Year 5 Conjecturing and generalising

Here are shadows of some 3D shapes. What shapes could have made them?

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 these sweets?

Abundant numbers are less than the sum of their factors (excluding themselves). Can you find some?

Norrie sees two lights flash at the same time. 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?

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.

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you choose?

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?

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.

When are Roman numerals shorter than Arabic numerals for the same number?

Can you find any two-digit numbers that satisfy all of these statements?

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?

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

Can you use four digits to make four two-digit numbers that add to 100?

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

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

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

We start with one cube and build around it. Then we build around that. How many cubes have we used?