Year 5 Conjecturing and Generalising

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

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?

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?

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.

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

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

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

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?

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

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.

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?