Number Operations & Calculation Methods

Consecutive Numbers

Stage: 2 and 3 Challenge Level: Challenge Level:1

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Can You Make 100?

Stage: 3 Challenge Level: Challenge Level:1

How many ways can you find to put in operation signs (+ - x ÷) to make 100?

Where Can We Visit?

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

Two and Two

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Number Daisy

Stage: 3 Challenge Level: Challenge Level:1

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

The Root of the Problemlive

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

Find the sum of this series of surds.

Remainders

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?

Largest Product

Stage: 3 Challenge Level: Challenge Level:1

Which set of numbers that add to 10 have the largest product?

Cinema Problem

Stage: 3 Challenge Level: Challenge Level:1

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

Consecutive Seven

Stage: 3 Challenge Level: Challenge Level:1

Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?

Method in Multiplying Madness?

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

The Remainders Game

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

A game that tests your understanding of remainders.

Countdown

Stage: 2 and 3 Challenge Level: Challenge Level:1

Here is a chance to play a version of the classic Countdown Game.

Going Round in Circles

Stage: 3 Challenge Level: Challenge Level:1

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

Missing Multipliers

Stage: 3 Challenge Level: Challenge Level:1

What is the smallest number of answers you need to reveal in order to work out the missing headers?

What Numbers Can We Make?

Stage: 3 Challenge Level: Challenge Level:1

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

Cryptarithms

Stage: 3 Challenge Level: Challenge Level:1

Can you crack these cryptarithms?

Impossibilities

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Just because a problem is impossible doesn't mean it's difficult...

Overlaps

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Can you find ways to put numbers in the overlaps so the rings have equal totals?

Have You Got It?

Stage: 3 Challenge Level: Challenge Level:1

Can you explain the strategy for winning this game with any target?

Egyptian Fractions

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.

Fractions Jigsaw

Stage: 3 Challenge Level: Challenge Level:1

A jigsaw where pieces only go together if the fractions are equivalent.

Round and Round and Round

Stage: 3 Challenge Level: Challenge Level:1

Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help?

Twisting and Turning

Stage: 3 Challenge Level: Challenge Level:1

Take a look at the video and try to find a sequence of moves that will take you back to zero.

More Twisting and Turning

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

It would be nice to have a strategy for disentangling any tangled ropes...

Playing Connect Three

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?

Consecutive Negative Numbers

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

Adding and Subtracting Positive and Negative Numbers

Stage: 3

How can we help students make sense of addition and subtraction of negative numbers?

Weights

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Different combinations of the weights available allow you to make different totals. Which totals can you make?

Keep it Simple

Stage: 3 Challenge Level: Challenge Level:1

Can all unit fractions be written as the sum of two unit fractions?

The Greedy Algorithm

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

The Egyptians expressed all fractions as the sum of different unit fractions. The Greedy Algorithm might provide us with an efficient way of doing this.

Magic Letters

Stage: 3 Challenge Level: Challenge Level:1

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

Strange Bank Account

Stage: 3 Challenge Level: Challenge Level:1

Imagine a very strange bank account where you are only allowed to do two things...

Up, Down, Flying Around

Stage: 3 Challenge Level: Challenge Level:1

Play this game to learn about adding and subtracting positive and negative numbers

Making a Difference

Stage: 3 Challenge Level: Challenge Level:1

How many different differences can you make?

Sum of 1s

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

Can you find the last 5 digits of this sum?

Comparing Totals

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

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

Walk or Run?

Stage: 3 Short Challenge Level: Challenge Level:1

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

Sum of Ten

Stage: 3 Short Challenge Level: Challenge Level:1

The sum of 10 distinct positive integers is 100. What is the largest possible value of one of the numbers?

Quiz Question

Stage: 3 Short Challenge Level: Challenge Level:1

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

Squares and Cubes

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

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

Last Digit

Stage: 3 Short Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

What is the last digit in this calculation involving powers?

Multiplication Mistake

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

Jane accidentally multiplied by 54 instead of 45, and her answer was 198 too big. What number did she multiply 54 by?

Split Clock Face

Stage: 3 Short Challenge Level: Challenge Level:1

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.

Missing Digits

Stage: 3 Short Challenge Level: Challenge Level:1

Can you find the missing digits in this calculation?

Palindromic Milometer

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

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

Hot-dogs

Stage: 3 Short Challenge Level: Challenge Level:1

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

Identical Digit Multiplication

Stage: 3 Short Challenge Level: Challenge Level:1

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

Multiple Choice

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

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

Adding Tricky Fractions

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

What is the sum of these fractions?

2014 Even Numbers

Stage: 3 Short Challenge Level: Challenge Level:1

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

See Axes

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

Which digit does X represent in this column sum?

ABC Addition

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

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

Almost Onelive

Stage: 3 Challenge Level: Challenge Level:1

Choose some fractions and add them together. Can you get close to 1?