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Resources tagged with Counting similar to Picture a Pyramid ...:

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Broad Topics > Numbers and the Number System > Counting

Picture a Pyramid ...

Age 7 to 11 Challenge Level:

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

How Would We Count?

Age 5 to 11 Challenge Level:

An activity centred around observations of dots and how we visualise number arrangement patterns.

Dramatic Mathematics

Age 5 to 11

This article for teachers describes a project which explores the power of storytelling to convey concepts and ideas to children.

Building Patterns

Age 7 to 11 Challenge Level:

Can you deduce the pattern that has been used to lay out these bottle tops?

Making Maths: Happy Families

Age 5 to 11 Challenge Level:

Here is a version of the game 'Happy Families' for you to make and play.

Icosagram

Age 11 to 14 Challenge Level:

Draw a pentagon with all the diagonals. This is called a pentagram. How many diagonals are there? How many diagonals are there in a hexagram, heptagram, ... Does any pattern occur when looking at. . . .

How Many Dice?

Age 11 to 14 Challenge Level:

A standard die has the numbers 1, 2 and 3 are opposite 6, 5 and 4 respectively so that opposite faces add to 7? If you make standard dice by writing 1, 2, 3, 4, 5, 6 on blank cubes you will find. . . .

Counting Cards

Age 7 to 11 Challenge Level:

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

Painting Cubes

Age 11 to 14 Challenge Level:

Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?

Cunning Card Trick

Age 11 to 14 Challenge Level:

Delight your friends with this cunning trick! Can you explain how it works?

Up and Down Donkey

Age 5 to 11 Challenge Level:

A number card game for 2-6 players.

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?

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?

Sitting Round the Party Tables

Age 5 to 11 Challenge Level:

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

1 to 8

Age 7 to 11 Challenge Level:

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

Poker Bingo

Age 5 to 11 Challenge Level:

A game played with a standard pack of cards.

Neighbours

Age 7 to 11 Challenge Level:

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

Cube Paths

Age 11 to 14 Challenge Level:

Given a 2 by 2 by 2 skeletal cube with one route `down' the cube. How many routes are there from A to B?

Card Trick 2

Age 11 to 14 Challenge Level:

Can you explain how this card trick works?

Euromaths

Age 11 to 14 Challenge Level:

How many ways can you write the word EUROMATHS by starting at the top left hand corner and taking the next letter by stepping one step down or one step to the right in a 5x5 array?

Birthday Cake Candles

Age 7 to 11 Challenge Level:

This challenge involves calculating the number of candles needed on birthday cakes. It is an opportunity to explore numbers and discover new things.

Page Numbers

Age 7 to 11 Short Challenge Level:

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

Swimming Pool

Age 5 to 11 Challenge Level:

In this problem, we're investigating the number of steps we would climb up or down to get out of or into the swimming pool. How could you number the steps below the water?

Slippery Snail

Age 7 to 16 Challenge Level:

A game for two people, who take turns to move the counters. The player to remove the last counter from the board wins.

Diagonal Sums Sudoku

Age 7 to 16 Challenge Level:

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

Month Mania

Age 5 to 11 Challenge Level:

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

Spelling Circle

Age 7 to 11 Challenge Level:

Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.

Fingers and Hands

Age 7 to 11 Challenge Level:

How would you count the number of fingers in these pictures?

Some Secret Codes

Age 7 to 11 Challenge Level:

Can you follow the rule to decode the messages?

Which Is Quicker?

Age 7 to 11 Challenge Level:

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

Tug Harder!

Age 7 to 11 Challenge Level:

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

Alien Counting

Age 7 to 11 Challenge Level:

Investigate the different ways these aliens count in this challenge. You could start by thinking about how each of them would write our number 7.

Count the Digits

Age 5 to 11 Challenge Level:

In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?

Amazing Card Trick

Age 11 to 14 Challenge Level:

How is it possible to predict the card?

Ip Dip

Age 5 to 11 Challenge Level:

"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

Dotty Six

Age 5 to 11 Challenge Level:

Dotty Six is a simple dice game that you can adapt in many ways.

Dotty Six for Two

Age 5 to 11 Challenge Level:

Dotty Six game for an adult and child. Will you be the first to have three sixes in a straight line?

An Investigation Based on Score

Age 11 to 14

Class 2YP from Madras College was inspired by the problem in NRICH to work out in how many ways the number 1999 could be expressed as the sum of 3 odd numbers, and this is their solution.

Small Change

Age 11 to 14 Challenge Level:

In how many ways can a pound (value 100 pence) be changed into some combination of 1, 2, 5, 10, 20 and 50 pence coins?

Lesser Digits

Age 11 to 14 Challenge Level:

How many positive integers less than or equal to 4000 can be written down without using the digits 7, 8 or 9?

Pairs

Age 11 to 14 Challenge Level:

Ann thought of 5 numbers and told Bob all the sums that could be made by adding the numbers in pairs. The list of sums is 6, 7, 8, 8, 9, 9, 10,10, 11, 12. Help Bob to find out which numbers Ann was. . . .

Ways of Summing Odd Numbers

Age 11 to 14

Sanjay Joshi, age 17, The Perse Boys School, Cambridge followed up the Madrass College class 2YP article with more thoughts on the problem of the number of ways of expressing an integer as the sum. . . .

Back to the Planet of Vuvv

Age 11 to 14 Challenge Level:

There are two forms of counting on Vuvv - Zios count in base 3 and Zepts count in base 7. One day four of these creatures, two Zios and two Zepts, sat on the summit of a hill to count the legs of. . . .