What is the total area of the four outside triangles which are
outlined in red in this arrangement of squares inside each other?
Draw three straight lines to separate these shapes into four groups
- each group must contain one of each shape.
A group activity using visualisation of squares and triangles.
What shape has Harry drawn on this clock face? Can you find its
area? What is the largest number of square tiles that could cover
Billy's class had a robot called Fred who could draw with chalk
held underneath him. What shapes did the pupils make Fred draw?
How can you make an angle of 60 degrees by folding a sheet of paper
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?
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?
Choose a box and work out the smallest rectangle of paper needed to
wrap it so that it is completely covered.
Can you visualise what shape this piece of paper will make when it is folded?
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
In this problem, we have created a pattern from smaller and smaller
squares. If we carried on the pattern forever, what proportion of
the image would be coloured blue?
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?
What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.
What is the greatest number of squares you can make by overlapping
Triangles are formed by joining the vertices of a skeletal cube. How many different types of triangle are there? How many triangles altogether?
Draw all the possible distinct triangles on a 4 x 4 dotty grid.
Convince me that you have all possible triangles.
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.
Anne completes a circuit around a circular track in 40 seconds.
Brenda runs in the opposite direction and meets Anne every 15
seconds. How long does it take Brenda to run around the track?
Can you cut a regular hexagon into two pieces to make a
parallelogram? Try cutting it into three pieces to make a rhombus!
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.
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. . . .
What is the shape of wrapping paper that you would need to completely wrap this model?
How many different triangles can you make on a circular pegboard that has nine pegs?
These points all mark the vertices (corners) of ten hidden squares.
Can you find the 10 hidden squares?
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?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
What happens to the area of a square if you double the length of
the sides? Try the same thing with rectangles, diamonds and other
shapes. How do the four smaller ones fit into the larger one?
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?
It is possible to dissect any square into smaller squares. What is
the minimum number of squares a 13 by 13 square can be dissected
Show that among the interior angles of a convex polygon there
cannot be more than three acute angles.
A package contains a set of resources designed to develop pupils'
mathematical thinking. This package places a particular emphasis on
“visualising” and is designed to meet the needs. . . .
Reasoning about the number of matches needed to build squares that
share their sides.
In a right angled triangular field, three animals are tethered to posts at the midpoint of each side. Each rope is just long enough to allow the animal to reach two adjacent vertices. Only one animal. . . .
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Make a cube out of straws and have a go at this practical
Bilbo goes on an adventure, before arriving back home. Using the
information given about his journey, can you work out where Bilbo
Mathematics is the study of patterns. Studying pattern is an
opportunity to observe, hypothesise, experiment, discover and
You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.
Exploring and predicting folding, cutting and punching holes and
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
The triangle ABC is equilateral. The arc AB has centre C, the arc
BC has centre A and the arc CA has centre B. Explain how and why
this shape can roll along between two parallel tracks.
Can you fit the tangram pieces into the outlines of the chairs?
Which of the following cubes can be made from these nets?
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?
What can you see? What do you notice? What questions can you ask?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?