# Resources tagged with: Creating and manipulating expressions and formulae

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##### Other tags that relate to Oranges and Lemons, Say the Bells of St Clement's
Factors and multiples. Games. Permutations. Interactivities. Visualising. Selecting and using information. Combinations. Working systematically. Music. Addition & subtraction.

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Broad Topics > Algebraic expressions, equations and formulae > Creating and manipulating expressions and formulae ##### Age 11 to 14Challenge 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? ### Number Pyramids

##### Age 11 to 14Challenge Level

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

##### Age 11 to 14Challenge 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? ### Special Sums and Products

##### Age 11 to 14Challenge 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. ### More Mathematical Mysteries

##### Age 11 to 14Challenge Level

Write down a three-digit number Change the order of the digits to get a different number Find the difference between the two three digit numbers Follow the rest of the instructions then try. . . . ### Magic W

##### Age 14 to 16Challenge Level

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total. ##### Age 11 to 14Challenge 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? ### Reversals

##### Age 11 to 14Challenge Level

Where should you start, if you want to finish back where you started? ### Steel Cables

##### Age 14 to 16Challenge Level

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

##### Age 11 to 14Challenge Level

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4 ### Partly Painted Cube

##### Age 14 to 16Challenge 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? ### Why 8?

##### Age 11 to 14Challenge Level

Choose any four consecutive even numbers. Multiply the two middle numbers together. Multiply the first and last numbers. Now subtract your second answer from the first. Try it with your own. . . . ### Sums of Pairs

##### Age 11 to 16Challenge 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?” ### Harmonic Triangle

##### Age 14 to 16Challenge Level

Can you see how to build a harmonic triangle? Can you work out the next two rows? ### Regular Hexagon Loops

##### Age 11 to 14Challenge Level

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

##### Age 14 to 16Challenge Level

Can you use the diagram to prove the AM-GM inequality? ### More Number Pyramids

##### Age 11 to 14Challenge Level

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

##### Age 11 to 14Challenge 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? ### Quick Times

##### Age 11 to 14Challenge Level

32 x 38 = 30 x 40 + 2 x 8; 34 x 36 = 30 x 40 + 4 x 6; 56 x 54 = 50 x 60 + 6 x 4; 73 x 77 = 70 x 80 + 3 x 7 Verify and generalise if possible. ### Sum Equals Product

##### Age 11 to 14Challenge 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 ï¿½ 1 [1/3]. What other numbers have the sum equal to the product and can this be. . . . ### Think of Two Numbers

##### Age 11 to 14Challenge Level

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

##### Age 14 to 16Challenge Level

Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice? ### Top-heavy Pyramids

##### Age 11 to 14Challenge Level

Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200. ### The Number Jumbler

##### Age 7 to 14Challenge Level

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

##### Age 11 to 14Challenge 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. . . . ##### Age 11 to 14Challenge 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. . . . ### Christmas Chocolates

##### Age 11 to 14Challenge Level

How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes? ### Always a Multiple?

##### Age 11 to 14Challenge Level

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens... ### Janine's Conjecture

##### Age 14 to 16Challenge 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. . . . ### 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. ### Crossed Ends

##### Age 11 to 14Challenge Level

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends? ### Chocolate 2010

##### Age 14 to 16Challenge Level

First of all, pick the number of times a week that you would like to eat chocolate. Multiply this number by 2... ### Lower Bound

##### Age 14 to 16Challenge 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 = ### Areas of Parallelograms

##### Age 14 to 16Challenge Level

Can you find the area of a parallelogram defined by two vectors? ### Never Prime

##### Age 14 to 16Challenge 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. ### A Tilted Square

##### Age 14 to 16Challenge Level

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices? ### Beach Huts

##### Age 11 to 14Challenge Level

Can you figure out how sequences of beach huts are generated? ### Painted Cube

##### Age 14 to 16Challenge Level

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces? ### How Much Can We Spend?

##### Age 11 to 14Challenge 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? ### Pair Products

##### Age 14 to 16Challenge 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 16Challenge 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. ### How Many Miles to Go?

##### Age 11 to 14Challenge 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? ### Is it Magic or Is it Maths?

##### Age 11 to 14Challenge Level

Here are three 'tricks' to amaze your friends. But the really clever trick is explaining to them why these 'tricks' are maths not magic. Like all good magicians, you should practice by trying. . . . ### Square Pizza

##### Age 14 to 16Challenge 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? ### Pinned Squares

##### Age 14 to 16Challenge Level

What is the total number of squares that can be made on a 5 by 5 geoboard? ### Cubes Within Cubes Revisited

##### Age 11 to 14Challenge 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? ### Interactive Number Patterns

##### Age 14 to 16Challenge Level

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

##### Age 7 to 14Challenge Level

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice? ### Triangles Within Pentagons

##### Age 14 to 16Challenge Level

Show that all pentagonal numbers are one third of a triangular number. ### Triangles Within Squares

##### Age 14 to 16Challenge Level

Can you find a rule which relates triangular numbers to square numbers?