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Resources tagged with Creating and manipulating expressions and formulae similar to Composite Notions:

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Broad Topics > Algebraic expressions, equations and formulae > Creating and manipulating expressions and formulae Perfectly Square

Age 14 to 16 Challenge Level:

The sums of the squares of three related numbers is also a perfect square - can you explain why? 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. Never Prime

Age 14 to 16 Challenge Level:

If a two digit number has its digits reversed and the smaller of the two numbers is subtracted from the larger, prove the difference can never be prime. Diophantine N-tuples

Age 14 to 16 Challenge Level:

Can you explain why a sequence of operations always gives you perfect squares? 2-digit Square

Age 14 to 16 Challenge Level:

A 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number? Back to Basics

Age 14 to 16 Challenge Level:

Find b where 3723(base 10) = 123(base b). Age 14 to 16 Challenge Level:

Kyle and his teacher disagree about his test score - who is right? 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... Multiplication Square

Age 14 to 16 Challenge Level:

Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice? Janine's Conjecture

Age 14 to 16 Challenge Level:

Janine noticed, while studying some cube numbers, that if you take three consecutive whole numbers and multiply them together and then add the middle number of the three, you get the middle number. . . . 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? DOTS Division

Age 14 to 16 Challenge Level:

Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}. Always Two

Age 14 to 18 Challenge Level:

Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2. Archimedes and Numerical Roots

Age 14 to 16 Challenge Level:

The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots? Lens Angle

Age 14 to 16 Challenge Level:

Find the missing angle between the two secants to the circle when the two angles at the centre subtended by the arcs created by the intersections of the secants and the circle are 50 and 120 degrees. AMGM

Age 14 to 16 Challenge Level:

Can you use the diagram to prove the AM-GM inequality? Leonardo's Problem

Age 14 to 18 Challenge Level:

A, B & C own a half, a third and a sixth of a coin collection. Each grab some coins, return some, then share equally what they had put back, finishing with their own share. How rich are they? 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. . . . Pythagoras Proofs

Age 14 to 16 Challenge Level:

Can you make sense of these three proofs of Pythagoras' Theorem? Salinon

Age 14 to 16 Challenge Level:

This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter? Consecutive Squares

Age 14 to 16 Challenge Level:

The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false? Training Schedule

Age 14 to 16 Challenge Level:

The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target? Age 14 to 16 Challenge Level:

Robert noticed some interesting patterns when he highlighted square numbers in a spreadsheet. Can you prove that the patterns will continue? Magic Squares for Special Occasions

Age 11 to 16

This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line. Simplifying Doughnut

Age 14 to 18 Challenge Level:

An algebra task which depends on members of the group noticing the needs of others and responding. Algebra Match

Age 11 to 16 Challenge Level:

A task which depends on members of the group noticing the needs of others and responding. Reasonable Algebra

Age 14 to 16 Challenge Level:

Use algebra to reason why 16 and 32 are impossible to create as the sum of consecutive numbers. There and Back

Age 14 to 16 Challenge Level:

Brian swims at twice the speed that a river is flowing, downstream from one moored boat to another and back again, taking 12 minutes altogether. How long would it have taken him in still water? ' Tis Whole

Age 14 to 18 Challenge Level:

Take a few whole numbers away from a triangle number. If you know the mean of the remaining numbers can you find the triangle number and which numbers were removed? Balance Point

Age 14 to 16 Challenge Level:

Attach weights of 1, 2, 4, and 8 units to the four attachment points on the bar. Move the bar from side to side until you find a balance point. Is it possible to predict that position? Terminology

Age 14 to 16 Challenge Level:

Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles? Magic Sums and Products

Age 11 to 16

How to build your own magic squares. Interactive Number Patterns

Age 14 to 16 Challenge Level:

How good are you at finding the formula for a number pattern ? 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. Screen Shot

Age 14 to 16 Challenge Level:

A moveable screen slides along a mirrored corridor towards a centrally placed light source. A ray of light from that source is directed towards a wall of the corridor, which it strikes at 45 degrees. . . . Pair Products

Age 14 to 16 Challenge Level:

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice? Inside Outside

Age 14 to 16 Challenge Level:

Balance the bar with the three weight on the inside. Gutter

Age 14 to 16 Challenge Level:

Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter? Algebra from Geometry

Age 11 to 16 Challenge Level:

Account of an investigation which starts from the area of an annulus and leads to the formula for the difference of two squares. Age 14 to 16 Challenge Level:

If a sum invested gains 10% each year how long before it has doubled its value? Series Sums

Age 14 to 16 Challenge Level:

Let S1 = 1 , S2 = 2 + 3, S3 = 4 + 5 + 6 ,........ Calculate S17. Sums of Pairs

Age 11 to 16 Challenge Level:

Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?” Fair Shares?

Age 14 to 16 Challenge Level:

A mother wants to share a sum of money by giving each of her children in turn a lump sum plus a fraction of the remainder. How can she do this in order to share the money out equally? Hike and Hitch

Age 14 to 16 Challenge Level:

Fifteen students had to travel 60 miles. They could use a car, which could only carry 5 students. As the car left with the first 5 (at 40 miles per hour), the remaining 10 commenced hiking along the. . . . Pareq Calc

Age 14 to 16 Challenge Level:

Triangle ABC is an equilateral triangle with three parallel lines going through the vertices. Calculate the length of the sides of the triangle if the perpendicular distances between the parallel. . . . Triangles Within Triangles

Age 14 to 16 Challenge Level:

Can you find a rule which connects consecutive triangular numbers? Pinned Squares

Age 14 to 16 Challenge Level:

What is the total number of squares that can be made on a 5 by 5 geoboard? Sum Equals Product

Age 11 to 14 Challenge Level:

The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 × 1 [1/3]. What other numbers have the sum equal to the product and can this be so for. . . .  