Resources tagged with Triangles similar to A Cartesian Puzzle:
Other tags that relate to A Cartesian Puzzle
Practical Activity. Symmetry. Visualising. Triangles. Rotations. Squares. Area - squares and rectangles. Coordinates. Reflections. Quadrilaterals.There are 59 results
Broad Topics > Angles, Polygons, and Geometrical Proof > Triangles
Cartesian Isometric
Age 7 to 11 Challenge Level:
The graph below is an oblique coordinate system based on 60 degree angles. It was drawn on isometric paper. What kinds of triangles do these points form?
Fraction Fascination
Age 7 to 11 Challenge Level:
This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.
Transformations on a Pegboard
Age 7 to 11 Challenge Level:
How would you move the bands on the pegboard to alter these shapes?
Rectangle Tangle
Age 7 to 11 Challenge Level:
The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the shapes?
Inside Seven Squares
Age 7 to 11 Challenge Level:
What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?
Triangle Island
Age 7 to 11 Challenge Level:
You have pitched your tent (the red triangle) on an island. Can you move it to the position shown by the purple triangle making sure you obey the rules?
Cut and Make
Age 7 to 11 Challenge Level:
Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?
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.
Jig Shapes
Age 5 to 11 Challenge Level:
Can you each work out what shape you have part of on your card? What will the rest of it look like?
Tessellating Transformations
Age 7 to 11 Challenge Level:
Can you find out how the 6-triangle shape is transformed in these tessellations? Will the tessellations go on for ever? Why or why not?
Part the Polygons
Age 7 to 11 Short Challenge Level:
Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape.
Triangle Relations
Age 7 to 11 Challenge Level:
What do these two triangles have in common? How are they related?
Triangle Shapes
Age 5 to 11 Challenge Level:
This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.
Sorting Logic Blocks
Age 5 to 11 Challenge Level:
This interactivity allows you to sort logic blocks by dragging their images.
Name That Triangle!
Age 7 to 11 Challenge Level:
Can you sketch triangles that fit in the cells in this grid? Which ones are impossible? How do you know?
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?
Folding Flowers 2
Age 7 to 11 Challenge Level:
Make a flower design using the same shape made out of different sizes of paper.
Making Maths: Equilateral Triangle Folding
Age 7 to 14 Challenge Level:
Make an equilateral triangle by folding paper and use it to make patterns of your own.
Making Maths: Test the Strength of a Triangle
Age 7 to 11 Challenge Level:
Have you noticed that triangles are used in manmade structures? Perhaps there is a good reason for this? 'Test a Triangle' and see how rigid triangles are.
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?
Constructing Triangles
Age 11 to 14 Challenge Level:
Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
Triangle Pin-down
Age 7 to 11 Challenge Level:
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
LOGO Challenge 5 - Patch
Age 11 to 16 Challenge Level:
Using LOGO, can you construct elegant procedures that will draw this family of 'floor coverings'?
Nine-pin Triangles
Age 7 to 11 Challenge Level:
How many different triangles can you make on a circular pegboard that has nine pegs?
Kissing Triangles
Age 11 to 14 Challenge Level:
Determine the total shaded area of the 'kissing triangles'.
Triangle Transformation
Age 7 to 14 Challenge Level:
Start with a triangle. Can you cut it up to make a rectangle?
Peg and Pin Boards
Age 5 to 11
This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.
Cutting it Out
Age 5 to 11 Challenge Level:
I cut this square into two different shapes. What can you say about the relationship between them?
Counting Triangles
Age 11 to 14 Challenge Level:
Triangles are formed by joining the vertices of a skeletal cube. How many different types of triangle are there? How many triangles altogether?
Number the Sides
Age 7 to 11 Challenge Level:
The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?
Tessellating Triangles
Age 7 to 11 Challenge Level:
Can you make these equilateral triangles fit together to cover the paper without any gaps between them? Can you tessellate isosceles triangles?
Cut it Out
Age 7 to 11 Challenge Level:
Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?
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?
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?
Regular Rings 1
Age 7 to 11 Challenge Level:
Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?
Property Chart
Age 11 to 14 Challenge Level:
A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?
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.
Shapely Pairs
Age 11 to 14 Challenge Level:
A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...
Adding Triangles
Age 11 to 14 Challenge Level:
What is the total area of the first two triangles as a fraction of the original A4 rectangle? What is the total area of the first three triangles as a fraction of the original A4 rectangle? If. . . .
Triangular Tantaliser
Age 11 to 14 Challenge Level:
Draw all the possible distinct triangles on a 4 x 4 dotty grid. Convince me that you have all possible triangles.
Tri-five
Age 7 to 11 Challenge Level:
Find all the different shapes that can be made by joining five equilateral triangles edge to edge.
Bracelets
Age 7 to 11 Challenge Level:
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
Ratty
Age 11 to 14 Challenge Level:
If you know the sizes of the angles marked with coloured dots in this diagram which angles can you find by calculation?
Floored
Age 11 to 14 Challenge Level:
A floor is covered by a tessellation of equilateral triangles, each having three equal arcs inside it. What proportion of the area of the tessellation is shaded?
Isosceles
Age 11 to 14 Challenge Level:
Prove that a triangle with sides of length 5, 5 and 6 has the same area as a triangle with sides of length 5, 5 and 8. Find other pairs of non-congruent isosceles triangles which have equal areas.
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?
NRICH is part of the family of activities in the Millennium Mathematics Project.