Resources tagged with Triangles similar to A Cartesian Puzzle:
Other tags that relate to A Cartesian Puzzle
Visualising. Symmetry. Coordinates. Practical Activity. Area - squares and rectangles. Quadrilaterals. Angles - points, lines and parallel lines. Rotations. Reflections. Triangles.There are 58 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?
Transformations on a Pegboard
Age 7 to 11 Challenge Level:
How would you move the bands on the pegboard to alter these shapes?
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.
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?
Triangle Relations
Age 7 to 11 Challenge Level:
What do these two triangles have in common? How are they related?
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.
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?
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.
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?
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.
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?
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?
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.
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?
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?
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?
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?
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?
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?
Folding Flowers 2
Age 7 to 11 Challenge Level:
Make a flower design using the same shape made out of different sizes of paper.
Kissing Triangles
Age 11 to 14 Challenge Level:
Determine the total shaded area of the 'kissing triangles'.
Sorting Logic Blocks
Age 5 to 11 Challenge Level:
This interactivity allows you to sort logic blocks by dragging their images.
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?
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?
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?
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?
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?
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.
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?
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?
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?
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.
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.
Interacting with the Geometry of the Circle
Age 5 to 16
Jennifer Piggott and Charlie Gilderdale describe a free interactive circular geoboard environment that can lead learners to pose mathematical questions.
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...
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?
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'?
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.
Triangles All Around
Age 7 to 11 Challenge Level:
Can you find all the different triangles on these peg boards, and find their angles?
Nine-pin Triangles
Age 7 to 11 Challenge Level:
How many different triangles can you make on a circular pegboard that has nine pegs?
Liethagoras' Theorem
Age 7 to 14
Liethagoras, Pythagoras' cousin (!), was jealous of Pythagoras and came up with his own theorem. Read this article to find out why other mathematicians laughed at him.
Uncanny Triangles
Age 7 to 11 Challenge Level:
Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?
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?
Dotty Triangles
Age 11 to 14 Challenge Level:
Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?
Squareo'scope Determines the Kind of Triangle
Age 11 to 14
A description of some experiments in which you can make discoveries about triangles.
NRICH is part of the family of activities in the Millennium Mathematics Project.