Resources tagged with Mathematical reasoning & proof similar to Counting Fish:
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Fractions. Hypothesis testing. Investigations. Biology. Experimental probability. Random variables. Mathematical reasoning & proof. Sampling and hypothesis tests. Handling data. Advanced Statistics.There are 172 results
Broad Topics > Using, Applying and Reasoning about Mathematics > Mathematical reasoning & proof
Truth Tables and Electronic Circuits
Age 11 to 18
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Unit Fractions
Age 11 to 14 Challenge Level:
Consider the equation 1/a + 1/b + 1/c = 1 where a, b and c are natural numbers and 0 < a < b < c. Prove that there is only one set of values which satisfy this equation.
Logic, Truth Tables and Switching Circuits Challenge
Age 11 to 18
Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .
Logic, Truth Tables and Switching Circuits
Age 11 to 18
Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and record your findings in truth tables.
Problem Solving, Using and Applying and Functional Mathematics
Age 5 to 18 Challenge Level:
Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.
Number Rules - OK
Age 14 to 16 Challenge Level:
Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number...
Similarly So
Age 14 to 16 Challenge Level:
ABCD is a square. P is the midpoint of AB and is joined to C. A line from D perpendicular to PC meets the line at the point Q. Prove AQ = AD.
Pattern of Islands
Age 11 to 14 Challenge Level:
In how many distinct ways can six islands be joined by bridges so that each island can be reached from every other island...
Mediant Madness
Age 14 to 16 Challenge Level:
Kyle and his teacher disagree about his test score - who is right?
Königsberg
Age 11 to 14 Challenge Level:
Can you cross each of the seven bridges that join the north and south of the river to the two islands, once and once only, without retracing your steps?
Mouhefanggai
Age 14 to 16
Imagine two identical cylindrical pipes meeting at right angles and think about the shape of the space which belongs to both pipes. Early Chinese mathematicians call this shape the mouhefanggai.
Proofs with Pictures
Age 14 to 18
Some diagrammatic 'proofs' of algebraic identities and inequalities.
Children at Large
Age 11 to 14 Challenge Level:
There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
Coins on a Plate
Age 11 to 14 Challenge Level:
Points A, B and C are the centres of three circles, each one of which touches the other two. Prove that the perimeter of the triangle ABC is equal to the diameter of the largest circle.
Round and Round
Age 14 to 16 Challenge Level:
Prove that the shaded area of the semicircle is equal to the area of the inner circle.
A Chordingly
Age 11 to 14 Challenge Level:
Find the area of the annulus in terms of the length of the chord which is tangent to the inner circle.
Matter of Scale
Age 14 to 16 Challenge Level:
Prove Pythagoras' Theorem using enlargements and scale factors.
Pent
Age 14 to 18 Challenge Level:
The diagram shows a regular pentagon with sides of unit length. Find all the angles in the diagram. Prove that the quadrilateral shown in red is a rhombus.
Classifying Solids Using Angle Deficiency
Age 11 to 16 Challenge Level:
Toni Beardon has chosen this article introducing a rich area for practical exploration and discovery in 3D geometry
Rhombus in Rectangle
Age 14 to 16 Challenge Level:
Take any rectangle ABCD such that AB > BC. The point P is on AB and Q is on CD. Show that there is exactly one position of P and Q such that APCQ is a rhombus.
Paradoxes
Age 7 to 14
A paradox is a statement that seems to be both untrue and true at the same time. This article looks at a few examples and challenges you to investigate them for yourself.
Composite Notions
Age 14 to 16 Challenge Level:
A composite number is one that is neither prime nor 1. Show that 10201 is composite in any base.
The Frieze Tree
Age 11 to 16
Patterns that repeat in a line are strangely interesting. How many types are there and how do you tell one type from another?
Take Three from Five
Age 14 to 16 Challenge Level:
Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
Why 24?
Age 14 to 16 Challenge Level:
Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.
Pythagorean Triples I
Age 11 to 16
The first of two articles on Pythagorean Triples which asks how many right angled triangles can you find with the lengths of each side exactly a whole number measurement. Try it!
Pythagorean Triples II
Age 11 to 16
This is the second article on right-angled triangles whose edge lengths are whole numbers.
Angle Trisection
Age 14 to 16 Challenge Level:
It is impossible to trisect an angle using only ruler and compasses but it can be done using a carpenter's square.
Postage
Age 14 to 16 Challenge Level:
The country Sixtania prints postage stamps with only three values 6 lucres, 10 lucres and 15 lucres (where the currency is in lucres).Which values cannot be made up with combinations of these postage. . . .
Sixational
Age 14 to 18 Challenge Level:
The nth term of a sequence is given by the formula n^3 + 11n . Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. . . .
Always Perfect
Age 14 to 16 Challenge Level:
Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.
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?
Whole Number Dynamics I
Age 14 to 18
The first of five articles concentrating on whole number dynamics, ideas of general dynamical systems are introduced and seen in concrete cases.
Whole Number Dynamics II
Age 14 to 18
This article extends the discussions in "Whole number dynamics I". Continuing the proof that, for all starting points, the Happy Number sequence goes into a loop or homes in on a fixed point.
Yih or Luk Tsut K'i or Three Men's Morris
Age 11 to 18 Challenge Level:
Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots and a little about prime knots, crossing numbers and. . . .
Picturing Pythagorean Triples
Age 14 to 18
This article discusses how every Pythagorean triple (a, b, c) can be illustrated by a square and an L shape within another square. You are invited to find some triples for yourself.
The Pillar of Chios
Age 14 to 16 Challenge Level:
Semicircles are drawn on the sides of a rectangle. Prove that the sum of the areas of the four crescents is equal to the area of the rectangle.
Whole Number Dynamics V
Age 14 to 18
The final of five articles which containe the proof of why the sequence introduced in article IV either reaches the fixed point 0 or the sequence enters a repeating cycle of four values.
Whole Number Dynamics IV
Age 14 to 18
Start with any whole number N, write N as a multiple of 10 plus a remainder R and produce a new whole number N'. Repeat. What happens?
Whole Number Dynamics III
Age 14 to 18
In this third of five articles we prove that whatever whole number we start with for the Happy Number sequence we will always end up with some set of numbers being repeated over and over again.
Happy Numbers
Age 11 to 14 Challenge Level:
Take any whole number between 1 and 999, add the squares of the digits to get a new number. Make some conjectures about what happens in general.
A Knight's Journey
Age 14 to 18
This article looks at knight's moves on a chess board and introduces you to the idea of vectors and vector addition.
Impossible Sandwiches
Age 11 to 18
In this 7-sandwich: 7 1 3 1 6 4 3 5 7 2 4 6 2 5 there are 7 numbers between the 7s, 6 between the 6s etc. The article shows which values of n can make n-sandwiches and which cannot.
Unit Interval
Age 14 to 18 Challenge Level:
Take any two numbers between 0 and 1. Prove that the sum of the numbers is always less than one plus their product?
Breaking the Equation ' Empirical Argument = Proof '
Age 7 to 18
This article stems from research on the teaching of proof and offers guidance on how to move learners from focussing on experimental arguments to mathematical arguments and deductive reasoning.
Sticky Numbers
Age 11 to 14 Challenge Level:
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
Cyclic Quadrilaterals
Age 11 to 16 Challenge Level:
Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?
Geometric Parabola
Age 14 to 16 Challenge Level:
Explore what happens when you draw graphs of quadratic equations with coefficients based on a geometric sequence.
NRICH is part of the family of activities in the Millennium Mathematics Project.