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An investigation that gives you the opportunity to make and justify predictions.

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The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

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Have a go at balancing this equation. Can you find different ways of doing it?

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How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

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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?

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Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

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Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

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Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

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Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

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Can you work out some different ways to balance this equation?

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Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

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Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.

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How many different rectangles can you make using this set of rods?

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Number problems at primary level that may require resilience.

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What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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Can you make square numbers by adding two prime numbers together?

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On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

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Got It game for an adult and child. How can you play so that you know you will always win?

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How many different sets of numbers with at least four members can you find in the numbers in this box?

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There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?

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When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?

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

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48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

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In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

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The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

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The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.

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A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

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Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

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There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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Given the products of diagonally opposite cells - can you complete this Sudoku?

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Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?

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Play this game and see if you can figure out the computer's chosen number.

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Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

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The items in the shopping basket add and multiply to give the same amount. What could their prices be?

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Can you complete this jigsaw of the multiplication square?

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What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

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A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

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I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

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Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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Given the products of adjacent cells, can you complete this Sudoku?

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In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

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Can you find different ways of creating paths using these paving slabs?

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Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

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The clues for this Sudoku are the product of the numbers in adjacent squares.

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Number problems at primary level to work on with others.

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A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.