Other tags that relate to Train Routes
Investigations. Practical Activity. Addition & subtraction. Working systematically. Mathematical modelling. Combinations. Interactivities. Visualising. Route inspection problems. Generalising.There are 151 results
Broad Topics > Using, Applying and Reasoning about Mathematics > Investigations
Cuboid-in-a-box
Age 7 to 11 Challenge Level:
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
Move a Match
Age 7 to 11 Challenge Level:
How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?
Homes
Age 5 to 7 Challenge Level:
There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?
Watch Your Feet
Age 7 to 11 Challenge Level:
I like to walk along the cracks of the paving stones, but not the outside edge of the path itself. How many different routes can you find for me to take?
Hexpentas
Age 5 to 11 Challenge Level:
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
Triple Cubes
Age 5 to 11 Challenge Level:
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
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?
Let's Investigate Triangles
Age 5 to 7 Challenge Level:
Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?
28 and It's Upward and Onward
Age 7 to 11 Challenge Level:
Can you find ways of joining cubes together so that 28 faces are visible?
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?
Sort the Street
Age 5 to 7 Challenge Level:
Sort the houses in my street into different groups. Can you do it in any other ways?
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?
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?
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.
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?
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?
Stairs
Age 5 to 11 Challenge Level:
This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.
Fencing Lambs
Age 7 to 11 Challenge Level:
A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.
Making Squares
Age 7 to 11
Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?
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.
Turning
Age 5 to 7 Challenge Level:
Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?
Two by One
Age 7 to 11 Challenge Level:
An activity making various patterns with 2 x 1 rectangular tiles.
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?
Sticky Triangles
Age 7 to 11 Challenge Level:
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
Cutting Corners
Age 7 to 11 Challenge Level:
Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?
My New Patio
Age 7 to 11 Challenge Level:
What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?
Cubes Here and There
Age 7 to 11 Challenge Level:
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
Sticks and Triangles
Age 7 to 11 Challenge Level:
Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?
Become Maths Detectives
Age 7 to 11 Challenge Level:
Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.
The Numbers Give the Design
Age 7 to 11 Challenge Level:
Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
Fit These Shapes
Age 5 to 11 Challenge Level:
What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?
Count the Digits
Age 5 to 11 Challenge Level:
In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?
Three Sets of Cubes, Two Surfaces
Age 7 to 11 Challenge Level:
How many models can you find which obey these rules?
Polygonals
Age 7 to 11 Challenge Level:
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Crossing the Town Square
Age 7 to 11 Challenge Level:
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Building with Rods
Age 7 to 11 Challenge Level:
In how many ways can you stack these rods, following the rules?
Birthday Cake Candles
Age 7 to 11 Challenge Level:
This challenge involves calculating the number of candles needed on birthday cakes. It is an opportunity to explore numbers and discover new things.
More Transformations on a Pegboard
Age 7 to 11 Challenge Level:
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Egyptian Rope
Age 7 to 11 Challenge Level:
The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?
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?
Lost Books
Age 7 to 11 Challenge Level:
While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?
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.
Roll These Dice
Age 7 to 11 Challenge Level:
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?
Redblue
Age 7 to 11 Challenge Level:
Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?
Magazines
Age 7 to 11 Challenge Level:
Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.
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.
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?
NRICH is part of the family of activities in the Millennium Mathematics Project.