List

Year 5 Conjecturing and Generalising

Dicey Array
game
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Dicey Array

Watch the video of this game being played. Can you work out the rules? Which dice totals are good to get, and why?

Brush Loads
problem
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Brush Loads

Age
7 to 11
Challenge level
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How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

Tug Harder!
problem
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Tug Harder!

Age
7 to 11
Challenge level
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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?
Three Dice
problem
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Three Dice

Age
7 to 11
Challenge level
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Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Area and perimeter
problem
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Area and perimeter

Age
7 to 11
Challenge level
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What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

Multiply Multiples 1
problem
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Multiply Multiples 1

Age
7 to 11
Challenge level
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Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Multiply Multiples 2
problem
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Multiply Multiples 2

Age
7 to 11
Challenge level
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Can you work out some different ways to balance this equation?
Round the Dice Decimals 2
problem
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Round the Dice Decimals 2

Age
7 to 11
Challenge level
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What happens when you round these numbers to the nearest whole number?

Multiply Multiples 3
problem
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Multiply Multiples 3

Age
7 to 11
Challenge level
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Have a go at balancing this equation. Can you find different ways of doing it?
Division Rules
problem
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Division Rules

Age
7 to 11
Challenge level
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This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Subtraction Surprise
problem
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Subtraction Surprise

Age
7 to 14
Challenge level
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Try out some calculations. Are you surprised by the results?
Roman Numerals
problem
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Roman Numerals

Age
7 to 11
Challenge level
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Can you find some examples when the number of Roman numerals is fewer than the number of Arabic numerals for the same number?
Tumbling Down
problem
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Tumbling Down

Age
7 to 11
Challenge level
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Watch this animation. What do you see? Can you explain why this happens?

Guess What?
problem
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Guess What?

Age
7 to 11
Challenge level
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Can you find out which 3D shape your partner has chosen before they work out your shape?
Factors and Multiples Game
game
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Factors and Multiples Game

A game in which players take it in turns to choose a number. Can you block your opponent?

Sweets in a box
problem
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Sweets in a box

Age
7 to 11
Challenge level
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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?
Abundant Numbers
problem
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Abundant Numbers

Age
7 to 11
Challenge level
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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?
Flashing Lights
problem
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Flashing Lights

Age
7 to 11
Challenge level
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Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?
Which is quicker?
problem
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Which is quicker?

Age
7 to 11
Challenge level
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Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Odd Squares
problem
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Odd Squares

Age
7 to 11
Challenge level
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Think of a number, square it and subtract your starting number. Is the number you're left with odd or even? How do the images help to explain this?

Up and Down Staircases
problem
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Up and Down Staircases

Age
7 to 11
Challenge level
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One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?
Six Ten Total
problem
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Six Ten Total

Age
7 to 11
Challenge level
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This challenge combines addition, multiplication, perseverance and even proof.
Pebbles
problem
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Pebbles

Age
7 to 11
Challenge level
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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?

Making Boxes
problem
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Making Boxes

Age
7 to 11
Challenge level
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Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

Reach 100
problem
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Reach 100

Age
7 to 11
Challenge level
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Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

Two Primes Make One Square
problem
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Two Primes Make One Square

Age
7 to 11
Challenge level
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Can you make square numbers by adding two prime numbers together?
Cubes within Cubes
problem
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Cubes within Cubes

Age
7 to 14
Challenge level
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We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?