Year 5 Exploring and noticing

Put operations signs between the numbers 3, 4, 5 and 6 to make the highest possible number and lowest possible number.

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?

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

How would you move the bands on the pegboard to alter these shapes?

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

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.

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.

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

Can you put these four calculations into order of difficulty? How did you decide?

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

Find at least one way to put in some operation signs to make these digits come to 100.

On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?

Can you draw a square in which the perimeter is numerically equal to the area?

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

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?

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

What do you think is going to happen in this video clip? Are you surprised?

Use 4 four times in a calculation. What answers can you get?

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?