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Games. Addition & subtraction. Factors and multiples. Creating and manipulating expressions and formulae. Interactivities. Working systematically. Mathematical reasoning & proof. Visualising. GeoGebra. Generalising.There are 184 results
Broad Topics > Thinking Mathematically > Visualising
3D Stacks
Age 7 to 14 Challenge Level:
Can you find a way of representing these arrangements of balls?
Drilling Many Cubes
Age 7 to 14 Challenge Level:
A useful visualising exercise which offers opportunities for discussion and generalising, and which could be used for thinking about the formulae needed for generating the results on a spreadsheet.
Seeing Squares for Two
Age 5 to 11 Challenge Level:
Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?
Display Boards
Age 7 to 11 Challenge Level:
Design an arrangement of display boards in the school hall which fits the requirements of different people.
Open Boxes
Age 7 to 11 Challenge Level:
Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
Taking Steps
Age 7 to 11 Challenge Level:
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Clocking Off
Age 7 to 16 Challenge Level:
I found these clocks in the Arts Centre at the University of Warwick intriguing - do they really need four clocks and what times would be ambiguous with only two or three of them?
Counters
Age 7 to 11 Challenge Level:
Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?
Finding 3D Stacks
Age 7 to 11 Challenge Level:
Can you find a way of counting the spheres in these arrangements?
Circles, Circles
Age 5 to 11 Challenge Level:
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
Sea Defences
Age 7 to 14 Challenge Level:
These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?
Coded Hundred Square
Age 7 to 11 Challenge Level:
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Cubes Within Cubes
Age 7 to 14 Challenge Level:
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
Seeing Squares
Age 5 to 11 Challenge Level:
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
Pattern Power
Age 5 to 14
Mathematics is the study of patterns. Studying pattern is an opportunity to observe, hypothesise, experiment, discover and create.
Shunting Puzzle
Age 7 to 11 Challenge Level:
Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?
Single Track
Age 7 to 11 Challenge Level:
What is the best way to shunt these carriages so that each train can continue its journey?
Waiting for Blast Off
Age 7 to 11 Challenge Level:
10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?
Jigsaw Pieces
Age 7 to 11 Challenge Level:
How will you go about finding all the jigsaw pieces that have one peg and one hole?
Thinking Through, and By, Visualising
Age 7 to 16
This article is based on some of the ideas that emerged during the production of a book which takes visualising as its focus. We began to identify problems which helped us to take a structured view. . . .
World of Tan 25 - Pentominoes
Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outlines of the people?
World of Tan 21 - Almost There Now
Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Odd Squares
Age 7 to 11 Challenge Level:
Think of a number, square it and subtract your starting number. Is the number you’re left with odd or even? How do the images help to explain this?
World of Tan 3 - Mah Ling
Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outline of Mah Ling?
Three Squares
Age 5 to 11 Challenge Level:
What is the greatest number of squares you can make by overlapping three squares?
World of Tan 19 - A Circular Problem
Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outline of this teacup?
Auditorium Steps
Age 7 to 14 Challenge Level:
What is the shape of wrapping paper that you would need to completely wrap this model?
World of Tan 17 - Weather
Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outline of the house?
World of Tan 10 - Butterflies
Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outline of the butterfly?
The Development of Spatial and Geometric Thinking: 5 to 18
Age 5 to 16
This is the first article in a series which aim to provide some insight into the way spatial thinking develops in children, and draw on a range of reported research. The focus of this article is the. . . .
Nine-pin Triangles
Age 7 to 11 Challenge Level:
How many different triangles can you make on a circular pegboard that has nine pegs?
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?
Putting Two and Two Together
Age 7 to 11 Challenge Level:
In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?
World of Tan 13 - A Storm in a Tea Cup
Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outlines of the convex shapes?
Ten Hidden Squares
Age 7 to 14 Challenge Level:
These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?
The Development of Spatial and Geometric Thinking: the Importance of Instruction.
Age 5 to 11
This article looks at levels of geometric thinking and the types of activities required to develop this thinking.
Bands and Bridges: Bringing Topology Back
Age 7 to 14
Lyndon Baker describes how the Mobius strip and Euler's law can introduce pupils to the idea of topology.
Dice, Routes and Pathways
Age 5 to 14
This article for teachers discusses examples of problems in which there is no obvious method but in which children can be encouraged to think deeply about the context and extend their ability to. . . .
Put Yourself in a Box
Age 7 to 11 Challenge Level:
A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.
Right or Left?
Age 7 to 11 Challenge Level:
Which of these dice are right-handed and which are left-handed?
Twice as Big?
Age 7 to 11 Challenge Level:
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
Eight Hidden Squares
Age 7 to 14 Challenge Level:
On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?
How Would We Count?
Age 5 to 11 Challenge Level:
An activity centred around observations of dots and how we visualise number arrangement patterns.
Take One Example
Age 5 to 11
This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.
World of Tan 12 - All in a Fluff
Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outlines of the rabbits?
World of Tan 9 - Animals
Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outlines of the camel and giraffe?
World of Tan
Age 5 to 11 Challenge Level:
Read about the adventures of Granma T and her grandchildren in this series of stories, accompanied by interactive tangrams.
World of Tan 26 - Old Chestnut
Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outline of the brazier for roasting chestnuts?
NRICH is part of the family of activities in the Millennium Mathematics Project.