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Broad Topics > Information and Communications Technology > smartphone

### Pair Products

##### Stage: 4 Challenge Level:

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

### Matchless

##### Stage: 4 Challenge Level:

There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?

### What's Possible?

##### Stage: 4 Challenge Level:

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

### Sitting Pretty

##### Stage: 4 Challenge Level:

A circle of radius r touches two sides of a right angled triangle, sides x and y, and has its centre on the hypotenuse. Can you prove the formula linking x, y and r?

### Nicely Similar

##### Stage: 4 Challenge Level:

If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?

### Areas of Parallelograms

##### Stage: 4 Challenge Level:

Can you find the area of a parallelogram defined by two vectors?

### Days and Dates

##### Stage: 3 Challenge Level:

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

### Dating Made Easier

##### Stage: 4 Challenge Level:

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

### Odd Differences

##### Stage: 4 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.

### How Many Miles to Go?

##### Stage: 3 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?

### Beelines

##### Stage: 4 Challenge Level:

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

### Always Perfect

##### Stage: 4 Challenge Level:

Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

### Sweet Shop

##### Stage: 3 Challenge Level:

Five children went into the sweet shop after school. There were choco bars, chews, mini eggs and lollypops, all costing under 50p. Suggest a way in which Nathan could spend all his money.

### Plus Minus

##### Stage: 4 Challenge Level:

Can you explain the surprising results Jo found when she calculated the difference between square numbers?

### Special Numbers

##### Stage: 3 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?

### Think of Two Numbers

##### Stage: 3 Challenge Level:

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

### Legs Eleven

##### Stage: 3 Challenge Level:

Take any four digit number. Move the first digit to the 'back of the queue' and move the rest along. Now add your two numbers. What properties do your answers always have?

### 2-digit Square

##### Stage: 4 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?

### Handshakes

##### Stage: 3 Challenge Level:

Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?

### Curvy Areas

##### Stage: 4 Challenge Level:

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?

### Searching for Mean(ing)

##### Stage: 3 Challenge Level:

Imagine you have a large supply of 3kg and 8kg weights. How many of each weight would you need for the average (mean) of the weights to be 6kg? What other averages could you have?

### Litov's Mean Value Theorem

##### Stage: 3 Challenge Level:

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...

### Painted Cube

##### Stage: 3 Challenge 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?

### Route to Infinity

##### Stage: 3 Challenge Level:

Can you describe this route to infinity? Where will the arrows take you next?

### Mirror, Mirror...

##### Stage: 3 Challenge Level:

Explore the effect of reflecting in two parallel mirror lines.

### Elevenses

##### Stage: 3 Challenge Level:

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

### Marbles in a Box

##### Stage: 3 Challenge Level:

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

### Orbiting Billiard Balls

##### Stage: 4 Challenge Level:

What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?

### Who Is the Fairest of Them All ?

##### Stage: 3 Challenge Level:

Explore the effect of combining enlargements.

### Picturing Square Numbers

##### Stage: 3 Challenge Level:

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

### Children at Large

##### Stage: 3 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?

### Summing Consecutive Numbers

##### Stage: 3 Challenge Level:

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

### Sissa's Reward

##### Stage: 3 Challenge Level:

Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...

### Repetitiously

##### Stage: 3 Challenge Level:

The number 2.525252525252.... can be written as a fraction. What is the sum of the denominator and numerator?

### Dozens

##### Stage: 3 Challenge Level:

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

### Fair Shares?

##### Stage: 4 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?

### Make 37

##### Stage: 2 and 3 Challenge Level:

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

### Consecutive Negative Numbers

##### Stage: 3 Challenge Level:

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

### Consecutive Seven

##### Stage: 3 Challenge Level:

Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?

### Take Three from Five

##### Stage: 4 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?

### Keep it Simple

##### Stage: 3 Challenge Level:

Can all unit fractions be written as the sum of two unit fractions?

### Differences

##### Stage: 3 Challenge Level:

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

### Counting Factors

##### Stage: 3 Challenge Level:

Is there an efficient way to work out how many factors a large number has?

### Fractions Jigsaw

##### Stage: 3 Challenge Level:

A jigsaw where pieces only go together if the fractions are equivalent.

### The Greedy Algorithm

##### Stage: 3 Challenge Level:

The Egyptians expressed all fractions as the sum of different unit fractions. The Greedy Algorithm might provide us with an efficient way of doing this.

### Squares in Rectangles

##### Stage: 3 Challenge Level:

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

### Cuboid Challenge

##### Stage: 3 Challenge Level:

What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?

### Salinon

##### Stage: 4 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?

### An Unusual Shape

##### Stage: 3 Challenge Level:

Can you maximise the area available to a grazing goat?

### Can They Be Equal?

##### Stage: 3 Challenge Level:

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