Open Middle

The calculation has empty boxes. Below it are the digits that go into them - each one exactly once.
Above every task you see the goal - the largest result, the smallest, or one as close as possible to a target number.
There are many arrangements, but only one is the best. First think about which digit belongs in the tens place.

Example

As large as possible!421=41Digits:124
As small as possible!128=4Digits:128
As close to 40 as possible!361=35Digits:136

For parents

What does this exercise practice?

The open middle practices place value as a strategy. The child does not work through a given calculation but decides where a digit has the biggest effect - a 9 in the tens place counts as ninety, in the ones place only as nine. Because many arrangements are allowed and only one is the best, the child has to justify its choice instead of guessing.

Common pitfalls

Each digit is used exactly once. Using a digit twice often gives a bigger result, but then the supply no longer fits. And with a minus it works the other way round - for a small result the small digit goes first, not the big one.

How to practice at home

Write three digits on three slips of paper and lay them out in a row. Who builds the biggest calculation? Then rearrange the same slips for the smallest result and compare out loud.

Related: Split a number into tens and ones, Ordering Numbers

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