Resources tagged with: Trial and improvement

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There are 85 results

Broad Topics > Thinking Mathematically > Trial and improvement

Magic Triangle

Age 7 to 11
Challenge Level

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

A Shapely Network

Age 7 to 11
Challenge Level

Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.

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?

Magic Circles

Age 7 to 11
Challenge Level

Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?

Sisters and Brothers

Age 7 to 11
Challenge Level

Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?

One Wasn't Square

Age 7 to 11
Challenge Level

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

A Numbered Route

Age 7 to 11
Challenge Level

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

Arranging the Tables

Age 7 to 11
Challenge Level

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

Rocco's Race

Age 7 to 11 Short
Challenge Level

Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.

Gift Stacks

Age 7 to 11
Challenge Level

Use the information to work out how many gifts there are in each pile.

Numbered Cars

Age 7 to 11
Challenge Level

I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?

Zios and Zepts

Age 7 to 11
Challenge Level

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

Number Juggle

Age 7 to 11
Challenge Level

Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).

Oranges and Lemons

Age 7 to 11
Challenge Level

On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

Let's Face It

Age 7 to 11
Challenge Level

In this problem you have to place four by four magic squares on the faces of a cube so that along each edge of the cube the numbers match.

The Puzzling Sweet Shop

Age 5 to 11
Challenge Level

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

Rabbits in the Pen

Age 7 to 11
Challenge Level

Using the statements, can you work out how many of each type of rabbit there are in these pens?

The Clockmaker's Birthday Cake

Age 7 to 11
Challenge Level

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

Buckets of Thinking

Age 7 to 11
Challenge Level

There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.

Prison Cells

Age 7 to 11
Challenge Level

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

How Many Eggs?

Age 7 to 11
Challenge Level

Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.

Difference

Age 7 to 11
Challenge Level

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Twenty Divided Into Six

Age 7 to 11
Challenge Level

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

Magic Matrix

Age 7 to 11
Challenge Level

Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?

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?

Fractions in a Box

Age 7 to 11
Challenge Level

The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.

Special 24

Age 7 to 11
Challenge Level

Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.

Sticky Dice

Age 7 to 11
Challenge Level

Throughout these challenges, the touching faces of any adjacent dice must have the same number. Can you find a way of making the total on the top come to each number from 11 to 18 inclusive?

Cat Food

Age 7 to 11
Challenge Level

Sam sets up displays of cat food in his shop in triangular stacks. If Felix buys some, then how can Sam arrange the remaining cans in triangular stacks?

Paw Prints

Age 7 to 11
Challenge Level

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

Sums of Pairs

Age 11 to 16
Challenge Level

Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”

1, 2, 3, 4, 5

Age 7 to 11
Challenge Level

Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?

Dice Stairs

Age 7 to 11
Challenge Level

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

3388

Age 11 to 14
Challenge Level

Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.

One to Eight

Age 11 to 14
Challenge Level

Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.

How Many Miles to Go?

Age 11 to 14
Challenge Level

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

Path to the Stars

Age 7 to 11
Challenge Level

Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?

Area and Perimeter

Age 7 to 11
Challenge Level

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

Factor Track

Age 7 to 14
Challenge Level

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

Escape from the Castle

Age 7 to 14
Challenge Level

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

Fifteen Cards

Age 7 to 11
Challenge Level

Can you use the information to find out which cards I have used?

Charitable Pennies

Age 7 to 14
Challenge Level

Investigate the different ways that fifteen schools could have given money in a charity fundraiser.

Fitted

Age 7 to 11
Challenge Level

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

Daisy

Age 7 to 11
Challenge Level

In this game for two players, take it in turns to shade one petal, or two petals next to each other. Is it better to go first or second?

Cinema Problem

Age 11 to 14
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.

Clever Santa

Age 7 to 11
Challenge Level

All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left.

Pair Sums

Age 11 to 14
Challenge Level

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

Four Colours

Age 5 to 11
Challenge Level

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

Tom's Number

Age 7 to 11
Challenge Level

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

Plenty of Pens

Age 7 to 11
Challenge Level

Amy's mum had given her £2.50 to spend. She bought four times as many pens as pencils and was given 40p change. How many of each did she buy?