This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
This activity investigates how you might make squares and pentominoes from Polydron.
If you had 36 cubes, what different cuboids could you make?
I have fifteen cards numbered $1 - 15$.
I put down seven of them on the table in a row.
The numbers on the first two cards add to $15$.
The numbers on the second and third cards add to $20$.
The numbers on the third and fourth cards add to $23$.
The numbers on the fourth and fifth cards add to $16$.
The numbers on the fifth and sixth cards add to $18$.
The numbers on the sixth and seventh cards add to $21$.
What are my cards?
Can you find any other solutions?
How do you know you've found all the different solutions?
This problem requires no mathematical ideas beyond simple addition and possibly subtraction, but it does require the perseverence to stick with a trial and improvement approach, combined with some systematic working.
After demonstrating that they have found all the possible solutions, learners could make up a similar problem for others to try. Remind them that you will expect them to know the solutions to their own problem before giving it to others to try out!
Using digit cards will encourage learners to try out different combinations without having to commit anything to paper at first. They may need reminding that, for example, that $12$ followed by $3$ will give a different order from $3$ followed by $12$. You could suggest that they focus on just one pair to begin with and consider all possible combinations, then try to work out
what the other cards could be based on each of those possibilities.