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Resources tagged with Creating and manipulating expressions and formulae similar to Multiplication Arithmagons:

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

What's Possible?

Age 14 to 16 Challenge Level:

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

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?

Pick's Theorem

Age 14 to 16 Challenge Level:

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

Special Numbers

Age 11 to 14 Challenge Level:

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

Can They Be Equal?

Age 11 to 14 Challenge Level:

Can you find rectangles where the value of the area is the same as the value of the perimeter?

More Number Pyramids

Age 11 to 14 Challenge Level:

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

Age 11 to 14 Challenge Level:

Think of a number Multiply it by 3 Add 6 Take away your start number Divide by 2 Take away your number. (You have finished with 3!) HOW DOES THIS WORK?

Number Pyramids

Age 11 to 14 Challenge Level:

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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?”

Lower Bound

Age 14 to 16 Challenge Level:

What would you get if you continued this sequence of fraction sums? 1/2 + 2/1 = 2/3 + 3/2 = 3/4 + 4/3 =

Good Work If You Can Get It

Age 11 to 14 Challenge Level:

A job needs three men but in fact six people do it. When it is finished they are all paid the same. How much was paid in total, and much does each man get if the money is shared as Fred suggests?

Square Pizza

Age 14 to 16 Challenge Level:

Can you show that you can share a square pizza equally between two people by cutting it four times using vertical, horizontal and diagonal cuts through any point inside the square?

Card Trick 1

Age 11 to 14 Challenge Level:

Can you explain how this card trick works?

Regular Hexagon Loops

Age 11 to 14 Challenge Level:

Make some loops out of regular hexagons. What rules can you discover?

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?

Summing Consecutive Numbers

Age 11 to 14 Challenge Level:

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

Age 11 to 14 Challenge Level:

Think of a number and follow my instructions. Tell me your answer, and I'll tell you what you started with! Can you explain how I know?

Think of Two Numbers

Age 11 to 14 Challenge Level:

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

Fibs

Age 11 to 14 Challenge Level:

The well known Fibonacci sequence is 1 ,1, 2, 3, 5, 8, 13, 21.... How many Fibonacci sequences can you find containing the number 196 as one of the terms?

Marbles in a Box

Age 11 to 16 Challenge Level:

How many winning lines can you make in a three-dimensional version of noughts and crosses?

Odd Differences

Age 14 to 16 Challenge Level:

The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.

Partly Painted Cube

Age 14 to 16 Challenge Level:

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

Steel Cables

Age 14 to 16 Challenge Level:

Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?

How Much Can We Spend?

Age 11 to 14 Challenge Level:

A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

Always a Multiple?

Age 11 to 14 Challenge Level:

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

Attractive Tablecloths

Age 14 to 16 Challenge Level:

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

Terminology

Age 14 to 16 Challenge Level:

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

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?

Always the Same

Age 11 to 14 Challenge Level:

Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?

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.

How Many Miles to Go?

Age 11 to 14 Challenge Level:

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

AMGM

Age 14 to 16 Challenge Level:

Can you use the diagram to prove the AM-GM inequality?

Chocolate Maths

Age 11 to 14 Challenge Level:

Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .

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?

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?

The Number Jumbler

Age 7 to 14 Challenge Level:

The Number Jumbler can always work out your chosen symbol. Can you work out how?

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?

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?

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?

Hand Swap

Age 14 to 16 Challenge Level:

My train left London between 6 a.m. and 7 a.m. and arrived in Paris between 9 a.m. and 10 a.m. At the start and end of the journey the hands on my watch were in exactly the same positions but the. . . .

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?

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?

How Big?

Age 11 to 14 Challenge Level:

If the sides of the triangle in the diagram are 3, 4 and 5, what is the area of the shaded square?

' 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?

Interactive Number Patterns

Age 14 to 16 Challenge Level:

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

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.

Cubes Within Cubes Revisited

Age 11 to 14 Challenge Level:

Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?

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.

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. . . .

Triangles Within Pentagons

Age 14 to 16 Challenge Level:

Show that all pentagonal numbers are one third of a triangular number.