Resources tagged with Visualising similar to Archery:
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Generalising. Resourceful. Visualising. Games. Working systematically. Interactivities. Experimental probability. Trial and improvement. Spreadsheets. Sampling.There are 184 results
Broad Topics > Using, Applying and Reasoning about Mathematics > Visualising
Isosceles Triangles
Age 11 to 14 Challenge Level:
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
Khun Phaen Escapes to Freedom
Age 11 to 14 Challenge Level:
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
Framed
Age 11 to 14 Challenge Level:
Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of. . . .
Tetra Square
Age 11 to 14 Challenge Level:
ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is 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.
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. . . .
Trice
Age 11 to 14 Challenge Level:
ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR?
On the Edge
Age 11 to 14 Challenge Level:
If you move the tiles around, can you make squares with different coloured edges?
Triangle Inequality
Age 11 to 14 Challenge Level:
ABC is an equilateral triangle and P is a point in the interior of the triangle. We know that AP = 3cm and BP = 4cm. Prove that CP must be less than 10 cm.
Coordinate Patterns
Age 11 to 14 Challenge Level:
Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
Buses
Age 11 to 14 Challenge Level:
A bus route has a total duration of 40 minutes. Every 10 minutes, two buses set out, one from each end. How many buses will one bus meet on its way from one end to the other end?
Conway's Chequerboard Army
Age 11 to 14 Challenge Level:
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
Cuboids
Age 11 to 14 Challenge Level:
Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
Triangles to Tetrahedra
Age 11 to 14 Challenge Level:
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
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.
Cubist Cuts
Age 11 to 14 Challenge Level:
A 3x3x3 cube may be reduced to unit cubes in six saw cuts. If after every cut you can rearrange the pieces before cutting straight through, can you do it in fewer?
Convex Polygons
Age 11 to 14 Challenge Level:
Show that among the interior angles of a convex polygon there cannot be more than three acute angles.
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?
Picturing Triangular Numbers
Age 11 to 14 Challenge Level:
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Zooming in on the Squares
Age 7 to 14
Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?
Right Time
Age 11 to 14 Challenge Level:
At the time of writing the hour and minute hands of my clock are at right angles. How long will it be before they are at right angles again?
An Unusual Shape
Age 11 to 14 Challenge Level:
Can you maximise the area available to a grazing goat?
All in the Mind
Age 11 to 14 Challenge Level:
Imagine you are suspending a cube from one vertex and allowing it to hang freely. What shape does the surface of the water make around the cube?
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?
Linkage
Age 11 to 14 Challenge Level:
Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?
Tetrahedra Tester
Age 11 to 14 Challenge Level:
An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?
Travelling Salesman
Age 11 to 14 Challenge Level:
A Hamiltonian circuit is a continuous path in a graph that passes through each of the vertices exactly once and returns to the start. How many Hamiltonian circuits can you find in these graphs?
Coloured Edges
Age 11 to 14 Challenge Level:
The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?
Concrete Wheel
Age 11 to 14 Challenge Level:
A huge wheel is rolling past your window. What do you see?
You Owe Me Five Farthings, Say the Bells of St Martin's
Age 11 to 14 Challenge Level:
Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?
The Old Goats
Age 11 to 14 Challenge Level:
A rectangular field has two posts with a ring on top of each post. There are two quarrelsome goats and plenty of ropes which you can tie to their collars. How can you secure them so they can't. . . .
Diagonal Dodge
Age 7 to 14 Challenge Level:
A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.
Icosagram
Age 11 to 14 Challenge Level:
Draw a pentagon with all the diagonals. This is called a pentagram. How many diagonals are there? How many diagonals are there in a hexagram, heptagram, ... Does any pattern occur when looking at. . . .
Christmas Boxes
Age 11 to 14 Challenge Level:
Find all the ways to cut out a 'net' of six squares that can be folded into a cube.
Christmas Chocolates
Age 11 to 14 Challenge Level:
How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?
Rati-o
Age 11 to 14 Challenge Level:
Points P, Q, R and S each divide the sides AB, BC, CD and DA respectively in the ratio of 2 : 1. Join the points. What is the area of the parallelogram PQRS in relation to the original rectangle?
Dissect
Age 11 to 14 Challenge Level:
What is the minimum number of squares a 13 by 13 square can be dissected into?
Tic Tac Toe
Age 11 to 14 Challenge Level:
In the game of Noughts and Crosses there are 8 distinct winning lines. How many distinct winning lines are there in a game played on a 3 by 3 by 3 board, with 27 cells?
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?
Shady Symmetry
Age 11 to 14 Challenge Level:
How many different symmetrical shapes can you make by shading triangles or squares?
Troublesome Dice
Age 11 to 14 Challenge Level:
When dice land edge-up, we usually roll again. But what if we didn't...?
Seven Squares
Age 11 to 14 Challenge Level:
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
Reflecting Squarely
Age 11 to 14 Challenge Level:
In how many ways can you fit all three pieces together to make shapes with line symmetry?
Hidden Rectangles
Age 11 to 14 Challenge Level:
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
3D Stacks
Age 7 to 14 Challenge Level:
Can you find a way of representing these arrangements of balls?
Polygon Rings
Age 11 to 14 Challenge Level:
Join pentagons together edge to edge. Will they form a ring?
Auditorium Steps
Age 7 to 14 Challenge Level:
What is the shape of wrapping paper that you would need to completely wrap this model?
Take Ten
Age 11 to 14 Challenge Level:
Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube so that the surface area of the remaining solid is the same as the surface area of the original?
Crossing the Atlantic
Age 11 to 14 Challenge Level:
Every day at noon a boat leaves Le Havre for New York while another boat leaves New York for Le Havre. The ocean crossing takes seven days. How many boats will each boat cross during their journey?
NRICH is part of the family of activities in the Millennium Mathematics Project.