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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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