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Habits of Mind

Persisting, Thinking flexibly

FOUR FOURS

Introduce the Habit of Mind: What does it mean to persist? Can you think of anytime that
you have persisted to achieve a goal. What skills, strategies did you use to achieve this?



Activity: This classical problem is most commonly formulated as follows:


"Given no more than four instances of the digit 4, represent all numbers using a maths
symbols and operators in common use."

For example: 0 = 4+ 4-4-4

Rules:

You can use the following symbols and operators:


+,- addition subtraction

*,/ multiplication, division

sqrt,^ square root, power

! factorial, eg: n! = n * (n-1) * (n-2) * ... * 2 * 1 , 4! = 4 x 3 x 2 x 1

. decimal point, eg: .4

′ repeating decimal, eg: .4′ = .444444444...




Debrief: Which numbers did you have trouble with?

How did you get over these problems?

What strategies would you use again in the future?













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