Other tags that relate to Building with Cubes
Tangram. Games. Investigations. Cubes & cuboids. Working systematically. Squares. Combinations. Interlocking cubes. Visualising. Practical Activity.There are 106 results
Broad Topics > Decision Mathematics and Combinatorics > Combinations
Map Folding
Age 7 to 11 Challenge Level:
Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?
Tetrahedron Faces
Age 7 to 11 Challenge Level:
One face of a regular tetrahedron is painted blue and each of the remaining faces are painted using one of the colours red, green or yellow. How many different possibilities are there?
Making Cuboids
Age 7 to 11 Challenge Level:
Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?
Multilink Cubes
Age 7 to 11 Challenge Level:
If you had 36 cubes, what different cuboids could you make?
Polydron
Age 7 to 11 Challenge Level:
This activity investigates how you might make squares and pentominoes from Polydron.
Child's Play
Age 7 to 11 Challenge Level:
A toy has a regular tetrahedron, a cube and a base with triangular and square hollows. If you fit a shape into the correct hollow a bell rings. How many times does the bell ring in a complete game?
Button-up Some More
Age 7 to 11 Challenge Level:
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Tiles on a Patio
Age 7 to 11 Challenge Level:
How many ways can you find of tiling the square patio, using square tiles of different sizes?
Cereal Packets
Age 7 to 11 Challenge Level:
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
Wag Worms
Age 7 to 11 Challenge Level:
When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.
Two on Five
Age 5 to 11 Challenge Level:
Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?
Noah
Age 5 to 7 Challenge Level:
Noah saw 12 legs walk by into the Ark. How many creatures did he see?
Train Carriages
Age 5 to 11 Challenge Level:
Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?
Penta Place
Age 7 to 11 Challenge Level:
Penta people, the Pentominoes, always build their houses from five square rooms. I wonder how many different Penta homes you can create?
Little Boxes
Age 7 to 11 Challenge Level:
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
New House
Age 7 to 11 Challenge Level:
In this investigation, you must try to make houses using cubes. If the base must not spill over 4 squares and you have 7 cubes which stand for 7 rooms, what different designs can you come up with?
3 Blocks Towers
Age 5 to 7 Challenge Level:
Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?
Buying a Balloon
Age 7 to 11 Challenge Level:
Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?
Tea Cups
Age 7 to 14 Challenge Level:
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
Triangle Edges
Age 5 to 7 Challenge Level:
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Red Express Train
Age 5 to 7 Challenge Level:
The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?
Ice Cream
Age 7 to 11 Challenge Level:
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
Bean Bags for Bernard's Bag
Age 7 to 11 Challenge Level:
How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?
Sweets in a Box
Age 7 to 11 Challenge Level:
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
Semaphore Signals
Age 7 to 11 Challenge Level:
Semaphore is a way to signal the alphabet using two flags. You might want to send a message that contains more than just letters. How many other symbols could you send using this code?
It Figures
Age 7 to 11 Challenge Level:
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
Mixed-up Socks
Age 5 to 7 Challenge Level:
Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?
Halloween Investigation
Age 7 to 11 Challenge Level:
Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?
Elf Suits
Age 7 to 11 Challenge Level:
If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?
Calcunos
Age 7 to 11 Challenge Level:
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
What Shape and Colour?
Age 5 to 7 Challenge Level:
Can you fill in the empty boxes in the grid with the right shape and colour?
Jumping Cricket
Age 5 to 7 Challenge Level:
El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?
Chocoholics
Age 7 to 11 Challenge Level:
George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?
Polo Square
Age 7 to 11 Challenge Level:
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
3 Rings
Age 7 to 11 Challenge Level:
If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?
Chocs, Mints, Jellies
Age 7 to 11 Challenge Level:
In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?
Triangle Animals
Age 5 to 7 Challenge Level:
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
Calendar Cubes
Age 7 to 11 Challenge Level:
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
Three by Three
Age 5 to 11 Challenge Level:
Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three square grid, so that there is only one of each colour in every row and every column
Room Doubling
Age 7 to 11 Challenge Level:
Investigate the different ways you could split up these rooms so that you have double the number.
Two Dice
Age 5 to 7 Challenge Level:
Find all the numbers that can be made by adding the dots on two dice.
A City of Towers
Age 5 to 7 Challenge Level:
In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?
Street Party
Age 7 to 11 Challenge Level:
The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.
Four-triangle Arrangements
Age 5 to 7 Challenge Level:
How many different shapes can you make by putting four right- angled isosceles triangles together?
Ladybirds in the Garden
Age 5 to 7 Challenge Level:
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
Those Tea Cups
Age 7 to 11 Challenge Level:
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
Home City
Age 7 to 11 Challenge Level:
Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.
The School Trip
Age 5 to 7 Challenge Level:
Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?
Newspapers
Age 7 to 11 Challenge Level:
When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?
NRICH is part of the family of activities in the Millennium Mathematics Project.