Vixen Value

The "Vixen Value" of a word is the number of vowels multiplied by the number on consonants in that word.

For example:

"Mathematics" is 28 (7 consonants, 4 vowels)

How many words can you find with a Vixen Value of 24?

What about 23?

A
E
I
O
U

A Mathematics Lesson Starter Of The Day


Topics: Starter | Factors | Vocabulary | Xmas

You can find many more ChristMaths activities at:

Transum.org/ChristMaths/

ChristMaths

  • Y11 A and B group, Rawthorpe High
  •  
  • We found that it a valuable cross-curicular learning opportunity. We found properties, reflection and chocolates.

    Merry xmas, Love Mr Heeley and Miss Jenkinson and Mr Newton

    Ps sorry, I forgot Charlotte's experiment xx
  • Grade 9 Girls, SRS, Dubai
  •  
  • We found substitute, proportion, triangular, expression, reciprocal and semicircle. Your starters are great!
  • 1D2 and Mrs Simpson, Torry Academy, Aberdeen
  •  
  • 1D2 found these words:
    QUADRATICS
    PROPERTIES
    PERCENTAGE
    DICTIONARY
    HORIZONTAL
    GLENBERVIE
    MULTIPLIED
    We also think it is impossible to make 23 as 23 is a prime number
  • 7 FP and Mrs Johnson, Stamord High School
  •  
  • We got cylindrical,estimating, remainders, arithmetic, multiplying, mysterious, millimetre, reversable, explosions......
    ......and they are still searching.
  • 2D1 and Mrs Simpson, Torry Academy, Aberdeen
  •  
  • 2D1 found these
    WHITEBOARD
    TRIANGULAR
    CORRECTION
    MANSEFIELD
    PENTAGONAL
    POWERLINES
    HYPOTENUSE
    KIRKPATRICK
  • Grade 9 Boys, SRS, Dubai
  •  
  • The boys class found understands, acceptable, restaurant, calculator, conversion, experiment and playgrounds.
  • Liam Brady, Liz Halfpenny, Paige Wilkinson, Chelse, 8H from Harrytown, Stockport
  •  
  • We found Reflection, Triangular, Perimeters, Trapeziums, Percentage and Number Line.
  • Class 5 6 A, St Catherines
  •  
  • It made maths fun and amusing!
  • 9B2, Harrytown High School Stockport
  •  
  • Triangular, Number Line, Properties, Diagonally, Reflection, Times Table

    from Alice, Alex, Jade, Verity, Ruby, Danielle
  • 9Y2, Hadleigh High School
  •  
  • 9Y2 found coursework, calculator, complexion, addictions, curriculum, incredible, chimpanzee, JordanMoat, DanielHall
  • Ken Wcislo, Queen Anne High School , Dinfermline Fife
  •  
  • 2B1 found Kincardine, percentage,calculator, Stonehaven, Challengers, interseted, democratic,multiplied, excellence, perfection,memorandum,university, proprtion, directions, inventions
    Great fun was had by all
  • Christopher Vile, Clacton-on Sea
  •  
  • Christopher is a veruca number
  • Mrs Humphreys' maths group, Nevill Road Junior School
  •  
  • We got

