Other tags that relate to Crossing the Atlantic
Creating and manipulating expressions and formulae. Working systematically. Mathematical modelling. Generalising. Speed and acceleration. Interactivities. Cubes & cuboids. Time. Mathematical reasoning & proof. Visualising.There are 125 results
Broad Topics > Algebraic expressions, equations and formulae > Creating and manipulating expressions and formulae
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?
Christmas Chocolates
Age 11 to 14 Challenge Level:
How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?
Painted Cube
Age 14 to 16 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?
A Tilted Square
Age 14 to 16 Challenge Level:
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
More Number Pyramids
Age 11 to 14 Challenge Level:
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Regular Hexagon Loops
Age 11 to 14 Challenge Level:
Make some loops out of regular hexagons. What rules can you discover?
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?
Magic W
Age 14 to 16 Challenge 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.
Partitioning Revisited
Age 11 to 14 Challenge 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
Quick Times
Age 11 to 14 Challenge 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.
Seven Squares
Age 11 to 14 Challenge Level:
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
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?
Triangles Within Triangles
Age 14 to 16 Challenge Level:
Can you find a rule which connects consecutive triangular numbers?
Triangles Within Squares
Age 14 to 16 Challenge Level:
Can you find a rule which relates triangular numbers to square numbers?
Triangles Within Pentagons
Age 14 to 16 Challenge Level:
Show that all pentagonal numbers are one third of a triangular number.
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?
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?
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?
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?
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?
Mind Reading
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. . . .
Multiply the Addition Square
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?
Lap Times
Age 14 to 16 Challenge Level:
Can you find the lap times of the two cyclists travelling at constant speeds?
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?
Hot Pursuit
Age 11 to 14 Challenge Level:
I added together the first 'n' positive integers and found that my answer was a 3 digit number in which all the digits were the same...
Hike and Hitch
Age 14 to 16 Challenge Level:
Fifteen students had to travel 60 miles. They could use a car, which could only carry 5 students. As the car left with the first 5 (at 40 miles per hour), the remaining 10 commenced hiking along the. . . .
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.
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?
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...
Mindreader
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. . . .
Boxed In
Age 11 to 14 Challenge Level:
A box has faces with areas 3, 12 and 25 square centimetres. What is the volume of the box?
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 for. . . .
Adding in Rows
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?
Top-heavy Pyramids
Age 11 to 14 Challenge Level:
Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.
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?
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?
Your Number Is...
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?
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?
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?
Your Number Was...
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?
One and Three
Age 14 to 16 Challenge Level:
Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400. . . .
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?
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. . . .
DOTS Division
Age 14 to 16 Challenge Level:
Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.
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. . . .
NRICH is part of the family of activities in the Millennium Mathematics Project.