Number Operations and Calculation Methods: Age 11-16

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Number Operations and Calculation Methods: Age 11-16.

We have put together a selection of these short problems as printable worksheets:

Printable worksheets: Age 11-14 ⭐   Printable worksheets: Age 11-14 ⭐⭐   Printable worksheet: Age 11-14 ⭐⭐⭐   Printable worksheet solutions


  • Small tomato seedlings in pink pots.
    problem

    Reverse Subtraction

    Age
    11 to 14
    Challenge level

    What is the value of c in this subtraction?

  • Small tomato seedlings in pink pots.
    problem

    Fly Away

    Age
    11 to 14
    Challenge level

    Can you work out the values of the digits in this addition sum?

  • Small tomato seedlings in pink pots.
    problem

    Bus Route

    Age
    11 to 14
    Challenge level

    How far apart are the first and last bus stops in this bus route?

  • Small tomato seedlings in pink pots.
    problem

    Debasing the Coinage

    Age
    11 to 14
    Challenge level

    How much lighter will £5 worth of 5p's be with these new lighter coins?

  • Small tomato seedlings in pink pots.
    problem

    Carry Over

    Age
    11 to 14
    Challenge level

    Each letter stands for a different digit, and S is non-zero. Which letter has the lowest value?

  • Small tomato seedlings in pink pots.
    problem

    In Sum-Mary

    Age
    11 to 14
    Challenge level

    What does the sum of these three numbers tell us about their product?

  • Small tomato seedlings in pink pots.
    problem

    Magic Error

    Age
    11 to 14
    Challenge level

    Two of the numbers in a 4×4 magic square have been swapped. Can you work out the sum of these numbers?

  • Small tomato seedlings in pink pots.
    problem

    Subtracting to 2008

    Age
    11 to 14
    Challenge level

    Can you work out the sum of the missing digits in this subtraction?

  • Small tomato seedlings in pink pots.
    problem

    Down and Along

    Age
    11 to 14
    Challenge level

    Can you work out the values of J, M and C in this sum?

  • Small tomato seedlings in pink pots.
    problem

    354972

    Age
    11 to 14
    Challenge level

    What is the remainder when 354972 is divided by 7?

  • Small tomato seedlings in pink pots.
    problem

    50, 50, 50 and 50

    Age
    11 to 14
    Challenge level

    Aroon says his age is 50 years, 50 months, 50 weeks and 50 days. What age will he be on his next birthday?

  • Small tomato seedlings in pink pots.
    problem

    Walk or Run?

    Age
    11 to 14
    Challenge level

    Can you work out how long it will take for John to walk to and from school?

  • Small tomato seedlings in pink pots.
    problem

    Split Clock Face

    Age
    11 to 14
    Challenge level

    Use 2 straight lines to split the clock face into 3 parts so that the sums of the numbers in each of the parts are equal.

  • Small tomato seedlings in pink pots.
    problem

    Missing Digits

    Age
    11 to 14
    Challenge level

    Can you find the missing digits in this calculation?

  • Small tomato seedlings in pink pots.
    problem

    Hot Dogs

    Age
    11 to 14
    Challenge level

    How many hot dogs did this hot dog lover eat on the first day of her binge?

  • Small tomato seedlings in pink pots.
    problem

    Identical Digit Multiplication

    Age
    11 to 14
    Challenge level

    77 is multiplied by another two-digit number with identical digits. What is the product?

  • Small tomato seedlings in pink pots.
    problem

    2014 Even Numbers

    Age
    11 to 14
    Challenge level

    What is the difference between the sum of the first 2014 odd numbers and the sum of the first 2014 even numbers?

  • Small tomato seedlings in pink pots.
    problem

    Whole Numbers Only

    Age
    11 to 14
    Challenge level

    Can you work out how many of each kind of pencil this student bought?

  • Small tomato seedlings in pink pots.
    problem

    Anti-Magic Square

    Age
    11 to 14
    Challenge level

    You may have met Magic Squares, now meet an Anti-Magic Square. Its properties are slightly different - can you still solve it?

  • Small tomato seedlings in pink pots.
    problem

    So Many Sums

    Age
    11 to 14
    Challenge level

    In this addition each letter stands for a different digit, with S standing for 3. What is the value of YxO?

  • Small pepper seedlings in orange pots.
    problem

    Currency Exchange

    Age
    11 to 14
    Challenge level

    Dan and Ann have 9 and 8 coins respectively. What is the smallest number of coins they must swap so they end up with equal amounts of money.