    detectives
    porcupines
    Netherlands
    Luxemburg
    Santa Claus
    dictionary
    Jesus Christ
    Christingle
    Nevill Road
    phone boxes
  • Rebecca Jarvis, Mr Cassidy's Year 9 Maths Class, Northoxfordshire Academy, Banbury
  •  
  • I found SUCCESSFULL. And Mr. Cassidy found Juggernaut.
  • Rebecca Jarvis, Mr Cassidy's Year 9 Maths Class, Northoxfordshire Academy, Banbury
  •  
  • I also found TOOTHPASTE!
  • Year 7 Set 1 Maths, British School Muscat, Oman
  •  
  • We really enjoyed this starter! The words we found were:
    TRANSPARENT
    TRANSLUCENT
    PERCENTAGE
    INCREDIBLE
    MECHANICAL
    HEMISPHERE
    REFLECTION
    EXPERIMENT
    MADAGASCAR
    CALCULATOR
    PROPERTIES
    DUMBLEDORE
    HARRY POTTER
    LIM YONG SONG (THATS bRIAN!)
  • Miss Cutshall's 8C Class, The International School of Luxembourg
  •  
  • Dear Mrs Humphreys' maths group, Nevill Road Junior School, We regret to inform you that you misspelled Luxembourg.
  • 7S4, Kettlethorpe high school
  •  
  • We got
    CHALLENGING
    TIMETABLES
    PROPERTIES
    CONTINUING
    ATTENDANCE
    ACTIVATING
    AMBULANCES
    ACCEPTABLE
    CALCULATOR
  • Mrs C Clark, 9ah/ma1, Mayfield School, Dagenham,Essex,
  •  
  • We found delivering, vocabulary, production, calculator, patchworks, Woodbridge, arithmetic, terminator, curriculum, university, percentage,altogether, shut ya mouf,
  • Philip Nutt, Cheney School Oxford
  •  
  • 7b5 at Cheney, here in Oxford, got DICTIONARY, EXPRESSION, CALCULATOR, INCREDIBLE, CHOCOLATES, MULTIPLYING, APOCALYPSE, MANCUNIANS, THEATRICAL, PROFFESION, HYPNOTISING and, rather topically, DEPRESSION
  • Jordan Bristow, Mr Cassidy's Year 11 Maths Class, Banbury
  •  
  • I found HEAVY METAL and Maxie realised that for 23 we could have AAAAAAAAAAAAAAAAAAAAAAAG!!!!
    Amy said we shouldn't be allowed to put in geographical places!
  • Kirsty Gull, Mr. Cassidy's Year 11 Maths Class, Banbury (again)
  •  
  • I found fingernail
  • Mr G, I&S
  •  
  • 8DEF3 got the following words:
    COMMISSION
    ILLUSTRATE
    WOODCUTTER
    VOCABULARY.
  • 8Y2 - With Miss Marsh, Bury Church Of England High School
  •  
  • We worked as a group and found
    DIFFERENCE
    ADJECTIVES
    CONTROLLERS
    ASSEMBLIES
    HORIZONTAL
    PERIMETERS.
  • 8Y3, Darrick Wood Secondary School, Orpington
  •  
  • We found:
    Percentage
    Perimeters
    celebrated
    vibrations
    calculator
    confidence
    multiplying
    university
    trampoline
    attendance.
  •  

