# Number Operations and 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.

### Dicey Operations

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

Who said that adding, subtracting, multiplying and dividing couldn't be fun?

### Countdown

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

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

### Got It

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

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

### The Remainders Game

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

A game that tests your understanding of remainders.

### Two and Two

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

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

### Cryptarithms

##### Stage: 3 Challenge Level:

Can you crack these cryptarithms?

### 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?

### 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?

### Can You Make 100?

##### Stage: 3 Challenge Level:

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

### 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?

### 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?

### Place Your Orders

##### Stage: 3 Challenge Level:

Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?

### Keep it Simple

##### Stage: 3 Challenge Level:

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

### Method in Multiplying Madness?live

##### 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?

### Legs Eleven

##### Stage: 3 Challenge Level:

Take any four digit number. Move the first digit to the 'back of the queue' and move the rest along. Now add your two numbers. What properties do your answers always have?

### 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?

### 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?

### Impossibilities

##### Stage: 3 Challenge Level:

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

### Thousands and Millions

##### Stage: 3 Challenge Level:

Here's a chance to work with large numbers...

### Overlaps

##### Stage: 3 Challenge Level:

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

### 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.

### 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.

### How Many Miles to Go?

##### Stage: 3 Challenge Level:

A car's milometer reads 4631 miles and the trip meter has 173.3 on it. How many more miles must the car travel before the two numbers contain the same digits in the same order?

### Largest Product

##### Stage: 3 and 4 Challenge Level:

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

### Cinema Problem

##### Stage: 3 and 4 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.

### The Legacy

##### Stage: 4 Challenge Level:

Your school has been left a million pounds in the will of an ex- pupil. What model of investment and spending would you use in order to ensure the best return on the money?

### Dating Made Easier

##### Stage: 4 Challenge Level:

If a sum invested gains 10% each year how long before it has doubled its value?

### The Root of the Problem

##### Stage: 4 and 5 Challenge Level:

Find the sum of the series.

### Number Operations and Calculation Methods - Short Problems

##### Stage: 3 and 4

A collection of short Stage 3 and 4 problems on number operations and calculation methods.

### 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.

### Sum of 1s

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

Can you find the last 5 digits of this sum?

### Latin Numberslive

##### Stage: 3 Challenge Level:

Can you create a Latin Square from multiples of a six digit number?

### 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?

### Last Digit

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

What is the last digit in this calculation involving powers?