denominators: Multiplying fractions (greatschools.org)Basic practice worksheet. Fraction Calculation Interactives (Multiplication / Division via Math Playground)Self-checking programme which generates questions on adding fractions. Decimals and Fractions
Ordering and Comparing Fractions and Decimals
Order decimals and fractions (KS3)Work interchangeably with terminating decimals and their corresponding fractions (KS3) Which Is Bigger? (The Storeroom)Blog post about one of my favourite activities - I do this to introduce work on equivalent fractions, then return to similar problems to introduce use of inequality symbols between the fractions. Comparing and Ordering Fractions and Decimals (The Storeroom)Blog post about a full set of lessons based on Standards Unit card sort N1 Ordering Fractions and Decimals.Comparing fractions worksheet (Math Aids)Worksheet generator for comparing two fractions; pupils use a common denominator to compare fractions, then insert the correct inequality symbol. Allows you to select denominators to change difficulty of problems. Worksheet collections (greatschools.org) - converting between fractions and decimals**Sheet one**: Simple conversion using place value.**Sheet two**: Converting between fractions and decimals using 10, 100 and easy denominators.**Sheet three**: Converting fractions to decimals using place value and division.**Sheet four**: Fractions and decimals greater than 1.
Worksheet collections (greatschools.org) - comparing and ordering decimals**Sheet one**: Comparing/ordering pairs and triples of decimals.**Sheet two**: Ordering sequences of decimals.**Sheet three**: Ordering sets of decimals with units.
Don Steward**Fractions to decimals**: Problem based on KS3 SATs question.**1/9 as a decimal**: Interesting visual representation of 1/9 as a decimal; great for a bit of discussion!
Fraction Order (Transum)Drag and drop to order common fractions and decimals. There is also a pupil version with three levels of activity which would also work as a whole-class starter.Farey Sequences (NRich)A lovely bit of pure maths related to sequences of ordered fractions. Fractions on a Number Line (BGfL)Interactive requiring pupils to place fractions on a number line using common denominators to compare; whole class activity or independent practice on computers. Ordering Fractions Interactive (Top Marks)Drag and drop activity; places fractions in height order, which is great for reinforcing ascending/descending vocabulary. Comparing Fractions Self-Checker (Math Playground)A self-checking interactive which generates questions on comparing fractions using inequality symbols. Could be used independently by pupils or to generate examples for discussion for the whole class. Four operations with Decimals
Use the four operations, including formal written methods, applied to decimals KS3)Decimal magic square worksheet generator (WorksheetWorks)Practising decimal addition with magic squares. Division of three-digit decimals (greatschools.org)Basic practice dividing decimal by whole number. Dividing decimals workout (StudyMaths)Question generator - good for basic repeated practice:Coming soon! Recurring Decimals (H)
Change recurring decimals into their corresponding fractions and vice versa (KS4 Higher only)Recurring Decimals (Median)Some interesting representations of the recurring patterns of sevenths. 998,001 and its mysterious recurring decimals (Numberphile)Ten minute video clip about what happens when you divide 1 by 998,001, with some very interesting result Percentages
Fractions, Decimals and Percentages
Define percentage as ‘number of parts per hundred’Interpret percentages as a fraction or a decimal (KS3) FDP number line (C. Norledge)Pupils match common fraction, decimal and percentage equivalents and place on a number line. Translating between fractions, dcimals and percents (MAP)Full lesson plan and set of resources for a series of lessons on fractions, decimals and percentages. FDP conversions crossnumber (C. Norledge)Crossnumber puzzle with a mixture of all fraction, decimal and percentage conversions. FSMA Fractions, decimals and percentages (Nuffield)Collection of worksheets with a variety of activities for converting between fractions, decimals and percentages. Worksheet generator (Mathaids)Generator with options to select just one or many different conversions. Fractions, decimals and percentages (Flash Maths)Good activity for use with mini-whiteboards; reveal a mixture of FDP or all of one and get pupils to convert the others. Converting percentage to decimal and fraction quickfire (C. Norledge)For use with mini-whiteboards or targeted questioning. Master the basics (C. Norledge)Standard practice questions. FDP Achievement unlocked (C. Norledge)Three levels of questions, differentiated bronze/silver/gold. Pupils pick their level of difficulty. Converting between fractions, decimals and percentages workout (StudyMaths)Question generator - good for basic repeated practice. Fractions, decimals and percentages Cookie Monster (dannytheref via TES)Nice little odd one out activity, great for a starter/plenary or quick revision. Workout (StudyMaths)Question generator to display on whiteboard, good for starter/revision, and includes answers. KESH Maths Takeaway (Link / Answers)GCSE practice problems booklet (N.B. 1MA0 specification). Why compare fractions and percentages? (BBC Skillswise)Short clip looking at real-life examples of the importance of fraction and percentage conversions. Fractions and percentages odd one out (C. Norledge)Pupils identify the odd one out in a set of three calculations - there are multiple answers for each problem, so a good opportunity to get pupils to explain their reasoning. Don Steward:**a to b as a percentage**: Problems to justify converting fractions to percentages.**Percentages to simplest fractions**: Some interesting visual representations of conversions.
