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Why do this problem?
can give some substance to children's ideas on place value especially when you are introducing or using numbers greater than $1000$. It shows in a pictorial way what the extra zeros do to a number when multiplying by $10$ and $100$.
The problem can also help children to appreciate how big large numbers really are!
You could introduce the problem by telling the class the 'story' about the tree and its trunks, its branches, its twig and its leaves. During, or after this, ask such questions as "How many branches are there altogether?" and "How many leaves will there be on each branch?".
Then, working in pairs, the children could work out the details of the problem. It might help them to draw rough sketches and/or make a table/list of the numbers of the trunks, branches, twigs and leaves, both at the beginning and after the woodcutter has been at work.
After the number of leaves taken off the tree has been calculated this needs to be subtracted from the total of all the leaves on the tree. This might be the time for a plenary so that you work on the calculation together as as class.
Some children may have do the problem differently, such as deducting the leaves removed from the tree as they go. This could lead to an interesting discussion on different methods to tackling problems such as this.
If there are ten twigs on each branch, how many will there be on ten branches?
How many leaves are there on ten twigs?
How many leaves did the Deca Tree have before the woodcutter came along?
How many leaves did the woodcutter chop off each time?
Children could be invited to invent a similar tree with different numbers of branches etc. such a five-branched 'Penta' tree or an eight-branched 'Octa' tree.
In addition to, or instead of, drawing sketches, it might help some children to make a model of the tree, or at least part of the tree. Pipecleaners could work well for this purpose.