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Broad Topics > Numbers and the Number System > Place value ### Diagonal Sums

##### Age 7 to 11 Challenge Level:

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice? ### Being Resourceful - Primary Number

##### Age 5 to 11 Challenge Level:

Number problems at primary level that require careful consideration. ##### Age 5 to 11 Challenge Level:

Try out this number trick. What happens with different starting numbers? What do you notice? ### Oddly

##### Age 7 to 11 Challenge Level:

Find the sum of all three-digit numbers each of whose digits is odd. ### Napier's Bones

##### Age 7 to 11 Challenge Level:

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications? ### Spell by Numbers

##### Age 7 to 11 Challenge Level:

Can you substitute numbers for the letters in these sums? ### Being Resilient - Primary Number

##### Age 5 to 11 Challenge Level:

Number problems at primary level that may require resilience. ### Coded Hundred Square

##### Age 7 to 11 Challenge Level:

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up? ### Being Collaborative - Primary Number

##### Age 5 to 11 Challenge Level:

Number problems at primary level to work on with others. ### Six Is the Sum

##### Age 7 to 11 Challenge Level:

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros? ### Which Scripts?

##### Age 7 to 11 Challenge Level:

There are six numbers written in five different scripts. Can you sort out which is which? ### ABC

##### Age 7 to 11 Challenge Level:

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication? ### Being Curious - Primary Number

##### Age 5 to 11 Challenge Level:

Number problems for inquiring primary learners. ### The Thousands Game

##### Age 7 to 11 Challenge Level:

Each child in Class 3 took four numbers out of the bag. Who had made the highest even number? ### Song Book

##### Age 7 to 11 Challenge Level:

A school song book contains 700 songs. The numbers of the songs are displayed by combining special small single-digit cards. What is the minimum number of small cards that is needed? ### Round the Three Dice

##### Age 7 to 11 Challenge Level:

What happens when you round these three-digit numbers to the nearest 100? ### One Million to Seven

##### Age 7 to 11 Challenge Level:

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like? ### Even Up

##### Age 11 to 14 Challenge Level:

Consider all of the five digit numbers which we can form using only the digits 2, 4, 6 and 8. If these numbers are arranged in ascending order, what is the 512th number? ### Trebling

##### Age 7 to 11 Challenge Level:

Can you replace the letters with numbers? Is there only one solution in each case? ### Alien Counting

##### Age 7 to 11 Challenge Level:

Investigate the different ways these aliens count in this challenge. You could start by thinking about how each of them would write our number 7. ### Subtraction Surprise

##### Age 7 to 14 Challenge Level:

Try out some calculations. Are you surprised by the results? ### All the Digits

##### Age 7 to 11 Challenge Level:

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures? ### Number Detective

##### Age 5 to 11 Challenge Level:

Follow the clues to find the mystery number. ### Nice or Nasty for Two

##### Age 7 to 14 Challenge Level:

Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent. ### Round the Dice Decimals 2

##### Age 7 to 11 Challenge Level:

What happens when you round these numbers to the nearest whole number? ### Arrange the Digits

##### Age 11 to 14 Challenge Level:

Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500? ### Multiply Multiples 3

##### Age 7 to 11 Challenge Level:

Have a go at balancing this equation. Can you find different ways of doing it? ### Round the Dice Decimals 1

##### Age 7 to 11 Challenge Level:

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number? ### Multiply Multiples 2

##### Age 7 to 11 Challenge Level:

Can you work out some different ways to balance this equation? ### Multiply Multiples 1

##### Age 7 to 11 Challenge Level:

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it? ### Digit Sum

##### Age 11 to 14 Challenge Level:

What is the sum of all the digits in all the integers from one to one million? ### Dicey Operations in Line for Two

##### Age 7 to 11 Challenge Level:

Dicey Operations for an adult and child. Can you get close to 1000 than your partner? ### Which Is Quicker?

##### Age 7 to 11 Challenge Level:

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why? ### Becky's Number Plumber

##### Age 7 to 11 Challenge Level:

Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings? ### Cayley

##### Age 11 to 14 Challenge Level:

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"? ### Just Repeat

##### Age 11 to 14 Challenge Level:

Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence? ### What Do You Need?

##### Age 7 to 11 Challenge Level:

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number? ### Football Sum

##### Age 11 to 14 Challenge Level:

Find the values of the nine letters in the sum: FOOT + BALL = GAME ### Eleven

##### Age 11 to 14 Challenge Level:

Replace each letter with a digit to make this addition correct. ### Six Times Five

##### Age 11 to 14 Challenge Level:

How many six digit numbers are there which DO NOT contain a 5? ### Two and Two

##### 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. ### Tis Unique

##### Age 11 to 14 Challenge Level:

This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility. ### Method in Multiplying Madness?

##### Age 7 to 14 Challenge Level:

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them? ### Reach 100

##### Age 7 to 14 Challenge Level:

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100. ### X Marks the Spot

##### Age 11 to 14 Challenge Level:

When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" . ### Skeleton

##### Age 11 to 14 Challenge Level:

Amazing as it may seem the three fives remaining in the following `skeleton' are sufficient to reconstruct the entire long division sum. ##### Age 11 to 14 Challenge Level:

Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E ##### Age 5 to 11 Challenge Level:

Who said that adding couldn't be fun? ### Double Digit

##### Age 11 to 14 Challenge Level:

Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. . . . ### Three Times Seven

##### Age 11 to 14 Challenge Level:

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?