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There are 123 results Picturing Triangular Numbers

Age 11 to 14 Challenge Level:

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers? 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? Route to Infinity

Age 11 to 14 Challenge Level:

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

Age 5 to 14 Challenge Level:

This task encourages you to investigate the number of edging pieces and panes in different sized windows. Shear Magic

Age 11 to 14 Challenge Level:

What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles? 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? Maths Trails

Age 7 to 14

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails. 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? Triangle Numbers

Age 11 to 14 Challenge Level:

Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue? Nim-7

Age 5 to 14 Challenge Level:

Can you work out how to win this game of Nim? Does it matter if you go first or second? Hidden Rectangles

Age 11 to 14 Challenge Level:

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard? 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? Chess

Age 11 to 14 Challenge Level:

What would be the smallest number of moves needed to move a Knight from a chess set from one corner to the opposite corner of a 99 by 99 square board? Tourism

Age 11 to 14 Challenge Level:

If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable. Enclosing Squares

Age 11 to 14 Challenge Level:

Can you find sets of sloping lines that enclose a square? Games Related to Nim

Age 5 to 16

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning. ...on the Wall

Age 11 to 14 Challenge Level:

Explore the effect of reflecting in two intersecting mirror lines. Dotty Triangles

Age 11 to 14 Challenge Level:

Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw? One, Three, Five, Seven

Age 11 to 16 Challenge Level:

A game for 2 players. Set out 16 counters in rows of 1,3,5 and 7. Players take turns to remove any number of counters from a row. The player left with the last counter looses. Frogs

Age 11 to 14 Challenge Level:

How many moves does it take to swap over some red and blue frogs? Do you have a method? 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. Nim-7 for Two

Age 5 to 14 Challenge Level:

Nim-7 game for an adult and child. Who will be the one to take the last counter? Go Forth and Generalise

Age 11 to 14

Spotting patterns can be an important first step - explaining why it is appropriate to generalise is the next step, and often the most interesting and important. Winning Lines

Age 7 to 16

An article for teachers and pupils that encourages you to look at the mathematical properties of similar games. 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. . . . Konigsberg Plus

Age 11 to 14 Challenge Level:

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges. Jam

Age 14 to 16 Challenge Level:

A game for 2 players More Number Pyramids

Age 11 to 14 Challenge Level:

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge... 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? Sliding Puzzle

Age 11 to 16 Challenge Level:

The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves. Keep it Simple

Age 11 to 14 Challenge Level:

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

Age 11 to 14 Challenge Level:

The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions. Mystic Rose

Age 14 to 16 Challenge Level:

Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes. 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? Magic Letters

Age 11 to 14 Challenge Level:

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws? Steps to the Podium

Age 7 to 14 Challenge Level:

It starts quite simple but great opportunities for number discoveries and patterns! 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:

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? Age 11 to 14 Challenge Level:

Great Granddad is very proud of his telegram from the Queen congratulating him on his hundredth birthday and he has friends who are even older than he is... When was he born? Who Is the Fairest of Them All ?

Age 11 to 14 Challenge Level:

Explore the effect of combining enlargements. 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? Cunning Card Trick

Age 11 to 14 Challenge Level:

Delight your friends with this cunning trick! Can you explain how it works? Have You Got It?

Age 11 to 14 Challenge Level:

Can you explain the strategy for winning this game with any target? Jam

Age 14 to 16 Challenge Level:

To avoid losing think of another very well known game where the patterns of play are similar. More Magic Potting Sheds

Age 11 to 14 Challenge Level:

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it? Pentanim

Age 7 to 16 Challenge Level:

A game for 2 players with similarities to NIM. Place one counter on each spot on the games board. Players take it is turns to remove 1 or 2 adjacent counters. The winner picks up the last counter. Dicing with Numbers

Age 11 to 14 Challenge Level:

In how many ways can you arrange three dice side by side on a surface so that the sum of the numbers on each of the four faces (top, bottom, front and back) is equal? One O Five

Age 11 to 14 Challenge Level:

You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .