Year 5 Visualising and representing

In this problem, we're investigating the number of steps we would climb up or down to get out of or into the swimming pool. How could you number the steps below the water?

Can you replace the letters with numbers? Is there only one solution in each case?

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?

What numbers would you put on this number line as it goes under the sea level?

This task offers opportunities to subtract fractions using A4 paper.

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

Can you match these calculation methods to their visual representations?

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?

Try adding fractions using A4 paper.

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?

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

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