  • Small tomato seedlings in pink pots.
    problem

    Kangaroo Subtraction

    Age
    11 to 14
    Challenge level

    Can you solve this 'KANGAROO' alphanumeric subtraction?

  • Small tomato seedlings in pink pots.
    problem

    Rolling Along the Trail

    Age
    11 to 14
    Challenge level

    What could be the scores from five throws of this dice?

  • Small tomato seedlings in pink pots.
    problem

    Jam and Egg Sandwich

    Age
    11 to 14
    Challenge level

    How many solutions can you find to this sum? Each of the different letters stands for a different number.

  • Small tomato seedlings in pink pots.
    problem

    Operational Decision

    Age
    11 to 14
    Challenge level

    What symbol should be inserted to make the equation true?

  • Small tomato seedlings in pink pots.
    problem

    Product and Sum

    Age
    11 to 14
    Challenge level

    When Jim rolled some dice, the scores had the same product and sum. How many dice did Jim roll?

  • Small tomato seedlings in pink pots.
    problem

    Latin Multiplication

    Age
    11 to 14
    Challenge level

    Can you choose one number from each row and column in this grid to form the largest possibe product?

  • Small tomato seedlings in pink pots.
    problem

    Birthday Tables

    Age
    11 to 14
    Challenge level

    How many tables of each type does Mark need at his birthday party?

  • Small tomato seedlings in pink pots.
    problem

    Filling Morecambe Bay

    Age
    11 to 14
    Challenge level

    "It would take 20 million years to fill Morecambe Bay from a bath tap". What does this imply is the approximate capacity of Morecambe Bay?

  • Small tomato seedlings in pink pots.
    problem

    Bookshop

    Age
    11 to 14
    Challenge level

    If Clara spends £23 on books and magazines, how many of each does she buy?

  • Small tomato seedlings in pink pots.
    problem

    Sum of Ten

    Age
    11 to 14
    Challenge level

    The sum of ten distinct positive integers is 100. What is the largest possible value of one of the numbers?

  • Small tomato seedlings in pink pots.
    problem

    Quiz Question

    Age
    11 to 14
    Challenge level

    Can you work out how many quizzes have to be played before we have a winner?

  • Small tomato seedlings in pink pots.
    problem

    Palindromic Milometer

    Age
    11 to 14
    Challenge level

    At the beginning and end of Alan's journey, his milometer showed a palindromic number. Can you find his maximum possible average speed?

  • Small tomato seedlings in pink pots.
    problem

    Multiple Choice

    Age
    11 to 14
    Challenge level

    How many questions did Sarah answer correctly in this multiple choice exam?

  • Small tomato seedlings in pink pots.
    problem

    See Axes

    Age
    11 to 14
    Challenge level

    Which digit does X represent in this column sum?

  • Small tomato seedlings in pink pots.
    problem

    ABC Addition

    Age
    11 to 14
    Challenge level

    Can you work out what a, b and c are in this sum?

  • Small tomato seedlings in pink pots.
    problem

    Product of Fractions

    Age
    11 to 14
    Challenge level

    Find the product of these mixed numbers

  • Small tomato seedlings in pink pots.
    problem

    Roses and Carnations

    Age
    11 to 14
    Challenge level

    How many different bunches of flowers can this class buy for their teacher?

  • Small tomato seedlings in pink pots.
    problem

    Sum One Special

    Age
    11 to 14
    Challenge level

    Three different integers have a sum of 1 and a product of 36 - what are they?

  • Small tomato seedlings in pink pots.
    problem

    Digit Deletion

    Age
    11 to 14
    Challenge level

    What is the largest number of digits that could be erased from this 1000-digit number, to get a surprising result?

  • Small tomato seedlings in pink pots.
    problem

    Sum of 1s

    Age
    11 to 14
    Challenge level

    Can you find the last 5 digits of this sum?

  • Small tomato seedlings in pink pots.
    problem

    Comparing Totals

    Age
    11 to 14
    Challenge level

    Can you work out the solution to this tricky summation problem?

  • Small tomato seedlings in pink pots.
    problem

    Squares and Cubes

    Age
    11 to 14
    Challenge level

    How many positive two-digit numbers are there whose square and cube both end in the same digit?

  • Small tomato seedlings in pink pots.
    problem

    Last Digit

    Age
    11 to 14
    Challenge level

    What is the last digit in this calculation involving powers?

  • Small tomato seedlings in pink pots.
    problem

    Divisible by 55

    Age
    11 to 14
    Challenge level

    Choose the digits $a$ and $b$ so that this number is divisible by 55.

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