# Number Operations & Calculation Methods

### Consecutive Numbers

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

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:

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

### Where Can We Visit?

##### Stage: 3 Challenge Level:

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:

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:

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:

Find the sum of this series of surds.

### Remainders

##### Stage: 3 Challenge Level:

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:

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

### Cinema Problem

##### Stage: 3 Challenge Level:

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:

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?

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

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:

A game that tests your understanding of remainders.

### Countdown

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

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

### Going Round in Circles

##### Stage: 3 Challenge Level:

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

### Missing Multipliers

##### Stage: 3 Challenge Level:

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:

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:

Can you crack these cryptarithms?

### Impossibilities

##### Stage: 3 Challenge Level:

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

### Overlaps

##### Stage: 3 Challenge Level:

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

### Have You Got It?

##### Stage: 3 Challenge Level:

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

### Egyptian Fractions

##### Stage: 3 Challenge Level:

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:

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

### Round and Round and Round

##### Stage: 3 Challenge Level:

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:

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:

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

### Playing Connect Three

##### Stage: 3 Challenge Level:

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:

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:

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

### Keep it Simple

##### Stage: 3 Challenge Level:

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

### The Greedy Algorithm

##### Stage: 3 Challenge Level:

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:

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:

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

### Up, Down, Flying Around

##### Stage: 3 Challenge Level:

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

### Making a Difference

##### Stage: 3 Challenge Level:

How many different differences can you make?

### Sum of 1s

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

Can you find the last 5 digits of this sum?

### Comparing Totals

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

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

### Walk or Run?

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

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:

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:

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

### Squares and Cubes

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

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:

What is the last digit in this calculation involving powers?

### Multiplication Mistake

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

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:

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:

Can you find the missing digits in this calculation?

### Palindromic Milometer

##### Stage: 3 Short 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?

### Hot Dogs

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

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:

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

### Multiple Choice

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

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

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

What is the sum of these fractions?

### 2014 Even Numbers

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

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:

Which digit does X represent in this column sum?