Resources tagged with: Trial and improvement

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Broad Topics > Thinking Mathematically > Trial and improvement

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.

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?

Gift Stacks

Age 7 to 11
Challenge Level

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

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.

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?

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?

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.

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?

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?

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.

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.

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?

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.

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?

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.

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?

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?

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 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?

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?

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?

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.

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?

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.

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?

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?

Make 100

Age 7 to 11
Challenge Level

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

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?

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.

Pizza Cut

Age 7 to 11
Challenge Level

Using only six straight cuts, find a way to make as many pieces of pizza as possible. (The pieces can be different sizes and shapes).

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.

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?

What Two ...?

Age 7 to 11 Short
Challenge Level

56 406 is the product of two consecutive numbers. What are these two numbers?

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?

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?

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.

Cycling Squares

Age 7 to 11
Challenge Level

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

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.

Domino Square

Age 7 to 11
Challenge Level

Use the 'double-3 down' dominoes to make a square so that each side has eight dots.

Fifteen Cards

Age 7 to 11
Challenge Level

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

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?

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?

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'.

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.

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.

Augustus' Age

Age 7 to 11
Challenge Level

In 1871 a mathematician called Augustus De Morgan died. De Morgan made a puzzling statement about his age. Can you discover which year De Morgan was born in?

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.

Strike it Out

Age 5 to 11
Challenge Level

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.