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Visualising. Video. Practical Activity. Mathematical reasoning & proof. Working systematically. Euclid's algorithm. Curious. Generalising. Addition & subtraction. Positive-negative numbers.There are 117 results
Broad Topics > Information and Communications Technology > smartphone
Consecutive Numbers
Age 7 to 14 Challenge Level:
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Consecutive Negative Numbers
Age 11 to 14 Challenge Level:
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Weights
Age 11 to 14 Challenge Level:
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Summing Consecutive Numbers
Age 11 to 14 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?
Number Daisy
Age 11 to 14 Challenge Level:
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
Marbles in a Box
Age 11 to 14 Challenge Level:
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Children at Large
Age 11 to 14 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?
Handshakes
Age 11 to 14 Challenge Level:
Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
Eight Hidden Squares
Age 7 to 14 Challenge Level:
On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?
Make 37
Age 7 to 14 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.
An Unusual Shape
Age 11 to 14 Challenge Level:
Can you maximise the area available to a grazing goat?
Two and Two
Age 11 to 14 Challenge Level:
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Take Three from Five
Age 14 to 16 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?
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?
On the Edge
Age 11 to 14 Challenge Level:
If you move the tiles around, can you make squares with different coloured edges?
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?
M, M and M
Age 11 to 14 Challenge Level:
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
Days and Dates
Age 11 to 14 Challenge Level:
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Largest Product
Age 11 to 14 Challenge Level:
Which set of numbers that add to 10 have the largest product?
Rule of Three
Age 11 to 14 Challenge Level:
If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?
Sweet Shop
Age 11 to 14 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.
Beelines
Age 14 to 16 Challenge Level:
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
Shady Symmetry
Age 11 to 14 Challenge Level:
How many different symmetrical shapes can you make by shading triangles or squares?
Picturing Square Numbers
Age 11 to 14 Challenge Level:
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
Squares in Rectangles
Age 11 to 14 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?
Who Is the Fairest of Them All ?
Age 11 to 14 Challenge Level:
Explore the effect of combining enlargements.
1 Step 2 Step
Age 11 to 14 Challenge Level:
Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?
Route to Infinity
Age 11 to 14 Challenge Level:
Can you describe this route to infinity? Where will the arrows take you next?
Mirror, Mirror...
Age 11 to 14 Challenge Level:
Explore the effect of reflecting in two parallel mirror lines.
Searching for Mean(ing)
Age 11 to 14 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?
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?
Consecutive Seven
Age 11 to 14 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?
Product Sudoku
Age 11 to 14 Challenge Level:
The clues for this Sudoku are the product of the numbers in adjacent squares.
Painted Cube
Age 11 to 14 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?
Ben's Game
Age 11 to 14 Challenge Level:
Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.
Do You Feel Lucky?
Age 11 to 14 Challenge Level:
Some people offer advice on how to win at games of chance, or how to influence probability in your favour. Can you decide whether advice is good or not?
Mixing Paints
Age 11 to 14 Challenge Level:
A decorator can buy pink paint from two manufacturers. What is the least number he would need of each type in order to produce different shades of pink.
Fractions Jigsaw
Age 11 to 14 Challenge Level:
A jigsaw where pieces only go together if the fractions are equivalent.
Mixing More Paints
Age 11 to 14 Challenge Level:
Is it always possible to combine two paints made up in the ratios 1:x and 1:y and turn them into paint made up in the ratio a:b ? Can you find an efficent way of doing this?
Keep it Simple
Age 11 to 14 Challenge Level:
Can all unit fractions be written as the sum of two unit fractions?
How Old Am I?
Age 14 to 16 Challenge Level:
In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?
Attractive Rotations
Age 11 to 14 Challenge Level:
Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...
Cuboid Challenge
Age 11 to 14 Challenge Level:
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
Repetitiously
Age 11 to 14 Challenge Level:
The number 2.525252525252.... can be written as a fraction. What is the sum of the denominator and numerator?
Elevenses
Age 11 to 14 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?
Dozens
Age 7 to 14 Challenge Level:
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
Sending a Parcel
Age 11 to 14 Challenge Level:
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
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?
Power Mad!
Age 11 to 14 Challenge Level:
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
Sissa's Reward
Age 11 to 14 Challenge Level:
Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...
NRICH is part of the family of activities in the Millennium Mathematics Project.