Resources tagged with: Trial and improvement

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Broad Topics > Mathematical Thinking > Trial and improvement

Number Round Up

Age 5 to 7 Challenge Level:

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

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.

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?

Big Dog, Little Dog

Age 5 to 7 Challenge Level:

Woof is a big dog. Yap is a little dog. Emma has 16 dog biscuits to give to the two dogs. She gave Woof 4 more biscuits than Yap. How many biscuits did each dog get?

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?

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).

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?

The Brown Family

Age 5 to 7 Challenge Level:

Use the information about Sally and her brother to find out how many children there are in the Brown family.

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.

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.

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?

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.

Age 7 to 11 Challenge Level:

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

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?

Starfish Spotting

Age 5 to 7 Challenge Level:

How many starfish could there be on the beach, and how many children, if I can see 28 arms?

Grouping Goodies

Age 5 to 7 Challenge Level:

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

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?

Find the Difference

Age 5 to 7 Challenge Level:

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Four-digit Targets

Age 7 to 11 Challenge Level:

You have two sets of the digits 0 – 9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?

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.

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?

Jumping Squares

Age 5 to 7 Challenge Level:

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

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?

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?

What's in a Name?

Age 5 to 7 Challenge Level:

What do you notice about these squares of numbers? What is the same? What is different?

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?

Age 5 to 7 Challenge Level:

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

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.

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?

The Puzzling Sweet Shop

Age 7 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?

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.

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.

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?

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.

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?

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?

The Tall Tower

Age 5 to 7 Challenge Level:

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

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.

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.

Escape from the Castle

Age 7 to 11 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?

Domino Join Up

Age 5 to 7 Challenge Level:

Can you arrange fifteen dominoes so that all the touching domino pieces add to 6 and the ends join up? Can you make all the joins add to 7?

Fifteen Cards

Age 7 to 11 Challenge Level:

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

Junior Frogs

Age 5 to 11 Challenge Level:

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

Strike it Out for Two

Age 5 to 11 Challenge Level:

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

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?

Sliding Game

Age 7 to 11 Challenge Level:

A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.

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?