  • MIss Butler's Year 8 Class, Park Community School, Havant, Hants
  •  
  • We enjoyed this.
    We found EASTENDERS, VALENTINES, HALLOWEENS, PERCENTAGE, TRIANGULAR, PERIMETERS, FOOTBALLER, NUMERATORS, CALCULATOR, FRIENDSHIPS, MULTIPLIED, ASSESSMENTS and EXPERIMENTS.
  • Yr 7N5 Mrs Brown, Kennet School
  •  
  • We came up with
    Turkey Meat
    Jingle Bells
    Big Rainbow.
  • The National School, Nottingham, 9t3
  •  
  • We found 24 and calculator, expressions, delivering, mathematic, pencil case, skateboard.
  • P. Shouksmith, St. Andrew's School, Eastbourne
  •  
  • We found the following words:
    Bookmarked
    Experiment
    Reflection
    Pentagonal
    Polyhedrons
    Trampoline.
  • D. Hickman Casey, 8E
  •  
  • We found the following:
    Calculater
    Bobbuilder
    Polyhedrons
    Conrollers
    Trampoline
    We are great fans of this fantastic website. We use it every math lesson. And we all love it so much!!!!!
  • Rhys , Daniel, Jordan ; Samantha, Grace Academy - Darlaston. Mr G's Yr10 Class
  •  
  • Triangular; Expression; Thirty-three; Transparent;.
  • Mr Hamshaw-Hart's 10set 3, Beverley Grammar School
  •  
  • We found
    MULTIPLIED
    CENTIMETRES
    TREEBEARD'S
    TYPEWRITERS
    SCIENTIFIC
    RECTANGULAR
    TERMINATOR
    DOORFRAMES
    and my name HAMSHAW-HART.
  • St.Mary's Primary P6, Lanark Scotland
  •  
  • Hi, we are St.Mary's Primary school and our pri6 class got 106 words altogether and the people who got the most are Owen and Charlie with 32 words. Here are ten of them:
    1.nursemaid
    2.participle
    3.dedicating
    4.victualler
    5.boatswains
    6.attribute
    7.accomplice
    8.admittance
    9.boulevards and vocabulary which Owen thought of in the playground and here are some warm up words, dictionary, chocolates and woodpecker.
  • King's College - Murcia, Year 8
  •  
  • We loved this starter. In fact, it was difficult to stop!
    difference
    headphones
    whiteboard
    multiplied
    evaluation
    Cinderella
    ambulances
    fairytale
    telephones
    calculator
    dictionary
    university
    Christopher.
  • Nareen, Wareen
  •  
  • I think this is amazing and is perfect. I found.
    Whiteboard
    Searchlight
    Helicopter
    calculator
    Adjectives
    University.
  • Mr Sim & Mr Morrison's 1b, Elgin Academy
  •  
  • PERCENTAGE
    EASTENDERS
    NEIGHBOURS
    CALCULATOR
    PERCENTAGE
    PROPERTIES
    ARITHMETIC
    CONVERSION
    ROSS CUMMING (one of the class!).
  • St .James, Yr 8 Set 5
  •  
  • Pencil case
    Monumental.
    Dictionary.
    Theatrical.
    Fosslized.
    Headphones.
    Light weight.
    Tchtyosaur
    Consider.:)
    these are the wordsthat we found.
  • 9A3, The Vyne School
  •  
  • Helicopter and dictionary.
  • Margaret Bates, Wallasey School
  •  
  • The activity was good fun and cooperation and competition took place. Quite compulsive!
  • Mr Smith, East Lanarkshire
  •  
  • We Got Transum.org, Hellraiser, twenty four, The Big Man, Good Times, Choco Cake, duck sauce, Prince Will, Cheey Toe, Hello Dude, Year Three, Year Eight and many more.
  • Dulwich College Beijing, Mr Martin
  •  
  • This was definite 5 out of 5 great challenge lots of class merits earned!
    We found 10 words.
    How about ...... Aphrodite!
    5JM
    Dulwich college Beijing.
  • 7B2, The Vyne School
  •  
  • Dictionary
    Despicable
    Mathematic
    Multiplied.
  • Mr Matthews, 7aMa1, Conisborough College, Catford, Lewisham
  •  
  • 10 correct answers from my clever top set:
    Reciprocal
    Calculator
    Multiplied
    Percentage
    Triangular
    Decreasing
    Increasing
    Expression
    Arithmetic
    Subtracting.
  • 1LF, Speyside High School
  •  
  • We had fun, but first we had to remind ourselves what vowels and consonants are. We found all these words:
    RHINOCEROS
    PROTRACTORS
    DICLOFENAC (mum's migraine medicine!)
    CANIS RUFUS (the proper name for a wolf it seems)
    ANTISEPTIC
    HARRY POTTER
    RON WEASLEY
    SANTA CLAUS
    APPRENTICE
    DICTIONARY
    ASIA MCGILL (one of our class)
    MRS FARQUHAR (our assistant).
  • Miss Emerson, Great Yarmouth
  •  
  • Class 6E found:
    Headphones
    Pencilcase
    Calculator
    HelloKitty
    Timestable
    Rainforest
    Apostrophe
    Microphone
    Collection
    ...and are still going!
  • Mrs Shaw, 8L2
  •  
  • 8L2 We found
    Mathematic
    Amplifiers
    Polyhedrons
    University
    Specialist.
  • 7S, Shrewsbury House School
  •  
  • We found:
    Multiplied
    Musicality
    Palindrome
    Bookmarked
    South Acton
    Hammersmith
    Accountant
    Vocabulary
    Now we are going to try and find words that have a score of 24 and have more vowels than consonants.
  • 5/6PR, Murwillumbah, Australia
  •  
  • We really enjoyed this activity. We had heaps of words equalling 24 then we did 32. Tomorrow's challenge will be to find words equalling 36 and 42.
  • Mr Toby Cardew, Grade 1/2 Nichols Point Primary School
  •  
  • We have a few here;
    contribute
    dictionary
    expression
    MovieWorld
    sequencing
    vocabulary
    non-Fiction
    remainders
    wideSpread
    chaimpanzee
    calculator
    permission
    jellybeans
    watermelon
    rainforest
    impossible
    franchisee
    confidence
    experiment
    production
    continuing
    aggression
    altogether
    restaurant
    acceptable
    tablespoon
    arithmetic.
  • 8A1, St Cecilia's RC High School
  •  
  • We found St Cecilia's, Santa Claus, Wonderlands, calculator, experiment, Jingle Bells, a Boxing Day, Isosceles and some names of some teachers and parents work too!
  •  