FDP jigsaws (@surreallyno via Twitter)A cute little idea for creating FDP jigsaws. Percentage, fraction, decimal grid (Visnos)Well-animated tool for looking at equivalence of fractions, decimals and percentages. TES IBoard has a similar interactive which also asks questions.FDP card sort (Stacy Brookes)Simple match cards with fractions (unsimplified and simplified), decimals and percentages. Writing and Comparing Percentages
Express one quantity as a percentage of anotherCompare two quantities using percentages (KS3) Converting fractions to percentages using a ratio table (The Storeroom)Blog post about a quick method that my pupils have found very useful for writing percentages without a calculator. Why compare fractions and percentages? (BBC Skillswise)Short clip looking at real-life examples of the importance of fraction and percentage conversions. Percentages of Amounts
Interpret percentages as operators (KS3)From bar modelling to ratio tables - tidying up percentage calculation (The Storeroom)Blog post describing my ideas about progression from bar modelling to ratio tables for efficient calculations. Active Maths worksheets (Subscription needed)These are great for basic practice, with lots of options to choose which percentages appear on the worksheets. **Percentages of money (10%, 15%, 25%, 50% and 75%)****Percentages of money (multiples of 10 and whole number % less than 10%)****Percentages of money with a calculator**
Basic practice worksheets (Worksheet Math)Excellent customisable worksheet generator with answers: Worksheets from greatschools.org Percentage spider (Flash Maths)Quick starter finding a variety of percentages of amounts; infinite generator. Could also work very nicely for reverse percentages. Starter of the Day (Transum)- In Your Head
**One**/**Two**: A couple of percentage grids; find 50%, 25%, 10% and 15%. **Percentable**: Similar to above activity, but also includes 33 1/3%, 75% and 90%. There's also another one here.**Odd Percent Out**: Find the odd one out in percentage calculations.
Percentages of amounts (BBC Skillswise)Three percentage problems with step-by-step solutions; pupils have to order the solutions for each problem. Why learn about percentages? (BBC Skillwise)One-minute clip with real-life examples of percentage calculations. Percentages of amounts fantastic trail (whidds via TES)Comprehensive lesson on percentages of amounts, including a differentiated trail/treasure hunt. Percentage Bar (NZ Maths)Brilliant interactive percentage bar with problems to solve. See the Teacher's Notes for suggestions for use.Percentage Increase and Decrease
Interpret percentage changes as a fraction or a decimalWork with percentages greater than 100% Solve problems involving percentage increase and decrease (KS3) Basic practice worksheets (Worksheet Math)Excellent customisable worksheet generator with answers: Percentage increase and decrease treasure hunt (skimble38 via TES) Good treasure hunt activity, but does include some reverse percentages - probably best for revision at the end of a unit on percentages. 3 Act Maths Duelling discounts (Dan Meyer)Pupils solve a variety of problems choosing a percentage discount or fixed discount. Discount and sales tax (Fawn Nguyen)Shopping contest activity; pupils pick items from a superstore's online catalogue to get the closest to $500, including calculation of percentage discounts and tax. Needs a little adapting for a UK setting. One percentage increase followed by another (Don Steward)Pupils find a single percentage increase to represent a double change. Percentage Growth, Decay and Compound Interest
Solve problems involving percentage change, including simple interest in financial mathematics (KS3)Set up, solve and interpret the answers in growth and decay problems, including compound interest (KS4) Savings and interest resources (Nuffield FSMA)Worksheet-based lesson looking at developing use of percentage multipliers for compound interest calculations; pupils calculate the amount of money in an account after one year, then five years, which develops nicely into the "standard" formula. Three act maths - Fry's bank account (Dan Meyer)Activity based on a clip from Futurama; pupils calculate the amount of money in Fry's bank account after 1000 years. Simple and compound interest cards (jlcaseyuk via TES)A selection of bank account information cards; takes a little work to turn this into a proper lesson. ## Proportion, Ratio and Rates of ChangeProportion
Simple Direct Proportion
Solve problems involving direct proportion, including graphical and algebraic representations (KS3)Exploring proportional reasoning (The Storeroom)Blog post with lesson ideas for working with proportional reasoning using bar modelling and ratio tables. Simple Inverse Proportion
Solve problems involving inverse proportion, including graphical and algebraic representations (KS3)Coming soon! Interpreting Proportion Equations
Understand that X is inversely proportional to Y is equivalent to X is proportional to 1/YInterpret equations that describe direct and inverse proportion (KS4) Coming soon! Constructing Proportion Equations (H)
Construct equations that describe direct and inverse proportion (KS4 Higher only)Coming soon! Proportion Graphs
Interpret the gradient of a straight line graph as a rate of change (KS4)Recognise and interpret graphs that illustrate direct and inverse proportion (KS4) Instantaneous and Average Rates of Change (H)
Interpret the gradient at a point on a curve as the instantaneous rate of change; apply the concepts of instantaneous and average rate of change (gradients of tangents and chords) in numerical, algebraic and graphical contexts (KS4 Higher only)Ratio
Working with Ratio
Use ratio notation, including reduction to simplest formDivide a given quantity into two parts in a given part:part or part:whole ratio Express the division of a quantity into two parts as a ratio (KS3) Basic worksheets (Worksheet Math)Excellent worksheet generator with answers: Aunt Dotty (Transum) Quick starter using ratio to split money between two children. Mixing Paints (NRich)A lovely rich problems about mixing red and white paint to make different shades of pink. The follow-up, Mixing More Paints, is also worth a look for a bit of extra challenge. Ratio and proportion ITP (via TeachFind)Explore ratio and proportion by pouring different amounts and combining two coloured liquids. Ratios and Fractions
Understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction Relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions Identify and work with fractions in ratio problems (KS4) Coming soon! |
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