Number Operations and Calculation Methods

Consecutive Numbers

Stage: 2 Challenge Level: Challenge Level:1

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

Rule of Three

Stage: 3 Challenge Level: Challenge Level:1

If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?

Legs Eleven

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

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?

Where Can We Visit?

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

Charlie and Lynne 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: 2 and 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: 2 and 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 Problem

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

Find the sum of the series.

Make 100

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

Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

GOT IT

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

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.

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:2 Challenge Level:2

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.

How Many Miles to Go?

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

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?

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: 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?

Dating Made Easier

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

The Legacy

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

Thousands and Millions

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

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

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.

Dicey Operations

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

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

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?

Place Your Orders

Stage: 3 Challenge Level: Challenge Level:1

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

Short Problems

Stage: 3 and 4 Challenge Level: Challenge Level:1

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

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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NRICH is part of the family of activities in the Millennium Mathematics Project.