  • Mr Saye, Castle Rock High School
  •  
  • My year 7 group got the following words:
    Calculator
    reflection
    expression
    millilitre
    millimetre
    instruction
    objectives
    perfection
    impossible
    Bart Simpson works although we know it's two words!
  • Year 8 Set 2, Dylan Thomas Community School, Swansea
  •  
  • Brilliant. we came up with:
    brigadiers
    psychadelic
    analytical
    linguistic
    timetables
    stratified
    horizontal
    multiplied
    triangular
    Archimedes
    production
    bendegedig (Welsh for brilliant)
    Fforestfach (a place near Swansea)
    properties
    developing
    Mathemateg (Welsh for mathematics)
    privileges
    privileged
    curriculum
    difference
    multiplied
    calculating
    experiment.
  • Josh,
  •  
  • Our homeschool got valentines, vegetables and halloweens:{only 3}.
  • 7X2 - Miss Marsh's Group, Bury Church Of England High School
  •  
  • We found:
    CATAPILLAR
    PROTECTION
    ALPHABETIC
    CALCULATOR
    PHOTOGRAPHS
    MULTIPLYING
    EVERYWHERE
    DEMOCRATIC
    SUBTRACTING
    IMPOSSIBLE
    NUMERATORS
    MASTERMINDS
    SEMICIRCLE
    DICTIONARY
    CONVERSION
    PERCENTAGE.
  • 7ax/Ma1, Alexandra Park School, London
  •  
  • We found:
    multiplied
    university
    expression
    experiment
    qualifying
    whiteboard
    scientific
    historians
    convention
    phenomenal
    mandelbrats
    disruption.
  • 7ps/Ma2, Alexandra Park School, London
  •  
  • We got:
    illustrate
    skateboard
    conclusion
    multiplied
    sequencing
    homophones
    qualifying
    dictionary.
  • Miss. Z Loi, Woodbridge High School
  •  
  • Rory McGowan found that Rory McGowan works...
    Francesca was very lazy and found that Mathematic works.
  • Matthew, Queensland, Australia
  •  
  • I found these words:
    intestines
    windowsills
    vocabulary
    dehydrating
    references
    commercial
    hurricanes
    advertises
    demolished
    suggestion
    adventures
    understands
    dictionary
    perfection
    reviewing
    excellence
    battleships
    saxophones
    hypermarket.
  • Y6 Ladies, Dorchester, St Birinus CE Primary
  •  
  • We think this was a very good activity!
  • Miss Wallace, Colonel Frank Seely
  •  
  • 9F2 from Colonel Frank Seely found the words:
    timestable
    timetables
    multiplying
    calculator
    simplifying
    during a starter.
  • Mr McK, CSSchool
  •  
  • We're from Church Stretton in super sunny Shropshire and we totally rule at this.
    We found:
    Multiplied
    Protractors
    Percentage
    Santa Claus
    Melissa-Ann (a very famous person)
    Subtracting
    One Hundred
    Playgrounds.
  • Mr Wood And The Year 8 Alans (set 2), Henry Beaufort School, Winchester
  •  
  • Year 8 set 2 found:
    Argentinians
    Watermelon
    Reflective
    Geometrics
    Phenomenal
    Journalists
    Netherlands
    Shopkeeper
    Elephants
    Dimensions
    Calculator
    Hellokitty
    Conclusion
    Santaclaus
    Triangular
    Multiplied
    Luxembourg
    Expressive
    Especially
    Furthermore
    Conclusive.
  • Matt LAUD And The Year 9 Alans, Henry Beaufort School, Winchester
  •  
  • Multiplied
    Triangular
    Initiative
    Fabulously
    Calculator
    FioranoGTB
    Porterloos
    Auspicious
    Confidence
    Twentythree
    Crocodiles
    Permission
    Reflective
    Switzerland
    Helicopter
    Scaffolding
    Whiteboard
    Vocabulary
    Calculating
    Algebraic
    Instruments
    Trampoline
    Headphones
    Typewriters
    Mathematic
    Industrial
    Fanfiction
    Reasonable
    Dictionary
    Expression
    Telephones
    Excellence
    We could go on, but we wouldn't want to bore you with excellence....
  • Mr Wood And The 7Y1 Alans, Henry Beaufort School, Winchester
  •  
  • Rigorously
    Pentagonal
    Multiplied
    Trapeziums
    Dimensions
    Archimedes
    Stationery
    Stationary
    Scientific
    Reflective
    Permission
    Santaclaus
    Accredited
    We could go on...
  • Mrs Rogers, 9set4
  •  
  • We found:
    Slothtastic
    Santaclaus
    reflective
    calculator
    whiteboard.
  • Miss S, Chorley
  •  
  • Great starter!
    7N at St. Michaels found:
    STRATEGIES
    REASONABLY
    CONVERSION
    ORGANISERS
    :).
  • Class 6, Fagley, Bradford
  •  
  • Class 6 found:
    difference
    theologist
    attendance
    We found it easier to find words with 4 vowels and 6 consonants.
  • ISK Y8 Phoenix, Geoje, South Korea
  •  
  • We found:
    hypotenuse
    percentage
    multiplied
    maleficent
    transition
    horizontal
    challenging
    difference
    pencil(case)
    reflection.
  • 7(1), Highfield School
  •  
  • We found: excitement, marvellous, transported, photography, chocolatey, dictionary, Donald Trump and Mr Quagmire. It also prompted a discussion on the ratio of consonants to vowels in words. We have one with 7:1.
  • Mr Mansell, Minsthorpe CC
  •  
  • My Y7 class were doing very well, when someone piped up "Wouldn't it be great if Twenty Four had a Verucca Value of 24???"
    So, we began an investigation into which numbers had a Verucca Value equal to their numerical value. :).
  • 4/5L, Mr Lee
  •  
  • 4/5L found these words:
    calculator
    twenty-eight
    one hundred
    ninety-nine
    thirty-eight
    semi-circle
    remainders
    multiplied
    triangular
    twenty-seven
    column graph
    protractors.
  • Y8 Phoenix 2019-20, International School Of Koje, Geoje Island, South Korea
  •  
  • We found:
    calculated
    connection
    downtrodden
    dictionary
    production
    adventures.
  • DIS 6A, Daegu, South Korea
  •  
  • We think these work:
    difference
    Pre-Algebra
    connection
    scientific
    basketballs
    similarity
    vocabulary
    watermelon
    discovered
    expression
    nanometers
    terminated
    inventions
    assessments
    properties
    proportion
    agreements
    relatively.

