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|Which is quicker, counting up to $30$ in ones or counting up to $300$ in tens? Why?|
This problem could be used as a short one, suitable for the start of a lesson, but it could also be explored more fully and therefore take more time. It will help learners to come to a deeper understanding of how the number system works and can also be extended to cover various multiplication tables.
Learners could extend this to such things as counting tens of thousands, counting in $7$s from $70$ to $140$, counting in steps of $0.1$ from $0.1$ to $1$ or counting in fractions such as tenths or eighths.
Some children may like to stick to counting in $10$s, $100$s, $2$ and $5$s, or other steps with which they they feel comfortable. Some learners may like to write down the numbers they are counting before being timed.
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?
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?