Year 5 Conjecturing and generalising

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?

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?

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

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?

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?

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?

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

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

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

What happens when you round these numbers to the nearest whole number?

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

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

Try out some calculations. Are you surprised by the results?

Can you find some examples when the number of Roman numerals is fewer than the number of Arabic numerals for the same number?

Watch this animation. What do you see? Can you explain why this happens?

Can you find out which 3D shape your partner has chosen before they work out your shape?

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.

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

This challenge combines addition, multiplication, perseverance and even proof.

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?