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.
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Christmas Present Ideas

It is often very difficult choosing Christmas presents for family and friends but so here are some seasonal, mathematics-related gifts chosen and recommended by Transum Mathematics.

Go Genius Maths

Transform maths practice into an exciting adventure with Go Genius Maths! This award-winning board game is designed to make learning maths enjoyable and engaging for children aged 7 and above. Perfect for family game nights or classroom activities, Go Genius Maths helps players develop essential arithmetic skills while having heaps of fun.

Whether you’re looking for a gift to inspire young minds or a tool to supplement maths education, Go Genius Maths is the ultimate choice. Spark curiosity, nurture mathematical talent, and turn learning into an unforgettable journey!

Go Genius
How Not To Be Wrong

How Not To Be Wrong

The maths we learn in school can seem like an abstract set of rules, laid down by the ancients and not to be questioned. In fact, Jordan Ellenberg shows us, maths touches on everything we do, and a little mathematical knowledge reveals the hidden structures that lie beneath the world's messy and chaotic surface. In How Not to be Wrong, Ellenberg explores the mathematician's method of analyzing life, from the everyday to the cosmic, showing us which numbers to defend, which ones to ignore, and when to change the equation entirely. Along the way, he explains calculus in a single page, describes Gödel's theorem using only one-syllable words, and reveals how early you actually need to get to the airport.

