# Resources tagged with: Creating and manipulating expressions and formulae

Filter by: Content type:
Age range:
Challenge level:

### There are 124 results

Broad Topics > Algebraic expressions, equations and formulae > Creating and manipulating expressions and formulae ### 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? ### Enriching Experience

##### Age 14 to 16 Challenge Level:

Find the five distinct digits N, R, I, C and H in the following nomogram ### 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. ### Unusual Long Division - Square Roots Before Calculators

##### Age 14 to 16 Challenge Level:

However did we manage before calculators? Is there an efficient way to do a square root if you have to do the work yourself? ### Regular Hexagon Loops

##### Age 11 to 14 Challenge Level:

Make some loops out of regular hexagons. What rules can you discover? ##### Age 11 to 14 Challenge Level:

A little bit of algebra explains this 'magic'. Ask a friend to pick 3 consecutive numbers and to tell you a multiple of 3. Then ask them to add the four numbers and multiply by 67, and to tell you. . . . ### 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? ### 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? ### Really Mr. Bond

##### Age 14 to 16 Challenge Level:

115^2 = (110 x 120) + 25, that is 13225 895^2 = (890 x 900) + 25, that is 801025 Can you explain what is happening and generalise? ### 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?” ##### Age 11 to 14 Challenge Level:

Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain. . . . ### 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? ### 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? ### Even So

##### Age 11 to 14 Challenge Level:

Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why? ### Back to Basics

##### Age 14 to 16 Challenge Level:

Find b where 3723(base 10) = 123(base b). ### 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? ##### Age 11 to 14 Challenge Level:

List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it? ### 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? ### 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? ### 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? ### 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. . . . ### 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? ### Inside Outside

##### Age 14 to 16 Challenge Level:

Balance the bar with the three weight on the inside. ### 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? ##### Age 11 to 14 Challenge Level:

Think of a number, add one, double it, take away 3, add the number you first thought of, add 7, divide by 3 and take away the number you first thought of. You should now be left with 2. How do I. . . . ### Crossed Ends

##### Age 11 to 14 Challenge Level:

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends? ### 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. ### 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? ### Magic Sums and Products

##### Age 11 to 16

How to build your own magic squares. ##### Age 11 to 14 Challenge Level:

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why? ### 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? ### Card Trick 1

##### Age 11 to 14 Challenge Level:

Can you explain how this card trick works? ### 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... ### 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? ### 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? ### 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? ### Special Sums and Products

##### Age 11 to 14 Challenge Level:

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48. ### 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? ### 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. . . . ### Perimeter Expressions

##### Age 11 to 14 Challenge Level:

Create some shapes by combining two or more rectangles. What can you say about the areas and perimeters of the shapes you can make? ### 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? ##### Age 7 to 14 Challenge Level:

Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know? ##### 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? ### Triangles Within Pentagons

##### Age 14 to 16 Challenge Level:

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

##### Age 11 to 16 Challenge Level:

A task which depends on members of the group noticing the needs of others and responding. ### Generating Triples

##### Age 14 to 16 Challenge Level:

Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more? ### 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...