What more could the inquisitive adult want for Christmas? This book makes a cosy, interesting read in front of the fire on those cold winter evenings. more... #ad

Graphic Display Calculator

This handheld device and companion software are designed to generate opportunities for classroom exploration and to promote greater understanding of core concepts in the mathematics and science classroom. TI-Nspire technology has been developed through sound classroom research which shows that "linked multiple representation are crucial in development of conceptual understanding and it is feasible only through use of a technology such as TI-Nspire, which provides simultaneous, dynamically linked representations of graphs, equations, data, and verbal explanations, such that a change in one representation is immediately reflected in the others.

For the young people in your life this is a great investment. Bought as a Christmas present but useful for many years to come as the young person turns into an A-level candidate then works their way through university. more... #ad

Calculator

Apple iPad Pro

The analytics show that more and more people are accessing Transum Mathematics via an iPad as it is so portable and responsive. The iPad has so many other uses in addition to solving Transum's puzzles and challenges and it would make an excellent gift for anyone.

The redesigned Retina display is as stunning to look at as it is to touch. It all comes with iOS, the world's most advanced mobile operating system. iPad Pro. Everything you want modern computing to be. more... #ad

Before giving an iPad as a Christmas gift you could add a link to iPad Maths to the home screen.

Craig Barton's Tips for Teachers

Teaching is complex. But there are simple ideas we can enact to help our teaching be more effective. This book contains over 400 such ideas." more... #ad

"The ideas come from two sources. First, from the wonderful guests on his Tips for Teachers podcast - education heavyweights such as Dylan Wiliam, Daisy Christodoulou and Tom Sherrington, as well as talented teachers who are not household names but have so much wisdom to share. Then there's what he has learned from working with amazing teachers and students in hundreds of schools around the world.

Another Craig Barton Book

The Story Of Maths [DVD]

The films in this ambitious series offer clear, accessible explanations of important mathematical ideas but are also packed with engaging anecdotes, fascinating biographical details, and pivotal episodes in the lives of the great mathematicians. Engaging, enlightening and entertaining, the series gives viewers new and often surprising insights into the central importance of mathematics, establishing this discipline to be one of humanity s greatest cultural achievements. This DVD contains all four programmes from the BBC series.

Marcus du Sautoy's wonderful programmes make a perfect Christmas gift more... #ad

Christmas Maths

This book provides a wealth of fun activities with a Christmas theme. Each photocopiable worksheet is matched to the Numeracy Strategy and compatible with the Scottish 5-14 Guidelines. This series is designed for busy teachers in the late Autumn term who are desperate for materials that are relevant and interesting and that can be completed with minimun supervision.

All the activities are suitable for use by class teachers, supply teachers, SEN teachers and classroom assistants and cover topics such as 'How many partridges did the true love give all together?' and 'Filling a sleigh with presents by rolling a dice!'. Children will have lots of fun working through the Christmas Maths themes but also gain valuable skills along the way.

A great source of ideas and another reasonably priced stocking filler. more... #ad

A Compendium Of 	Mathematical Methods

A Compendium Of Mathematical Methods

How many different methods do you know to solve simultaneous equations? To multiply decimals? To find the nth term of a sequence?

A Compendium of Mathematical Methods brings together over one hundred different approaches from classrooms all over the world, giving curious mathematicians the opportunity to explore fascinating methods that they've never before encountered.

If you teach mathematics to any age group in any country, you are guaranteed to learn lots of new things from this delightful book. It will deepen your subject knowledge and enhance your teaching, whatever your existing level of expertise. It will inspire you to explore new approaches with your pupils and provide valuable guidance on explanations and misconceptions. more... #ad

Math with Bad Drawings

I had been tutoring the wonderful Betsy for five years. When the day came for our last ever session together before the end of her Year 13, I received this beautiful book as a gift of appreciation.

This a very readable book by Ben Orlin. I'm really enjoying the humour in the writing and the drawings are great.

Ben Orlin answers maths' three big questions: Why do I need to learn this? When am I ever going to use it? Why is it so hard? The answers come in various forms-cartoons, drawings, jokes, and the stories and insights of an empathetic teacher who believes that mathematics should belong to everyone. more... #ad

Click the images above to see all the details of these gift ideas and to buy them online.

Maths T-Shirts

Maths T-shirts on Amazon
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Laptops In Lessons

Teacher, do your students have access to computers?
Do they have iPads or Laptops in Lessons?

Whether your students each have a TabletPC, a Surface or a Mac, this activity lends itself to eLearning (Engaged Learning).

Laptops In Lessons

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